Using probabilistic optimization to compute and implement ranked preventive resilience measures to enhance operational resilience of power systems

Abstract

The present disclosure relates to a method comprising using at least one hardware processor to: obtain asset data associated with a plurality of power delivery assets of a power network; obtain forecast data associated with at least one future event; generate input data based on the asset data and the forecast data; and input, prior to the at least one future event, the input data to a probabilistic optimization model that optimizes at least one parameter of operation of the power network for the at least one future event; determine, for each of a plurality of resilience measures, a measure of effectiveness of the resilience measure for the at least one future event on operation of the power network based on a solution of the probabilistic optimization model; output the measures of effectiveness of the plurality of resilience measures to a network controller of the power network; and implement one of the resilience measures in accordance with the measure of effectiveness of the resilience measure.

Description

Technical Field

[0001] The embodiments described herein generally relate to the control of power systems, and more specifically to calculating ranked preventative resilience measures and implementing these ranked preventative resilience measures based on that ranking. These resilience measures include, but are not limited to, load shedding, network topology optimization, preventative deployment and real-time scheduling of distributed energy resources, and preventative network islanding, thereby using probabilistic optimization to enhance the operational resilience of the power system. Background Technology

[0002] Extreme weather events such as storms, hurricanes, floods, and wildfires are among the leading causes of global power outages. Due to the climate crisis, the severity, frequency, and duration of extreme weather events continue to increase. Currently, these events are estimated to cause between $20 billion and $55 billion in losses annually. Therefore, enhancing the resilience of power grids has never been more important.

[0003] Typically, utilities monitor weather forecasts and, when severe weather events are predicted, attempt to estimate the potential damage to their power systems. They then use this information to begin preparing for potential power outages. This preparation usually includes assessing inventory, procuring hardware resources, scheduling maintenance personnel, and arranging assistance from nearby utilities (e.g., acquiring equipment). However, even if these measures are implemented before the weather event, they are still reactive measures because they are preparations made to repair grid damage during or after the event.

[0004] Traditional preparedness is neither proactive nor defensive. In other words, traditional preparedness for weather events does not prepare or reinforce the power system to absorb the impact of events, for example, by eliminating or mitigating the damage to the power system from the outset. Proactive preparedness improves the operational resilience of the power system, defined as the ability to withstand the destructive effects of high-impact, low-frequency events by absorbing, adapting to, and rapidly recovering from such events, thereby maintaining a reliable power supply during recovery activities. However, proactive preparedness is accompanied by a high degree of uncertainty, which complicates accurately capturing the impact of extreme weather events. Summary of the Invention

[0005] Therefore, in one aspect, a system, method, and nontransient computer-readable medium are disclosed for implementing one or more resilience measures using probabilistic optimization to enhance the operational resilience of a power system. Also in one aspect, a system, method, and nontransient computer-readable medium are disclosed for calculating ranked preventative resilience measures (including preventative deployment and real-time dispatch of distributed energy resources) using probabilistic optimization to enhance the operational resilience of a power system. A first objective achievable by the disclosed embodiments is to optimize the switching states in the power system to strengthen the power system against predicted events, such as severe weather events. A second objective achievable by the disclosed embodiments is to determine the optimal deployment of mobile distributed energy resources within the power system. A third objective achievable by the disclosed embodiments is to determine the optimal dispatch of distributed energy resources within the power system. A fourth objective achievable by the disclosed embodiments is to ensure radiation using constraints representing virtual loads.

[0006] In a preferred embodiment, a method includes using at least one hardware processor to: acquire asset data associated with a plurality of power transmission assets of a power network; acquire predictive data associated with at least one future event; generate input data based on the asset data and the predictive data; and input the input data into a probabilistic optimization model prior to the at least one future event, the probabilistic optimization model optimizing at least one parameter of the operation of the power network for the at least one future event; for each of a plurality of resilience measures, based on the solution of the probabilistic optimization model, determine a measure of the effectiveness of the resilience measures for the operation of the power network for the at least one future event; output the measure of the effectiveness of the plurality of resilience measures to a network controller of the power network; and implement one of the resilience measures according to the measure of the effectiveness of the resilience measures.

[0007] The method may further include: ranking the plurality of resilience measures according to the corresponding effectiveness measures before outputting the effectiveness measure, and implementing one of the plurality of resilience measures according to the ranking.

[0008] The effectiveness of each of the plurality of resilience measures may be measured based on one or both of the following: the expected improvement in the operation of the power network during the at least one future event when the resilience measures are implemented, and / or the ease with which the resilience measures are implemented.

[0009] The plurality of resilience measures include one or more of the following: a) controlling the power network to reduce power supplied to at least one load of the power network during the at least one future event; b) controlling the power network to reconfigure the power network to an optimized network topology such that the power network has the optimized network topology during the at least one future event; c) controlling the power network to reconfigure the power network to an optimized network topology to maximize the total load served in the power network during the at least one future event; and d) controlling one or more switches in the power network to split the power network into a plurality of microgrids.

[0010] In a), the asset data may include critical information indicating the criticality of one or more loads of the power network, and wherein the objective function weights the one or more loads according to the criticality.

[0011] In a), the probabilistic optimization model can optimize the objective function for calculating the expected load supply.

[0012] In a), the probabilistic optimization model can model the topology of the power network, wherein the solution of the probabilistic optimization model includes an optimized network topology, and wherein the plurality of resilient measures include reconfiguring the power network to the optimized network topology.

[0013] In a), the probabilistic optimization model can model the electrical islanding within the power network, wherein the solution of the probabilistic optimization model can include one or more electrical islands within the power network, and wherein the plurality of resilient measures includes preventative electrical islanding; and preferably, the solution of the probabilistic optimization model includes a microgrid configuration, the microgrid configuration including a plurality of microgrids, each microgrid having at least one grid-type distributed energy resource, and wherein the method further includes: determining to implement the preventative electrical islanding; and controlling one or more switches in the power network to split the power network into a plurality of microgrids.

[0014] In a), the probabilistic optimization model can model the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model can include the scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures include scheduling the one or more energy resources; and preferably, the one or more energy resources include at least one mobile energy resource.

[0015] In a), the asset data may include one or more parameters of each of one or more of the plurality of power transmission assets, and may indicate the connection between the plurality of power transmission assets.

[0016] In a), the input data may include multiple failure probability distributions of the plurality of power transmission assets; and / or the at least one future event may include a weather event, and wherein the prediction data (630) may include a weather forecast for a certain period of time for the at least one future event.

[0017] The power network may include a distribution network.

[0018] In b), the probabilistic optimization model can model the topology of the power network, wherein the solution of the probabilistic optimization model includes the optimized network topology.

[0019] In b), the asset data may include critical information indicating the criticality of one or more loads of the power network.

[0020] In b), the probabilistic optimization model can model the electrical islanding within the power network, wherein the solution of the probabilistic optimization model can include one or more electrical islands within the power network, and wherein the plurality of resilient measures can include preventative electrical islanding.

[0021] In b), the solution of the probabilistic optimization model may include a microgrid configuration comprising multiple microgrids, each microgrid having at least one grid-type distributed energy resource, and wherein the method further comprises: determining to implement the preventive electrical islanding partitioning; and controlling one or more switches in the power network to split the power network into multiple microgrids.

[0022] In b), the probabilistic optimization model can model the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model can include the scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures can include scheduling the one or more energy resources.

[0023] In b), the asset data may include one or more parameters of each of one or more of the plurality of power transmission assets, and may indicate the connection between the plurality of power transmission assets.

[0024] In c), the probabilistic optimization model can determine the optimized network topology of the power network to be used during the at least one future event by optimizing an objective function to maximize the total load served in the power network during the at least one future event; and the objective function can associate each of the plurality of nodes in the power network with a critical factor representing the relative criticality of the load at that node, associate each of the plurality of power lines in the power network with a risk factor representing the failure probability of that power line, including a term representing the voltage deviation at the plurality of nodes, and is subject to one or more constraints.

[0025] In c), controlling the power network may include controlling one or more switches in the power network.

[0026] Optimizing the objective function may include maximizing the objective function, wherein the objective function may include:

[0027] in, t It is a time period T Index of time intervals within, N These are the multiple nodes. i It is the index of the node within the plurality of nodes. It is the first i Key factors for load at each node This represents the dot product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node and It is a scalar factor. ij It is the connection of the first i The node and the first j The index of the power lines of each node. E It is a collection of power lines that have not experienced any faults. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij Active power flow on the power lines It is in the t During the time interval, the first ijReactive power flow on the power lines It is the set of nodes representing flexible asset connection points among the plurality of nodes, and It is in the t During the time interval, the first i The absolute value of the voltage at each node.

[0028] The objective function may further include a term representing the generation of one or more distributed energy resources in the power network, and optimizing the objective function may include maximizing the objective function, wherein the objective function may include:

[0029] in, t It is a time period T Index of time intervals within, N These are the multiple nodes. i It is the index of the node within the plurality of nodes. It is the first i Key factors for load at each node This represents the dot product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node , and It is a scalar factor. ij It is the connection of the first i The node and the first j The index of the power lines of each node. E It is a collection of power lines that have not experienced any faults. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij Active power flow on the power lines It is in the t During the time interval, the first ij Reactive power flow on the power lines It is the set of nodes representing flexible asset connection points among the plurality of nodes. It is in the t During the time interval, the first i The absolute value of the voltage at each node. It is the set of nodes representing photovoltaic power sources among the plurality of nodes, and It is in the t During the time interval, the first i The active power output of the photovoltaic power source at each node.

[0030] The one or more constraints may include at least one deployment constraint for each mobile distributed energy resource to be deployed at a flexible asset connection point in the power network during the event, wherein the at least one deployment constraint ensures that: each mobile distributed energy resource can only be deployed at the node representing the flexible asset connection point among the plurality of nodes, if deployed; at most one mobile distributed energy resource can be deployed at each node representing the flexible asset connection point; and each mobile distributed energy resource can only be deployed at a single node, if deployed.

[0031] The following conditions may apply:

[0032] in, It is a collection of mobile generators to be deployed in the power grid during the event. d It is the index of the mobile generator within the set of mobile generators. It is a collection of mobile energy storage systems to be deployed in the power grid during the event. m It is the index of the mobile energy storage system within the set of mobile energy storage systems. It is the set of nodes representing flexible asset connection points among the plurality of nodes. i It is the set of nodes Index of the node within, It means the first d Was the mobile generator deployed at the [number]th [location]? i The binary variable at each node, and It means the first m Whether the mobile energy storage system was deployed in the [number]th [location] i Binary variables at each node.

[0033] The one or more constraints may include at least one virtual load constraint for each of the plurality of nodes representing distributed energy resources, and the at least one virtual load constraint may require that the virtual load at each of the plurality of nodes representing distributed energy resources be powered by a virtual power supply from the node representing a substation among the plurality of nodes.

[0034] The at least one virtual load constraint may include:

[0035] in, E It is a collection of power lines that have not experienced any faults. i It is the index of the node within the plurality of nodes. ji It is the first j The node is connected to the first i The index of the power lines of each node. ij It is the first i The node is connected to the first j The index of the power lines of each node. From the first j The node to the first i Virtual power flow of each node From the first i The node to the first j Virtual power flow of each node It is the first i Virtual load at each node It is a collection of mobile generators to be deployed in the power grid during the event. d It is the index of the mobile generator within the set of mobile generators. It is a collection of mobile energy storage systems to be deployed in the power grid during the event. m It is the index of the mobile energy storage system within the set of mobile energy storage systems. It means the first d Was the mobile generator deployed at the [number]th [location]? i Binary variables at each node It means the first m Whether the mobile energy storage system was deployed in the [number]th [location] i Binary variables at each node N These are the multiple nodes. It is the set of nodes representing distributed energy resources among the plurality of nodes. It is the set of nodes representing flexible asset connection points among the plurality of nodes, and It is the set of nodes representing the substation among the multiple nodes.

[0036] The at least one virtual load constraint may further include:

[0037] in, M This is the total number of energy storage systems. D It is the total amount of non-renewable energy, and P It represents the total amount of renewable energy.

[0038] In c), the network topology may include the state of each of a plurality of switches in the power network, and preferably, reconfiguring the power network may include controlling the plurality of switches to match the state in the network topology.

[0039] In c), the network topology may include the deployment of each of one or more mobile distributed energy resources, and / or the network topology may include power dispatch for each of the one or more distributed energy resources represented in the network topology, and preferably, the one or more distributed energy resources may be a plurality of distributed energy resources including one or more stationary distributed energy resources and one or more mobile distributed energy resources.

[0040] In d), the probabilistic optimization model can determine the switching state of each of a plurality of switches in the power network, at least by optimizing an objective function to maximize the total load served in the power network during the at least one future event, so as to form one or more microgrids in the power network, and the objective function can associate each of a plurality of power lines in the power network with a risk factor representing the failure probability of that power line, such that power flow on power lines associated with lower risk factors takes precedence over power flow on power lines associated with higher risk factors, and is subject to one or more islanding constraints.

[0041] In d), optimizing the first objective function includes maximizing the first objective function, wherein the first objective function includes:

[0042] Where Φ is the set of phases, p It is a phase within the set of said phases. T It refers to the time period of the event. t It is the index of the time interval within the stated time period. N These are the multiple nodes. i It is the index of the node within the plurality of nodes. Represents the product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node γ It is a scalar factor. ij It is the first i The node is connected to the firstj The index of the power lines of each node. E It is a collection of power lines. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij The active power flow on the power lines, and It is in the t During the time interval, the first ij Reactive power flow on a power line.

[0043] The one or more islanding constraints can ensure that each of the plurality of nodes is assigned to exactly one of the one or more microgrids.

[0044] The one or more islanding constraints can ensure that exactly one node representing a grid-type distributed energy resource is assigned to each of the one or more microgrids.

[0045] The one or more islanding constraints can ensure that each of the one or more microgrids includes at least two nodes.

[0046] The one or more islanding constraints can ensure that each of the multiple power lines is assigned to one of the one or more microgrids or a power grid including substations based on the assignment of at least one node among the multiple nodes connected to the power line.

[0047] The one or more island partitioning constraints may include: , for ,

[0048] in, K It is the set of nodes representing grid-type distributed energy resources among the plurality of nodes. k yes K Intranode index, N These are the multiple nodes. i It is the node index within the plurality of nodes, and It means the first i Is the node assigned to the node by the first...? k A binary variable of a microgrid formed by individual nodes.

[0049] The one or more island partitioning constraints may include:

[0050] in, K It is the set of nodes representing grid-type distributed energy resources among the plurality of nodes. k yes K Intranode index, E s In the scene s A collection of power lines that have not experienced any faults. i It is the node index within the plurality of nodes. S It is a collection of power lines, each having one of the aforementioned multiple switches. j It is the node index within the plurality of nodes. ij The first of the multiple power lines is i The node is connected to the first j An index of a power line for a node. It means that the first ij Whether the power line is assigned to the first k A binary variable in a microgrid formed by individual nodes. It means the first i Is the node assigned to the node by the first...? k A microgrid formed by nodes has two variables, and It means the first ij A binary variable representing the switching state on a power line.

[0051] The method may further include, before determining the switching state: classifying each of the plurality of nodes as critical or non-critical, so as to divide the plurality of nodes into critical nodes and non-critical nodes; and reducing the number of the plurality of nodes in the power network by recursively aggregating at least one parameter of a non-critical node with at least one parameter of at least one critical node, and removing the non-critical node until only critical nodes remain in the plurality of nodes.

[0052] The aggregation can be performed at each of the plurality of nodes for each phase.

[0053] The at least one parameter may include load.

[0054] The aggregation may include: when the non-critical node is not between two critical nodes, aggregating the entire value of the at least one parameter of the non-critical node with the value of the at least one parameter of the nearest critical node, and removing the non-critical node and one of the multiple power lines between the non-critical node and the nearest critical node; and when the non-critical node is between two critical nodes, aggregating a portion of the value of the at least one parameter of the non-critical node with the value of the at least one parameter of each of the two critical nodes, removing the non-critical node, removing each of the multiple power lines between the non-critical node and the two critical nodes, and adding a new aggregated power line between the two critical nodes.

[0055] The method may further include: storing a mapping of each removed non-critical node to a critical node aggregated with the non-critical node, and a mapping of each removed power line among the plurality of power lines to any power line aggregated with the removed power line.

[0056] The method may further include: after determining the switching state, for each of the one or more microgrids, planning the scheduling in the one or more microgrids in the following manner: in a first phase, for each of a plurality of time intervals within the time period of the event, allocating generation resources in the microgrid to the time interval by optimizing a second objective function based on a plurality of scenarios and the probability of each of the plurality of scenarios to maximize the total load served in the power network during the time interval, wherein the second objective function associates each of the plurality of power lines with a risk factor representing the failure probability of that power line; and in a second phase, for each of a plurality of time segments within each of the plurality of time intervals, allocating generation resources to the time segment by optimizing a third objective function to maximize the total load served in the power network during the time interval, wherein the second objective function is deterministic and associates each of the plurality of power lines with a risk factor representing the failure probability of that power line.

[0057] The method may further include, in the second stage, selecting a set of loads to be supplied with electricity during each of the plurality of time segments in each of the plurality of time intervals, wherein the third objective function is constrained by requiring each load in the selected set of loads to be supplied with a predefined minimum service duration.

[0058] The method may further include: for each of the one or more microgrids, during each of the plurality of time segments, scheduling power generation in the microgrid based on the power generation resources allocated for that time segment.

[0059] Reconfiguring the power network may include controlling the plurality of switches to match the determined switch states.

[0060] In this embodiment, the event is a weather event.

[0061] In one embodiment, the forecast data includes forecasts of the load on the power network during the at least one future event.

[0062] In one embodiment, the input data includes multiple failure scenarios of the plurality of power transmission assets during the at least one future event.

[0063] In one embodiment, the asset data includes the failure probabilities of the plurality of power transmission assets, and the method further includes generating the plurality of failure scenarios based on the failure probabilities.

[0064] In an embodiment, the input data includes multiple failure probability distributions of the plurality of power transmission assets; and / or wherein the at least one future event includes a weather event, and wherein the prediction data includes a weather forecast for a certain period of time for the at least one future event, and / or wherein the power network includes a distribution network.

[0065] In a preferred embodiment, an apparatus includes at least one processor configured to perform the method according to any of the above embodiments.

[0066] In a preferred embodiment, a computer program product includes instructions that, when executed by a means including at least one processor, cause the processor to perform the method according to any of the above embodiments.

[0067] It should be understood that any feature in the above methods can be implemented individually or in any combination with any subset of other features. Therefore, even though the appended claims indicate a specific dependency between features, the disclosed embodiments are not limited to those specific dependencies. Rather, any feature described herein can be combined with any other feature described herein, or implemented in any combination of any features without any one or more other features described herein. Furthermore, any methods described above and elsewhere herein can be embodied individually or in any combination in an executable software module of a processor-based system (such as a server) and / or stored in executable instructions on a non-transitory computer-readable medium. Attached Figure Description

[0068] By studying the accompanying drawings, details of both the structure and operation of the invention can be partially gathered. In the drawings, similar reference numerals refer to similar parts, and in the drawings: Figure 1 The illustration shows an example infrastructure in which any of the processes described herein can be implemented according to an embodiment; Figure 2 The illustration shows an example processing system according to an embodiment that can be used to perform any of the processes described herein; Figure 3 An example data stream for probability optimization according to an embodiment is illustrated; Figure 4 An example process for probability optimization according to an embodiment is illustrated; Figure 5 The illustration shows an example process for calculating a measure of the effectiveness of resilience measures according to an embodiment; Figure 6 The illustration shows an architecture for probabilistic optimization of load reduction according to an embodiment; Figure 7 The illustration shows an architecture for probabilistic optimization of network topology according to an embodiment; Figure 8 The illustration shows an example of microgrid formation in preventive network islanding according to an embodiment; Figure 9A The illustration shows an architecture for probabilistic preventative network islanding according to an embodiment; Figure 9B The illustration shows an architecture for probabilistic preventative network islanding according to an embodiment; Figure 10 The illustration shows an architecture for probabilistic DER deployment and scheduling according to an embodiment; Figure 11 The concept of virtual load according to an embodiment is illustrated; Figure 12 The illustration shows an architecture for network simplification according to an embodiment; Figure 13 The illustration depicts an example simplification and aggregation of a portion of a power network according to an embodiment; Figure 14 The illustration shows a two-stage optimization process according to an embodiment; Figure 15 The illustration shows the segmentation of time periods according to an embodiment; Figure 16 The diagram illustrates the relationship between the first-stage optimization and the second-stage optimization for the state of charge of a battery energy storage system, based on an example. Figure 17A and Figure 17B The illustration shows a network diagram of the circuit used in an exemplary implementation of the disclosed embodiments.

[0069] Figure 18A and Figure 18B The diagram illustrates a network plot of the circuitry used in an exemplary implementation of the disclosed embodiments. Figure 19 The diagram illustrates an architecture that combines network simplification, electrical islanding, and microgrid scheduling planning according to an embodiment; and Figure 20 The illustration shows an example operation of preventative network islanding according to an embodiment. Detailed Implementation

[0070] In the embodiments, a system, method, and nontransient computer-readable medium are disclosed for using probabilistic optimization to compute ranked preventative resilience measures to potentially leverage network simplification and two-stage microgrid dispatch planning to enhance the operational resilience of power systems. After reading this specification, those skilled in the art will understand how to practice the invention in various alternative embodiments and applications.

[0071] In further embodiments, systems, methods, and nontransient computer-readable media are disclosed for using probabilistic optimization to compute ranked preventative resilience measures (including preventative deployment and real-time dispatch of distributed energy resources) to enhance the operational resilience of power systems.

[0072] However, while various embodiments of the invention will be described herein, it should be understood that these embodiments are presented by way of example and illustration only and not by way of limitation. Therefore, this detailed description of various embodiments should not be construed as limiting the scope or breadth of the invention as set forth in the appended claims.

[0073] 1. Infrastructure Figure 1The illustration depicts an example infrastructure in which any of the disclosed processes can be implemented according to an embodiment. The infrastructure may include a management system 110 (e.g., including one or more servers) that hosts and / or executes one or more of the various processes described herein, which may be implemented in software and / or hardware. Examples of the management system 110 include, but are not limited to, Supervisory Control and Data Acquisition (SCADA) systems, Power Management Systems (PMS), Energy Management Systems (EMS), Distribution Management Systems (DMS), Advanced DMS (ADMS), Asset Management Systems (ASM), etc. The management system 110 may include dedicated servers, or alternatively, may be implemented in a computing cloud, where the computing resources of one or more servers are dynamically and elastically allocated to multiple tenants based on demand. In either case, the servers may be centrally deployed (e.g., in a single data center) and / or geographically distributed (e.g., across multiple data centers). The management system 110 may also include or communicatively connect to software 112 and / or database 114. Additionally, the management system 110 may be communicatively connected to one or more user systems 130, target systems 140, and / or third-party systems 150 via one or more networks 120.

[0074] Network 120 may include the Internet, and management system 110 may communicate with user system 130, target system 140, and / or third-party system 150 via the Internet and / or other networks using standard transport protocols such as Hypertext Transfer Protocol (HTTP), HTTP Secure Protocol (HTTPS), File Transfer Protocol (FTP), FTP Secure Protocol (FTPS), Secure Shell FTP (SFTP), Extensible Messaging and Presence Protocol (XMPP), Open FieldMessage Bus (OpenFMB), IEEE Smart Energy Specification Application Protocol (IEEE 2030.5), and proprietary protocols. Although management system 110 is illustrated as being connected to various systems via a single set of networks 120, it should be understood that management system 110 may be connected to various systems via different sets of one or more networks. For example, management system 110 may be connected to a subset of user system 130, target system 140, and / or third-party system 150 via the Internet, but may also be connected to one or more other user system 130, target system 140, and / or third-party system 150 via an intranet. Furthermore, although only a few user systems 130, target systems 140, and third-party systems 150, an instance of software 112, and a database 114 are illustrated, it should be understood that the infrastructure may include any number of user systems 130, target systems 140, third-party systems 150, software instances 112, and databases 114.

[0075] User system 130 may include any one or more types of computing devices capable of wired and / or wireless communication, including but not limited to desktop computers, laptop computers, tablet computers, smartphones or other mobile phones, servers, game consoles, televisions, set-top boxes, electronic kiosks, point-of-sale terminals, embedded controllers, programmable logic controllers (PLCs), etc. However, it is generally envisioned that user system 130 will include personal computers, mobile devices, or workstations through which intelligent agents of the operator (e.g., utility) of target system 140 (e.g., power system, such as a power grid, such as a distribution network) can interact with management system 110. These interactions may include inputting data (e.g., parameters for configuring the processes described herein) and / or receiving data (e.g., outputs of the processes described herein) via a graphical user interface provided by management system 110 or a system between management system 110 and user system 130. A graphical user interface may include screens (e.g., web pages) that include a combination of content and elements such as text, images, videos, animations, references (e.g., hyperlinks), frames, inputs (e.g., text boxes, text areas, check boxes, radio buttons, drop-down menus, buttons, forms, etc.), scripts (e.g., JavaScript), and elements that contain data stored in database 114 or elements derived from that data.

[0076] Target system 140 may include any type of system on which data related to one or more assets is monitored, analyzed, and / or action is taken. However, in the context of the specific non-limiting examples provided throughout this disclosure, it will be assumed that target system 140 includes or is constituted by an electric system (such as a power grid). An electric system may include one or more, and typically multiple, power transmission assets connected in a network, which may include distribution networks (e.g., balanced or unbalanced), transmission networks, etc. Assets may include power resources such as generators, energy storage systems, electrical loads (e.g., rechargeable energy storage systems or other controllable loads, uncontrollable loads, etc.), and other types of power transmission assets such as transformers, inverters, branch lines or other power lines (e.g., overhead or underground power lines), poles on which power lines are mounted, capacitor banks, voltage regulators, switches, fuses, reclosers, and / or any other components supporting the power system. Generators can include different types of generators, such as those from thermal power plants (e.g., coal, natural gas, nuclear, geothermal, etc.), hydropower plants, renewable energy power plants (e.g., solar, wind, geothermal, etc.), diesel generators, etc., and can be stationary (i.e., stationary) or mobile. Electrical loads can include anything that consumes electricity, including but not limited to electric vehicles, household appliances, machinery, commercial buildings, residential buildings, hospitals, police stations, fire stations, gas pipeline pumping stations, water supply systems, etc.

[0077] Third-party system 150 may include any one or more types of computing devices capable of wired and / or wireless communication. However, it is generally envisioned that third-party system 150 will include one or more servers that supply external data to management system 100. External data may represent historical, current, and / or predicted values ​​of one or more parameters related to target system 140, such as weather parameters (e.g., temperature, humidity, wind speed, pressure, etc.), market parameters (e.g., energy prices), socio-political events (e.g., protests, law enforcement warnings, etc.).

[0078] The management system 110 can execute software 112, which includes one or more software modules implementing one or more of the disclosed processes. Additionally, the management system 110 may include a database 114, be communicatively coupled to, or otherwise access to the database, which stores data input to and / or output from the one or more disclosed processes. Any suitable database may be used in database 114, including but not limited to MySQL™, Oracle™, IBM™, Microsoft SQL™, Access™, PostgreSQL™, MongoDB™, etc., and includes cloud-based databases, proprietary databases, and unstructured databases.

[0079] 2. Example Processing System Figure 2 An example processing system 200 according to embodiments is illustrated and can be used to perform any of the processes described herein. For example, system 200 can be used as one or more of, or in combination with, the functions, methods, or software described herein (e.g., for storing and / or executing software 112, storing database 114, etc.), and can represent a component of management system 110, user system 130, target system 140, third-party system 150, and / or other processing devices described herein. System 200 can be a server, a conventional personal computer, or any other processor-enabled device capable of wired or wireless data communication. Those skilled in the art will appreciate that other computer systems and / or architectures can also be used.

