System and method for blackout rotation enabled control of power distribution system

Abstract

To provide a control system which controls fair blackout rotations that are optimized considering key factors associated with power distribution in a power distribution system.SOLUTION: A power distribution system collects a graph-based representation of the power distribution system as a radial tree of nodes connected by edges. Each node represents a section of the power distribution system isolated by switches and each edge represents a switch that connects a section represented by the node with a neighboring section represented by the neighboring node. Each node has a property of power demand of a corresponding section, which is governed by a difference between demanded and available energy for the section, and each edge has a property constraining throughput of energy through the switch in a direction of a power flow. A control system solves an optimization problem to determine the states of the edges and controls the switches based on the optimized states of the corresponding edges.SELECTED DRAWING: Figure 1A

Description

[Technical field]

[0001] The present disclosure relates generally to power systems, and more specifically to outage rotation control in electrical distribution systems. [Background technology]

[0002] Outage rotation or rolling blackouts are an almost unavoidable measure that distribution utilities must resort to to ensure optimal demand response. Their causes are generally due to insufficient generation capacity or insufficient transmission infrastructure to distribute electricity to areas where it is needed. Outage rotation is also used as a response strategy to address power generation capacity reductions that exceed the reserve capacity of power plants that are unexpectedly offline, such as in the case of extreme weather events, natural disasters, and other cases. Fair outage rotation is a goal that all distribution and generation utilities strive to achieve. Outage rotation schemes are usually constructed by using heuristic rule-based techniques. However, such techniques may not work well when outage scenarios are complex and require longer time horizons and larger geographic area coordination. Also, distribution systems usually do not have sufficient flexibility and resilience to facilitate effective load shedding, source rerouting, and local resource backup. As a result, fair rolling blackouts may be nearly impossible. For example, most consumers within the affected service area may experience blackouts. In contrast, some key consumers may experience multiple outages while others may not experience any outages at all, depending on where they are located.

[0003] A conventional power system has a structure that combines a central generating station, a transmission system, and a distribution and utilization system. Such a system performs outage rotation according to a rule-based approach that can be prescribed based on historical consumption and outage data, some predefined priorities of geographical areas, and similar static data. Any optimization technique that can be applied to such a system is constrained by the dimensionality of the power system structure. Thus, many optimization techniques that can provide a higher degree of flexibility in terms of fairness of outage rotation may not be feasible due to such fixed dimensionality.

[0004] Therefore, there is a need for flexible methods and techniques for achieving fair outage rotation that are optimized by considering important factors related to electricity distribution. There is also a need for more advanced tools for achieving fair outage rotation and more cost-effective means for enabling fairer outage rotation. Summary of the Invention

[0005] With the increasing frequency, intensity, and duration of natural disasters and power outages, disaster-induced power generation shortages and network failures are inevitable. Therefore, power outage rotation is a necessary measure to help customers share the burden of the disaster impacts and the responsibility of maintaining the stability of the system.

[0006] It is an object of some embodiments to provide a system and method for controlling a power distribution system. Additionally or alternatively, it is an object of some embodiments to provide a control method suitable for controlling outage rotation in the operation of a power distribution system. Additionally or alternatively, it is an object of some embodiments to disclose a method for fair outage rotation in a power distribution system under extreme operating events. Additionally or alternatively, it is an object of some embodiments to provide a method for fair outage rotation suitable for large-scale power distribution systems that suffer from the curse of dimensionality in optimization problems.

[0007] Planned or rotating outages are systematic, temporary outages that help balance the supply and demand of electricity in a power system. Typically, power system operators call for planned outages and implement temporary outages one area at a time, limiting the duration of outages in each area. In these situations, outage rotations are based on accepted rules for a particular distribution system. However, rule-based outage rotations are often not optimal for a particular type of outage or for a particular consumer of the distribution system.

[0008] Therefore, it is an objective of some embodiments to provide a method for controlling a power distribution system suitable for optimizing the outage rotation principle. In other words, it is an objective of some embodiments to replace rule-based outage rotation with optimization-based outage rotation. However, optimization-based techniques require power flow analysis of large-scale power distribution systems and suffer from the curse of dimensionality problem. Therefore, it is not surprising that optimization-based techniques have not been adopted to control outage rotation in power distribution system operations.

[0009] To address this issue, some embodiments replace the structural model of the power distribution system with a meta-structure of different dimensionality and replace the power flow model with a model that balances the internal powers of the meta-structure to optimize the power flow analysis in the system. The purpose of such a replacement is to provide a new optimization space suitable for power flow analysis, which allows to reduce the computational burden and reduce the possibility of the curse of dimensionality in optimization problems in controlling the power distribution system.