[0080] System 200 preferably includes one or more processors 210. Processor 210 may include a central processing unit (CPU). Additional processors may be provided, such as a graphics processing unit (GPU), an auxiliary processor for managing input / output, an auxiliary processor for performing floating-point mathematical operations, a dedicated microprocessor (e.g., a digital signal processor) with an architecture suitable for rapidly executing signal processing algorithms, a processor subordinate to the main processor (e.g., a back-end processor), an additional microprocessor or controller and / or coprocessor for dual-processor or multi-processor systems. Such auxiliary processors may be discrete processors or integrated with the main processor. Examples of processors 210 that may be used with system 200 include, but are not limited to, any processor supplied by Intel Corporation of Santa Clara, California (e.g., Pentium™, Core i7™, Xeon™, etc.), any processor supplied by Advanced Micro Devices Inc. (AMD) of Santa Clara, California, any processor supplied by Apple Inc. of Cupertino (e.g., A-series, M-series, etc.), any processor supplied by Samsung Electronics Ltd. of Seoul, South Korea (e.g., Exynos™), any processor supplied by NXP Semiconductors Ltd. of Eindhoven, Netherlands, etc.

[0081] Processor 210 can be connected to communication bus 205. Communication bus 205 may include a data channel for facilitating information transfer between the storage devices of system 200 and other peripheral components. Furthermore, communication bus 205 can provide a set of signals for communicating with processor 210, including a data bus, address bus, and / or control bus (not shown). Communication bus 205 may include any standard or non-standard bus architecture, such as Industry Standard Architecture (ISA), Extended Industry Standard Architecture (EISA), Micro Channel Architecture (MCA), Peripheral Component Interconnect (PCI) local bus, or bus architectures published by the Institute of Electrical and Electronics Engineers (IEEE) including IEEE 488 Universal Interface Bus (GPIB) or IEEE 696 / S-100.

[0082] System 200 may include main memory 215. Main memory 215 provides storage for instructions and data of programs executed on processor 210, such as one or more processes discussed herein (e.g., embodied in software 112). It should be understood that programs stored in memory and executed by processor 210 can be written and / or compiled in any suitable language, including but not limited to C / C++, Java, JavaScript, Perl, Python, Visual Basic, .NET, etc. Main memory 215 is typically a semiconductor-based memory, such as dynamic random access memory (DRAM) and / or static random access memory (SRAM). Other semiconductor-based memory types include, for example, synchronous dynamic random access memory (SDRAM), Rambus dynamic random access memory (RDRAM), ferroelectric random access memory (FRAM), etc., including read-only memory (ROM).

[0083] System 200 may also include auxiliary storage 220. Auxiliary storage 220 may optionally include internal media 225 and / or removable media 230. Internal media 225 may include, for example, hard disk drives (HDDs), solid-state drives (SSDs), etc. Removable media 230 may include, for example, magnetic tape drives, compact optical disc (CD) drives, digital versatile optical disc (DVD) drives, flash memory drives, etc. Auxiliary storage 220 is a non-transitory computer-readable medium on which computer-executable code (e.g., software 112) and / or other data is stored. Computer software or data stored on auxiliary storage 220 is read into main memory 215 for execution by processor 210.

[0084] System 200 may include an input / output (I / O) interface 235. I / O interface 235 provides an interface between one or more components of system 200 and one or more input and / or output devices. Examples of input devices include, but are not limited to, sensors, keyboards, touchscreens or other touch-sensitive devices, cameras, biometric sensing devices, computer mice, trackballs, pen-based pointing devices, etc. Examples of output devices include, but are not limited to, other processing devices, cathode ray tubes (CRTs), plasma displays, light-emitting diode (LED) displays, liquid crystal displays (LCDs), printers, vacuum fluorescent displays (VFDs), surface-conducting electron emission displays (SEDs), field emission displays (FEDs), etc. In some cases, input and output devices may be combined, such as in the case of touch panel displays (e.g., in smartphones, tablets, or other mobile devices).

[0085] System 200 may include a communication interface 240. Communication interface 240 allows software and other data to be transferred between system 200 and external devices, networks, or other external systems 245. For example, data that may include computer software or executable code may be transferred from external system 245 (e.g., a network server, personal computer, or other device) to system 200 and / or from system 200 to external system 245 via communication interface 240. Examples of communication interface 240 include built-in network adapters, network interface cards (NICs), PCMCIA network cards, card bus network adapters, wireless network adapters, Universal Serial Bus (USB) network adapters, modems, wireless data cards, communication ports, infrared interfaces, IEEE 1394 FireWire, and any other device capable of connecting system 200 to a network (e.g., network 120) or another computing device. The communication interface 240 preferably implements industry-published protocol standards, such as Ethernet IEEE 802 standard, Fibre Channel, Digital Subscriber Line (DSL), Asynchronous Digital Subscriber Line (ADSL), Frame Relay, Asynchronous Transfer Mode (ATM), Integrated Services Digital Network (ISDN), Personal Communication Services (PCS), Transmission Control Protocol / Internet Protocol (TCP / IP), Serial Line Internet Protocol / Point-to-Point Protocol (SLIP / PPP), etc., but it may also implement customized or non-standard interface protocols.

[0086] Data transmitted via communication interface 240 typically takes the form of electrical communication signals 255. These signals 255 can be provided to communication interface 240 via communication channel 250. In embodiments, communication channel 250 can be a wired or wireless network (e.g., network 120), or any other type of communication link. Communication channel 250 carries signals 255 and can be implemented using a variety of wired or wireless communication means, including wires or cables, optical fibers, traditional telephone lines, cellular telephone links, wireless data communication links, radio frequency (“RF”) links, or infrared links, to name a few.

[0087] A computer program, including computer-executable code or instructions (e.g., included in software 112), is stored in main memory 215 and / or secondary memory 220. The computer program may also be received via communication interface 240 and stored in main memory 215 and / or secondary memory 220. When executed, the computer program enables system 200 to perform one or more processes described elsewhere herein.

[0088] In this specification, the term "computer-readable medium" is used to refer to any non-transitory computer-readable storage medium used to provide computer-executable code and / or other data to or within system 200. Examples of such media include main memory 215, secondary memory 220 (including internal memory 225 and / or removable media 230), and any peripheral device communicatively coupled to communication interface 240, such as external system 245. These non-transitory computer-readable media are means for providing executable code, programming instructions, software, and / or other data to processor 210.

[0089] System 200 may also include optional wireless communication components that facilitate wireless communication over voice and / or data networks (e.g., in cases where user system 130 is a smartphone or other mobile device, or sensors and / or actuators within target system 140). The wireless communication components include antenna system 270, radio system 265, and baseband system 260. In system 200, radio frequency (RF) signals are transmitted and received over the air by antenna system 270 under the control of radio system 265.

[0090] In one embodiment, antenna system 270 may include one or more antennas and one or more multiplexers (not shown) that perform switching functions to provide transmit signal paths and receive signal paths to antenna system 270. In the receive path, the received RF signal may be coupled from the multiplexer to a low-noise amplifier (not shown), which amplifies the received RF signal and transmits the amplified signal to radio system 265.

[0091] In an alternative embodiment, radio system 265 may include one or more radios configured to communicate on various frequencies. In another embodiment, radio system 265 may combine a demodulator (not shown) and a modulator (not shown) in a single integrated circuit (IC). The demodulator and modulator may also be separate components. In the incoming path, the demodulator removes the RF carrier signal, leaving the baseband received signal transmitted from radio system 265 to baseband system 260.

[0092] The baseband system 260 is also communicatively coupled to a processor 210, which has access to data storage areas 215 and 220. Therefore, data including a computer program can be received from the baseband processor 260 and stored in main memory 210 or secondary memory 220, or executed upon receipt. When executed, such a computer program enables the system 200 to perform one or more of the disclosed processes.

[0093] 3. Sample data flow for managing the target system Figure 3An example data flow for probabilistic optimization according to an embodiment is illustrated. Target system 140 may include a monitoring module 310 and a control module 320. Software 112 of management system 110 may include an analysis and control module 330 and a human-machine interface (HMI) 340. Analysis and control module 330 may interact with or include system model 350, which may be stored in database 114 of management system 110. It should be understood that communication between various systems may be performed via network 120. Additionally, communication between a pair of modules may be performed via an application programming interface (API) provided by one of these modules or through other inter-process communication means.

[0094] Monitoring module 310 can monitor and collect data output from one or more sensors in target system 140. For example, sensors in a power system network can sense voltage at nodes, current on power lines, one or more parameters of assets, the state of switches (e.g., open or closed), etc. Monitoring module 310 can also derive additional data from the collected data. Monitoring module 310 can transmit or “push” the collected and / or otherwise obtained data as system telemetry to analysis and control module 330 (e.g., via analysis and control module 330’s API). Alternatively, analysis and control module 330 can obtain or “pull” system telemetry from monitoring module 310 (e.g., via monitoring module 310’s API). System telemetry can include measurements at each of one or more nodes (e.g., buses in a power system) or other points within the network of target system 140. System telemetry can be transmitted from monitoring module 310 to analysis and control module 330 in real time or periodically as data is collected and / or otherwise obtained. As used herein, the term “real-time” includes events that occur simultaneously, as well as events that have time intervals due to inherent delays caused by latency in processing, memory access, communication, etc.

[0095] The analysis and control module 330 can receive system telemetry from the monitoring module 310 and use the system telemetry in conjunction with the system model 350 to determine the configuration of the target system 140 (e.g., one or more assets in a power system), and then control the target system 140 to transition to the determined configuration. Specifically, the analysis and control module 330 can generate control signals that are transmitted to the control module 320 of the target system 140. For example, the control signals can be sent via the API of the control module 320. The control signals can be transmitted from the analysis and control module 330 of the management system 110 to the control module 320 of the target system 140 in real time, periodically (e.g., before a sliding time window), or in response to user operation when system telemetry is received and analyzed. The analysis and control module 330 can control the target system 140 automatically (e.g., without any user intervention), semi-automatically (e.g., requiring user approval or confirmation), and / or in response to manual user input.

[0096] Each third-party system 150 may supply external data to the analysis and control module 330. The third-party system 150 may transfer or push external data to the analysis and control module 330 (e.g., via the API of the analysis and control module 330). Alternatively, the analysis and control module 330 may obtain or pull external data from the third-party system 150 (e.g., via the API of the third-party system 150). External data may include any data utilized by the analysis and control module 330 and not available from internal sources (such as monitoring module 310 or database 114). External data may include or be constituted by exogenous data from the target system 140. In the context that the target system 140 is an electric system, exogenous data may include one or more historical and / or forecast weather parameters, such as temperature, humidity, solar radiation intensity, wind speed, air pressure, precipitation, warnings, etc. In this case, the third-party system 150 may include a meteorological service, such as the U.S. National Weather Service. As another example, external data may include one or more historical and / or forecast market parameters, such as energy prices in primary or ancillary service markets. In this context, a third-party system 150 may include an energy market in which energy is traded.

[0097] The analysis and control module 330 may receive internal data from the monitoring module 310 and / or the database 114 and / or external data from one or more third-party systems 150, and derive input data from the received internal and / or external data. The input data may include values ​​extracted from and / or otherwise obtained from the received data (e.g., calculated, inferred, interpolated, imputed, etc.). The analysis and control module 330 may access a system model 350 of the target system 140 (e.g., stored in the database 114) and apply a probabilistic optimization model 360 to the input data and the system model 350 to produce output. This output may include multiple ranked resilience measures, as will be discussed elsewhere herein.

[0098] The analysis and control module 330 can make decisions and / or perform operations on the target system 140 based on the output of the probabilistic optimization model 360. As an example, the analysis and control module 330 can use this output to determine the optimal configuration of the target system 140 at a future time. Based on this determination, the analysis and control module 330 can initiate control operations automatically (i.e., without any user intervention), semi-automatically (e.g., with user approval or confirmation via human-machine interface 340), or manually (e.g., in response to a manual user request via human-machine interface 340) to change the real-time or planned operation of the target system 140 based on the optimal configuration. Initiating a control operation may include transmitting control commands to the control module 320 of the target system 140, which can responsively control the target system 140 according to the control commands.

[0099] The control module 320 of the target system 140 (which may be a network controller) receives control signals from the analysis and control module 330 and controls one or more components of the target system 140 according to the control signals. In the context of a power system, examples of such control include, but are not limited to: setting setpoints (e.g., active and / or reactive power of a generator, voltage, etc.), regulating the power output of a generator, regulating the charging or discharging of an energy storage system, regulating the power input of a load, activating or deactivating a load, closing or opening a switch (e.g., a circuit breaker), etc.

[0100] The human-machine interface 340 can generate a graphical user interface (GUI) that is transmitted to the user system 130, and receive input to the GUI via the user system 130. The GUI can provide information about the current state of the target system 140 determined from system telemetry, the predicted state of the target system 140 determined by the analysis and control module 330, the output of the probabilistic optimization model 360, the configuration of the target system 140 determined by the analysis and control module 330, and control decisions or recommendations for the target system 140 determined by the analysis and control module 330. Additionally, the GUI can provide inputs that enable the user of the user system 130 to configure the settings of the analysis and control module 330, build and / or modify the system model 350, train, configure, test and / or deploy the probabilistic optimization model 360, accept or reject decisions or recommendations, specify, approve and / or reject control to be transmitted to the control module 320 of the target system 140, analyze the target system 140, etc.

[0101] System model 350 can be stored as a data structure in database 114 and accessed by modules such as analysis and control module 330 via any known means (e.g., via the API of database 114, direct queries to database 114, etc.). For example, system model 350 can be loaded from database 114 into storage (e.g., 215 and / or 220) and executed by management system 110 as a service accessible via API by analysis and control module 330 (e.g., as a microservice). Management system 110 can provide a separate system model 350 for each target system 140 managed by management system 110, and / or a common system model 350 for two or more target systems 140.

[0102] Similarly, the probabilistic optimization model 360 can be stored as a data structure in database 114 and accessed by modules such as analysis and control module 330 via any known means (e.g., via the API of database 114, direct queries to database 114, etc.). For example, the probabilistic optimization model 360 can be loaded from database 114 into storage (e.g., 215 and / or 220) and executed by management system 110 as a service accessible via API by analysis and control module 330 (e.g., as a microservice). Management system 110 can provide a separate probabilistic optimization model 360 for each target system 140 managed by management system 110, and / or a common probabilistic optimization model 360 for two or more target systems 140.

[0103] 4. Example Process Figure 4An example process 400 for probabilistic optimization according to an embodiment is illustrated. Process 400 can be implemented by software 112, for example, within analysis and control module 330, using probabilistic optimization model 360. Although process 400 is illustrated by a certain arrangement and order of subprocesses, process 400 can be implemented by fewer, more, or different subprocesses, as well as different arrangements and / or orders of subprocesses. Furthermore, it should be understood that any subprocess that does not depend on the completion of another subprocess can be executed before, after, and / or in parallel with that other independent subprocess, even if these subprocesses are described or illustrated in a particular order.

[0104] While not strictly necessary, this document will generally assume that target system 140 is an electrical system, such as a power grid, and more particularly, a power network. A power network can refer to any interconnected electrical components, such as distribution networks and / or transmission networks. Distribution networks deliver electricity to individual consumers, while transmission networks transmit large quantities of electrical energy from power plants to substations. The disclosed embodiments will be applicable to any type of power network, including any type of distribution network and any type of transmission network, provided that suitable data for that power network is available.

[0105] In subprocess 410, input data is acquired. The input data may be acquired based on data from one or more data sources, including one or more internal data sources, such as the monitoring module 310 of the target system 140, database 114, etc., and / or one or more external data sources, such as one or more third-party systems 150. In this embodiment, the input data originates from or is otherwise based on asset data, prediction data, probability data, and / or other data.

[0106] Asset data is associated with one or more, and typically multiple, assets of the target system 140. At least a portion of the asset data may be obtained from an operator's geographic information system (GIS), network controller (e.g., implementation control module 320), etc. Assets can be any component of the target system 140. In embodiments where the target system 140 is an electric system, assets can be any type of power transmission asset, including but not limited to generators, energy storage systems, electrical loads, transformers, inverters, branch lines or other power lines (e.g., overhead or underground power lines), poles on which power lines are installed, capacitor banks, voltage regulators, switches, fuses, reclosers, and / or any other components supporting the power system. Asset data may include an identifier for each asset, one or more parameters for each asset, and connectivity information (e.g., a connectivity model) indicating connections between assets (e.g., electrical connections, communication connections, etc.) in the case of a power network or other network. The parameters for each asset can include the asset's status (e.g., open or closed in the case of a switch, on or off in the case of a generator, charging or discharging in the case of an energy storage system), the asset's measured values ​​(e.g., power output, power input, voltage, current, etc.), and the asset's calculated values, enabling the determination and control of power flow. The parameters for each asset can also include the asset's failure probability or failure probability distribution.

[0107] The parameters for each asset may also include criticality information, which indicates the criticality of the power network asset (such as power lines, generators, electrical loads, etc.). It should be understood that asset criticality refers to the importance or impact of the asset's failure on the normal operation of the target system 140 relative to other assets of the target system 140. For example, loads that are more important during extreme events (e.g., hospitals, fire stations, pumping stations, etc. during extreme weather events) may have higher asset criticality than other loads; power lines supplying more or more critical downstream loads may have higher asset criticality than power lines supplying fewer or less critical downstream loads; power lines closer to power network substations may have higher criticality than power lines at the edge of the power network, and so on. Typically, asset criticality can be proportional to or otherwise related to the optimization objective. For example, if the loss of one asset causes a greater reduction in the value of the objective function (e.g., the total load served) than another asset, then that asset can be assigned a higher criticality than the other asset. Key information may include key factors that classify each asset into one of several key categories (e.g., low, medium, or high), or otherwise quantify the keyness of each asset (e.g., as a numerical value from zero to one, zero to one hundred, etc.). The keyness of electrical loads may be determined by utilities and / or consumers, while the keyness of other nodes within the power network may be determined using graph theory or other methods. Different asset types may use different key factors, or the same key factors may be used for each asset type.

[0108] The following table is a non-exhaustive list of exemplary parameters that can be included in the asset data for each of the various asset types associated with the target system 140, which includes the power distribution network:

[0109] The forecast data is associated with at least one future event. It should be understood that a future event is any event that occurs after the current time, including events that occur a few milliseconds or seconds after the current time, as well as events that occur minutes, hours, days, weeks, months, years, etc., after the current time. Future events can include weather events, such as extreme weather events. Examples of extreme weather events include, but are not limited to, storms, hurricanes, floods, wildfires, etc. Alternatively or additionally, future events can include non-extreme weather events (such as mild storms, high temperatures, etc.) or non-weather events (such as cybersecurity attacks, socio-political events (e.g., riots, terrorist attacks, etc.)). More generally, an event can be any predictable event that may damage or otherwise disrupt the operation of target system 140. In any case, the forecast data can include any predictable parameters of the event within any time period of the event. The time period can span the entire event or any part of the event (e.g., spanning one of multiple time intervals of the event). For example, if the event is a weather event, the forecast data may include a weather forecast for that time period, which may include predicted values ​​for one or more weather parameters, such as temperature, precipitation, humidity, wind speed, pressure, etc. In the case where the target system 140 is a power system including renewable energy resources, the weather forecast may be used to predict power generation in the power system. Alternatively or additionally, in embodiments where the target system 140 is a power system, the forecast data may include predictions of electrical loads on the power system, such as predictions of active and / or reactive power consumed by all electrical loads in the power network. While shorter time intervals for the forecast data will provide higher resolution, the disclosed embodiments will be applicable to any time interval.

[0110] Probabilistic data takes into account the uncertainties associated with future events. Probabilistic data can use realistic assumptions to represent the impact of future events on the assets of the target system 140. It should be understood that the content of the probabilistic data can vary depending on the type of optimization used by the probabilistic optimization model 360. For example, if optimization is performed using stochastic (i.e., scenario-based) modeling, the probabilistic data can include multiple scenarios representing possible asset failures based on their probability of occurrence. If optimization is performed using robust modeling, the probabilistic data can include the failure probability distribution for each of one or more of these assets (e.g., possibly all assets). If optimization is performed using chance-constrained modeling, the probabilistic data can include the failure probability distribution and tolerance probability for each of one or more of these assets. If optimization is performed using risk-driven modeling, the probabilistic data can include multiple scenarios representing possible asset failures based on their probability of occurrence, as well as critical information (e.g., critical factors) for each of one or more assets. If optimization is performed using a stochastic-robust hybrid modeling approach, the probabilistic data can include multiple scenarios representing possible asset failures based on their probability of occurrence, as well as the failure probability distribution for each of one or more of these assets.

[0111] When the probabilistic data includes multiple scenarios, these scenarios can be generated using any suitable technique, such as Monte Carlo sampling. Each scenario can indicate the set of assets that have failed in that scenario and be associated with a probability of occurrence. In this embodiment, the sum of the probabilities of occurrence for all the multiple scenarios is always one.

[0112] Input data can be obtained from a dataset that includes asset data, forecast data, probability data, and / or other data. Input data can be obtained by extracting or parsing values ​​from the dataset, calculating values ​​from one or more values ​​in the dataset, etc. In simple cases, input data can simply include the dataset, or consist of it. Alternatively, the dataset can be processed in some way to obtain the input data.

[0113] In sub-process 420, based on the input data acquired in sub-process 410, probabilistic optimization is performed on the operation of the target system 140 in response to future events. Specifically, the input data can be fed into a probabilistic optimization model 360, which uses probabilistic inputs (such as the probabilistic data mentioned above) to optimize at least one parameter of the operation of the target system 140 in response to future events. At a higher level, the probabilistic optimization model 360 can optimize the objective function that computes at least one parameter of the operation of the target system 140.

[0114] It should be understood that the probabilistic optimization model 360 may include one or more models. For example, the probabilistic optimization model 360 may include different models for each of the multiple resilience measures available for use by the analysis and control module 330. Each of the multiple resilience measures may utilize a different model, or two or more (including possibly all) of the multiple resilience measures may utilize the same model.

[0115] As described above, multiple resilience measures can be available for the analysis and control module 330. For a given target system 140, all the multiple resilience measures supported by the management system 110 can always be available for the analysis and control module 330. Alternatively, for a given target system 140, the multiple resilience measures available for the analysis and control module 330 can depend on one or more factors, such as user settings or preferences, system settings, attributes of the target system 140, etc. When using user settings to limit the multiple available resilience measures, the operator of the target system 140 can limit which resilience measures are available based on the operator's implementation capabilities. If the operator has the resources to implement all the resilience measures supported by the management system 110, the analysis and control module 330 can consider all resilience measures. Conversely, if the operator does not have the resources to implement all the resilience measures supported by the management system 110, the operator can limit the available resilience measures to a subset of those that the operator has the resources to implement. It should be understood that the operator can also limit the available resilience measures for other reasons, such as user preferences, operator requirements, operating scenarios, etc.

[0116] In subprocess 430, it is determined whether there is another flexibility measure to consider. It should be understood that process 400 may consider each of the multiple flexibility measures available to the analysis and control module 330. When there is still another flexibility measure to consider (i.e., "yes" in subprocess 430), process 400 may proceed to subprocess 440 to consider the next flexibility measure. Otherwise, when there is no flexibility measure to consider (i.e., "no" in subprocess 430), process 400 may proceed to subprocess 450.

[0117] Examples of possible resilience measures are described in detail elsewhere herein and may include, for example, load reduction, network topology optimization, preventative network islanding, and / or distributed energy resource (DER) deployment and scheduling. It should be understood that the resilience measures available in the embodiments may include any one or a combination of two or more of these exemplary resilience measures, or may constitute such a measure. For example, in various embodiments, available resilience measures may include, or may constitute such a measure, load reduction and network topology optimization, preventative network islanding, DER deployment and scheduling, load reduction and network topology optimization and preventative network islanding, load reduction and network topology optimization and DER deployment and scheduling, load reduction and network topology optimization and preventative network islanding and DER deployment and scheduling, load reduction and preventative network islanding and DER deployment and scheduling, network topology optimization and preventative network islanding, network topology optimization and DER deployment and scheduling, network topology optimization and preventative network islanding and DER deployment and scheduling, preventative network islanding and DER deployment and scheduling, etc., or may constitute such a measure.

[0118] In subprocess 440, an effectiveness measure of the considered resilience measures is determined based on the solution of the probabilistic optimization model 360 in subprocess 420. The effectiveness measure quantifies the effectiveness of the resilience measures against future events on the operation of the target system 140. For example, the effectiveness measure may be based on (e.g., including or constituted by) the expected improvement in the operation of the target system 140 assuming the resilience measures are implemented during future events. As another example, the effectiveness measure may be based on the ease of implementing the resilience measures. In a preferred embodiment, the effectiveness measure is based on both the expected improvement in the operation of the target system 140 assuming the resilience measures are implemented during future events and the ease of implementing the resilience measures. In this case, even if a certain resilience measure has higher effectiveness, it may be ranked after another resilience measure with lower effectiveness but easier implementation. For example, effectiveness metrics can be determined for the following: load reduction only, network topology optimization only, preventative network islanding only, DER deployment and scheduling only, each of load reduction and network topology optimization, each of load reduction and preventative network islanding, each of load reduction and DER deployment and scheduling, each of load reduction and network topology optimization and preventative network islanding, each of load reduction and network topology optimization and DER deployment and scheduling, each of load reduction and network topology optimization and preventative network islanding and DER deployment and scheduling, each of load reduction and preventative network islanding and DER deployment and scheduling, each of network topology optimization and preventative network islanding, each of network topology optimization and DER deployment and scheduling, each of preventative network islanding and DER deployment and scheduling, etc.

[0119] In subprocess 450, multiple resilience measures and their corresponding effectiveness metrics calculated in the iterations of subprocess 440 are output. For example, these resilience measures and their corresponding effectiveness metrics can be output to the network controller of the target system 140. The network controller can be a control function of the analysis and control module 330, in which case the output can be intra-process or inter-process communication. Alternatively, the network controller can be the control module 320 of the target system 140, or another component separate from the analysis and control module 330.

[0120] As another example, multiple resilience measures and their corresponding effectiveness metrics can be output to human-machine interface 340 for review by the operator of target system 140. In this case, the operator can manually select one or more resilience measures to be implemented from among the multiple resilience measures based on, for example, their corresponding effectiveness metrics and other potential factors. Thus, the operator can assess the trade-offs between the value of the resilience measures and other non-grid-related factors. For example, operators may choose to implement the following: load reduction only, network topology optimization only, preventative network islanding only, DER deployment and scheduling only, each of load reduction and network topology optimization, each of load reduction and preventative network islanding, each of load reduction and DER deployment and scheduling, each of load reduction and network topology optimization and preventative network islanding, each of load reduction and network topology optimization and DER deployment and scheduling, each of load reduction and network topology optimization and preventative network islanding and DER deployment and scheduling, each of load reduction and preventative network islanding and DER deployment and scheduling, each of network topology optimization and preventative network islanding, each of network topology optimization and DER deployment and scheduling, each of preventative network islanding and DER deployment and scheduling, etc.

[0121] Before outputting multiple resilience measures and their corresponding effectiveness measures, these measures can be ranked according to their effectiveness measures. For example, effectiveness measures can utilize the same effectiveness measure unit and / or be normalized to the same value range, making it easy to compare the effectiveness measure of a first resilience measure with the effectiveness measure of a second resilience measure that is different from the first. It should be understood that resilience measures with higher effectiveness measures can be ranked higher than those with lower effectiveness measures.

[0122] Multiple resilience measures may include, or constitute, load reduction, network topology optimization, preventative network islanding, and / or deployment and / or scheduling of one or more energy resources. Each of these resilience measures will be described in more detail elsewhere in this document. It should be understood that these resilience measures are provided by way of example, and multiple resilience measures may include, exclude, or include a subset of these resilience measures, or constitute them. In addition, multiple resilience measures may include additional resilience measures not specifically described herein. Essentially, any measure that, when implemented, can reduce disruption to the operation of the target system 140 during future events can be included among the multiple resilience measures available to the analysis and control module 330.

[0123] As described above, the probabilistic optimization model 360 applied to the input data in subprocess 420 can include different models for different resilience measures among multiple resilience measures. For example, if the target system 140 is a power network and multiple resilience measures include load shedding, the probabilistic optimization model 360 can include a model whose objective function calculates the expected load supply of the power network and maximizes that expected load supply. In embodiments where the asset data includes critical information indicating the criticality of the loads in the power network, the objective function can weight these loads according to the corresponding criticality factors. As another example, if the target system 140 is a power network and multiple resilience measures include network topology optimization, the probabilistic optimization model 360 can model the topology of the power network, and the solution of the probabilistic optimization model 360 can include the optimized network topology to which the power network should be reconfigured. As another example, where the target system 140 is a power network and multiple resilience measures include preventative islanding, probabilistic optimization model 360 can model the electrical islanding within the power network, and the solution of probabilistic optimization model 360 can include a microgrid configuration comprising multiple electrical islands (e.g., microgrids) within the power network. As another example, where the target system 140 is a power network and multiple resilience measures include the deployment and scheduling of distributed energy resources, probabilistic optimization model 360 can model the deployment and / or scheduling of distributed energy resources within the power network, and the solution of probabilistic optimization model 360 can include the preventative deployment of one or more mobile distributed energy resources within the power network and / or the real-time scheduling of each of one or more distributed energy resources within the power network.

[0124] Process 400 can be executed automatically and iteratively at each expiry date in multiple time intervals or according to another cycle. For example, Process 400 can be executed for future time windows based on currently available input data. In each iteration of Process 400, the future time window can slide according to a time step. The time step can be any amount of time, and in embodiments, it can be equal to the length of the time interval and the time window. For example, if the time window is a 24-hour period, Process 400 can be executed daily for future events of the following day. It should be understood that as the length of the time window decreases, the resolution of the optimization increases. Therefore, it is generally preferred to have smaller time windows, such as minutes, tens of minutes, hours, etc. However, this may not be practical for some resilient measures (such as network topology optimization) because reconfiguring the network topology every few minutes is not feasible. Therefore, an appropriate balance (e.g., a 6-hour time window) can be found based on available resilient measures and / or other factors. In additional or alternative embodiments, process 400 may be performed in response to manual user action via human-machine interface 340 and / or in response to another triggering event, such as a notification from third-party system 150 (e.g., a weather service) regarding an impending event (e.g., an extreme weather event).

[0125] 5. Example validity measures The effectiveness measure of a resilience measure should quantify the potential benefits of implementing that measure. In this embodiment, the effectiveness measure is calculated relative to the case where no resilience measure is implemented. Specifically, the effectiveness measure can be determined by comparing the target system 140 with the resilience measure implemented with an equivalent target system 140 without the resilience measure implemented.

[0126] Since effectiveness metrics must be determined prior to future events, a scenario-based approach can be used to account for the uncertainty of how future events will actually unfold. Specifically, the performance of resilience measures can be evaluated on at least a subset of possible scenarios. For example, if the future event is a weather event, each scenario can represent a set of one or more possible weather conditions and their corresponding effects on target system 140. This approach provides knowledge of: (i) what improvements are needed in target system 140 in the long term to permanently strengthen it against such events; and (ii) the expected performance of target system 140 during such events to enable the implementation of short-term resilience measures. To ensure that the evaluation of resilience measures is unbiased, the scenarios used to determine effectiveness metrics can differ from those used in the scenario-based implementation of probabilistic optimization model 360.

[0127] Figure 5An example process 500 for calculating a measure of the effectiveness of resilience measures according to an embodiment is illustrated. System model 350A of the target system 140 with resilience measures implemented and system model 350B of the target system 140 without resilience measures implemented are both input into the evaluation process 505. The evaluation process 505 can be performed on system model 350A and system model 350B separately, either serially or in parallel.

[0128] For each of system models 350A and 350B, evaluation process 505 evaluates the performance of target system 140 in each of a plurality of scenarios 510, illustrated as scenarios 510A, 510B, 510C, ..., 510X, which represent at least a subset of possible scenarios during future events. As used herein, reference numerals with additional letters will be used to refer to specific components, while the same reference numerals without any additional letters will be used to refer collectively to the plurality of said components or to a general or arbitrary instance of said components. Thus, for example, the term “scenario 510” collectively refers to scenarios 510A, 510B, 510C, ..., 510X, and the term “scenario 510” can refer to any single scenario 510A, 510B, 510C, ..., 510X.

[0129] It should be understood that each scenario 510 represents a possible real-world situation. Scenario 510 may be generated, for example, by the analysis and control module 330. Each scenario 510 may indicate the state of at least a subset of multiple assets in the target system 140. For example, scenario 510 may indicate the potential state (e.g., operation or failure) of each power line in the power system (e.g., power network) of the target system 140 during future events.

[0130] For each of the multiple scenarios 510, the evaluation process 505 calculates a metric 515, illustrated as metrics 515A, 515B, 515C, ..., 515X, representing the predictive performance of the target system 140 in the corresponding scenario 510. For example, metric 515A represents the predictive performance of the target system 140 in scenario 510A, metric 515B represents the predictive performance of the target system 140 in scenario 510B, metric 515C represents the predictive performance of the target system 140 in scenario 510C, and metric 515X represents the predictive performance of the target system 140 in scenario 510X. Each of the metrics 515 for scenario 510 is output by the evaluation process 505 to the metric analysis module 520.

[0131] The measurement analysis module 520 can calculate a validity measure 530 based on the measure 515 calculated by the evaluation process 505. For example, the validity measure 530 can be calculated based on an algorithm that determines a composite value of the measure 515. The composite value can be the mean, weighted mean (e.g., weighted according to the probability of occurrence of each scenario 510), median, etc. of the measure 515.

[0132] Metric 515 and / or effectiveness metric 530 may each include a value for each of one or more key performance indicators (KPIs). It should be understood that the KPIs used for each metric 515 may be the same. The KPIs used may be selected by the operator of the target system 140. Different KPIs may be used depending on the specific resilience measures to be ranked.

[0133] Any one or more key performance indicators (KPIs) can be used to measure 515 and / or the effectiveness measure 530. Examples of KPIs include, but are not limited to, total load supplied (or total load not supplied), critical load supplied (or critical load not supplied), average load outage duration, average total load outage duration (e.g., System Average Outage Duration Index (SAIDI)), average node voltage overrun percentage, average branch power flow overrun percentage, network connectivity percentage to power source, photovoltaic (PV) utilization percentage, battery energy storage system (BESS) state of charge (SOC) margin overrun percentage, number of customers experiencing power outages, etc. PV utilization percentage and BESS SOC margin overrun percentage are DER-specific measures. Similar DER-specific measures can be used for other types of distributed energy resources.

[0134] Total load supply can be calculated as:

[0135] in, N It is the set of nodes in the target system 140. i It is an index in the node set. It is the first i The value of active power load at each node (e.g., in kilowatts (kW)), and It is the first i The value of reactive power load at each node (e.g., in kilovolt-ampere reactive power (kVAr)).

[0136] Critical load supply can be calculated as follows:

[0137] in, It is the set of key nodes in the target system 140.

[0138] The average load outage duration can be calculated (e.g., in time units such as hours, minutes, etc.):

[0139] in, T It is a time period that includes multiple time intervals, and Δ t It refers to the duration. The average total load outage duration (e.g., SAIDI) can be calculated (e.g., in time units such as hours, minutes, etc.):

[0140] The average node voltage over-limit interval percentage can be calculated (e.g., expressed as a percentage):

[0141] in, It is in the t Within the time interval, the first i Voltage at each node V It is the minimum limit (per unit) for node voltage, and It is the maximum limit (per unit) of node voltage.

[0142] The percentage of network connectivity to the power supply can be calculated (e.g., expressed as a percentage):

[0143] PV utilization percentage can be calculated (e.g., expressed as a percentage) as follows:

[0144] in, The PV generator is in the first t Within the time interval i The active power output at the node, and The PV generator is in the first t Within the time interval i The predicted active power output at the node.

[0145] The percentage of the BESS SOC reserve margin exceeding the limit can be calculated (e.g., expressed as a percentage):

[0146] in, It is the first t Within the time interval, the first i The charge state of the BESS element at each node This is the maximum limit of the state of charge, and SOC It is the minimum constraint on the state of charge.

[0147] 6. Flexible measures As described above, multiple resilience measures may include load reduction, network topology optimization, preventative network islanding, and / or DER deployment and / or scheduling. In embodiments, multiple resilience measures include at least load reduction and network topology optimization. Typically, utilities already have the necessary infrastructure and systems to implement load reduction (e.g., demand response) and network topology reconfiguration (e.g., via remote control switches in target system 140). Utilities may implement preventative network islanding and / or DER scheduling based on the availability of the islanding system and fixed and / or mobile distributed energy resources. It is noteworthy that load reduction and DER scheduling can ensure the safe operation of target system 140 by maintaining supply and demand balance within target system 140. Generally, in terms of ease of implementation (which can be considered when ranking resilience measures), network topology optimization is the easiest to implement, load reduction is the second easiest, DER deployment and scheduling is the third easiest, preventative network islanding using only existing distributed energy resources is the fourth easiest, and preventative network islanding using one or more mobile distributed energy resources is the fifth easiest or the most difficult to implement.

[0148] The probabilistic optimization model 360 may include one or more optimization models for multiple resilience measures. For example, an optimization model may be constructed for each resilience measure, or an optimization module may be constructed for two or more resilience measures. The optimization models for different resilience measures may be different from each other or the same. In any case, each optimization model may accept probabilistic inputs in the input data that take into account the inherent uncertainty of the future events under consideration, and output the optimal decision for improving the operational resilience of the target system 140 in an uncertainty-aware manner for the applicable resilience measures.

[0149] In an embodiment, the probabilistic optimization model 360 may include at least an optimal power flow (OPF) model. A typical OPF problem finds the optimal decision for the operation of the target system 140 by optimizing (e.g., minimizing or maximizing) an objective function subject to any operational constraints on the target system 140. Typical objective functions include, but are not limited to, maximizing the supplied load, maximizing load shedding, minimizing network losses, and minimizing operating costs. Typical operational constraints include, but are not limited to, constraints on power flow, constraints on generation limitation, constraints on load control, constraints on voltage, constraints on switching limitation, and constraints on ramp rate.

[0150] When making operational decisions in response to anomalous events (such as extreme weather events), the optimal power flow must take into account the fact that components of the target system 140 may fail to operate as expected due to significant changes in the operating environment. Therefore, in this embodiment, the OPF model is modified to account for unpredictable scenarios caused by future events, adding new constraints supporting resilient measures, and / or adding new constraints that consider operator preferences (e.g., regarding acceptable risk, prioritization of resilient measures, etc.). One example of this modified OPF model described herein is based on scenario-based stochastic optimization. A second example of this modified OPF model described herein is based on risk-driven optimization. However, alternative OPF optimizations can be used, including but not limited to robust optimization, stochastic-robust hybrid optimization, chance-constrained optimization, etc., with appropriate modifications to the constraints.

[0151] 6.1. Load Reduction Extreme weather events can introduce a high degree of uncertainty into the operation of target systems 140 (such as power distribution networks). This uncertainty largely stems from the different assets that may fail (e.g., damage caused by the event). Under normal operating conditions, asset failure rates are low. However, severe or extreme events can lead to high failure rates among assets and may cause multiple failures in a short period of time. Furthermore, during such events, it is very difficult to physically assess the location of faults and provide immediate repairs due to potential damage to non-electrical infrastructure such as roads, buildings, etc.

[0152] Therefore, the OPF model should consider the uncertainty of asset failures. The most vulnerable assets in a distribution network are utility poles and power lines. Damage to these assets is a major cause of power outages due to weather events. Therefore, the basic structure of the OPF model should at least consider the uncertainty of utility pole and line failures.

[0153] During extreme weather events, network operators aim to maximize the load supplied to consumers while keeping load priorities in mind. For example, the highest priority might be given to critical loads such as hospitals, fire stations, and pumping stations. Conversely, the lowest priority might be given to residential loads, commercial buildings, and community parks. It is important to note that load priorities can be dynamic and may change depending on the type of event.

[0154] In this embodiment, the OPF model accounts for the uncertainty of load priority and asset failure by maximizing the supplied load as follows:

[0155] Where Ω represents the set of scenes. T It is a set of time intervals. N It is the set of nodes in the target system 140. It is a scene in the scene set Ω s The probability of occurrence, It is a set of nodes N The Middle i The weight of the load at each node (e.g., indicating the criticality of the load). It is in the s In the first scenario t In the nth time interval i The value of active power load at each node (e.g., in kW), and It is in the s In the first scenario t In the nth time interval i The reactive power load at each node (e.g., in kVAr). At a higher level, the OPF model maximizes the expected load supply summed across all nodes, time intervals, and scenarios while considering the probability of each scenario, prioritizing loads with higher weights (e.g., more critical).

[0156] As described above, the probabilistic OPF model can use a scenario-based approach to calculate the expected load supply across multiple different scenarios. These scenarios can include normal operation scenarios and multiple failure scenarios, in which one or more assets fail due to future events. Each scenario can indicate which assets (if any) are operational and which assets (if any) have failed within that scenario. In the case of a power network, each scenario s can be described as an edge set. This edge set, for each power line in the power network, indicates whether the power line is in operation or has failed.

[0157] The probabilistic OPF model can include the following first set of constraints, which use a branch power flow model to represent the node power balance: Constraint (1):

[0158] in, It is in the s In the first scenario t In the nth time interval i The value of active power output (e.g., in kW) of distributed energy resources (e.g., generated) at each node. It is connected to the first i The set of nodes from which edges originate. It is connected to the terminator. i The set of nodes whose edges are given by a given node. It is in the s In the first scenario t The time interval connects to the firsti The and the first j The value of active power flow on the power lines of each node (e.g., in kW). N DER It is the set of all nodes associated with distributed energy resources, and It represents the set of all nodes in a substation.

[0159] Constraint (2):

[0160] in, It is in the s In the first scenario t In the nth time interval i The value of reactive power output (e.g., in kVAr) of distributed energy resources (e.g., generated) at each node, and It is in the s In the first scenario t The time interval connects to the first i The and the first j The predicted value of reactive power flow on the power lines of each node (e.g., in kVAr).

[0161] Constraint (3):

[0162] Constraint (4):

[0163] The objective of this first set of constraints is to ensure that the power balance condition is met at every node in the power system. Constraints (1) and (2) represent the power balance of all nodes connected to loads and generators, while constraints (3) and (4) represent the power balance of all nodes connected only to loads. In general, these constraints ensure that the net power flow through each node is always zero. For simplicity, power losses are ignored in these constraints.

[0164] The probabilistic OPF model can include the following second set of constraints, which represent line power flow capacity constraints and ensure that the total power flow on the power line does not exceed the rated capacity of the power line: Constraint (5):

[0165] in, It is the connection of the first i The node and the first j Limitations on the active power flow of power lines at each node (e.g., in kW).

[0166] Constraint (6):

[0167] in, It is the connection of the first i The node and the first j The limits of reactive power flow of power lines at each node (e.g., in kVAr).

[0168] The probabilistic OPF model can include the following third set of constraints, which represent voltage constraints and ensure that the solution of the OPF model does not lead to overvoltage or undervoltage in the power system: Constraint (7):

[0169] in, It is in the s In the first scenario t In the nth time interval i Voltage at each node It is in the s In the first scenario t In the nth time interval j Voltage at each node It is used to calculate the connection of the first i The and the first j The linearized matrix of active power voltage drop on the power lines at each node, and It is used to calculate the connection of the first i The and the first j The linearized matrix of reactive power voltage drop on the power lines of each node.

[0170] Constraint (8):

[0171] in, It is the minimum limit (per unit) for node voltage. It is the maximum limit (per unit) for node voltage, and It is in the s In the first scenario t In the nth time interval i The square of the node voltage at each node (per unit).

[0172] Constraint (9):

[0173] in, This is the reference voltage (per unit) of the substation node. Constraints (7) and (8) calculate the node voltage and limit it to acceptable limits. To model the voltage drop between nodes based on the magnitude of the power flow, a linearization method can be used. An example of such a linearization method is described in the following literature: DB Arnold, “Model-Free Optimal Control of Distributed Energy”, UC Berkeley, 2015, which is hereby incorporated in its entirety by reference. Matrix and These represent the linearization coefficients used to model the impact of actual power flow and reactive power flow on node voltage drop. The values ​​of these matrices can be calculated as follows:

[0174]

[0175] The probabilistic OPF model can include the following fourth set of constraints, which represent load constraints and ensure that the solution of the OPF model can supply the load demand within the range defined by the minimum load that must be supplied and the maximum predicted load: Constraint (10):

[0176] in, It is in the s In the first scenario t Within the time interval, it is necessary to send to the first i The minimum active power supplied by each node (e.g., in kW), and It is in the s In the first scenario t Within the time interval, the first i The maximum predicted value of reactive power load at each node (e.g., in kW).

[0177] Constraint (11):

[0178] in, It is in the s In the first scenario t Within the time interval, it is necessary to send to the first i The minimum reactive power supplied by each node (e.g., in kAVr), and It is in the s In the first scenario t Within the time interval, the first iThe maximum predicted reactive power load at each node (e.g., in kAVr). It is worth noting that the maximum predicted load can vary for different scenarios within the scenario set Ω. Therefore, the probabilistic OPF model can also account for uncertainties in load forecasting.

[0179] The aforementioned probabilistic OPF model can be used to generate resilient load reduction measures. Specifically, multiple scenarios can be acquired in subprocess 410, and these scenarios can be provided to a probabilistic optimization model 360, which includes the probabilistic OPF model, from the input data. For example, asset data can include failure probabilities or failure probability distributions for multiple assets, and multiple failure scenarios can be generated based on these failure probabilities or failure probability distributions. Alternatively, failure scenarios can be pre-generated and provided in the asset data or other data acquired in subprocess 410.

[0180] Regardless of how the multiple fault scenarios are acquired, a probabilistic OPF model can be applied to these scenarios to obtain the optimal (e.g., maximum) value of the expected load supply for all scenarios during the future event. If this optimal value is less than the expected load during the future event, a load shortage may exist during the future event. Therefore, load reduction resilience measures can be output as one of several resilience measures proposed to improve operational resilience during the future event. The proposed load reduction value (e.g., the amount of power to be reduced) can be determined as the difference between the optimal load supply calculated by the probabilistic OPF model and the expected load during the future event, or based on that difference.

[0181] Figure 6 The illustration depicts an architecture for probabilistic optimization of load shedding according to an embodiment utilizing load shedding as a resilient measure. In the illustrated embodiment, multiple scenarios 610 representing a scenario set Ω are generated (e.g., by analysis and control module 330), illustrated as scenarios 610A, 610B, 610C, ..., 610X. Each scenario 610 may indicate the state of at least a subset of multiple assets in the target system 140. For example, scenario 610 may indicate the potential state (e.g., operational or faulty) of each power line in the power system (e.g., power network) of the target system 140 during future events.

[0182] Multiple scenarios 610, along with asset data 620 and prediction data 630, are input into the OPF model 660 of the probabilistic optimization model 360. It should be understood that the use of multiple scenarios 610 takes into account the uncertainty in the prediction data 630 and enables the OPF model 660 to be probabilistic. Each of the multiple scenarios 610 can be associated with a corresponding probability that scenario 610 will occur, such that the OPF model 660 takes into account the probability of occurrence of multiple scenarios 610. In an alternative embodiment, instead of or in addition to the multiple scenarios 610, the failure probability distribution of each of one or more of these assets can be input into the OPF model 660.

[0183] The decisions to be made by the OPF model 660 are made relative to the current state of the target system 140 (which may be a power distribution network). The output of the OPF model 660 is load shedding 670. In an embodiment, load shedding 670 identifies one or more electrical loads to be shedding, for example, by shutting down the electrical load or otherwise reducing the power consumption of the electrical load. In other words, load shedding 670 may indicate the amount of power to be shedding from one or more electrical loads in the network of the target system 140. It should be understood that load shedding 670 may be determined by the OPF model 660 based on multiple scenarios 610, such that load shedding 670 takes into account the probability of failure of assets (e.g., power lines) in the target system 140 due to future events.

[0184] Load shedding 670 can be output to a network controller 680 managing the target system 140. The network controller 680 can be implemented as a system 200 implementing control module 320. Before and / or during a future event, the network controller 680 can reconfigure the target system 140 to reflect load shedding 670 and receive feedback from the target system 140 reflecting its current state. The network controller 680 can provide feedback to a module (e.g., analysis control module 330) that generates multiple scenarios 610 based on the current state of the target system 140, including or constituting the current state of the target system 140. As discussed above, this can include scenarios 610 indicating the potential state (e.g., operation or failure) of assets (e.g., power lines) in the power system (e.g., power grid) of the target system 140 during a future event.

[0185] 6.2. Network Topology Optimization Network topology optimization can utilize the same probabilistic OPF model described above regarding load reduction. Given scenarios in the scenario set Ω, the basic objective of network topology optimization is to optimize the network topology of target system 140 such that power flow on power lines with the highest failure probability is minimized, while maximizing load supply. This strengthens target system 140 against future events by minimizing the impact of failures on the power lines with the highest failure probability on the operation of target system 140 during the event.

[0186] To provide network topology optimization as a resilient measure, variables and constraints related to the operation of switches in the target system 140 can be added to the probabilistic OPF model described above. These switches can be interpreted as network branches; therefore, the set of switches can be denoted as... .

[0187] The following fifth set of constraints, representing branch power flow limitations, can be added to the probabilistic OPF model: Constraint (12):

[0188] Constraint (13):

[0189] in, It indicates the connection of the first i The node and the first j A binary value indicating whether the switch state of a node is open or closed (e.g., ...). = 1 indicates that the switch is closed, and = 0 indicates that the switch is off.

[0190] It is worth noting that, ( The value of ) after optimization represents the optimized network topology of the target system 140. Since these switching state decisions do not change based on the scenario considered, the switching state variables... It does not have a scene index.

[0191] Additionally, the sixth set of constraints, representing the additional voltage constraints of nodes connected by switches, can be added to the probabilistic OPF model: Constraint (14):

[0192] Constraint (15):

[0193] in, It is to capture the scene s The Middle i The and the firstj Relaxation variables for the voltage difference between nodes. Add relaxation variables. In order to ensure that when the first ij When the switch on the edge is turned off, constraint (14) is not violated. Constraint (15) ensures that when the first... ij When the switch on the edge is closed (i.e., ), ,and and The relationship was maintained. However, if the first ij The switch on the edge is off (i.e., If so, there is no need to maintain it. and The relationship between them.

[0194] When optimizing network topology, the final network topology may contain network loops. However, distribution networks typically operate in a radial pattern from power sources to individual consumers (i.e., without network loops). Therefore, to ensure that the network topology maintains a radial structure and does not contain loops, one or more radial constraints can be added to the probabilistic OPF model. In graph theory-based approaches, two conditions must be met to maintain a radial network: (i) the total number of power lines must equal the total number of nodes minus the total number of substations; and (ii) the network must remain fully connected.

[0195] To incorporate the above conditions and ensure the radiality of the optimized network topology, the following seventh set of constraints can be added to the probabilistic OPF model: Constraint (16):

[0196] Constraint (17):

[0197] Constraint (18):

[0198] In alternative embodiments where the utility allows loops (e.g., mesh operation), this seventh set of constraints may be omitted.

[0199] Figure 7The illustration depicts an architecture for probabilistic optimization of network topology according to an embodiment that utilizes network topology optimization as a resilient measure. In the illustrated embodiment, multiple scenarios 610 representing a scenario set Ω are generated (e.g., by analysis and control module 330), illustrated as scenarios 610A, 610B, 610C, ..., 610X. These scenarios can be the same scenarios 610 described elsewhere, and therefore any description of scenario 610 in other contexts also applies to scenario 610 in this context, and vice versa.

[0200] Multiple scenarios 610, along with asset data 620 and prediction data 630, are input into the OPF model 760 of the probabilistic optimization model 360. It should be understood that the use of multiple scenarios 610 takes into account the uncertainty in the prediction data 630 and enables the OPF model 760 to be probabilistic. Each of the multiple scenarios 610 can be associated with a corresponding probability that scenario 610 will occur, such that the OPF model 760 takes into account the probability of occurrence of multiple scenarios 610. In an alternative embodiment, instead of or in addition to the multiple scenarios 610, the failure probability distribution of each of one or more of these assets can be input into the OPF model 760.

[0201] The decisions to be made by the OPF model 760 are made relative to the current state of the target system 140 (which may be a distribution network). The current state of the target system 140 should satisfy radial constraints (e.g., equations (16)-(18)). Therefore, to ensure that the radial constraints are satisfied, one of the scenarios 610 (illustrated as scenario 610A) can be matched with the current state of the target system 140. Only the radial constraints need to be added to the OPF model 760 for this one scenario 610A representing the current state of the target system 140. This is sufficient because if the network of the target system 140 is radial with respect to the current state, the network will remain radial after any faulty assets (e.g., power lines) are removed.

[0202] The output of the OPF model 760 is an optimized network topology 770. In an embodiment, the optimized network topology 770 includes optimized switching states of the target system 140. In other words, the optimized network topology 770 can indicate the state (e.g., open or closed) of each switch in the network of the target system 140. It should be understood that the optimized network topology 770 can be determined by the OPF model 760 based on multiple scenarios 610, such that the optimized network topology 770 takes into account the probability of assets (e.g., power lines) in the target system 140 failing due to future events.

[0203] The optimized network topology 770 can be output to a network controller 680 managing the target system 140. The network controller 680 can be implemented as a system 200 implementing control module 320. Before and / or during future events, the network controller 680 can reconfigure the target system 140 to reflect the optimized network topology 770 and receive feedback from the target system 140 reflecting its current state. The network controller 680 can provide feedback to a module (e.g., analysis control module 330) that generates multiple scenarios 610 based on the current state of the target system 140, including or constituting the current state of the target system 140. As discussed above, this can include scenario 610A representing the current state of the target system 140 and applying radial constraints, as well as other scenarios 610 indicating the potential state (e.g., operation or failure) of assets (e.g., power lines) in the power system (e.g., power grid) of the target system 140 during future events.

[0204] While network topology optimization is an important tool for hardening target system 140 against the impact of events, changing the network topology every few minutes during an event may be impractical due to physical constraints in target system 140 and / or computational resource constraints in management system 110. Therefore, in this embodiment, decisions regarding network topology updates can be made at a feasible time resolution (e.g., every N hours), which can be set by the operator. In this case, at the expiration of each of the multiple time intervals, multiple scenarios 610 can be generated based on the current state of target system 140, and an OPF model 760 can be applied to these multiple scenarios 610, along with asset data 620 (e.g., which may represent current asset information) and / or prediction data 630 (e.g., which may represent predictions for one or more subsequent time intervals), to determine a new optimized network topology 770, which can then be used by network controller 680 to reconfigure target system 140. This process can be repeated for each of the multiple time intervals until the event has ended and a post-event (e.g., recovery) phase has begun.

[0205] The time interval used can be set by the operator of the target system 140. For example, the time interval could be six hours. Therefore, for an 18-hour event, a first iteration of network topology probabilistic optimization for the first six-hour period of the event can be performed before the event begins, and the network controller 680 can reconfigure the target system 140 at the start of the first six-hour period. A second iteration of network topology probabilistic optimization for the second six-hour period of the event can be performed before the first six-hour period ends, and the network controller 680 can reconfigure the target system 140 at the start of the second six-hour period. A third iteration of network topology probabilistic optimization for the third six-hour period of the event can be performed before the second six-hour period ends, and the network controller 680 can reconfigure the target system 140 at the start of the third six-hour period. Finally, after the third six-hour period ends, the post-event phase can begin, and the network topology probabilistic optimization can end or continue, depending on the implementation.

[0206] 6.3. Preventive Network Silo Delineation Preventative network islanding (also referred to as "preventative microgrid formation" or "preventative dynamic microgrid formation") divides a target system 140 (e.g., a power system, such as a power network comprising or consisting of distribution networks) into multiple electrical islands prior to future events. It should be understood that an electrical island is a part of the power system, including generation, network, and loads, whose network connections to other parts of the power system have been disconnected. Therefore, each of the multiple electrical islands can have independent grid-connected generation resources; in this case, the electrical island may be referred to herein as a "microgrid."

[0207] The basic concept of preventative network islanding is to transform the power system into multiple self-sustaining microgrids to ensure continued operation during future events. Benefits of preventative network islanding can include, for example, limiting the impact of damage to network assets to small electrical islands so that the damage does not affect the entire network, eliminating dependence on network assets with a high probability of failure, reducing operational uncertainty caused by events, and / or facilitating post-event (e.g., recovery) phases. Preventative network islanding can divide the target system 140 into small islanded microgrids by creating microgrids around existing grid-connected distributed energy resources and / or by utilizing mobile grid-connected distributed energy resources (e.g., with or without any existing grid-connected distributed energy resources). It is worth noting that the portion of the power network connected to the substation may be referred to herein as the “main grid.”