[0010] That is, to avoid direct modeling of large-scale power flows for system optimization, which causes the curse of dimensionality problem, some embodiments simplify the distribution system into a connected network by first dividing the distribution system into a set of feeder sections separated by switchable devices that are normally open or normally closed, and then modeling the feeder sections as its nodes and the switches as links. The power flow model of the system is replaced by an internal power balance model that balances the local generation and load of each section when isolated, and an external power balance model that regulates the power exchange with adjacent sections through the switches when energized. Using small-scale power flow calculations, it can be confirmed whether there is a power flow violation in any feeder section. If a violation is found, the violation can be eliminated by adjusting / reducing the switch power flow limit according to the sensitivity of the violation to power injection at the switch. The energization status of each feeder section can be determined by the state of the switches present on the path between the section and the available substations / feeders. In some implementations, the energy lost due to isolation of a section is determined based on local renewable generation, storage dispatch, and load demand.

[0011] As such, some embodiments use a graph-based representation of the structure of the power distribution system. Each node of the graph is a section of the power system, e.g., a feeder section, separated from other sections of the power system by a switch. The switches may be of different types, such as normally closed or normally open switches. Some example embodiments model the switch with a binary variable representing its open / closed status and a set of continuous variables representing the amount of current / power flowing through the switch. The variables may be subject to a set of thresholds for the maximum current / power allowed to flow through the switch. In some example embodiments, the thresholds may be configurable to represent operational requirements, such as maximum power, imposed by a demand response program.

[0012] When all the switches associated with a section are in the open position, the section is isolated from the rest of the power system. Therefore, the power demand can be estimated for the entire section, instead of for each individual load in the section. In other words, the section can be treated as a load with an energy demand that is the difference between the power generation that the generators in the section are estimated to produce and the energy consumption that the loads in the section are estimated to consume. This nodal representation allows for a reduction in the dimension of the optimization problem.

[0013] Switches connect the power flow between each feeder section and other sections of the distribution system. Thus, switches are represented as edges connecting nodes of a graph-based representation. A characteristic of a node is its power demand (fixed or time-varying), while a characteristic of an edge is the potential throughput of delivering power through the switch. In some example embodiments, the graph is a radial tree starting from a root node representing a source feeding the distribution system, such as a mains grid. Thus, the throughput of a switch connecting a node to its children is the minimum of the throughput of the switch defined by its type (open or closed) and the throughput of the edge leading to the node, which defines the maximum flow of energy the switch can receive. In particular, edges are directional, and a pair of nodes can be connected by an edge in one or both directions with different throughputs.

[0014] Consider this graph-based representation and note that the state of the entire distribution system can be represented as a function of the states of the switches that pass or block the flow of energy. Thus, the effects of the internal complexities of different elements of the distribution system, such as the individual demands of different loads, power storage, generation, types, and costs of production of electricity, can be reduced (or aggregated) or simply ignored by optimization.

[0015] In addition, this graph-based representation is advantageous for power generation shortages caused by disasters, which may be reflected in the properties of the nodes and edges. The graph is a radial tree that spreads outward, i.e., radiates, from the root node, so that each node is connected to the root node through one or more radial paths. When at least one edge on a path leading to a node is deleted or opened, this entire path is blocked. The deletion of edges may be intentional or unintentional, i.e., controlled or uncontrolled. For example, unintentional deletion may occur due to adversarial events such as natural disasters and / or unexpected events. Intentional deletion may occur due to optimization of power distribution in case of energy shortages. This intentional deletion may be achieved by opening a switch.

[0016] Thus, the configuration of the radial tree can be changed in case of natural disasters and / or unexpected events. However, if there is an edge on this tree, it is considered that the edge can pass energy, taking into account its throughput, which can be changed by natural events and / or as a result of optimization. Whether a switch should pass energy or not depends on the state of the switch and the corresponding state of the edge.

[0017] As an example, the constraints imposed by the graph-based representation include one or a combination of the following: the possibility of power exchange between nodes, the direction of power flow between nodes, the throughput, i.e., the maximum value of power flow between nodes, constraints on the power balance between the power flowing into each non-isolated node and the power flowing out of each non-isolated node, the dependency of the power flow between nodes on the power exchanges between other nodes, and radial constraints on the radial paths formed by the edges. However, in some implementations, the constraints may not depend on the type of switch, e.g., the characteristics of the edges may not specify the type of the corresponding switch. Such an approach simplifies the optimization problem, thereby reducing the computational load and complexity, which leads to faster control operations.

[0018] Therefore, the graph-based representation of the power distribution system according to some embodiments allows for the formulation of optimization problems using the principle of optimizing a cost function of node characteristics such as power demand, power shortage amount, power shortage duration, power shortage frequency, etc., as a function of edge states, considering a radial tree of graphs that specifies node and edge relationships and characteristics as constraints. In particular, the graph-based representation of the grid meta-structure is distinguishable and enables various optimization techniques.