[0208] Figure 8An example of microgrid formation in preventative network islanding is illustrated according to an embodiment. Initially, the target system 140 may have a first configuration 800A in which no electrical islands exist. In the first configuration 800A, the network may have multiple nodes 810 connected by multiple power lines 820. In the illustrated example, the multiple nodes 810 include two existing distributed energy resources 830A and 830B, which have grid-forming capabilities and at least one is operating in grid-forming mode, these distributed energy resources supplying power in the target system 140.

[0209] Before or at the start of a future event, the target system 140 (e.g., a network controller 680 that can implement control module 320) can be reconfigured from a first configuration 800A to a second configuration 800B based on preventative electrical islanding determined by the solution of probabilistic optimization model 360. In the second configuration 800B, power lines 820A and 820B have been shut down to disconnect their respective nodes 810. Specifically, switches on power lines 820A and 820B have been opened to disconnect the respective nodes 810 from each other. In addition, mobile distributed energy resources 830M have been dispatched and deployed. Thus, three electrical islands 840A, 840B, and 840C are formed. Electrical island 840A is powered by existing distributed energy resources 830A, electrical island 840B is powered by existing distributed energy resources 830B, and electrical island 840C is powered by the deployed mobile distributed energy resources 830M.

[0210] Distributed energy resources 830 can be any asset that supplies electricity, such as generators using non-renewable and / or renewable resources, battery storage systems, etc. Distributed energy resources 830 can be stationary or mobile. Stationary or static distributed energy resources 830 (e.g., 830A and 830B) are resources that already exist within the network during the determination of preventative network islanding. Mobile distributed energy resources 830 (e.g., 830M) are capable of being moved from one location to another. Battery storage systems are particularly useful as mobile distributed energy resources 830. Mobile distributed energy resources 830 can be added to the network between the time of determining preventative network islanding and any other time before, at the start of, or during a future event.

[0211] Figure 9AThe illustration shows an architecture 900 for probabilistic preventative network islanding, based on an embodiment utilizing preventative network islanding as a resilience measure. Other OPF models described herein are scenario-based OPF (S-OPF) models, which proactively consider the uncertainty of asset failure using multiple scenarios 610. In contrast, preventative network islanding can passively consider asset uncertainty using risk-based metrics. This type of OPF model may be referred to herein as a “risk-driven” OPF (RD-OPF) model.

[0212] The S-OPF model utilizes multiple scenarios 610, while the RD-OPF optimization model 960 considers only a single scenario 610 that can be input into the optimization model 960 along with asset data 620 (which may include DER capacity, network information (e.g., network topology, switch status, etc.), asset criticality, asset risk factors, etc.) and forecast data 630 (which may include weather forecasts, load forecasts, generation forecasts, etc.). A single scenario 610 may include a network topology representing the healthy operating state of the power network (e.g., no faulty assets) or its current operating state at the time of optimization. The network topology may identify each node and edge in the power network's power graph, the status of each switch in the power network (e.g., open or closed), the deployment of each distributed energy resource 830 (e.g., the nodes to which each distributed energy resource 830 is connected), etc. In this embodiment, the optimization model 960 assumes that DER deployment has already occurred. DER deployment can be performed as described elsewhere herein to deploy one or more mobile distributed energy resources 830 at flexible asset connection points within the power network.

[0213] The objective of optimization model 960 is to optimally partition the network of target system 140 into multiple smaller microgrids by minimizing power flow on vulnerable lines and maximizing the total supplied load under one or more constraints. Optimization model 960 can be implemented as a mixed-integer linear optimization problem, where the decision variables are switch states. The output of optimization model 960 is microgrid configuration 970. In an embodiment, microgrid configuration 970 may identify each microgrid to be formed (e.g., as a set of node identifiers) and / or indicate the optimal state of each switch in the network.

[0214] Microgrid configuration 970 can be output to network controller 680. Before and / or during future events, network controller 680 can reconfigure target system 140 to reflect microgrid configuration 970. Specifically, network controller 680 can update physical switches in target system 140 (e.g., by opening or closing each of one or more switches) to reflect the state of switches in microgrid configuration 970, thereby forming multiple microgrids in target system 140 and defining setpoints for one or more distributed energy resources 830 within the resulting microgrids. In other words, the power network can be reconfigured based on the determined switch states such that the power network will have the determined switch states during future events.

[0215] Dividing a power grid into microgrids enhances grid resilience. However, there is a limit to the total number of microgrids into which a network can be divided. It is highly likely that microgrids will primarily form along branches of the network, while the majority of the network remains connected to the main grid. In these instances, combining preventative network islanding with network topology optimization has a synergistic effect. Specifically, each microgrid in a microgrid configuration 970, output by optimization model 960, can be provided in the asset data 620 input to OPF model 760 to generate an optimized network topology 770 for each microgrid in microgrid configuration 970. In this case, network controller 680 can control target system 140 (e.g., control switches in target system 140) to form multiple microgrids in microgrid configuration 970, thus having corresponding optimized network topologies 770. The combination of microgrid configuration 970 and optimized network topologies 770 can improve the resilience of each part of the network.

[0216] In an embodiment, optimization model 960 can determine the switching state of each of a plurality of switches in the power network before an event by optimizing an objective function to maximize the total load served in the power network during the event, so as to form one or more microgrids 840 in the power network. The objective function can associate each of the plurality of power lines 820 in the power network with a risk factor representing the criticality and failure probability of the power line 820, such that the power flow on the power line 820 associated with the lower risk factor takes precedence over the power flow on the power line 820 associated with the higher risk factor, and is subject to one or more islanding constraints. The one or more islanding constraints can ensure that: each of the plurality of nodes 810 is assigned to exactly one of the microgrids 840; exactly one of the plurality of nodes 810 representing a grid-type distributed energy resource 830 is assigned to each of the one or more microgrids 840; each of the microgrids 840 includes at least two nodes 810; and / or each of the plurality of power lines 820 is assigned to one of the microgrids 840 or the main grid including substations based on the assignment of at least one node of the plurality of nodes 810 connected to the power line 820.

[0217] In this embodiment, the objective function includes:

[0218] Where Φ is the set of phases, p It is a phase within the set of phases. T It refers to the time period of the event. t It is an index of the time interval within that time period. N It is these multiple nodes, i It is the index of the node within these multiple nodes. Represents the product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node It is a scalar factor , ij It is the first i The node is connected to the first j Index of power lines for each node. E It is a collection of power lines. Is with the first ij Risk factors associated with each power line It is in thet During the time interval, the first ij The active power flow on the power lines, and It is in the t During the time interval, the first ij Reactive power flow on a power line. In this case, the optimization objective function involves maximizing the load served, while the second term of the objective function is derived from a risk factor. The weights represent the weights used to minimize power flow on risky power lines. The scaling factor γ sets the relative weight of the second term.

[0219] It should be understood that in a three-phase system, 1, , , and All parameters are 3×1 vectors, representing the values ​​of the corresponding parameters for all three network phases. Furthermore, in this three-phase system, it should be understood that other node- or line-specific parameters described herein can also be 3×1 vectors, representing the values ​​of the corresponding parameters for all three network phases.

[0220] As discussed above, the objective function can be subject to island partitioning constraints. Island partitioning constraints can include one or more of the following node association constraints, and preferably all of them:

[0221] It ensures that each node is assigned to one and only one microgrid, and in which, K It is the set of nodes representing the grid-type distributed energy resource 830 (e.g., used to form an electrical island) among these multiple nodes, including substation nodes. k yes K Intranode index, N It is these multiple nodes, i It is the node index within these multiple nodes, and It means the first i Is the node assigned to the node by the first...? k The binary variables of a microgrid formed by nodes (i.e., Indicates assignment, and (Indicates no assignment) ,for

[0222] It ensures that each grid-connected distributed energy resource 830 is assigned to the microgrid it forms, and this should always hold true; and / or

[0223] It ensures that each microgrid has at least one other node in addition to the DER node of this grid configuration.

[0224] In this embodiment, the islanding constraints may include one or more of the following line constraints and association constraints, and preferably all of them:

[0225] in, It means the first ij Whether the power line was assigned to the first k The binary variables of a microgrid formed by nodes (i.e., Indicates assignment, and (Indicates no assignment). It means the first i Is the node assigned to the node by the first...? k The binary variables of a microgrid formed by nodes (i.e., Indicates assignment, and (indicating unassigned), and It means the first ij A binary variable representing the switching state on a power line (i.e., = 1 indicates a closed loop, and (Indicates disconnection);

[0226] It ensures that power lines with switches only... Only then does it belong to the first k A microgrid formed by individual nodes;

[0227] It ensures that, in addition to power lines with switches, each power line is assigned to the microgrid, and among them, S It is a collection of power lines, each having one of the multiple switches; and / or

[0228] It ensures that if the first ij If a switch on a power line does not belong to a microgrid, then the switch is located at the boundary between two microgrids.

[0229] In an embodiment, islanding constraints may include one or more, preferably all, of the following island-by-island radial constraints, which ensure that each formed microgrid is radial, but these constraints may be omitted if the power network will operate in a mesh mode:

[0230]

[0231] in, It is for switches ( i,j ) is used to formulate by the first k A binary variable constraining the radial distribution of a microgrid formed by nodes (i.e., if { and },but ;if{ or },but These constraints represent a linearized version of the following:

[0232] In this embodiment, island partitioning constraints may include:

[0233] in, L It is a collection of power lines, and this constraint applies to the radial nature of each microgrid, i.e.:

[0234] The optimization model 960 may include additional constraints. For example, in the presence of multiple power sources (such as multiple distributed energy resources 830) in any microgrid (i.e., an electrical island without grid-connected distributed energy resources 830 and without substation nodes) or main grid (i.e., a portion of the power network with substation nodes), one or more virtual load constraints may be added to the optimization model 960, as discussed elsewhere in this document. Additionally, the optimization model 960 may include one or more node power balance constraints, one or more branch power flow constraints, and / or one or more load constraints.

[0235] Constraints for node power balance may include one or more of the following, and preferably all of them, or constitute a subset thereof:

[0236] Its identification substation node (denoted as) G active power P (e.g., in kW) and reactive power Q (e.g., in kVAr) balance, and where Indicates the first t During the time interval, the first i Active / reactive power injection at each node, and and They represent the first t During the time interval, the first ij Article and Section ji Active / reactive power flow on a power line;

[0237] It indicates that, except for substation nodes and nodes equipped with distributed energy resources 830, all connected loads (denoted as...) D Active power of the nodes P and reactive power Q The balance;

[0238] It represents the active power of all nodes that are not connected to loads and do not have distributed energy resources deployed. P and reactive power Q The balance;

[0239] It indicates that all connected loads or deployed distributed energy resources 830 (denoted as...) DER Active power of the nodes P and reactive power Q The balance, in which It is a set of nodes that are connected to fixed or mobile distributed energy resources 830; and / or

[0240] It represents the active power of all nodes without connected loads. P and reactive power Q The constraints ensure that the net power flow through any node is always zero. For computational simplicity, these constraints assume zero power loss.

[0241] Branch power flow constraints can limit the active and reactive power flow capacity of power lines to ensure that the total power flow on each power line does not exceed the rated capacity of the power line. In embodiments, branch power flow constraints include one or more of the following, preferably all of them, or constitute a subset thereof:

[0242] For power lines not associated with switches, where, It is an active power flow limitation (e.g., in kW), and It is reactive power flow limitation (e.g., in kVAr); and / or

[0243] For power lines associated with switches, wherein, It means the first ijA binary variable representing the state of a switch on a power line (e.g., open or closed). If the switch is open, then... This allows us to disregard constraints, and if the switch is closed, then... This necessitates consideration of constraints.

[0244] The constraints on the load ensure that the solution generated by the optimization model 960 has a load demand within the range between the minimum required supply load and the maximum predicted load. In the embodiments, these constraints include or consist of the following:

[0245] It limits active and reactive loads, among which Indicates the first t During the time interval, the first i Predicted active and reactive loads at each node Indicates the first t During the time interval, the first i The lower limits of active and reactive loads at each node (e.g., the load that must be supplied), and Indicates the first t During the time interval, the first i The upper limits of active and reactive loads at each node (e.g., maximum predicted load). Assume minimum service load for all nodes. It is positive for at least one time interval to ensure that the radiation constraint works as expected.

[0246] The number of binary variables in the island partitioning constraint is This number can increase significantly as the size of the power network grows. Therefore, in this embodiment, network simplification is performed on the power network before the optimization model 960 determines the switching state. Network simplification is described in more detail elsewhere in this document. At a higher level, network simplification may include classifying each of a plurality of nodes in the power network as critical or non-critical, thereby dividing the plurality of nodes into critical and non-critical nodes, and reducing the number of nodes in the power network by recursively aggregating at least one parameter of a non-critical node with at least one parameter of at least one critical node, and removing the non-critical node until only critical nodes remain in the plurality of nodes. These parameters may include load, and aggregation may be performed at each of the plurality of nodes for each phase. Aggregation may include: when a non-critical node is not between two critical nodes, aggregating the entire value of the parameter of the non-critical node with the value of the parameter of the nearest critical node, and removing the non-critical node and one of the plurality of power lines between the non-critical node and the nearest critical node. This aggregation can be performed on any non-critical node that meets the following conditions: (i) it is located adjacent downstream of a critical load (i.e., farther from the critical node than the slack bus (which is a substation that acts as a connection point between the power network and the backbone); (ii) there are no more branch points downstream of the given non-critical node; and (iii) there are no critical nodes downstream of the given non-critical node. Additionally, aggregation may include: when a non-critical node is between two critical nodes, aggregating a portion of the non-critical node's parameter value with the parameter values ​​of each of the two critical nodes, removing the non-critical node, removing each of the multiple power lines between the non-critical node and the two critical nodes, and adding a new aggregated power line between the two critical nodes. This aggregation can be performed recursively until all non-critical nodes between the two critical nodes have been removed. Network simplification may further include: storing a mapping from each removed non-critical node to a critical node aggregated with the non-critical node, and a mapping from each removed power line in the multiple power lines to any power line aggregated with the removed power line. This network simplification can reduce the size of the power grid by reducing the number of nodes. N |and number of lines |L| This reduces the complexity of the optimization model 960, thereby significantly reducing the number of binary variables. Advantageously, this significantly reduces the time required to solve the optimization model 960.

[0247] Preventative network islanding can also be combined with microgrid dispatch planning, which is described in more detail elsewhere in this paper. At a high level, after the switching states forming the microgrid are determined by optimization model 960, dispatch in the microgrid can be planned for each of the microgrids by performing the following operations: In a first phase, for each of multiple time intervals within the time period of the event, generation resources in the microgrid are allocated to that time interval by optimizing a first objective function based on multiple scenarios and the probability of each of those scenarios to maximize the total load served in the power network during that time interval, wherein the first objective function associates each of the multiple power lines with a risk factor representing the failure probability of that power line. Then, the planning can further include: for each of the microgrids, in a second phase, for each of multiple time segments within each of the multiple time intervals, generation resources are allocated to that time segment by optimizing a second objective function to maximize the total load served in the power network during that time interval, wherein the second objective function is deterministic and associates each of the multiple power lines with a risk factor representing the failure probability of that power line. In the second phase, the planning may further include: for each of the multiple time segments within each of the multiple time intervals, selecting a set of loads to be supplied with electricity during that time segment, wherein the second objective function is constrained by requiring each load in the selected set of loads to be supplied with a predefined minimum service duration. The planning may further include: for each of the microgrids, during each of the multiple time segments, scheduling generation in the microgrid based on the generation resources allocated for that time segment.

[0248] Figure 9B As Figure 9A An alternative is illustrated, showing an architecture for probabilistic preventative electrical islanding based on an embodiment utilizing preventative network islanding as a resilient measure. In the illustrated embodiment, multiple scenarios 610 representing a scenario set Ω are generated (e.g., by analysis and control module 330), illustrated as scenarios 610A, 610B, 610C, ..., 610X. These scenarios can be the same scenarios 610 described elsewhere, and therefore any description of scenario 610 in other contexts applies equally to scenario 610 in this context, and vice versa.

[0249] Multiple scenarios 610, along with asset data 620 and prediction data 630, are input into optimization model 960 of probabilistic optimization model 360. It should be understood that the use of multiple scenarios 610 takes into account the uncertainty in the prediction data 630 and enables optimization model 960 to be probabilistic. Each of the multiple scenarios 610 can be associated with a corresponding probability that scenario 610 will occur, such that optimization model 960 takes into account the probability of occurrence of multiple scenarios 610. In an alternative embodiment, instead of or in addition to the multiple scenarios 610, the failure probability distribution of each of one or more of these assets can be input into optimization model 960.

[0250] The objective of optimization model 960 is to optimally partition the network of target system 140 into multiple smaller microgrids by minimizing power flow on vulnerable lines and maximizing the total supplied load under one or more constraints. These constraints may include one or more, possibly all, of the following: all microgrids must be radial; each microgrid is formed by opening or closing existing switches; each microgrid has a large number (e.g., a threshold number) of nodes; microgrid formation does not isolate any critical loads; if grid-type distributed energy resources 830 exist in the power network, the number of microgrids containing at least one grid-type distributed energy resource 830 is maximized; and / or the number of microgrids not containing grid-type distributed energy resources 830 cannot exceed the number of available mobile distributed energy resources 830. Since each microgrid will be radial and formed using existing switches, these microgrids will meet the network's operating criteria without the need for preventative network islanding.

[0251] The output of optimization model 960 is microgrid configuration 970. In an embodiment, microgrid configuration 970 may identify each microgrid to be formed (e.g., as a set of node identifiers) and / or indicate the optimal state of each switch in the network. Microgrid configuration 970 may also define the amount of electricity to be absorbed or injected by each distributed energy resource 830 during future events, and / or identify one or more mobile distributed energy resources 830 to be dispatched and the location to which each mobile distributed energy resource 830 is to be dispatched. It should be understood that microgrid configuration 970 is determined by optimization model 960 based on multiple scenarios 610, such that microgrid configuration 970 takes into account the probability of assets (e.g., power lines) in target system 140 failing due to future events.

[0252] Microgrid configuration 970 can be output to network controller 680. Before and / or during future events, network controller 680 can reconfigure target system 140 to reflect microgrid configuration 970. Specifically, network controller 680 can update physical switches in target system 140 (e.g., by opening or closing each of one or more switches) to reflect the state of switches in microgrid configuration 970, thereby creating multiple microgrids in target system 140 and defining setpoints for one or more distributed energy resources 830 within the resulting microgrids.

[0253] Dividing a power grid into microgrids enhances grid resilience. However, there is a limit to the total number of microgrids into which a network can be divided. It is highly likely that microgrids will primarily form along branches of the network, while the majority of the network remains connected to the main grid. In these instances, combining preventative network islanding with network topology optimization has a synergistic effect. Specifically, each microgrid in a microgrid configuration 970, output by optimization model 960, can be provided in the asset data 620 input to OPF model 760 to generate an optimized network topology 770 for each microgrid in microgrid configuration 970. In this case, network controller 680 can control target system 140 (e.g., control switches in target system 140) to form multiple microgrids in microgrid configuration 970, thus having corresponding optimized network topologies 770. The combination of microgrid configuration 970 and optimized network topologies 770 can improve the resilience of each part of the network.

[0254] 6.4. Deployment and scheduling of distributed energy resources Figure 10 The illustration depicts an architecture for probabilistic DER deployment and scheduling based on an embodiment utilizing DER deployment and scheduling as a resilient measure. It is noteworthy that preventative network islanding discussed elsewhere herein can utilize DER deployment in the first phase to optimize DER deployment when determining how to partition the power network into microgrids. Therefore, it should be understood that the disclosed DER deployment and / or scheduling can be combined with preventative network islanding discussed elsewhere herein.

[0255] DER deployment and scheduling can use risk-based metrics in the OPF model 1060 to passively account for uncertainties in assets by minimizing power flows through vulnerable assets. In an embodiment, the OPF model 1060 also mitigates voltage deviations at nodes (e.g., buses) caused by power injection from distributed energy resources 830. The OPF model 1060 can assume that any asset that fails during the considered future events will not be repaired during those future events.

[0256] OPF model 1060 considers only a single scenario 610. This single scenario 610 may include a DER configuration, including a network topology representing the healthy operating state of the power network (e.g., no faulty assets) or the current operating state when optimization is performed. The network topology may identify each node and edge in the power graph of the power network, the state of each switch in the power network (e.g., open or closed), the deployment of each distributed energy resource 830 (e.g., the nodes to which each distributed energy resource 830 is connected), etc.

[0257] In an embodiment, asset data 620 may include a set 622 of nodes representing Flexible Asset Connection Points (FACPs), a set 624 of fixed distributed energy resources 830, a set 626 of mobile distributed energy resources 830, and a definition 628 of the distributed energy resources 830. Set 622 identifies all nodes in the power network representing FACPs to which mobile distributed energy resources 830 can be connected. A FACP is any node in the power network at which a mobile distributed energy resource 830 can easily connect to the power network to inject power into it. Set 624 identifies all fixed distributed energy resources 830 in the power network. Set 626 identifies all mobile distributed energy resources 830 that can be connected to one of the FACPs identified in set 622. Definition 628 may define parameters for each type of fixed and mobile distributed energy resource 830, such as type, identifier, size, manufacturer, model, rating, whether the distributed energy resource 830 is a grid-connected (GFM) or grid-following (GFL) type, etc.

[0258] The OPF model 1060 can receive a single scenario 610, asset data 620, and prediction data 630, as described elsewhere in this document, and generate a DER configuration 1070. The DER configuration 1070 can include an optimal network topology. The optimal network topology can identify each node and edge in the power graph of the power network, the state of each switch in the power network (e.g., open or closed), the deployment of each distributed energy resource 830 (e.g., the nodes to which each distributed energy resource 830 is connected), etc. Relative to the network topology in scenario 610, the optimal network topology can include adding one or more mobile distributed energy resources 830 from set 626 to flexible asset connection points in set 622, one or more preventative changes to switch states (e.g., actively opening or closing switches), etc.

[0259] Distributed energy resources 830 can include any type of energy, including but not limited to diesel generators (DG), battery energy storage systems (BESS), and solar photovoltaic (PV) systems. Distributed energy resources 830 can be further divided into stationary or static distributed energy resources 830 and mobile distributed energy resources 830. Stationary distributed energy resources 830 have predefined and fixed locations in the power network (e.g., busbars), ensuring that the OPF model 1060 does not change its location, while mobile distributed energy resources 830 can be deployed by the OPF model 1060 at any node within the power network representing a flexible asset connection point.

[0260] In this embodiment, the OPF model 1060 determines the optimal deployment of mobile distributed energy resources 830 within the power grid and the optimal scheduling of distributed energy resources 830 within the power grid, while minimizing the power grid's operational dependence on assets at risk, as determined by future events. The OPF model 1060 can integrate both stationary and mobile distributed energy resources 830 within the existing power grid and leverage their capabilities to simultaneously address multiple operational objectives.

[0261] Specifically, prior to the event, the OPF model 1060 can determine the DER configuration 1070 (e.g., including network topology) to be used during the event (e.g., to increase the resilience of the power network) by optimizing an objective function to maximize the total load served in the power network during the event. This objective function may associate each of the multiple nodes in the power network with a criticality factor representing the relative criticality of the load at that node, associate each of the multiple power lines in the power network with a risk factor representing the probability of failure of that power line, and include a term representing voltage deviations at the multiple nodes. This objective function may also be subject to one or more constraints. It should be understood that the power network can be reconfigured to the determined network topology before or during the event, such that the power network will have the determined network topology during the event.

[0262] In the embodiments, the objective function includes or is composed of the following items:

[0263] in, T It refers to the time period of the event. t It is an index of the time interval within a time period. N These are multiple nodes in the power grid. i It is the node index among these multiple nodes. It is the first i Key factors affecting load at each node This represents the dot product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i The demand for active power supply at each node (e.g., in kW). Indicates the first t During the time interval, the first i The reactive power supply demand at each node (e.g., in kVAr). and It is a scalar factor ( ), representing the participation / weighting factors of the second and third terms of the objective function, which are minimized by their negative signs. ij It is the connection of the first i The node and the first j Index of power lines for each node. E It is the collection of fault-free power lines in the power grid. Is with the first ij Risk factors associated with each power line It is the first t During the time interval, the first ij Active power flow on a power line (e.g., in kW). It is the first t During the time interval, the first ij Reactive power flow on a power line (e.g., in kVAR). It is a set of nodes representing flexible asset connection points among multiple nodes, and It is the first t During the time interval, the first i The absolute value of the voltage at each node.

[0264] It should be understood that in a three-phase system, 1, , , , and All parameters are 3×1 vectors, representing the values ​​of the corresponding parameters for all three network phases. Furthermore, in this three-phase system, it should be understood that other node- or line-specific parameters described herein can also be 3×1 vectors, representing the values ​​of the corresponding parameters for all three network phases.

[0265] Risk factors can be calculated based on the failure probability and criticality of the corresponding power lines. This failure probability can be obtained using the vulnerability curve of the corresponding power line and / or multiple failure scenarios. In other words, risk factor. It was also included in the first ijThe risks and criticality of power lines. The criticality of power lines can be based on nominal power flow usage. Fault analysis or saliency analysis is used to calculate, as discussed in the following literature: DT Grady, “Robust Classification of Salient Links in Computer Networks,” Nature Communications, 2012, which is hereby incorporated in its entirety by reference. ij The probability of a power line failure is expressed as: And will the first ij The criticality of power lines is represented as follows Risk factors It can be calculated as:

[0266] It is worth noting that the above expression considers both the fault probability of the power line and the adjusted criticality value. Risk Factor The criticality of a power line increases with increasing criticality and decreases with decreasing criticality. As an example, a higher risk factor can be assigned to power lines near substation nodes in a power network that serve numerous loads and therefore have a higher criticality than power lines near the ends of the network that typically serve few loads. More generally, the criticality of a power line can increase with the number of loads it serves.

[0267] In the above embodiment of the objective function, optimizing the objective function includes maximizing the objective function. The effect of optimizing the objective function is to optimize the state of network switches in the power network to ensure maximum weighting (e.g., based on the criticality factor) is served via the first term. (Weighted) load, while simultaneously minimizing the weighted power flow on the risky lines via a second term (e.g., the risk of power lines is determined by risk factors). (represented), and minimizes the voltage deviation on the network bus via the third term.

[0268] In additional embodiments, the objective function may further include a term representing the generation of one or more distributed energy resources 830 in the power grid. For example, in embodiments where the power grid includes a photovoltaic (PV) system, the objective function may include a fourth term designed to maximize the PV generation utilized.

[0269] in, It is a scalar factor representing the participation / weighting factor of the fourth term of the objective function. The fourth term is maximized by its positive sign. It is the set of nodes representing photovoltaic power sources among multiple nodes in the power grid, and It is the first t During the time interval, the first i The active power output of the photovoltaic power source utilized at each node (e.g., in kW).

[0270] In any embodiment, the objective function of the OPF model 1060 may be subject to one or more constraints, including but not limited to one or more constraints on the following: node power balance, branch power flow, node voltage of switching nodes, node voltage of non-switching nodes, absolute voltage, load, radiation, deployment of mobile distributed energy resources 830, virtual load, active and reactive power limits of non-renewable generators, active and reactive power limits of energy storage systems, polygon relaxation of the secondary apparent power of distributed energy resources 830, time-sequential discharge / charge of energy storage systems, active and reactive power of renewable generators, etc.

[0271] Constraints for node power balance may include one or more of the following, and preferably all of them, or constitute a subset thereof:

[0272] It represents the active power of a substation node (denoted as G). P (e.g., in kW) and reactive power Q (For example, in kVAr) balance;

[0273] It indicates that, except for substation nodes and nodes equipped with distributed energy resources 830, all connected loads (denoted as...) D Active power of the nodes P and reactive power Q The balance;

[0274] It represents the active power of all nodes that are not connected to loads and do not have distributed energy resources deployed. P and reactive power Q The balance;

[0275] It represents all connected loads (denoted as ). D ) or deployed distributed energy resources 830 (denoted as DER Active power of the nodes P and reactive power Q The balance, in which It is a set of nodes that are connected to fixed or mobile distributed energy resources 830; and / or

[0276] It represents the active power of all nodes without connected loads. P and reactive power Q The balance is maintained. In general, these node power constraints ensure that the net power flow through any node is always zero. For computational simplicity, these constraints assume zero power loss.

[0277] Branch power flow constraints can limit the active and reactive power flow capacity of power lines to ensure that the total power flow on each power line does not exceed the rated capacity of the power line. In embodiments, branch power flow constraints include one or more of the following, preferably all of them, or constitute a subset thereof:

[0278] For power lines not associated with switches, where, It is an active power flow limitation (e.g., in kW), and It is reactive power flow limitation (e.g., in kVAr); and / or

[0279] For power lines associated with switches, wherein, It means the first ij A binary variable representing the state of a switch on a power line (e.g., open or closed). If the switch is open, then... This allows us to disregard constraints, and if the switch is closed, then... This necessitates consideration of constraints.

[0280] Constraints on the node voltage of switching nodes ensure that the decisions of the OPF model 1060 do not lead to overvoltage and undervoltage conditions in the power network. In embodiments, these constraints include one or more, and preferably all, of the following, or consist of:

[0281] It calculates the node voltages of all nodes connected to the switch, where It is the first t During the time interval, the first i The square of the node voltage (e.g., per unit value) of each node. It is the first t During the time interval, the first j The square of the node voltage (e.g., per unit value) of each node. and It is used to calculate the connection of the first i The node and the first j The linearized matrix of voltage drop on the power line at each node, and This is a relaxation variable used for the voltage difference between two disconnected nodes, which is introduced to ensure that in the first... ij This constraint is not violated when the switch on a power line is disconnected;

[0282] It limits the node voltage of all nodes connected to the switch to acceptable limits in the following way: ensuring that when the first node... ij The switch on the power line is closed (i.e., )hour, And must be maintained and The relationship between them, and when the first ij The switch on the power line is open (i.e., When ), there is no need to maintain and The relationship between them, and in which It is the maximum limit (per unit) of node voltage; and / or

[0283] It is based on the first ij The amplitude of the power flow on the power line is linearized using the linearization method. i The node and the first j The voltage drop between nodes is modeled. Specifically, and This represents the linearization coefficient used to model the impact of active and reactive power flow on node voltage drop, as discussed elsewhere in this paper.

[0284] Constraints on node voltages of non-switching nodes may include one or more of the following, and preferably all of them, or constitute a subset thereof:

[0285] It calculates the node voltage of all nodes not connected to the switch;

[0286] It limits the node voltage to acceptable limits for all nodes not connected to the switch, where, It is the minimum limit (per unit) for node voltage; and / or

[0287] It sets the voltage of each substation node as the reference voltage. (per unit value), where, It is the set of nodes representing all substations in the power network among these multiple nodes.

[0288] Constraints on absolute voltage may include or consist of the following:

[0289] It defines an absolute voltage limit at each node representing a flexible asset connection point, thereby limiting node voltage deviation.

[0290] The constraints on the load ensure that the solution generated by the OPF model 1060 has a load demand within the range between the minimum required supply load and the maximum predicted load. In the embodiments, these constraints include or consist of the following:

[0291] It limits active and reactive loads, among which Indicates the first t During the time interval, the first i Predicted active and reactive loads at each node Indicates the first t During the time interval, the first i The lower limits of active and reactive loads at each node (e.g., the load that must be supplied), and Indicates the first t During the time interval, the first i The upper limit of active and reactive loads at each node (e.g., maximum predicted load).

[0292] Constraints on radiality maintain the radial nature of the power network. Otherwise, network switching optimization in the OPF model 1060 might create loops in the power network. In the embodiments, these constraints include or constitute the following:

[0293] in, E SW It is a collection of power lines connected to a network switch, and It is the collection of power lines that are not connected to switches. Radiality is modeled using a concept from graph theory, which requires that the total number of power lines must equal the total number of nodes minus the total number of substations, and that the power network must be fully connected.

[0294] Constraints on the deployment of mobile distributed energy resources 830 may include at least one deployment constraint for each mobile distributed energy resource 830 to be deployed at flexible asset connection points in the power network during future events. These deployment constraints ensure that: each mobile distributed energy resource 830 can only be deployed at nodes representing flexible asset connection points (if deployed); at most one mobile distributed energy resource 830 can be deployed at each node representing a flexible asset connection point; and each mobile distributed energy resource 830 can only be deployed at a single node (if deployed). In embodiments, deployment constraints include one or more, and preferably all, of the following, or constitute a subset thereof:

[0295] It ensures that each flexible asset connection point can have a maximum of one mobile distributed energy resource 830 (e.g., a diesel generator or battery storage system), where It refers to the collection of mobile generators (e.g., diesel generators) that need to be deployed in the power grid during an event. d It is the index of the mobile generator within the set of mobile generators. It refers to the collection of mobile energy storage systems (e.g., battery energy storage systems) to be deployed in the power grid during an event. m It is an index of mobile energy storage systems within the collection of mobile energy storage systems. It means the first d Is the mobile generator deployed at the [location name missing]? i A binary variable at each node (i.e., 1 indicates deployment, 0 indicates no deployment). It means the first m Whether the mobile energy storage system is deployed in the [number]th [location] i A binary variable for each node (i.e., 1 indicates deployment, 0 indicates no deployment).

[0296] It ensures that each mobile generator (if allocated) will be assigned to a unique flexible asset connection point; and / or

[0297] It ensures that each mobile energy storage system (if allocated) will be assigned to a unique flexible asset connection point.

[0298] When distributed energy resources 830 exist in the power grid and inject power into it, there is a possibility that these distributed energy resources 830 may inject their maximum power into the grid, while excess power will be absorbed by substations. This can result in bidirectional power flows in the power grid. Therefore, to ensure radiation, in the case of fixed and / or mobile distributed energy resources 830, and to avoid or minimize the problem of excess power flows toward substations, the concept of virtual power flows can be introduced into the OPF model 1060 using one or more constraints representing virtual loads. The idea is to deploy fixed virtual loads at each DER node (i.e., the node associated with the distributed energy resource 830), and these virtual loads can only be powered by virtual power supplies provided by substations. Constraints on virtual loads may include at least one virtual load constraint for multiple nodes each representing a distributed energy resource 830, requiring that the virtual load at each node representing the distributed energy resource 830 in the multiple nodes be powered by virtual power supplies from the node representing the substation in the multiple nodes. In embodiments, virtual load constraints include one or more of the following, and preferably all of them, or constitute them:

[0299] It defines all nodes connected to the fixed distributed energy resource 830, flexible asset connection points connected to the mobile distributed energy resource 830, and virtual power balance for all other nodes except those representing substations, where From the first j The node to the first i Virtual power flow of each node From the first i The node to the first j Virtual power flow of each node It is the first i Virtual load of each node It is the set of nodes representing distributed energy resource 830 among these multiple nodes;

[0300] It defines the virtual power balance of substation nodes supplying virtual power, where, It comes from the first i Virtual power supply for each substation node;

[0301] It ensures that the virtual power flow capacity does not exceed the power flow capacity of all distributed energy resources in the power grid, which is 830. M It is the total number of energy storage systems (e.g., battery energy storage systems). DIt is the total number of non-renewable generators (e.g., diesel generators), and P It is the total number of renewable generators (e.g., photovoltaic systems); and / or

[0302] It assigns a virtual load with a per-unit value of one to each distributed energy resource 830, and assigns a virtual load with a per-unit value of zero to all other nodes. The substation node will be responsible for supplying power to the virtual loads of all distributed energy resources 830. Figure 11 The illustration illustrates the concept of a virtual load according to an embodiment. In the illustrated example, node 1 is a substation node that supplies power to the virtual load, node 2 is a non-substation node not connected to the distributed energy resource 830, and node 3 is a node connected to the fixed distributed energy resource 830.

[0303] Constraints on active and reactive power limits for non-renewable generators (such as diesel generators) ensure upper and lower limits on the active and reactive power generated by the non-renewable generators. In embodiments, these constraints include one or more, and preferably all, of the following, or consist of:

[0304] in, It is in the t During the time interval, the first i The active power output (in kW) from non-renewable generators at each node. It is in the i Active power limitations of non-renewable generators at each node It is a set of nodes associated with a non-renewable generator among multiple nodes, and the lower bound is set to zero because non-renewable generators (such as diesel generators) cannot absorb active power;

[0305] in, It is in the t During the time interval, the first i The reactive power output from non-renewable generators at each node (e.g., in kVAr), and It is in the i Reactive power limitations of non-renewable generators at each node;

[0306] It ensures apparent power limitation and can be linearized using polygonal relaxation constraints described elsewhere in this paper, where, It is in thet During the time interval, in the... i Apparent power from non-renewable generators at each node (e.g., in kilovolt-amperes (kVA)); and / or

[0307] It ensures that non-renewable generators do not operate below their rated power factor, whereby, This is the power factor of the non-renewable generator. If the non-renewable generator is a mobile distributed energy resource that must be deployed at flexible asset connection points, then the upper limit of each of the first three constraints should be multiplied by [the factor]. .

[0308] Constraints on active and reactive power limits for energy storage systems (such as battery energy storage systems) ensure upper and lower limits for active and reactive power input to the energy storage system (e.g., charging) or output from the energy storage system (e.g., discharging). In embodiments, these constraints include one or more, and preferably all, of the following, or consist of:

[0309] in, It is in the t During the time interval, in the... i Active power (in kW) input to or output from the energy storage system at each node. It is in the i Active power limitations of energy storage systems at each node It is a set of nodes associated with the energy storage system among multiple nodes, and the lower bound is negative because the energy storage system can store active power;

[0310] in, It is in the t During the time interval, in the... i The reactive power input to or output from the energy storage system at each node (e.g., in kVAr), and It is in the i The reactive power limit of the energy storage system at each node, wherein the lower limit is negative because the energy storage system can absorb reactive power;

[0311] It ensures apparent power limitation and can be linearized using polygonal relaxation constraints described elsewhere in this paper, where, It is in the iApparent power input to or output from the energy storage system at each node (e.g., in kVA); and / or

[0312] It ensures that the energy storage system does not operate outside its rated power factor, whereby, This is the power factor of the energy storage system. If the energy storage system is a mobile distributed energy resource that must be deployed at flexible asset junctions, then the lower and upper limits of each of the first two constraints, and the upper limit of the third constraint, should be multiplied by [the factor]. .

[0313] The polygonal relaxation constraint on the quadratic apparent power of the distributed energy resource 830 transforms the quadratic constraint on the apparent power limit in the active and reactive power constraint of the non-renewable generator and / or energy storage system into a linear equation to simplify optimization. Specifically, the apparent power limit can be represented as a Euclidean sphere, which can be expressed by a polygonal approximation using a series of linear constraints. In embodiments, these constraints include one or more, and preferably all, of the following, or constitute a subset thereof:

[0314]

[0315] in, P It is active power. Q It is reactive power. S It is apparent power, and These are the coefficients that determine the linearization precision (e.g., ).

[0316] Constraints on the timing of discharge / charge of energy storage systems may include one or more of the following, and preferably all of them, or constitute a subset thereof:

[0317] It reflects the change of the state of charge (SoC) of the energy storage system over time, where the SoC is defined by the charging and discharging actions during each time interval based on the corresponding charge and discharge efficiencies. It is the first t During the time interval, the first m The state of charge of an energy storage system Is the ( t - 1) During the time interval, the first m The state of charge of an energy storage system It is the first t During the time interval, the first m The charging power of an energy storage system It is the first t During the time interval, the first m The discharge power of an energy storage system It is the first m Storage limitations of an energy storage system (e.g., in kilowatt-hours (kWh)). It is the first m The charging efficiency of an energy storage system It is the first m The discharge efficiency of the energy storage system, and It is a collection of fixed and mobile energy storage systems;

[0318] It imposes maximum and minimum limits on the state of charge of the energy storage system over all time intervals, where It is the first t During the time interval, the first m Minimum state of charge (e.g., percentage) limits for each energy storage system, and It is the first t During the time interval, the first m Maximum state of charge (e.g., percentage) limit for each energy storage system;

[0319] Its applied charging power limit range for energy storage systems, of which It is to ensure the first t During the time interval, the first m A binary variable representing the mutual exclusion of charging and discharging in an energy storage system, and It is the first t During the time interval, the first m The maximum charging power of each energy storage system;

[0320] Its applied discharge power limit range for energy storage systems, of which It is the first t During the time interval, the first m The maximum output of each energy storage system; and / or

[0321] It ensures the first t During the time interval, the first m The active power of the energy storage system equal to the t During the time interval, the first m The difference between the discharge power and the charging power of an energy storage system.

[0322] Constraints on the active and reactive power of renewable energy generation may include one or more of the following, and preferably all of them, or constitute a subset thereof:

[0323] It determines the utilized active renewable energy generation of each renewable generator, of which It is in the t During the time interval period from the first i The utilized active power output of each renewable generator, and It is in the t During the time interval period from the first i The predicted active power output of each renewable generator (e.g., distribution curve); and / or

[0324] It determines the reactive power output of each renewable generator based on the power factor of the renewable generator, where It is in the t During the time interval period from the first i The utilized reactive power output of a renewable generator, and It is the power factor of a renewable generator.

[0325] The output of OPF model 1060 is DER configuration 1070. DER configuration 1070 may include an optimal network topology, which includes the deployment of each of one or more mobile distributed energy resources 830, the state of each of multiple switches in the power network, etc. DER configuration 1070 may also include power dispatch for each of the one or more distributed energy resources 830 represented in the network topology, which may be a plurality of distributed energy resources 830 including one or more fixed distributed energy resources 830 and one or more mobile distributed energy resources 830.

[0326] The DER configuration 1070 can be input into the DER deployment / scheduling module 1080. The DER deployment / scheduling module 1080 can deploy one or more mobile distributed energy resources 830 at the locations identified in the DER configuration 1070, and / or schedule one or more distributed energy resources 830 within the target system 140 according to the specifications in the DER configuration 1070. With the help of the DER deployment / scheduling module 1080, mobile distributed energy resources 830 can be physically deployed and scheduled according to their priority locations in the network based on the DER configuration 1070 to ensure continuous load supply, support emergency power restoration, provide backup power, provide black start (i.e., restore power to a portion of the network without relying on external power sources), support microgrids (e.g., formed by preventative network islanding), etc.

[0327] The DER configuration 1070 can also be input to a network controller 680, which is described in more detail elsewhere in this document. The network controller 680 can reconfigure the power network before or at the start of an event, based on the network topology determined by the OPF model 1060 and included in the DER configuration 1070, such that the power network will have the determined network topology during the event. This reconfiguration may include reconfiguring the states of switches in the power network according to the network topology in the DER configuration 1070. Specifically, the network controller 680 can control multiple switches in the power network to match the states in the network topology of the DER configuration 1070.

[0328] Distributed energy resources 830 (whether fixed or mobile) typically have limited resources that are difficult to replenish during extreme weather events. Furthermore, the movement of mobile distributed energy resources 830 is hampered by the high degree of uncertainty caused by extreme weather events. Therefore, in this embodiment, the OPF model 1060 can work in conjunction with the DER deployment / schedule module 1080 during an event to monitor power outages in the target system 140 and, based on the observed power outages, move the mobile distributed energy resources 830 to new locations within their respective vicinity areas and / or reschedule the distributed energy resources 830. Specifically, feedback from the target system 140 reflecting its current state can be returned to the OPF model 1060 as scenario 610. The OPF model 1060 can be applied to scenario 610 along with asset data 620 and / or forecast data 630 to provide a new DER configuration 1070. This new DER configuration can be provided to the DER deployment / scheduling module 1080, which can move one or more mobile distributed energy resources 830 to a new location and / or reschedule distributed energy resources 830 based on the new DER configuration 1070. This ensures that the distributed energy resources 830 in the network optimally supply power to the load throughout the entire duration of the event, while maintaining sufficient operational reserves.

[0329] As disclosed, OPF model 1060 is a probabilistic, risk-driven OPF (RD-OPF) model. It should be understood that OPF model 1060 is probabilistic because it incorporates risk factors (e.g., risk factors) into its objective function. This factor considers the probability of asset failure. The OPF model 1060 can maximize the total load served while minimizing power flow on critical power lines and reducing voltage deviations at nodes with fixed or mobile distributed energy resources 830, subject to constraints such as ensuring the active and reactive power injection of distributed energy resources 830 is within the corresponding DER ratings, the radiation of the power network, and voltage stability. The OPF model 1060 can also optimize the deployment of mobile distributed energy resources 830 at pre-identified FACP nodes while ensuring consistency with the objective function. Strategic deployment of mobile distributed energy resources 830 through binary deployment constraints can further enhance the load service capacity of the power network, minimize power flow on critical power lines, and alleviate voltage deviations at nodes. Furthermore, optimal network topology optimization through optimal network switch configuration can maximize the efficiency, stability, and reliability of the power system while maintaining the radiation of the distribution network.

[0330] The advantages of the OPF model 1060 include, but are not limited to: serving as a decision-making tool for operators to optimally deploy mobile distributed energy resources 830 in the power grid to proactively enhance the resilience of the power grid; reducing line losses and alleviating stress on at-risk power lines during extreme weather events by strategically deploying distributed energy resources 830 near high-demand areas and generating power near consumption points; dynamically balancing supply and demand through the use of distributed energy resources 830 to support load shedding, load shifting, and preventative network islanding measures; injecting reactive power into the power grid through optimal deployment of distributed energy resources 830 to maintain voltage levels within acceptable limits, thereby improving grid stability and reducing voltage deviations; providing frequency support by deploying distributed energy resources 830 (such as battery storage systems) to absorb excess energy during high-generation periods and release energy during power outages and / or shortages; and / or mitigating voltage fluctuations through proactive voltage control, volt-var optimization, and distributed coordination by deploying distributed energy resources 830 near critical loads. Furthermore, since the OPF model 1060 is inherently probabilistic, its performance is unaffected by the increased uncertainty of severe weather events. However, the OPF model 1060 can also be used to improve the operational efficiency of power grids during normal weather conditions with lower uncertainty.

[0331] It should be understood that the disclosed DER deployment and scheduling can be incorporated into process 400. Specifically, the OPF model 1060 can be run in subprocess 420, and a measure of the effectiveness of the resulting DER configuration can be determined in subprocess 440. More specifically, in an embodiment, in subprocess 410, asset data 620 associated with multiple power transmission assets of the power network is acquired, prediction data 630 associated with at least one future event is acquired, and input data is generated based on the asset data 620 and the prediction data 630. Prior to the future event, in subprocess 420, the input data is fed into at least one probabilistic optimization model that optimizes at least one parameter of the operation of the power network for the future event. The probabilistic optimization model may include the OPF model 1060, which determines the optimized network topology of the power network to be used during the future event by at least optimizing an objective function to maximize the total load served in the power network during the future event. The objective function associates each of the multiple nodes in the power network with a critical factor representing the relative criticality of the load at that node, and each of the multiple power lines in the power network with a risk factor representing the failure probability of that power line, including a term representing voltage deviations at the multiple nodes, and is subject to one or more constraints. Then, in subprocesses 430 to 440, for each of the multiple resilience measures (including DER deployment and scheduling) performed by the OPF model 1060, a measure of the effectiveness of that resilience measure against future events on the operation of the power network is determined based on the solution of the probabilistic optimization model (e.g., OPF model 1060). In subprocess 450, the measure of the effectiveness of the multiple resilience measures can be output to, for example, the network controller 680 and / or human-machine interface 340 of the power network. These multiple resilience measures may include reconfiguring the power network to the optimized network topology determined by the OPF model 1060. The optimized network topology can be determined, in which case the network controller 680 can control the power network to reconfigure the power network to the optimized network topology, so that the power network has the optimized network topology during future events. Such control may include controlling one or more switches in the power network (e.g., changing the state of a switch from open to closed, or from closed to open).

[0332] 7. Network Simplification In embodiments, for at least one resilient measure, the size of the power network of the target system 140 is reduced to decrease the computational load for optimizing the resilient measure, including the number of variables, computational speed, computational complexity, etc. For example, network simplification can be used to reduce the number of nodes in the network topology of the system model 350 and / or in each scenario 610 considered by the optimization model for any resilient measure (including load shedding, network topology optimization, preventative network islanding, and / or DER deployment and scheduling). However, it should be understood that the disclosed network simplification can also be used alone or in other contexts and applications outside of the disclosed resilient measure for any type of network (e.g., radial network) in any type of target system 140. A description of network simplification can be referenced to one or more terms or concepts introduced in the following literature: Pecenak et al., “Multiphase Distribution Feeder Reduction”, IEEE Transactions on Power Systems, Vol. 33, No. 2, pp. 1320-1328, 2018, which is hereby incorporated herein by reference in its entirety.

[0333] Figure 12 The illustration shows an architecture 1200 for network simplification according to an embodiment. Network simplification can be performed by the analysis and control module 330 prior to subprocess 420 of process 400 for one or more of a plurality of resilience measures and / or for any other analysis in which the scale of the power network poses a computational challenge. At a high level, network simplification reduces the number of nodes and / or edges in the graph of the power network to compress the power network representation that must be analyzed while retaining the information needed for optimization.

[0334] The input 1210 for network simplification may include a representation, identifier, and / or other description of key assets 1214 in the original network 1212 (e.g., a power network), and / or include all edges in the original network 1212 (e.g., for each power line). i , j ]for The data for risk factor 1216. Each of risk factors 1216 can represent the failure probability and / or criticality of each edge in the original network 1212.

[0335] In subprocess 1220, critical nodes in the original network 1212 are identified based on critical assets 1214 and risk factors 1216. Subprocess 1220 may include identifying those nodes that possess critical assets as critical nodes. Subprocess 1220 may also include identifying those nodes that represent branch points as critical nodes. In other words, critical nodes (e.g., critical buses) are identified as those nodes in the original network 1212 that possess critical assets (e.g., switches, distributed energy resources 830, shunt capacitors, etc.) and / or branch points.

[0336] In subprocess 1230, the topology of the original network 1212 is identified. Subprocess 1230 may include, for each node in the original network 1212, identifying the set of parent nodes and the set of child nodes of that node phase by phase. In other words, generating a set of directly connected upstream nodes and a set of directly connected downstream nodes for each node in the original network 1212. In an embodiment, subprocess 1230 may utilize the following algorithm for topology identification:

[0337] In the above algorithm, Adj This represents the adjacency matrix of the original network 1212. This represents the original set of nodes in the original network 1212. Indicates that for the first i The node and the first p The set of parent nodes of the phase, Indicates that for the first i The node and the first p The set of child nodes of a phase. Within each phase, the algorithm uses a recursive Identify() function to connect to each bus. i The upstream bus is identified as the parent node, mathematically represented as... , , And will be connected to each busbar i The downstream busbar is identified as a child node, represented as... , , . It is aimed at the first i The node and the first p The set of intermediate parent nodes of a phase.

[0338] In subprocess 1240, the original network 1212 is simplified. Subprocess 1240 may include eliminating non-critical nodes that are not between two critical nodes. This step primarily focuses on removing edges connected to terminal nodes. Subprocess 1240 may also include eliminating non-critical nodes between two critical nodes. This step may be performed iteratively until all non-critical nodes have been removed from the original network 1212.

[0339] Subprocess 1250 may include aggregating at least a portion of the values ​​of one or more parameters from each eliminated non-critical node with the values ​​of the parameters of the critical node corresponding to the eliminated non-critical node. Aggregation parameters may include the load at each node, the criticality of the load at each node, one or more constraints on each edge, and a risk factor for each edge.

[0340] Subroutines 1240 and 1250 can be executed together. Figure 13 The illustration depicts an example simplification and aggregation of a portion of a power network according to an embodiment. In this example, a sample portion of a three-phase power network is illustrated, where B1 is a three-phase critical bus, B2 is a two-phase non-critical bus, and B3 is a two-phase critical bus. It is noteworthy that the load is not uniformly connected between the phases. p The loads connected to each bus (i.e., node) can be described as follows:

[0341] in Indicates the first p Xiangdi i The load of each busbar Indicates the first p Xiangdi i The weight of the load at each busbar, and Indicates the first p Xiangdi i Load distribution curves for each bus. Each of the original network 1212 The initial value can be set to one. p The burden of being in a relationship can be simply expressed as:

[0342] in, and yes n ×1 column vector, and It is an n×n matrix.

[0343] When the original network 1212 is simplified to the simplified network 1270, the weight of the load on the bus being eliminated... WThe phases are transferred to each adjacent bus. The goal is to remove each non-critical bus. Therefore, in the illustrated example, the goal is to remove non-critical bus B2 and its first phase weight. and the weight of its second phase The weights are transferred to adjacent buses B1 and / or B3. It should be understood that this weight transfer between nodes represents aggregation in subprocess 1250.

[0344] In this embodiment, how the weights from the eliminated non-critical buses are transferred to adjacent buses depends on the position of the non-critical bus relative to the adjacent buses. Specifically, end bus simplification refers to eliminating the end bus, such as the second phase of bus B2, while intermediate bus simplification refers to eliminating the bus located between two buses, such as the first phase of bus B2.

[0345] Since the non-critical busbar B2 needs to be removed and the second phase of busbar B2 is the terminal busbar, the entire weight of the load connected to busbar B2 in the second phase is therefore affected. The shift should be made to the critical bus B1 and aggregated with it. The updated weight matrix for the second phase is:

[0346] It is worth noting that the load weight of the eliminated bus B2 is converted to zero.

[0347] Since non-critical busbar B2 needs to be removed, and the first phase of busbar B2 is an intermediate busbar (i.e., located between the first phases of buses B1 and B3), the weight of the load connected to busbar B2 in the first phase is... They should be assigned to and aggregated with critical buses B1 and B3. In the embodiment, the weights... Divided equally and in half ( ) was transferred to bus B1, while the other half ( The weights are transferred to bus B3. The updated weight matrix for the first phase is:

[0348] It is worth noting that the load weight of the eliminated bus B2 is converted to zero.

[0349] In subprocess 1260, any post-processing can be performed. Subprocess 1260 may include generating a simplified network 1270 from the nodes and edges retained after simplification in subprocess 1240 and their corresponding parameters after aggregation in subprocess 1250. Subprocess 1260 may also generate a mapping 1275 between the simplified network 1270 and the original network 1212, which maps each compressed portion (e.g., node, edge, etc.) of the simplified network 1270 to a corresponding uncompressed portion (e.g., node, edge, etc.) of the original network 1212. Mapping 1275 may map each retained node to an eliminated node aggregated with that retained node and / or map each retained edge to an eliminated edge aggregated with that retained edge.

[0350] The output of network simplification is a simplified network 1270 and a mapping 1275. The simplified network 1270 can be provided as input to one or more analyses (e.g., optimization by the analysis and control module 330) and / or stored in the system model 350. The mapping 1275 can be stored (e.g., in the system model 350) and subsequently retrieved and used (e.g., by the analysis and control module 330) to extend the simplified network 1270 back to the original network 1212 after analysis (e.g., optimization). Therefore, any optimized solution of the simplified network 1270 can be readily transformed into an optimized solution of the original network 1212, enabling control to be performed relative to the original network 1212.

[0351] In this embodiment, it is assumed that the network has n busbar and m A three-phase radial network with n nodes, where each node represents a single-phase connection point on a busbar. m ≤ 3n In a radial network, each bus is connected to the upstream bus via only one power line. Nodes are indexed in this paper. The power lines are indicated by an index in this article. It means that, among them, i It is the index of the sending node. j This is the index of the receiving node. It is assumed that the power network uses multiphase connections and ideal lines, with resistance and reactance ignored. This assumption is valid at least for the preventative network islanding described elsewhere in this document, since power line parameters are not considered in the disclosed microgrid formation embodiments. Three levels of load criticality are used: normal; moderately critical; and highly critical.

[0352] Phase number is This indicates that, in actual multi-phase power distribution feeders, the distance between adjacent busbars... This may differ. The simplified network 1270 needs to maintain the original load distribution. Therefore, in this embodiment, network simplification is performed at the phase level. This network simplification recursively removes non-critical nodes or buses (NCBs) until only the set of critical nodes or buses (CBs) remains in the network.

[0353] In this embodiment, sub-processes 1240 to 1260 can be implemented using the following end-bus simplification algorithm:

[0354] The above end-bus simplification algorithm considers edges downstream of branch points that have no critical nodes. This ensures that all nodes connected to the downstream of each branch point are aggregated with that branch point. The algorithm's input includes the set of nodes in the original network 1212. Adjacent-to-adjacent matrix Phase-by-phase load weighting Key bus set CB and the phase-by-phase topology identification results from subprocess 1230. , For edges with critical nodes, only the downstream node of the critical node, located furthest from the branch point, is aggregated with the critical node. The loads of eliminated nodes can be aggregated as described above, and the load weight matrix can be updated to... , The eliminated nodes are stored in middle, , And the eliminated edges are stored in middle, , Active load reactive load and load weight matrix It will also be updated. Finally, by extracting from the collection... N Subtract the set of nodes calculated for all phases from the middle. R Update the node set to The algorithm's output includes the set of nodes that have been eliminated. R Stores the node-level node set of the eliminated nodes aggregated with each remaining node. And a node-level edge set that stores the eliminated edges aggregated with each remaining edge. .

[0355] In this embodiment, sub-processes 1240 to 1260 can be implemented using the following algorithms for intermediate bus simplification, aggregation, and post-processing:

[0356] The aforementioned intermediate bus simplification algorithm eliminates any nodes located between two critical nodes. When a node is eliminated, its load is distributed to and aggregated with its two adjacent nodes, as described above. The algorithm's input consists of the set of updated nodes in the intermediate network. Adjacent-to-adjacent matrix Phase-by-phase load weighting Key Node Set CB and the phase-by-phase topology identification results from subprocess 1230. , The intermediate bus simplification algorithm can be run recursively until all non-critical buses between the two critical buses have been removed. After convergence, it is updated... ( The aggregate load is recalculated, and the eliminated nodes are stored in [the relevant database]. middle, , New edges are introduced to connect two critical nodes that eliminate non-critical nodes, completing the simplified network 1270, denoted as . The eliminated edges are stored in... middle, , The algorithm's output includes the set of nodes that have been eliminated. R Stores the node-level node set of the eliminated nodes aggregated with each remaining node. And a node-level edge set that stores the eliminated edges aggregated with each remaining edge. The output can also include active load. 、 reactive load and load weight matrix .

[0357] Once the network has been simplified, one or more parameters are aggregated, including load criticality, one or more constraints on each edge, risk factors on each edge, etc., such that these parameters represent the simplified network 1270. For edge constraints (e.g., branch constraints), the maximum value among all constraints aggregated for a given phase that form that edge in the simplified network 1270 is taken. If the original edge is denoted as... ,but For radial power networks, branch constraints typically decrease gradually downstream from the substation. Therefore, the branch constraints of the branch closest to the substation must be considered. A similar approach is used for the risk factors of the edges, where... It is worth noting that risk is not defined phase by phase.

[0358] Given the criticality of the load at the aggregation node, firstly, regarding the... p Phase computation has been performed from the original node Transfer to node The first step is to decompose the load distribution curve into its share. The second step is to obtain the total load from each original node (e.g., in kWh). The third step is to calculate the weighted average of the original loads, where the weight of each original load is the weight transferred from that original node to the nodes in the simplified network 1270. i The total load. This provides the simplified network of 1270 nodes. i Its criticality is denoted as Although the original key can be an integer (e.g., one, two, three), It can have real values ​​( This approximates the optimization time period. T The key to aggregation.

[0359] In the post-processing of subprocess 1260, information about the eliminated nodes and edges, as well as the nodes and edges to which these eliminated nodes and edges are aggregated, is stored. In this regard, a phase-by-phase set of nodes (denoted as ) is defined for the simplified network 1270. , , ) and the set of edges for each phase (denoted as ) , , ,in This is the set of nodes in the simplified network 1270), and they are stored together with the set of eliminated nodes and the set of eliminated edges, which are respectively aggregated with the nodes and edges in the simplified network 1270. Continuing the example above, after the end bus is simplified, node B2 is stored in... And the edge connecting B1 and B2 is stored in In the simplification of the intermediate busbar, given the key nodes... i and downstream key nodes k In the phase p There are non-critical nodes among them, and critical nodes... i and k New edges are introduced between them, and the eliminated non-critical nodes are stored in two sets. and In the middle, and connects non-critical buses with critical nodes. i and k The old edges are stored In this context, the set is assigned to the new route. k The set of edges. Continuing the example above, for the phase... The eliminated node B2 is stored in and In the middle, the edges connecting B1 and B2, and the edges connecting B2 and B3 are stored... In this context, the set is newly introduced along with the edge linking B2 and B3. This stored information can then be used to construct parameter values ​​for an optimization model (e.g., an optimization model 960 for preventative network islanding).

[0360] In this embodiment, the entire network simplification can be implemented using the following algorithm:

[0361] The network simplification algorithm described above includes each of subprocesses 1220 to 1260, and produces a simplified network 1270 and a mapping 1275. The algorithm's input includes the data from the original network 1212, which is a set of nodes. Adjacency matrix Adj and load distribution curves for each node The algorithm initializes the load weight matrix by assigning an identity matrix. , .

[0362] 8. Microgrid Dispatch Planning In this embodiment, the analysis and control module 330 can implement microgrid dispatch planning. Microgrid dispatch planning can be used in conjunction with one or more of the disclosed resilient measures. For example, the disclosed DER deployment can be used to deploy grid-type distributed energy resources 830 onto the power network, the disclosed preventative network islanding can be used to dynamically form microgrids around grid-type distributed energy resources 830 within the power network, and microgrid dispatch planning can be used to proactively plan dispatch within the dynamically formed microgrids. However, it should be understood that for any power network including microgrids, microgrid dispatch planning can also be used alone or in any other context and application beyond the disclosed resilient measures.

[0363] Microgrid dispatch planning is particularly important for microgrids created through preventative network islanding to cope with severe weather events, as these microgrids will operate in highly unstable and uncertain environments with limited generation resources available for their continued operation. Without proper advance dispatch planning, the benefits of preventative network islanding may not be realized.

[0364] In this embodiment, a two-stage optimization framework is employed for enhanced active dispatch planning of microgrids. The first stage utilizes a hybrid of scenario-based optimal power flow (S-OPF) and risk-driven optimal power flow (RD-OPF) for full-event optimization. Its primary responsibility is to allocate limited generation resources across one or more microgrids for each of multiple time intervals (e.g., hours) spanning future events. The second stage utilizes deterministic optimal power flow for partial-event optimization (which can be computed one time interval at a time), along with the allocation of limited generation resources from the first stage. The second stage can refine dispatch and load control decisions for generation resources while ensuring that dispatch does not significantly deviate from the allocation in the first stage. Dividing the optimization into two stages coupled in this way provides the benefit of reducing the computational complexity of each optimization problem, while ensuring that decisions in the second stage fully consider the impact of decisions in the first stage.

[0365] Figure 14 The illustration shows a two-stage optimization process 1400 according to an embodiment. Process 1400 can be implemented by the analysis and control module 330. Process 1400 can be executed when preventative network islanding is selected as a resilience measure to be implemented before future events. Alternatively, process 1400 can be executed independently of any resilience measure.

[0366] Process 1400 is executed within a future time period for which optimization is to be performed. A time period can represent a span of time for a future event (such as a weather event, and possibly a severe weather event). This time period includes one or more, and typically multiple time intervals. Each time interval includes multiple time segments. While not strictly required, it is generally assumed that each time interval will have the same duration, and each time segment will have the same duration. Figure 15 The illustration depicts the segmentation of a time period according to an embodiment. In the illustrated example, the time period is divided into twelve equal time intervals, and each time interval is further divided into four equal time segments. As an example, the duration of a time period can be twelve hours or half a day, the duration of each time interval can be one hour, and the duration of each time segment can be fifteen minutes. A Phase 1 optimization is performed for the entire time period to determine the allocation for each time interval within that time period, and a Phase 2 optimization is performed for each time interval to determine the allocation for each time segment within that time interval.

[0367] In subprocess 1410, the model can be initialized. Subprocess 1410 may include determining microgrid configuration 970 (e.g., using optimization model 960), determining minimum service duration requirements for loads, determining load and renewable generation forecasts, and estimating the time periods of events (e.g., power outages, severe weather events, etc.).

[0368] In subprocess 1420, supporting data to be used by the first phase optimization can be generated. Subprocess 1420 may include scenario generation and / or fault risk analysis, wherein scenario generation can generate one or more scenarios to be used by the first phase optimization, and fault risk analysis can generate risk factors (e.g., for one or more assets in the power network, such as power lines)... Different scenarios can be generated for load and renewable power generation (e.g., PV power generation).

[0369] For generating load scenarios, one or more, and possibly all, of four different methods can be used. In the first method, the minimum and maximum predicted load demands within the time period can be calculated, and multiple time-series scenarios can be generated by uniformly sampling the data between the minimum and maximum predicted load demands. In the second method, the minimum and maximum load demands in available historical data can be calculated, and multiple time-series scenarios can be generated by uniformly sampling the data between the minimum and maximum historical load demands. In the third method, the time series of minimum and maximum load demands for each time interval can be obtained from available historical data, and multiple time-series scenarios can then be generated by uniformly sampling the data between the minimum and maximum historical load demands for each time interval. In the fourth method, the time series of minimum and maximum load demands for each time interval can be obtained from available historical data, and a first time-series scenario including the maximum load demand for each time interval can be obtained, and a second time-series scenario including the minimum load demand for each time interval can also be obtained. The first, second, and third methods can be selected based on operator choice, while the fourth method can be used to test very extreme cases.

[0370] For scenario generation targeting renewable energy generation, the distribution curve of renewable energy generation can be assumed to be the average value of renewable energy generation. The standard deviation can be calculated as one-fifth of the average value. Then, the scenario can be generated by assuming that renewable energy generation follows a normal distribution.

[0371] In subprocess 1430, the first-stage optimization can be solved for each of the multiple time intervals within the entire time period, based on the supporting data generated in subprocess 1420. The first-stage optimization may include a hybrid of S-OPF and RD-OPF models, as discussed in more detail elsewhere in this document. It should be understood that the first-stage optimization can be performed well before the time period, with sufficient time to accommodate the computational time required to solve the first-stage optimization, preferably with some buffer time. For example, the first-stage optimization may be performed fifteen minutes, thirty minutes, one hour, several hours, twelve hours, twenty-four hours, etc., before the start of the time period. If the time period represents a severe weather event, the first-stage optimization can be performed once the confidence level of the weather forecast for that time period reaches a certain confidence threshold.

[0372] Subprocess 1435 can determine whether the next time interval is imminent. For example, it can be determined that the next time interval is imminent if the start time of the next time interval is within a predefined time period from the current time. This predefined time period can represent a duration sufficient to accommodate the computation time required to solve the second-stage optimization, preferably with some buffer time. As an example, the predefined time period can be a few minutes, five minutes, ten minutes, fifteen minutes, thirty minutes, one hour, or any other duration in between or longer. When it is determined that the next time interval is not imminent (i.e., "No" in subprocess 1435), process 1400 can continue to wait for the next time interval to imminent. Otherwise, when it is determined that the next time interval is imminent (i.e., "Yes" in subprocess 1435), process 1400 can proceed to subprocess 1440.

[0373] In subprocess 1440, the second-stage optimization can be solved for each time segment in the current time interval using the first objective function and the first set of constraints. The second-stage optimization may include a deterministic optimization model, as discussed in more detail elsewhere in this document, which determines the optimal scheduling for each of the multiple time segments within the current time interval. Notably, the execution time of the second-stage optimization is closer to the actual scheduling time than that of the first-stage optimization; therefore, predictions of the power network state and events within the current time interval will generally be more accurate and less uncertain than those available during the first-stage optimization.

[0374] Subprocess 1445 can determine whether the most recent solution from the second-stage optimization is feasible. Specifically, the solution can be compared with one or more constraints to ensure that the solution satisfies all constraints. If the solution does not satisfy all constraints, it can be determined as infeasible, and if it satisfies all constraints, it can be determined as feasible. When the solution is determined to be infeasible (i.e., "No" in subprocess 1445), process 1400 can proceed to subprocess 1450. Otherwise, when the solution is determined to be feasible (i.e., "Yes" in subprocess 1445), process 1400 can proceed to subprocess 1460.

[0375] In sub-procedure 1450, the second-stage optimization can be resolved for this time interval. In this case, a second objective function and a second set of constraints can be used. The second objective function and / or the second set of constraints can be different from the first objective function and / or the first set of constraints used in sub-procedure 1440. For example, the second set of constraints can be relaxed relative to the first set of constraints, thereby increasing the search space for solutions. Furthermore, in each subsequent iteration of sub-procedure 1450, the second set of constraints can be further relaxed, thereby further increasing the search space for solutions.

[0376] In subprocess 1460, scheduling is performed for the current time interval based on the optimal solution of the second-stage optimization. Scheduling may include sending one or more commands to network controller 680 and / or DER deployment / scheduling module 1080, which can control one or more distributed energy resources 830 in one or more microgrids 840 within the power network during the current time interval according to the scheduling in the final solution of the second-stage optimization for the current time interval. This scheduling, for example, defines the operation of the power network within the current time interval at the granularity of time segments within the current time interval.

[0377] Subprocess 1465 can determine whether scheduling has been performed for the last time interval within the time period. When it is determined that scheduling has been performed for the last time interval (i.e., "yes" in subprocess 1465), process 1400 can terminate. Otherwise, when it is determined that at least one time interval still needs to be considered (i.e., "no" in subprocess 1465), process 1400 can proceed to subprocess 1475.

[0378] Subprocess 1475 can determine whether to resolve the Phase 1 optimization. Resolving the Phase 1 optimization can be determined when one or more criteria are met, and not when one or more criteria are not met. These one or more criteria may include each of one or more deviations between a field measurement of a parameter (e.g., the state of charge of a battery storage system) and the value of that parameter used in the most recent Phase 1 optimization exceeding a predefined threshold. In other words, resolving the Phase 1 optimization can be determined when the actual value of one or more parameters used in the previous Phase 1 optimization significantly deviates from its expected value. When it is determined not to resolve the Phase 1 optimization (i.e., "No" in subprocess 1475), process 1400 can return to subprocess 1435 to wait for Phase 2 optimization to be performed for the next time interval. Otherwise, when it is determined to resolve the Phase 1 optimization (i.e., "Yes" in subprocess 1475), process 1400 can return to subprocess 1420 to generate supporting data and resolve the Phase 1 optimization.

[0379] If subprocess 1475 determines that the first-stage optimization needs to be resolved, one or more constraints can be added to the first-stage optimization model to represent the actual measured values ​​of one or more parameters. For example, during time intervals... t = When the actual state of charge (SOC) of the battery storage system at the end of stage 3 is 75%, and the expected SOC of the battery storage system at this time is 85% (i.e., a 10% deviation, indicating a significant deviation), a hard equality constraint can be added to the stage 1 optimization model. Therefore, for more than t = 3 time intervals, the decisions in the solution of the first stage optimization will be based on the t = Update the actual field measurement values ​​obtained at 3 locations. Examples that could trigger a re-solution of the first stage optimization include failure of the grid-type distributed energy resource 830, and significant deviation of the resource consumption of the grid-type distributed energy resource 830 from its allocation.

[0380] Figure 16 The diagram illustrates the relationship between Stage 1 and Stage 2 optimizations for the state of charge (SOC) of a battery storage system, based on an example. As illustrated, Stage 1 optimization provides an operating range 1610 of the SOC for the battery storage system before the start of a time period. Then, during that time period, as each time interval approaches, Stage 2 optimization provides a more accurate allocation 1620 of the SOC for the battery storage system. As long as allocation 1620 remains within or tolerable of the operating range 1610, Stage 1 optimization does not need to be resolved. However, if the deviation of allocation 1620 from the operating range 1610 exceeds a predefined threshold, Stage 1 optimization can be resolved, as discussed elsewhere in this document.

[0381] 8.1. Phase 1 Optimization Model Specific embodiments of the Phase 1 optimization model will now be described. The primary objective of Phase 1 optimization is to account for uncertainties in load, generation, and asset failures, while allocating the limited generation resources available in the microgrid to each time interval of the optimized period. The S-OPF method is employed to account for uncertainties in load and generation (e.g., typically PV generators), and the RD-OPF method is employed to account for uncertainties in asset failures. This ensures the computational tractability of Phase 1 optimization. Specifically, since Phase 1 optimization models the entire time period, the size of the optimization problem increases rapidly with the duration of the time period and / or the size of the microgrid. Therefore, the disclosed embodiments enable Phase 1 optimization to scale with the time period and / or size of the microgrid.

[0382] Scenario-based modeling of load and generation utilization enables the Phase 1 optimization model to capture the operational range of generation resources that can be dispatched during each time interval without leading to resource depletion and premature microgrid shutdown. On the other hand, risk-driven modeling for asset failure utilization minimizes the dependence of high-power flows on high-risk power lines. Phase 1 optimization can maximize load supply and minimize power flows on risky power lines while considering load criticality, load generation scenarios, and power line failure risks.

[0383] In the first embodiment, the first-stage optimization model may include:

[0384] Ω represents multiple load and power generation scenarios. s It is a scene index across multiple scenarios. It is the first s The probability of each scenario occurring T It refers to the time period of the event. t It is the time interval index within that time period. N It consists of multiple nodes. i It is a node index among multiple nodes. It is the first i The criticality of each node Represents the product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first s In the first scenario t During the time interval, the first i The active power supply demand of each node (e.g., in kW). Indicates the first s In the first scenario tDuring the time interval, the first i The reactive power supply demand of each node (e.g., in kVAr). It is a scalar factor. ij It is the first i The node is connected to the first j Index of power lines for each node. E It is a collection of power lines. Is with the first ij Risk factors associated with each power line It is the first s In the first scenario t During the time interval, the first ij The active power flow on the power lines, and It is the first s In the first scenario t During the time interval, the first ij Reactive power flow on a power line.

[0385] In a second embodiment, the objective function may further include a term representing the power generation of one or more distributed energy resources 830 in the power grid. For example, in an embodiment where the power grid includes a photovoltaic (PV) system, the objective function may include a third term designed to maximize the PV power generation utilized.

[0386] in, It is the set of nodes representing photovoltaic power sources among multiple nodes in the power grid, and It is the first s In the first scenario t During the time interval, the first i The utilized active power output of the photovoltaic power source at each node (e.g., in kW).

[0387] It should be understood that in a three-phase system, 1, , , , and All are 3×1 vectors, representing the values ​​of the corresponding parameters for all three network phases. Furthermore, in such a three-phase system, it should be understood that other node- or line-specific parameters described herein (including variations of the aforementioned parameters for non-renewable generators and energy storage systems) can also be 3×1 vectors, representing the values ​​of the corresponding parameters for all three network phases.

[0388] The first-stage optimization model may include one or more constraints on the objective function. Unless otherwise specified, these constraints may be defined for all nodes (i.e., ), for all edges defined (i.e., ), defined for all time intervals within that time period (i.e., ), and definitions for all scenarios (i.e., ).

[0389] The first set of constraints ensures that the power balance condition is satisfied at every node of the power network in all scenarios. These constraints can be described using a branch power flow model as follows:

[0390] It represents the power balance of all nodes with loads, substations, or connected to distributed energy resources 830 (i.e., ,in It is a set of nodes that include substations. It is a set of nodes that have renewable generators. N DG It is a set of nodes with non-renewable generators. It is a collection of nodes with energy storage systems, among which It is the first s In the first scenario t During the time interval, the first i Active power injection at each node of the substation (e.g., in kW). It is the first s In the first scenario t During the time interval, the first i Reactive power injection at each node of the substation (e.g., in kVAr). It is the first s In the first scenario t During the time interval, the first ij Reactive power flow on the power lines It is connected to the first i The set of nodes from which edges originate, and It is connected to the terminator. i The set of nodes whose edges are given by each node; and

[0391] It represents power balance only when all nodes with loads are connected (i.e., This ensures that the net injection through each node is always zero. For simplicity, power losses are ignored in these constraints. It is worth noting that, in the context of a microgrid, N Sub This includes nodes connected to the grid-type distributed energy resource 830.

[0392] The second set of constraints ensures that the total power flowing on each power line does not exceed the rated capacity of that power line:

[0393]

[0394] in, It is the first ij Active power flow limitation on the power lines, and It is the first ij Reactive power flow limitation on power lines.

[0395] The third set of constraints ensures that S-OPF decisions do not lead to overvoltage or undervoltage in the power network:

[0396] It calculates the node voltages and limits them to an acceptable range, where It is the first s In the first scenario t During the time interval, the first i The square of the node voltage at each node (e.g., per unit value). It is the first s In the first scenario t During the time interval, the first j The square of the node voltage (e.g., per unit value) of each node. and It is used to calculate the connection of the first i The node and the first j The linearized matrix of voltage drop on the power line at each node. It is the minimum limit of node voltage (e.g., per unit value), and This is the maximum limit of node voltage (e.g., per unit); and

[0397] It will reference voltage value Assigned to nodes connected to the grid-type distributed energy resource 830 (i.e., ).matrix and The linearization coefficients represent the linearization coefficients used to model the impact of active and reactive power flow on node voltage drop.

[0398] It is worth noting that this method takes into account the influence of power flowing in other phases, which enables detailed three-phase modeling.

[0399] The fourth set of constraints ensures that the S-OPF model can supply load demand within the range of minimum required load and maximum predicted load in a manner that does not violate any operational constraints on branch power flow and node voltage. These constraints may vary depending on the scenario:

[0400] in It is the first s In the first scenario t During the time interval, the first i The minimum active power load that each node must supply. It is the first s In the first scenario t During the time interval, the first i The maximum predicted active power load of each node It is the first s In the first scenario t During the time interval, the first i Each node must supply a minimum reactive power load, and It is the first s In the first scenario t During the time interval, the first i The maximum predicted reactive power load of each node.

[0401] The fifth set of constraints models all types of distributed energy resources 830 in the microgrid:

[0402] It models the behavior of non-renewable generators in a microgrid by ensuring that the output of each non-renewable generator is limited by its operating constraints. It is the first s In the first scenario t During the time interval, connect to the first i The active power output of non-renewable generators at each node. It is the first s In the first scenario t During the time interval, connect to the first i The maximum active power output of the non-renewable generator at each node. It is the first s In the first scenario t During the time interval, connect to the first i The reactive power output of non-renewable generators at each node, It is the first s In the first scenario t During the time interval, connect to the first i The maximum reactive power output of non-renewable generators at each node, and It is the first t During the time interval, connect to the first i Apparent power of non-renewable generators at each node;

[0403] It models the behavior of renewable generators in a microgrid by ensuring that the output of each renewable generator is limited by the maximum predicted generation based on the renewable generator's rating and by providing reactive power support (assuming the renewable generator does not provide any reactive power support). It is the first s In the first scenario t During the time interval, the first i The utilized active power output of a renewable generator It is the first s In the first scenario t During the time interval, the first i Predicted active power output of a renewable generator It is the first s In the first scenario t During the time interval, the first i The utilized reactive power output of a renewable generator, and It is the power factor of a renewable generator;

[0404] It models the behavior of energy storage systems in microgrids by ensuring that the input and output of each energy storage system are limited by its operational constraints, that the time-varying SoC changes are consistent with the power exchange of each energy storage system, and that energy storage systems never charge and discharge simultaneously. It is the first s In the first scenario t During the time interval, the first i Active power (in kW) input to or output from the energy storage system at each node. It is the first i Active power limitations of energy storage systems at each node It is the first s In the first scenario t During the time interval, the first i The reactive power input to or output from the energy storage system by each node (e.g., in kVAr). It is the first i Reactive power limitations of energy storage systems at each node It is the first i Apparent power input to or output from the energy storage system at each node (e.g., in kVA). It is the power factor of the energy storage system. It is the first s In the first scenario t During the time interval, the first i The state of charge of the energy storage system at each node It is the first s In the ( ) scenario t - 1) During the time interval, the first i The state of charge of the energy storage system at each node It is the first s In the first scenario t During the time interval, the first i The charging power of the energy storage system at each node It is the first s In the first scenario t During the time interval, the first i The discharge power of the energy storage system at each node It is the first i Storage limitations of energy storage systems at each node (e.g., kWh). It is the first i Charging efficiency of the energy storage system at each node. It is the first i Discharge efficiency of the energy storage system at each node. It is the first i Minimum state of charge (e.g., percentage) limit for energy storage systems at each node. It is the first i Maximum state of charge (e.g., percentage) limit for energy storage systems at each node. It is to ensure the first s In the first scenario t During the time interval, the first i The bivariate variables of the charging and discharging mutual exclusion of the energy storage system at each node, and It is the first t During the time interval, the first i The maximum charging power of the energy storage system at each node; and

[0405] It ensures that the active power injection is equal to the sum of the power output from all distributed energy resources 830.

[0406] The fifth set of constraints relates to switching operations. Typically, small-scale microgrids do not require switches. However, additional constraints are added when switches are present at locations that could affect the radial behavior of the microgrid. Switches can be interpreted as controllable network branches; therefore, the set of switches is denoted as […]. The second set of constraints can be modified for all switches to make it applicable to all power lines with switches (i.e., Add the following constraints:

[0407] in It means the first ij A binary variable representing the switching state on a power line (e.g., Indicates disconnection. (Indicates closed). Since the switch state is fixed and independent of the scene, therefore... The variable has no scene index. s Additionally, the third set of constraints can be modified to add the following constraints to all nodes connected by the switch:

[0408] in It is the first s Two disconnected nodes in a scene i and j The slack variable of the voltage difference between them. This slack variable ensures the first ij The constraint is not violated when the switch on the first power line is disconnected. The second constraint ensures that when the first... ij The switch on the power line is closed (i.e., When ), then And must be maintained and The relationship between them. However, if the first ij The switch on the power line is open (i.e., If so, there is no need to maintain it. and The relationship between them.

[0409] The sixth set of constraints ensures radiality. After switching optimization, there is a possibility that the final switching state may lead to loops within the power network, and distribution networks typically operate in a radial pattern. Therefore, to ensure that the optimal switching state maintains the radial structure of the power network, additional radial constraints can be added. In this embodiment, a graph theory-based approach is used to model the radial constraints. To maintain a radial network, two conditions must be met: (i) the total number of edges must equal the total number of nodes minus the total number of substations; and (ii) the network must remain fully connected.

[0410] To incorporate the first of these two radiation conditions into the first-stage optimization model, the following constraint can be added:

[0411] The second radiation condition is more difficult to ensure. This is because the presence of distributed energy resource 830 may cause the upstream switch of distributed energy resource 830 to be disconnected, since the downstream distributed energy resource 830 can meet the load demand of the downstream load. Therefore, in the embodiment, virtual load flow is adopted to ensure that the second condition is met. The basic idea is to assign a virtual load with a per-unit value of one to each grid-type distributed energy resource 830, where all other nodes are fixed with a per-unit value of zero, and the grid-type distributed energy resource 830 is responsible for powering each virtual load. To reduce computational complexity, these virtual load constraints are implemented only for a time interval and a scenario, because the switching state is time-invariant and scenario-invariant. To ensure the second radiation condition, the following virtual load constraints can be added to the first-stage optimization model:

[0412] in, It comes from the first i Each substation node (i.e., Virtual power supply, It is the first i The virtual load at each node (i.e., ), From the first i The flow from the node to the first j The virtual power flow of each node, and It is the first ij Virtual power flow constraints for power lines.

[0413] 8.2. Second-stage optimization model The solution for Phase 1 optimization can include the operating range of all grid-connected distributed energy resources 830 for each time interval within the time period. The main objective of Phase 2 optimization is to perform microgrid dispatch for each time interval by ensuring that the grid-connected distributed energy resources 830 are not dispatched outside the operating range determined by Phase 1 optimization. Specifically, Phase 2 optimization selects the loads to be supplied and cut in a manner that conforms to the generation availability specified in Phase 1 optimization.

[0414] Generation resources in a microgrid need to be carefully allocated throughout the entire time period to avoid a complete microgrid shutdown. There is a possibility that events could cause distributed energy resources (830) to fail, potentially leading to premature microgrid shutdown. Since the execution time of the second-stage optimization is closer to actual scheduling than that of the first-stage optimization, its uncertainty is lower. Therefore, the second-stage optimization model can utilize deterministic methods. This provides the additional benefit that the second-stage optimization model is computationally faster than the first-stage optimization model.

[0415] From a mathematical modeling perspective, there is no significant difference between the Phase 1 and Phase 2 optimization models. The main differences are: the Phase 1 optimization model implements a combination of scenario-based optimal power flow and risk-driven optimal power flow, while the Phase 2 optimization model is essentially deterministic due to lower uncertainty; the Phase 2 optimization model has several additional constraints and a slightly modified objective function to ensure that the DER scheduling computed in Phase 2 does not significantly deviate from the solution of Phase 1; Phase 2 optimization does not consider switching states and radial constraints because the network topology has been fixed in Phase 1; and the load control constraints in Phase 2 optimization differ slightly from those in Phase 1 optimization because they include variables representing binary load connectivity.

[0416] Phase 2 optimization can maximize load supply and minimize power flow on at-risk power lines while considering load criticality and power line fault risk. It should be understood that all terms used in the Phase 2 optimization model can be the same as those used in the Phase 1 optimization model, the only difference being that these terms do not have scenario indices because the Phase 2 optimization model is not scenario-based. In other words, Phase 2 optimization can consider only a single scenario representing the current or health state of the power network (e.g., including switching states determined by Phase 1 optimization). Furthermore, Phase 1 optimization optimizes over time intervals (i.e., the indices in Phase 1 optimization...). t The second phase of optimization (representing time intervals) optimizes on time slices (i.e., the indexes in the second phase of optimization). t (This refers to a time segment within a time interval). In all other respects, any description of the terms in the first-stage optimization also applies to the same terms in the second-stage optimization.

[0417] In the first embodiment, the second-stage optimization model may include:

[0418] In a second embodiment, the objective function may further include a term representing the power generation of one or more distributed energy resources 830 in the power grid. For example, in an embodiment where the power grid includes a photovoltaic (PV) system, the objective function may include a third term designed to maximize the PV power generation utilized.

[0419] In either embodiment, the second-stage optimization model can include one or more constraints. The first set of constraints ensures that the power balance condition is satisfied at every node of the power network:

[0420] It is worth noting that, except for not considering multiple scenarios, this first set of constraints is the same as the first set of constraints in the first-stage optimization model.

[0421] The second set of constraints ensures that the total power flowing on each power line does not exceed the rated capacity of that power line:

[0422] It is worth noting that, except for not considering multiple scenarios, this second set of constraints is the same as the second set of constraints in the first-stage optimization model.

[0423] The third set of constraints ensures that the Phase 2 optimization decision will not lead to overvoltage or undervoltage in the power network:

[0424] It is worth noting that, except for ignoring multiple scenarios, this third set of constraints is the same as the third set of constraints in the first-stage optimization model. (Matrix) and It can be defined in the same way as in the first-stage optimization model.

[0425] The fourth set of constraints ensures that the Phase 2 optimization model can selectively supply load demand, which ensures that power generation consumption is close to the operating range set by the Phase 1 optimization:

[0426] in, It indicates whether or not to send to the first i The binary variable of load power supply to each node (i.e., This indicates that there is no power supply, and (indicating power supply), and N MSD It is the set of nodes whose loads are connected to the power grid but have not yet met their minimum service duration requirements. It is worth noting that... The load is not indexed by time to ensure that if it is connected to or disconnected from the power network, it remains in that state throughout the entire time interval. This is done to prevent frequent load switching in and out. The last equality constraint in this fourth set of constraints ensures that loads whose connections have not yet reached the minimum service duration cannot be disconnected, which ensures that the minimum service duration must be met before a load can be disconnected.

[0427] The fifth set of constraints models and / or restricts the behavior of each type of distributed energy resource 830 in the power network:

[0428] It limits the output of non-renewable generators to within their operating limits;

[0429] It ensures that the output of the non-renewable generator is optimized by Phase 1 (denoted as...). S 1) Within the defined operating range, where, It is the power factor of a non-renewable generator;

[0430] It ensures that the output of the renewable generator is limited to the maximum predicted power generation based on the renewable generator's rating;

[0431] It ensures that the maximum output of these renewable generators is within the operating range determined by the first phase optimization, and wherein the lower limit is set to zero because the photovoltaic generators are not dispatchable;

[0432] It provides reactive power output from renewable generators;

[0433]

[0434] It ensures that the input and output of the energy storage system are limited by its operating constraints, that the SoC variation over time matches the power of the energy storage system, and that the energy storage system is never charged and discharged simultaneously.

[0435] It ensures that the state of charge of each energy storage system remains within the operating range determined by the optimization in Phase 1; and

[0436] It ensures that the active power injection is equal to the sum of the power output from all distributed energy resources 830.

[0437] It is worth noting that the second-stage optimization model does not need to include any constraints related to switching operations and radiation. This is because the switching states are inherited from the first-stage optimization. This makes the second-stage optimization model computationally lightweight, making it suitable for near real-time scheduling. This allows the second-stage optimization to be performed near the start of each time interval, minimizing uncertainty.

[0438] Strict constraints on the distributed energy resource 830 regarding its operating range determined by the first-stage optimization may render the second-stage optimization model infeasible. For example, imposing strict constraints on the output of the distributed energy resource 830 if it unexpectedly shuts down due to a fault would render the second-stage optimization model infeasible. To avoid infeasibility, one or more constraints on the second-stage optimization model can be relaxed (e.g., in subprocess 1450). Specifically, new variables can be introduced for each type of distributed energy resource 830: Indicates the first t During the first time segment i The output of the non-renewable generator at each node and the average output value of the operating range determined by the first stage optimization. Deviation; Indicates the first t During the first time segment i The input or output of the energy storage system at each node and the average input or output value of the operating range determined by the first stage optimization. The deviation; and Indicates the first t During the first time segment i The output of the regenerative generator at each node and the average output value of the operating range determined by the first stage optimization. The deviation. To incorporate this relaxation, the objective function of the second-stage optimization model can be modified as follows (e.g., for each iteration of subprocess 1450):

[0439] in, It is the first i The energy capacity of the energy storage system at each node. In an alternative embodiment, the objective function may further include a term for maximizing renewable power generation in the power grid:

[0440] The operator can decide whether to prioritize maximizing renewable energy utilization or minimizing the deviation of renewable generation from the operating range determined by the Phase 1 optimization. This relaxation method in subprocess 1450 ensures that the deviation relative to the Phase 1 optimization is minimized by adding a penalty to the objective function, while also ensuring that the Phase 2 optimization returns a feasible solution.

[0441] Additionally, relaxation (e.g., in each iteration of subprocess 1450) may include applying the corresponding constraints from the fifth set of constraints (i.e., including those using...) S Replace the constraint representing the parameter (1) with the following constraint:

[0442] Additionally, relaxation (e.g., relaxation in each subsequent iteration of subprocess 1450 after the initial iteration of subprocess 1450) may include replacing the fourth set of constraints with:

[0443] To ensure the feasibility of the problem.

[0444] 9. Experimental Results [139, 065] Figure 17A The illustration shows a network diagram of the IEEE 123-node distribution network feeder circuit used in an exemplary implementation of the disclosed embodiments before the preventative deployment and scheduling of distributed energy resources 830. This network diagram has been simplified, removing details unnecessary for understanding the test. In the illustrated example, fixed distributed energy resources 830 are present at nodes 29, 78, and 101, and flexible asset connection points are nodes 23, 35, 51, 57, 91, and 99.

[0445] The criticality of power lines is assigned based on graph theory. Loads on the circuit are assigned different criticality levels to indicate the priority to be given to these loads. Load criticality is divided into three categories: low (e.g., residential buildings, recreational areas, etc.); medium (e.g., shelters, grocery stores, etc.); and high (e.g., hospitals, gas pipeline pumping stations, water supply systems, etc.). Critical loads are indicated by diamond shapes at nodes 83, 100, 102, and 102. It should be understood that the criticality of power lines and loads can be included in asset data 620.

[0446] The candidates for Mobile Distributed Energy Resources 830 are:

[0447] Figure 17B The illustration shows a network diagram of the IEEE 123-node distribution network feeder circuit used in an exemplary implementation of the disclosed embodiments after preventative deployment and scheduling of distributed energy resources 830 by the RD-OPF model 1060. The DER configuration 1070 output by the RD-OPF model 1060 consists of the following distributed energy resources 830:

[0448] Notably, four mobile distributed energy resources 830 (including two battery storage systems and two diesel generators) were deployed on predefined FACP nodes. To demonstrate the effectiveness of the RD-OPF model 1060, the expected system performance was evaluated under a set of predefined line outage scenarios. The expected system mean outage duration index (E[SAIDI]) was used as a measure of effectiveness. Advantageously, the preventative deployment and scheduling determined by the RD-OPF model 1060 resulted in a 4.7% reduction in the expected system mean outage duration index.

[0449] Figure 18A The illustration shows a network diagram of the IEEE 123 node distribution network feeder circuit used in an exemplary implementation of a disclosed preventive network islanding method before preventive network islanding is implemented. Figure 18B The diagrams illustrate network plots of the same feeder circuit after preventative network islanding. These network plots have been simplified, removing details unnecessary for understanding the testing. As shown, after preventative network islanding, the feeder circuit has been split into a main grid and three microgrids via disconnect switches [13, 152], [39, 66], [64, 108], [151, 300], [97, 197], [67, 72], and [71, 114].

[0450] Two different solvers were tested over six-hour and twenty-four-hour time periods, with and without the disclosed network simplification. The first solver was Gurobi™, a multi-threaded commercial solver; the second was the Computational Infrastructure for Operations Research (COIN) Branch Cut (CBC), a single-threaded open-source solver. For Gurobi™, network simplification reduced computation time by 32% over the six-hour time period and by 44% over the twenty-four-hour time period. For CBC, network simplification reduced computation time by 52% over the six-hour time period and by 82% over the twenty-four-hour time period. The resulting microgrid configurations were similar with and without network simplification. The only difference was in the main grid, where, with network simplification, switch [23, 25] was open and switch [18, 135] was closed, while without network simplification, switch [23, 25] was closed and switch [18, 135] was open. This may be a result of aggregation methods that ignore voltage constraints or risk factors and limitations of power lines during microgrid formation.

[0451] For comparative analysis, network simplification and preventative network islanding were also tested on an IEEE 8500 bus system. This system included both medium-voltage and low-voltage nodes. During network simplification, low-voltage nodes were eliminated and aggregated to their corresponding medium-voltage nodes, reducing the system to 2,522 nodes. For Gurobi™, network simplification reduced computation time by 82% over a six-hour period and by 76% over a twenty-four-hour period. For CBC, network simplification reduced computation time by 57% over a six-hour period. For CBC, the reduction in computation time over a twenty-four-hour period was uncertain because without network simplification, the optimization failed to converge even after 1.5 hours; with network simplification, the computation time was only 349 seconds.

[0452] In all cases, the disclosed network simplification significantly reduces the computation time of the disclosed preventative network islanding implementation. This is particularly important in applications related to operational resilience, where rapid decisions may be required for large power networks.

[0453] 10. Example Application While the disclosed embodiments are not specific to any particular target system 140 and event (e.g., abnormal weather, normal weather, non-weather, etc.) (e.g., in terms of asset portfolio, load type, geographic location, etc.), it is generally envisioned that the target system 140 will be a power network, and the event will be an extreme weather event. The power network can be any type of distribution network, including a three-phase balanced distribution network or a three-phase unbalanced distribution network, or alternatively, a transmission network. The disclosed embodiments enable proactive resilience measures to be implemented prior to weather events, thereby improving the operational resilience of the power network before weather events occur. This, in turn, can reduce the downtime of the power network (e.g., power outages) during weather events.

[0454] Specifically, one or more OPF models can be used to identify multiple resilience measures, which can be ranked in a recommended priority order based on effectiveness metrics. These effectiveness metrics can be based on one or more key performance indicators and / or ease of implementation. One or more of these resilience measures can then be selected and implemented in the power grid before, at the start of, and / or during a weather event to strengthen the power grid, enabling it to better absorb the effects of damage caused by the weather event (e.g., fewer power outages) and / or recover from the effects of damage caused by the weather event (e.g., faster power restoration). These resilience measures can be selected manually (e.g., by the distribution network operator), automatically (e.g., by analysis and control module 330, network controller 680, etc.), and / or semi-automatically (e.g., automatically recommending selections but requiring manual approval or rejection of the recommendations).

[0455] Regardless of how the resilience measure is selected, each resilience measure can be implemented manually, automatically, or semi-automatically. In the automatic or semi-automatic case, when it is determined that a specific resilience measure should be implemented, network controller 680 (e.g., system 200 implementing control module 320) can control the power network of target system 140 to implement that specific resilience measure. For example, if it is determined that load shedding should be implemented, network controller 680 can control the power network to reduce the power supplied to at least one load of the power network during a future event. If it is determined that an optimized network topology should be implemented, network controller 680 can control the power network to reconfigure the power network to the optimized network topology 770, such that the power network has the optimized network topology 770 during a future event. If it is determined that preventive network islanding should be implemented, network controller 680 can control the power network to reconfigure the power network to a microgrid configuration 970, and, if necessary, dispatch one or more mobile distributed energy resources 830 (e.g., via DER dispatch module 980) or otherwise facilitate the dispatch of one or more mobile distributed energy resources 830. If it is determined that DER deployment and scheduling will be implemented, the network controller may schedule one or more distributed energy resources 830, deploy and / or schedule one or more mobile distributed energy resources 830 (e.g., via DER deployment / scheduling module 1080), control multiple switches to match the state in the network topology (e.g., DER configuration 1070), and / or otherwise facilitate the deployment and / or scheduling of one or more distributed energy resources 830.

[0456] Therefore, the disclosed embodiments can be used as a decision-making tool for the operator of the target system 140. Specifically, the operator can utilize process 400 to support proactive resilience measures to improve the operational resilience of the target system 140 before future events. Additionally, process 400 can continue operating during an event to provide updated recommendations and rankings of resilience measures using real-time input data collected during the event.

[0457] Alternatively or concurrently, the disclosed embodiments can be used as a planning tool to quantify the operational resilience of target system 140. In other words, process 400 can be performed without considering any future events to recommend and rank resilience measures for improving the overall operational resilience of target system 140. The operator of target system 140 can use this planning tool for short-term or long-term planning. For example, the operator can use the ranked resilience measures to prioritize investments in enhancements to target system 140.

[0458] Effectiveness measures used to quantify the effectiveness of each resilience measure can utilize intuitive and / or commonly used key performance indicators, such as critical load supply, loss of load value, mean outage duration index, etc. The effectiveness measures can be provided to the operator of the target system 140 in an easily readable visual format (e.g., in one or more tables, graphs, charts, etc.) via human-machine interface 340. Therefore, the operator may be able to begin using the disclosed embodiments without any additional training.

[0459] In embodiments, resilience measures include, or are constituted by, DER deployment and scheduling using the RD-OPF model 1060. The RD-OPF model 1060 performs risk-driven optimization to determine whether and how to reconfigure the network topology of the power network, including how to deploy and schedule distributed energy resources 830 within the power network, to effectively prepare the power network for future events, one or more other resilience measures (e.g., preventative islanding) and / or recovery plans to ensure a continuous, secure, and reliable power supply to the load. The objective is to enhance the operational resilience of the power network by solving a multi-time optimization problem based on inputs such as the risk value of assets, network topology, asset information, physical constraints, the location of FACP nodes, and information about distributed energy resources 830 (e.g., quantity, fixed or mobile, type, combination, etc.) that can be specified by the operator, ensuring maximum load service while minimizing weighted power flow on risky lines and voltage deviations on network buses.

[0460] Compared to state-of-the-art network topology optimization and load control techniques, the disclosed method for DER deployment and dispatch effectively improves load service and availability metrics (e.g., Loss of Load Value, SAIDI, etc.), and enables power system operators to prevent islanding in a systematic manner to further enhance availability metrics and ensure load management, grid stability, and voltage regulation throughout extreme weather events. The disclosed method is also flexible for different types of forecast events, including weather events such as storms, hurricanes, blizzards, wildfires, heat waves, and floods, and is modular in its applicability to distribution networks with varying balance and imbalance structures. This method can be integrated with network simplification to provide faster solutions for very large and complex power systems.

[0461] In the embodiments, the disclosed method for DER deployment and scheduling is designed to provide or support one or more of the following objective decisions based on the availability of fixed and / or mobile distributed energy resources 830 and network configuration requirements: (i) scheduling fixed distributed energy resources 830 if only fixed distributed energy resources 830 exist in the power network; (ii) reconfiguring the network topology using network switching optimization, in addition to scheduling fixed distributed energy resources 830; (iii) reconfiguring the network topology using network switching optimization, in addition to deploying and scheduling mobile distributed energy resources 830; and / or (iv) reconfiguring the network topology using network switching optimization, in addition to scheduling fixed distributed energy resources 830, in addition to deploying and scheduling mobile distributed energy resources 830.

[0462] In embodiments, resilience measures include or constitute preventative network islanding, which can utilize the disclosed network simplification. In this case, asset data associated with multiple power transmission assets of the power network can be acquired, and forecast data associated with at least one future event can be acquired. Input data can be generated based on the asset data and forecast data. Prior to at least one future event (e.g., a weather event, such as an extreme weather event), the input data can be fed into a probabilistic optimization model that optimizes at least one parameter of the operation of the power network for the at least one future event. This probabilistic optimization model determines the switching state of each of multiple switches in the power network by optimizing an objective function to maximize the total load served in the power network during the at least one future event, in order to introduce one or more microgrids into the power network. The objective function associates each of multiple power lines in the power network with a risk factor representing the failure probability of that power line, prioritizing power flow on power lines associated with lower risk factors over power flow on power lines associated with higher risk factors, and is subject to one or more islanding constraints. Furthermore, for each of the multiple resilience measures, an effectiveness metric for the operation of the power network against at least one future event can be determined based on the solution of a probabilistic optimization model. The effectiveness metrics of the multiple resilience measures can be output to the network controller 680 of the power network, wherein the multiple resilience measures include reconfiguring the power network according to determined switching states, which may represent a microgrid configuration 970. Reconfiguring the power network may include controlling multiple switches to match the determined switching states. Specifically, the determined switching states can be determined to be implemented, in which case the network controller 680 can control multiple switches to match the determined switching states such that the multiple switches have the determined switching states during at least one future event.

[0463] The disclosed preventative network islanding proactively divides power network islands into a main grid and one or more microgrids by reconfiguring the power network topology using available switches in the power network. This enables the formation of smaller, self-sufficient microgrids that can operate independently of substations and to each other to serve their respective loads. Each microgrid requires grid-based distributed energy resources 830 to form the microgrid's frequency. This grid-based functionality can be supported by diesel generators, battery storage systems, etc. This introduces redundancy into the power network because loads no longer rely solely on substations to form frequencies and supply demand, which improves the operational resilience of the power network by reducing the likelihood of power outages during events. The embodiments are modular in their applicability to different balanced and unbalanced distribution networks.

[0464] Optimized preventative network islanding allows for the appropriate determination of microgrid size, ensuring that loads within each microgrid are served to the maximum extent possible throughout the event period. Furthermore, the concept of risk can be integrated into the optimization problem to account for the predicted impact of the event. In this case, the quantified risk of the event to assets is incorporated into the optimization to minimize the microgrid's dependence on at-risk assets. Therefore, even if high-risk assets fail during the event, the majority of the power network can continue to operate at maximum performance. In summary, using risk-aware optimal decision-making to create electrical islands within the power network enables greater operational resilience to extreme events that could damage one or more assets within the power network. The advantages of the disclosed preventative network islanding include, but are not limited to: increased redundancy through multiple network sources beyond substation feeders, thereby reducing the value of lost loads during power outages; reduced dependence on at-risk assets during extreme events; ensuring critical loads remain energized, which is crucial for important consumers such as hospitals and communication networks; and facilitating faster recovery by allowing unaffected microgrids to connect to the main grid first, followed by the affected portion of the power network. Although this paper primarily discusses electrical islanding in a preventative or proactive context, the optimizations disclosed for electrical islanding can also be used passively, for example, after and / or during an event.

[0465] Figure 19An architecture 1800 combining network simplification, electrical islanding, and microgrid dispatch planning according to an embodiment is illustrated. Architecture 1800 may be particularly useful for large power systems or when rapid (e.g., real-time) decision-making is required. Initially, the network simplification architecture 1200 simplifies the original network 1212 into a simplified network 1270, as discussed elsewhere herein. This simplified network 1270 (consisting of a smaller number of nodes and edges and associated with aggregated parameters such as load, load criticality, edge criticality, etc.) is provided as input to an electrical islanding architecture 900, which determines a microgrid configuration 970, as discussed elsewhere herein. Finally, this microgrid configuration 970, including network topology and switching states, is provided as input to a process 1400 that performs a two-stage microgrid dispatch planning process, as described elsewhere herein, to dispatch distributed energy resources 830 in a manner that maximizes the loads served in the microgrid while ensuring compliance with physical DER constraints. In embodiments where the power network is small or computational speed is not an issue, the network simplification architecture 1200 can be omitted. It is worth noting that architecture 1800 is independent of the power grid model and events, and can be easily applied to different types of power networks facing different events, including different types of distribution networks, regardless of their asset mix, load type, and geographic location.

[0466] Figure 20 An example operation of preventative network islanding according to an embodiment is illustrated. In this example, target system 140 includes substation node 1, FACP node 3, and other nodes 2, 4, and 5. Hurricane 1900 is predicted to pass through the middle of target system 140. Preventative network islanding is performed to generate a microgrid configuration 970 by changing the state of switches [2, 3] from closed to open. This microgrid configuration divides target system 140 into a main grid consisting of nodes 1, 2, and 5 and a microgrid consisting of nodes 3 and 4 and having grid-type distributed energy resources 830. Thus, target system 140 is hardened to withstand hurricane 1900.

[0467] The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will become readily apparent to those skilled in the art, and the general principles described herein can be applied to other embodiments without departing from the spirit or scope of the invention. Therefore, it should be understood that the description and drawings presented herein represent currently preferred embodiments of the invention, and thus represent a broad range of subjects considered in the invention. It should be further understood that the scope of the invention fully encompasses other embodiments that may be obvious to those skilled in the art, and therefore the scope of the invention is not limited.

[0468] As used herein, the terms “comprising,” “comprise,” and “comprises” are open-ended. For example, “A comprises B” means that A may include either (i) B alone, or (ii) a combination of B with one or more (and potentially any number) other components. In contrast, the terms “consisting of,” “consist of,” and “consistsof” are closed-ended. For example, “A constitutes B” means that A includes only B and excludes no other components in the same context.

[0469] The combinations described herein, such as "at least one of A, B, or C," "one or more of A, B, or C," "at least one of A, B, and C," "one or more of A, B, and C," and "A, B, C, or any combination thereof," include any combination of A, B, and / or C, and may include multiple A, multiple B, or multiple C. Specifically, combinations such as "at least one of A, B, or C," "one or more of A, B, or C," "at least one of A, B, and C," "one or more of A, B, and C," and "A, B, C, or any combination thereof" may be only A, only B, only C, A and B, A and C, B and C, or A and B and C, and any such combination may contain one or more members of its constituent parts A, B, and / or C. For example, a combination of A and B may include one A and multiple B, multiple A and one B, or multiple A and multiple B.

[0470] The following items relate to preferred embodiments: Example 1A: A method comprising using at least one hardware processor to perform the following operations: acquiring asset data associated with a plurality of power transmission assets of a power network; acquiring predictive data associated with at least one future event; generating input data based on the asset data and the predictive data; and inputting the input data into a probabilistic optimization model prior to the at least one future event, the probabilistic optimization model optimizing at least one parameter of the operation of the power network for the at least one future event; determining, for each of a plurality of resilience measures, an effectiveness measure of the resilience measures for the operation of the power network for the at least one future event based on the solution of the probabilistic optimization model; and outputting the effectiveness measures of the plurality of resilience measures to a network controller of the power network.

[0471] Project 2A: The method of Project 1A further includes using the at least one hardware processor to rank the plurality of resilience measures according to the validity measures before outputting the validity measures.

[0472] Project 3A: The method as described in Project 2A, wherein the effectiveness measure of each of the plurality of resilience measures is based on one or both of the following: the expected improvement in the operation of the power network during the at least one future event when the resilience measures are implemented; or the ease with which the resilience measures are implemented.

[0473] Project 4A: The method as described in any of the preceding projects, wherein the probabilistic optimization model optimizes the objective function of the expected load supply, and wherein the plurality of resilience measures include load shedding.

[0474] Project 5A: The method as described in Project 4A, wherein the asset data includes critical information indicating the criticality of one or more loads of the power network, and wherein the objective function weights the one or more loads according to the criticality.

[0475] Item 6A: The method of Item 4A further includes using the at least one hardware processor to perform the following operations: determining to implement the load reduction; and controlling the power network to reduce the power supplied to at least one load of the power network during the at least one future event.

[0476] Project 7A: The method of any of the preceding projects, wherein the probabilistic optimization model models the topology of the power network, wherein the solution of the probabilistic optimization model includes an optimized network topology, and wherein the plurality of resilience measures include reconfiguring the power network to the optimized network topology.

[0477] Item 8A: The method of Item 7A further includes using the at least one hardware processor to perform the following operations: determining to implement the optimized network topology; and controlling the power network to reconfigure the power network to the optimized network topology such that the power network has the optimized network topology during the at least one future event.

[0478] Project 9A: The method of any of the preceding projects, wherein the probabilistic optimization model models the electrical islanding within the power network, wherein the solution of the probabilistic optimization model includes one or more electrical islands within the power network, and wherein the plurality of resilience measures includes preventative electrical islanding.

[0479] Project 10A: The method of any of the preceding projects, wherein the probabilistic optimization model models the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model includes scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures includes scheduling the one or more energy resources.

[0480] Item 11A: The method as described in any of the preceding items, wherein the asset data includes one or more parameters of each of one or more of the plurality of power transmission assets, and indicates the connection between the plurality of power transmission assets.

[0481] Item 12A: The method as described in any of the preceding items, wherein the forecast data includes forecasts of load on the power network during the at least one future event.

[0482] Project 13A: The method as described in any of the preceding projects, wherein the input data includes multiple failure scenarios of the plurality of power transmission assets during the at least one future event.

[0483] Project 14A: The method of Project 13A, wherein the asset data includes the failure probabilities of the plurality of power transmission assets, and wherein the method further includes generating the plurality of failure scenarios based on the failure probabilities using the at least one hardware processor.

[0484] Project 15A: The method as described in any of the preceding projects, wherein the input data includes multiple failure probability distributions of the plurality of power transmission assets.

[0485] Item 16A: The method of any of the preceding items, wherein the at least one future event includes a weather event, and wherein the forecast data includes a weather forecast for a certain period of time for the at least one future event.

[0486] Item 17A: The method as described in any of the preceding items, wherein the power network includes a distribution network.

[0487] Project 18A: The method as described in any of the preceding projects, wherein the plurality of resilience measures include load reduction and network topology optimization.

[0488] Project 1B: A method comprising using at least one hardware processor to: acquire asset data associated with a plurality of power transmission assets of a power network; acquire forecast data associated with at least one future event; generate input data based on the asset data and the forecast data; and input the input data into a probabilistic optimization model prior to the at least one future event, the probabilistic optimization model optimizing at least one parameter of the operation of the power network for the at least one future event; for each of a plurality of resilience measures, determining a measure of the effectiveness of the resilience measures for the operation of the power network for the at least one future event based on a solution of the probabilistic optimization model; and outputting the measure of the effectiveness of the plurality of resilience measures to a network controller of the power network, wherein the probabilistic optimization model optimizes the computation of an objective function for expected load supply, and wherein the plurality of resilience measures include load shedding.

[0489] Project 2B: The method of Project 1B further includes using the at least one hardware processor to perform the following operations: determining to implement the load reduction; and controlling the power network to reduce the power supplied to at least one load of the power network during the at least one future event.

[0490] Project 3B: The method as described in Project 1B or 2B, wherein the asset data includes critical information indicating the criticality of one or more loads of the power network, and wherein the objective function weights the one or more loads according to the criticality.

[0491] Project 4B: The method of any one of Projects 1B to 3B further includes ranking the plurality of resilience measures according to the validity measures of the plurality of resilience measures using the at least one hardware processor before outputting the validity measures.

[0492] Item 5B: The method as described in any one of Items 1B to 4B, wherein the effectiveness measure of each of the plurality of resilience measures is based on one or both of the following: the expected improvement in the operation of the power network during the at least one future event when the resilience measures are implemented; or the ease with which the resilience measures are implemented.

[0493] Project 6B: The method of any one of Projects 1B to 5B, wherein the probabilistic optimization model models the topology of the power network, wherein the solution of the probabilistic optimization model includes an optimized network topology, and wherein the plurality of resilient measures include reconfiguring the power network to the optimized network topology.

[0494] Item 7B: The method of Item 6B further includes using the at least one hardware processor to perform the following operations: determining to implement the optimized network topology; and controlling the power network to reconfigure the power network to the optimized network topology such that the power network has the optimized network topology during the at least one future event.

[0495] Project 8B: The method of any one of Projects 1B to 7B, wherein the probabilistic optimization model models the electrical islanding within the power network, wherein the solution of the probabilistic optimization model includes one or more electrical islands within the power network, and wherein the plurality of resilience measures includes preventative electrical islanding.

[0496] Project 9B: The method as described in Project 8B, wherein the solution of the probabilistic optimization model includes a microgrid configuration comprising multiple microgrids, each microgrid having at least one grid-type distributed energy resource, and wherein the method further comprises using the at least one hardware processor to: determine the implementation of the preventive electrical islanding partitioning; and control one or more switches in the power network to split the power network into multiple microgrids.

[0497] Project 10B: The method of any one of Projects 1B to 9B, wherein the probabilistic optimization model models the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model includes scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures includes scheduling the one or more energy resources.

[0498] Item 11B: The method as described in Item 10B, wherein the one or more energy resources include at least one mobile energy resource.

[0499] Item 12B: The method as described in any one of Items 1B to 11B, wherein the asset data includes one or more parameters of each of one or more of the plurality of power transmission assets and indicates the connection between the plurality of power transmission assets.

[0500] Item 13B: The method of any one of items 1B to 12B, wherein the forecast data includes forecasts of load on the power network during the at least one future event.

[0501] Item 14B: The method of any one of Items 1B to 13B, wherein the input data includes multiple failure scenarios of the plurality of power transmission assets during the at least one future event.

[0502] Project 15B: The method as described in Project 14B, wherein the asset data includes the failure probabilities of the plurality of power transmission assets, and wherein the method further includes generating the plurality of failure scenarios based on the failure probabilities using the at least one hardware processor.

[0503] Item 16B: The method of any one of Items 1B to 15B, wherein the input data comprises multiple failure probability distributions of the plurality of power transmission assets.

[0504] Item 17B: The method of any one of items 1B to 16B, wherein the at least one future event includes a weather event, and wherein the forecast data includes a weather forecast for a certain period of time for the at least one future event.

[0505] Item 18B: The method of any one of Items 1B to 17B, wherein the power network includes a distribution network.

[0506] Project 1C: A method comprising using at least one hardware processor to: acquire asset data associated with a plurality of power transmission assets of a power network; acquire predictive data associated with at least one future event; generate input data based on the asset data and the predictive data; and input the input data into a probabilistic optimization model prior to the at least one future event, the probabilistic optimization model optimizing at least one parameter of the operation of the power network for the at least one future event; for each of a plurality of resilience measures, determining a measure of the effectiveness of the resilience measures for the operation of the power network for the at least one future event based on a solution of the probabilistic optimization model; and outputting the measure of the effectiveness of the plurality of resilience measures to a network controller of the power network, wherein the probabilistic optimization model models a topology of the power network, wherein a solution of the probabilistic optimization model includes an optimized network topology, and wherein the plurality of resilience measures includes reconfiguring the power network to the optimized network topology.

[0507] Project 2C: The method of Project 1C further includes using the at least one hardware processor to perform the following operations: determining to implement the optimized network topology; and controlling the power network to reconfigure the power network to the optimized network topology such that the power network has the optimized network topology during the at least one future event.

[0508] Item 3C: The method as described in Item 1C or 2C, wherein controlling the power network includes controlling one or more switches in the power network.

[0509] Project 4C: The method of any one of Projects 1C to 3C further includes ranking the plurality of resilience measures according to the validity measures of the plurality of resilience measures using the at least one hardware processor before outputting the validity measures.

[0510] Item 5C: The method of any one of Items 1C to 4C, wherein the effectiveness measure of each of the plurality of resilience measures is based on one or both of the following: the expected improvement in the operation of the power network during the at least one future event when the resilience measures are implemented; or the ease with which the resilience measures are implemented.

[0511] Item 6C: The method as described in any one of Items 1C to 5C, wherein the plurality of resilience measures include load reduction.

[0512] Item 7C: The method as described in Item 6C, wherein the asset data includes critical information indicating the criticality of one or more loads of the power network.

[0513] Item 8C: The method of Item 6C further includes using the at least one hardware processor to perform the following operations: determining to implement the load reduction; and controlling the power network to reduce the power supplied to at least one load of the power network during the at least one future event.

[0514] Project 9C: The method of any one of Projects 1C to 8C, wherein the probabilistic optimization model models the electrical islanding within the power network, wherein the solution of the probabilistic optimization model includes one or more electrical islands within the power network, and wherein the plurality of resilience measures include preventative electrical islanding.

[0515] Project 10C: The method as described in Project 9C, wherein the solution of the probabilistic optimization model includes a microgrid configuration comprising multiple microgrids, each microgrid having at least one grid-type distributed energy resource, and wherein the method further comprises using the at least one hardware processor to perform the following operations: determining to implement the preventive electrical islanding partitioning; and controlling one or more switches in the power network to split the power network into multiple microgrids.

[0516] Project 11C: The method of any one of Projects 1C to 10C, wherein the probabilistic optimization model models the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model includes scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures includes scheduling the one or more energy resources.

[0517] Item 12C: The method of any one of Items 1C to 11C, wherein the asset data includes one or more parameters of each of one or more of the plurality of power transmission assets and indicates the connection between the plurality of power transmission assets.

[0518] Item 13C: The method of any one of items 1C to 12C, wherein the forecast data includes forecasts of load on the power network during the at least one future event.

[0519] Item 14C: The method of any one of items 1C to 13C, wherein the input data includes multiple failure scenarios of the plurality of power transmission assets during the at least one future event.

[0520] Project 15C: The method as described in Project 14C, wherein the asset data includes the failure probabilities of the plurality of power transmission assets, and wherein the method further includes generating the plurality of failure scenarios based on the failure probabilities using the at least one hardware processor.

[0521] Item 16C: The method of any one of Items 1C to 15C, wherein the input data comprises multiple failure probability distributions of the plurality of power transmission assets.

[0522] Item 17C: The method of any one of items 1C to 16C, wherein the at least one future event includes a weather event, and wherein the forecast data includes a weather forecast for a certain period of time for the at least one future event.

[0523] Item 18C: The method of any one of items 1C to 17C, wherein the power network includes a distribution network.

[0524] Project 1D: A method comprising using at least one hardware processor to: acquire asset data associated with a plurality of power transmission assets of a power network; acquire forecast data associated with at least one future event; generate input data based on the asset data and the forecast data; and input the input data into a probabilistic optimization model prior to the at least one future event, the probabilistic optimization model optimizing at least one parameter of the operation of the power network for the at least one future event; wherein the probabilistic optimization model determines the switching state of each of a plurality of switches in the power network, at least by optimizing an objective function to maximize the total load served in the power network during the at least one future event, so as to enable the power network to... One or more microgrids are formed, wherein the objective function associates each of a plurality of power lines in the power network with a risk factor representing the failure probability of that power line, such that power flow on power lines associated with lower risk factors takes precedence over power flow on power lines associated with higher risk factors, and is subject to one or more islanding constraints; for each of a plurality of resilience measures, based on the solution of the probabilistic optimization model, a measure of the effectiveness of the resilience measure against the operation of the power network for the at least one future event is determined; and the measure of the effectiveness of the plurality of resilience measures is output to the network controller of the power network; wherein the plurality of resilience measures includes reconfiguring the power network according to a determined switching state.

[0525] Item 2D: The method of Item 1D further includes using the at least one hardware processor to perform the following operations: determining to implement the determined switch state; and controlling the plurality of switches to match the determined switch state such that the plurality of switches have the determined switch state during the at least one future event.

[0526] Project 3D: A method for improving the resilience of a power network comprising multiple nodes prior to an event, the method comprising, prior to the event: determining the switching state of each of a plurality of switches in the power network to form one or more microgrids in the power network by optimizing a first objective function to maximize the total load served in the power network during the event, wherein the first objective function associates each of a plurality of power lines in the power network with a risk factor representing the criticality and failure probability of that power line, such that power flow on power lines associated with lower risk factors takes precedence over power flow on power lines associated with higher risk factors, and is subject to one or more islanding constraints; and reconfiguring the power network according to the determined switching state such that the power network will have the determined switching state during the event.

[0527] Project 4D: The method as described in Project 3D, wherein optimizing the first objective function includes maximizing the first objective function, and wherein the first objective function includes:

[0528] in, It is a collection of phases. p It is a phase within the set of phases. T It refers to the time period of the event. t It is the index of the time interval within the stated time period. N These are the multiple nodes. i It is the index of the node within the plurality of nodes. Represents the product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node γ It is a scalar factor. ij It is the first i The node is connected to the first j Index of power lines for each node. E It is a collection of power lines. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij The active power flow on the power lines, and It is in the t During the time interval, the first ij Reactive power flow on a power line.

[0529] Project 5D: The method of any one of Projects 1D to 4D, wherein the one or more islanding constraints ensure that each of the plurality of nodes is assigned to exactly one of the one or more microgrids.

[0530] Project 6D: The method of any one of Projects 1D to 5D, wherein the one or more islanding constraints ensure that exactly one of the plurality of nodes representing a grid-type distributed energy resource is assigned to each of the one or more microgrids.

[0531] Project 7D: The method of any one of Projects 1D to 6D, wherein the one or more islanding constraints ensure that each of the one or more microgrids includes at least two nodes.

[0532] Project 8D: The method of any one of Projects 1D to 7D, wherein the one or more islanding constraints ensure that each of the plurality of power lines is assigned to one of the one or more microgrids or a power grid including a substation based on the assignment of at least one node among the plurality of nodes connected to the power line.

[0533] Project 9D: The method as described in any one of Projects 1D to 8D, wherein the one or more island partitioning constraints include: , for ,

[0534] in, K It is the set of nodes representing grid-type distributed energy resources among the plurality of nodes. k yes K Intranode index, N These are the multiple nodes. i It is the node index within the plurality of nodes, and It means the first i Is the node assigned to the node by the first...? k A binary variable of a microgrid formed by individual nodes.

[0535] Project 10D: The method as described in any of the preceding claims, wherein the one or more island partitioning constraints include:

[0536] in, K It is the set of nodes representing grid-type distributed energy resources among the plurality of nodes. k yes K Intranode index, In the scene s A collection of power lines that have not experienced any faults. i It is the node index within the plurality of nodes. S It is a collection of power lines, each having one of the aforementioned multiple switches. j It is the node index within the plurality of nodes. ij The first of the multiple power lines is i The node is connected to the first j An index of a power line for a node. It means that the first ij Whether the power line is assigned to the first k A binary variable in a microgrid formed by individual nodes. It means the first i Is the node assigned to the node by the first...? k A binary variable in a microgrid formed by nodes, and It means the first ij A binary variable representing the switching state on a power line.

[0537] Project 11D: The method as described in any of the preceding claims further comprises: prior to determining the switching state: classifying each of the plurality of nodes as critical or non-critical, so as to divide the plurality of nodes into critical nodes and non-critical nodes; and reducing the number of the plurality of nodes in the power network by recursively aggregating at least one parameter of a non-critical node with at least one parameter of at least one critical node, and removing the non-critical nodes until only critical nodes remain in the plurality of nodes.

[0538] Item 12D: The method as described in Item 11D, wherein the aggregation is performed at each of the plurality of nodes for each phase.

[0539] Project 13D: The method as descri...

Claims

1. A method comprising using at least one hardware processor to perform the following operations: Acquire asset data associated with multiple power transmission assets of the power network; Obtain predictive data associated with at least one future event; Input data is generated based on the asset data and the prediction data; as well as Prior to the at least one future event, the input data is fed into a probabilistic optimization model, which optimizes at least one parameter of the operation of the power network in response to the at least one future event. For each of the plurality of resilience measures, based on the solution of the probabilistic optimization model, a measure of the effectiveness of the resilience measure against the operation of the power network in response to the at least one future event is determined; The effectiveness measures of the multiple resilience measures are output to the network controller of the power network; as well as One of the resilience measures shall be implemented according to the effectiveness measure of the resilience measure.

2. The method according to claim 1, further comprising: Before outputting the effectiveness measure, the plurality of resilience measures are ranked according to the corresponding effectiveness measure, and One of the multiple resilience measures will be implemented based on the ranking.

3. The method according to any one of the preceding claims, wherein, The effectiveness of each of the plurality of resilience measures is measured based on one or both of the following: The anticipated improvement in the operation of the power network during the at least one future event, with the implementation of the aforementioned resilience measures, and / or The ease with which the aforementioned flexible measures can be implemented.

4. The method according to any one of the preceding claims, wherein, The aforementioned multiple resilience measures include one or more of the following: a) Control the power network to reduce the power supplied to at least one load of the power network during the at least one future event; b) Control the power network to reconfigure the power network to an optimized network topology such that the power network has the optimized network topology during the at least one future event; c) Control the power network to reconfigure it into an optimized network topology to maximize the total load served by the power network during the at least one future event; as well as d) Control one or more switches in the power network to split the power network into multiple microgrids.

5. The method according to claim 4, wherein, In a), the asset data includes critical information indicating the criticality of one or more loads of the power network, and wherein the objective function weights the one or more loads according to the criticality.

6. The method according to claim 5, wherein, In a), the probabilistic optimization model optimizes the objective function for calculating the expected load supply.

7. The method according to any one of claims 4 to 6, wherein, In a), the probabilistic optimization model models the topology of the power network, wherein the solution of the probabilistic optimization model includes an optimized network topology, and wherein the plurality of resilient measures include reconfiguring the power network to the optimized network topology.

8. The method according to any one of claims 4 to 7, wherein, In a), the probabilistic optimization model models the electrical islanding within the power network, wherein the solution of the probabilistic optimization model includes one or more electrical islands within the power network, and wherein the plurality of resilient measures includes preventative electrical islanding. And preferably The solution of the probabilistic optimization model includes a microgrid configuration, wherein the microgrid configuration includes multiple microgrids, each microgrid having at least one grid-type distributed energy resource (830), and wherein the method further includes: Determine the implementation of the aforementioned preventative electrical islanding; and Control one or more switches in the power network to split the power network into multiple microgrids.

9. The method according to any one of claims 4 to 8, wherein, In a), the probabilistic optimization model models the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model includes scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures include scheduling the one or more energy resources. And preferably The one or more energy resources include at least one mobile energy resource.

10. The method according to any one of claims 4 to 9, wherein, The asset data includes one or more parameters for each of one or more of the plurality of power transmission assets, and indicates the connections between the plurality of power transmission assets.

11. The method according to any one of claims 4 to 10, wherein, The input data includes multiple failure probability distributions of the multiple power transmission assets; and / or The at least one future event includes a weather event, and the forecast data (630) includes a weather forecast for a certain period of time for the at least one future event.

12. The method according to any one of claims 5 to 11, wherein, The power network includes the distribution network.

13. The method according to claim 4 or 5, wherein, In b), the probabilistic optimization model models the topology of the power network, wherein the solution of the probabilistic optimization model includes the optimized network topology.

14. The method according to claim 4 or 13, wherein, In b), the asset data includes critical information indicating the criticality of one or more loads of the power network.

15. The method according to claim 4 or any one of 13 to 14, wherein, The probabilistic optimization model models the electrical islanding within the power network, wherein the solution of the probabilistic optimization model includes one or more electrical islands within the power network, and wherein the plurality of resilient measures includes preventative electrical islanding.

16. The method according to claim 4 or any one of 13 to 15, wherein, The solution of the probabilistic optimization model includes a microgrid configuration, wherein the microgrid configuration includes multiple microgrids, each microgrid having at least one grid-type distributed energy resource, and wherein the method further includes: Determine the implementation of the aforementioned preventative electrical islanding; and Control one or more switches in the power network to split the power network into multiple microgrids.

17. The method according to claim 4 or any one of 13 to 16, wherein, The probabilistic optimization model models the scheduling of energy resources within the power network, wherein the solution of the probabilistic optimization model includes the scheduling of each of one or more energy resources within the power network, and wherein the plurality of resilient measures include scheduling the one or more energy resources.

18. The method according to claim 4 or any one of 13 to 17, wherein, The asset data includes one or more parameters for each of one or more of the plurality of power transmission assets, and indicates the connections between the plurality of power transmission assets.

19. The method according to claim 4, wherein, In c): The probabilistic optimization model determines the optimized network topology of the power network to be used during the at least one future event by optimizing the objective function to maximize the total load served by the power network during the at least one future event. and The objective function associates each of the plurality of nodes in the power network with a critical factor representing the relative criticality of the load at that node, associates each of the plurality of power lines in the power network with a risk factor representing the failure probability of that power line, includes a term representing voltage deviation at the plurality of nodes, and is subject to one or more constraints.

20. The method according to claim 4 or claim 19, wherein, In c), controlling the power network includes controlling one or more switches in the power network.

21. The method according to claim 19 or 20, wherein, Optimizing the objective function includes maximizing the objective function, wherein the objective function includes: in, t It is a time period T Index of time intervals within, N These are the multiple nodes. i It is the index of the node within the plurality of nodes. It is the first i Key factors for load at each node This represents the dot product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node and It is a scalar factor. ij It is the connection of the first i The node and the first j Index of power lines for each node. E It is a collection of power lines that have not experienced any faults. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij Active power flow on a power line It is in the t During the time interval, the first ij Reactive power flow on the power lines It is the set of nodes representing flexible asset connection points among the plurality of nodes, and It is in the t During the time interval, the first i The absolute value of the voltage at each node.

22. The method according to any one of claims 19 to 21, wherein: The objective function further includes a term representing the generation of one or more distributed energy resources in the power network, and Optimizing the objective function includes maximizing the objective function, wherein the objective function includes: in, t It is a time period T Index of time intervals within, N These are the multiple nodes. i It is the index of the node within the plurality of nodes. It is the first i Key factors for load at each node This represents the dot product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node , and It is a scalar factor. ij It is the connection of the first i The node and the first j Index of power lines for each node. E It is a collection of power lines that have not experienced any faults. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij Active power flow on a power line It is in the t During the time interval, the first ij Reactive power flow on the power lines It is the set of nodes representing flexible asset connection points among the plurality of nodes. It is in the t During the time interval, the first i The absolute value of the voltage at each node. It is the set of nodes representing photovoltaic power sources among the plurality of nodes, and It is in the t During the time interval, the first i The active power output of the photovoltaic power source at each node.

23. The method according to any one of claims 19 to 22, wherein: The one or more constraints include at least one deployment constraint for each mobile distributed energy resource to be deployed at a flexible asset connection point in the power network during the event, wherein the at least one deployment constraint ensures that: Each mobile distributed energy resource can only be deployed at the node representing the flexible asset connection point among the multiple nodes, if deployed. At most one mobile distributed energy resource can be deployed at each node representing a flexible asset connection point; and Each mobile distributed energy resource can only be deployed at a single node, if deployed.

24. The method according to any one of claims 19 to 23, wherein: in, It is a collection of mobile generators to be deployed in the power grid during the event. d It is the index of the mobile generator within the set of mobile generators. It is a collection of mobile energy storage systems to be deployed in the power grid during the event. m It is the index of the mobile energy storage system within the set of mobile energy storage systems. It is the set of nodes representing flexible asset connection points among the plurality of nodes. i It is the set of nodes Index of the node within, It means the first d Was the mobile generator deployed at the [number]th [location]? i A binary variable at each node, and It means the first m Whether the mobile energy storage system was deployed in the [number]th [location] i Binary variables at each node.

25. The method according to any one of claims 19 to 24, wherein: The one or more constraints include at least one virtual load constraint for each of the plurality of nodes representing distributed energy resources, wherein the at least one virtual load constraint requires that the virtual load at each of the plurality of nodes representing distributed energy resources be powered by a virtual power supply from the node representing a substation among the plurality of nodes.

26. The method of claim 25, wherein: The at least one virtual load constraint includes: in, E It is a collection of power lines that have not experienced any faults. i It is the index of the node within the plurality of nodes. ji It is the first j The node is connected to the first i Index of power lines for each node. ij It is the first i The node is connected to the first j Index of power lines for each node. From the first j The node to the first i Virtual power flow of each node From the first i The node to the first j Virtual power flow of each node It is the first i Virtual load at each node It is a collection of mobile generators to be deployed in the power grid during the event. d It is the index of the mobile generator within the set of mobile generators. It is a collection of mobile energy storage systems to be deployed in the power grid during the event. m It is the index of the mobile energy storage system within the set of mobile energy storage systems. It means the first d Was the mobile generator deployed at the [number]th [location]? i Binary variables at each node It means the first m Whether the mobile energy storage system was deployed in the [number]th [location] i Binary variables at each node N These are the multiple nodes. It is the set of nodes representing distributed energy resources among the plurality of nodes. It is the set of nodes representing flexible asset connection points among the plurality of nodes, and It is the set of nodes representing the substation among the multiple nodes.

27. The method according to any one of claims 25 to 26, wherein: The at least one virtual load constraint further includes: in, M It is the total number of energy storage systems. D It is the total amount of non-renewable energy, and P It represents the total amount of renewable energy.

28. The method according to claim 4 or claims 19 to 27, wherein, In c): The network topology includes the state of each of the multiple switches in the power network, and preferably... Reconfiguring the power network includes controlling the plurality of switches to match the state in the network topology.

29. The method according to claim 4 or claims 19 to 28, wherein, In c): The network topology includes the deployment of each of one or more mobile distributed energy resources, and / or The network topology includes power dispatching for each of one or more distributed energy resources represented in the network topology, and preferably... The one or more distributed energy resources mentioned herein are multiple distributed energy resources including one or more fixed distributed energy resources and one or more mobile distributed energy resources.

30. The method according to claim 4, wherein, In d): The probabilistic optimization model determines the switching state of each of a plurality of switches in the power network by optimizing an objective function to maximize the total load served in the power network during the at least one future event, so as to form one or more microgrids in the power network. The objective function associates each of the multiple power lines in the power network with a risk factor representing the failure probability of that power line, such that power flow on power lines associated with lower risk factors takes precedence over power flow on power lines associated with higher risk factors, and is subject to one or more islanding constraints.

31. The method according to claim 30, wherein, In d): Optimizing the first objective function includes maximizing the first objective function, wherein the first objective function includes: Where Φ is the set of phases, p It is a phase within the set of said phases. T It refers to the time period of the event. t It is the index of the time interval within the stated time period. N These are the multiple nodes. i It is the index of the node within the plurality of nodes. Represents the product of two vectors. Represents the element-wise absolute value of a vector. Indicates the first t During the time interval, the first i Active power supply and demand at each node Indicates the first t During the time interval, the first i The reactive power supply demand at each node γ It is a scalar factor. ij It is the first i The node is connected to the first j Index of power lines for each node. E It is a collection of power lines. Is with the first ij Risk factors associated with each power line It is in the t During the time interval, the first ij The active power flow on the power lines, and It is in the t During the time interval, the first ij Reactive power flow on a power line.

32. The method according to any one of claims 30 to 31, wherein: The one or more islanding constraints ensure that each of the plurality of nodes is assigned to exactly one of the one or more microgrids.

33. The method according to any one of claims 30 to 32, wherein: The one or more islanding constraints ensure that exactly one node representing a grid-type distributed energy resource is assigned to each of the one or more microgrids.

34. The method according to any one of claims 30 to 33, wherein: The one or more islanding constraints ensure that each of the one or more microgrids includes at least two nodes.

35. The method according to any one of claims 30 to 34, wherein: The one or more islanding constraints ensure that each of the multiple power lines is assigned to one of the one or more microgrids or a power grid including substations based on the assignment of at least one node among the multiple nodes connected to the power line.

36. The method according to any one of claims 30 to 35, wherein: The one or more island partitioning constraints include: ， for , in, K It is the set of nodes representing grid-type distributed energy resources among the plurality of nodes. k yes K Intranode index, N These are the multiple nodes. i It is the node index within the plurality of nodes, and It means the first i Is the node assigned to the node by the first...? k A binary variable of a microgrid formed by individual nodes.

37. The method according to any one of claims 30 to 36, wherein: The one or more island partitioning constraints include: in, K It is the set of nodes representing grid-type distributed energy resources among the plurality of nodes. k yes K Intranode index, In the scene s A collection of power lines that have not experienced any faults. i It is the node index within the plurality of nodes. S It is a collection of power lines, each having one of the aforementioned multiple switches. j It is the node index within the plurality of nodes. ij The first of the multiple power lines is i The node is connected to the first j An index of a power line for a node. It means that the first ij Whether the power line is assigned to the first k A binary variable in a microgrid formed by individual nodes. It means the first i Is the node assigned to the node by the first...? k A binary variable in a microgrid formed by nodes, and It means the first ij A binary variable representing the switching state on a power line.

38. The method according to any one of claims 30 to 37, further comprising, before determining the switching state: Each of the plurality of nodes is classified as critical or non-critical, thereby dividing the plurality of nodes into critical nodes and non-critical nodes; and The number of nodes in the power network is reduced by recursively aggregating at least one parameter of a non-critical node with at least one parameter of a critical node and removing the non-critical node until only the critical node remains among the nodes.

39. The method according to claim 38, wherein, The aggregation is performed at each of the plurality of nodes for each phase.

40. The method according to claim 38 or claim 39, wherein, The at least one parameter includes load.

41. The method according to any one of claims 38 to 40, wherein, The aggregation includes: When the non-critical node is not between two critical nodes, the entire value of at least one parameter of the non-critical node is aggregated with the value of at least one parameter of the nearest critical node, and the non-critical node and one of the multiple power lines between the non-critical node and the nearest critical node are removed; and When the non-critical node is between two critical nodes, a portion of the value of at least one parameter of the non-critical node is aggregated with the value of at least one parameter of each of the two critical nodes, and the non-critical node is removed, each of the multiple power lines between the non-critical node and the two critical nodes is removed, and a new aggregated power line is added between the two critical nodes.

42. The method according to any one of claims 38 to 41, further comprising storing a mapping of each removed non-critical node to a critical node aggregated with the non-critical node, and a mapping of each removed power line among the plurality of power lines to any power line aggregated with the removed power line.

43. The method according to any one of claims 30 to 42, further comprising, after determining the switching state, planning the scheduling of the one or more microgrids for each of the one or more microgrids in the following manner: In the first phase, for each of a plurality of time intervals within the time period of the event, a second objective function is optimized based on a plurality of scenarios and the probability of each of the plurality of scenarios to maximize the total load served by the power network during the time period, thereby allocating the generation resources in the microgrid to the time interval, wherein, The second objective function associates each of the multiple power lines with a risk factor representing the failure probability of that power line; as well as In the second phase, for each of the multiple time segments within each of the multiple time intervals, generation resources are allocated to the time segment by optimizing a third objective function to maximize the total load served by the power network during the time interval, wherein the second objective function is deterministic and associates each of the multiple power lines with a risk factor representing the failure probability of that power line.

44. The method of claim 43, further comprising: In the second phase, for each of the multiple time segments within each of the multiple time intervals, a set of loads to be supplied with electricity during the time segment is selected, wherein the third objective function is constrained by requiring each load in the selected set of loads to be supplied with a predefined minimum service duration.

45. The method according to claim 43 or 44, further comprising: For each of the one or more microgrids, during each of the plurality of time segments, power generation in the microgrid is scheduled based on the power generation resources allocated for that time segment.

46. ​​The method according to claim 4 or any one of 30 to 45, wherein, Reconfiguring the power network includes controlling the plurality of switches to match the determined switch states.

47. The method according to any one of claims 1 to 46, wherein, The event in question is a weather event.

48. The method according to any one of claims 1 to 47, wherein, The forecast data includes forecasts of the load on the power network during the at least one future event.

49. The method according to any one of claims 1 to 48, wherein, The input data includes multiple failure scenarios of the plurality of power transmission assets during the at least one future event.

50. The method according to any one of claims 1 to 49, wherein, The asset data includes the failure probabilities of the plurality of power transmission assets, and the method further includes generating the plurality of failure scenarios based on the failure probabilities.

51. The method according to any one of claims 1 to 50, wherein, The input data includes multiple failure probability distributions of the multiple power transmission assets, and / or Wherein, the at least one future event includes a weather event, and wherein the prediction data includes a weather forecast for a certain period of time for the at least one future event, and / or The power network includes a distribution network.

52. An apparatus comprising at least one processor configured to perform the method according to any one of claims 1 to 51.

53. A computer program product comprising instructions that, when executed by a means comprising at least one processor, cause the processor to perform the method according to any one of claims 1 to 51.

54. A non-transitory computer-readable storage medium comprising instructions that, when executed by a means comprising at least one processor, cause the processor to perform the method according to any one of claims 1 to 51.

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