[0019] To allow for fair outage rotation while considering various interests, some embodiments balance one or a combination of objectives by modeling outage rotation as a multi-objective optimization problem, including minimizing lost energy and minimizing switch operations, which represent the needs of the power system, minimizing section outage duration and minimizing section outage frequency, which represent customer demands, minimizing the difference in outage frequency between feeder sections, and minimizing the difference in outage frequency between feeder sections to achieve the goal of fair outage rotation.

[0020] Some embodiments are based on the understanding that a graph-based representation of a power distribution system can take into account the details of the impact of an adversarial event on the distribution. For example, an adversarial event may trip a switch, an edge in the graph-based representation corresponding to a link may be removed, and / or the definition of a node may be changed. For example, an adversarial event may reduce the available power from the main grid, and the amount of power distributed may be reduced accordingly. For example, storage or generation in a feeder section may be reduced, and the characteristics of the node reflecting the power demand are changed accordingly.

[0021] Some example embodiments utilize a cost function of node characteristics with multiple objectives. For example, in some embodiments, the cost function has six different cost metrics that define the cost function to be optimized. Such multi-objective optimization provides greater fairness in outage rotation. The objectives include: (1) minimizing the total amount of lost energy, (2) minimizing the total number / frequency of switching operations, (3) minimizing the maximum outage duration, (4) minimizing the maximum outage frequency / number, (5) minimizing the maximum difference in outage duration between any two feeder sections, and (6) minimizing the maximum difference in outage frequency between two feeder sections.

[0022] However, solving such a multi-objective cost function can be time-consuming and extensive, thus posing computational challenges. To that end, some example embodiments convert the multi-objective optimization into a single-objective optimization by defining the singular objective as maximizing the sum of a first item, defined as the weighted sum of the sufficiencies for all the objectives, and a second item, defined as the minimum of the weighted sufficiencies among all the objectives. The multi-objective optimization is converted into a single-objective optimization by modeling the sufficiency of each objective using a nonlinear generalized rectified linear unit (ReLU) function and defining a so-called global sufficiency as its objective. The global sufficiency of the single-objective optimization is defined as the combination of the sum of the sufficiencies for each objective of the multi-objective optimization multiplied by its weighting factor and the minimum sufficiency among all objectives determined according to the division of the sufficiency for each objective by its weighting factor. Such a definition allows maximizing the global sufficiency of all stakeholders while maximally protecting the interests of the least sufficient.

[0023] Due to the nonlinear characteristics of the generalized ReLU function, the logical operations required by the section separation status judgment and storage contribution, and the multiplication operations between binary and continuous variables, the above formulated problem is a nonlinear optimization problem that may be difficult to solve, and the consistency of the solution may not be guaranteed. Therefore, some embodiments use a directed feasible region approach to convert each nonlinear item as an optimization problem, search for a solution within a feasible region bounded by a linear equation, and direct the search for the solution using a linear objective function. The generated optimization is then embedded in an optimization model for blackout rotation that replaces the original nonlinear item. By doing so, the nonlinear optimization is converted into a mixed integer linear optimization problem, which reduces the computational complexity and the possibility of divergence.

[0024] Some example embodiments are also based on the recognition that different approaches can be used to solve optimization problems associated with power distribution. Example solutions include nonlinear optimization problems using mixed binary and continuous variables and logical operations, mixed-integer linear programming problems (MILPs), and machine learning solutions using physics-informed neural networks (PINNs), which solve optimization problems by training neural networks to minimize loss functions, including cost functions.

[0025] Some example embodiments determine states of edges of the graph-based representation that govern the power flow of available energy that optimizes a cost function of the characteristics of the nodes to optimize planned outages by solving the optimization problem thus formulated, taking into account the graph-based representation as a constraint. The optimized states of the edges thus determined are translated into control commands for the states of one or more switches of the distribution system. The control commands are sent to the switches to cause a change in the power flow of available energy in the distribution system.

[0026] In some implementations, the control command is determined based on the state of the edge and the type of the switch represented by the edge. For example, the type includes normally open or normally closed. Thus, for example, if the switch is a normally open type, the current state of the switch is open, and it is determined that the optimized state of the switch is also open, no command is sent. A similar situation exists for a normally closed type switch. In other words, a command is sent only to change the state of the switch from the current state to the opposite state.

[0027] To achieve the above objects and advantages, some example embodiments provide a control system, method, and program for controlling power flow of available energy in a power distribution system.

[0028] For example, some example embodiments provide a control system for controlling power flow of available energy in a power distribution system. The control system includes one or more processors and a memory having instructions stored thereon, the processor executing the instructions to cause the control system to collect a graph-based representation of the power distribution system as a radial tree of a plurality of nodes connected by a plurality of edges. Each node of the plurality of nodes in the radial tree represents a section of the power distribution system, the section being isolated from other parts of the power distribution system by one or more switches when the one or more switches are in an open position. Furthermore, each node of the plurality of nodes has a characteristic of a power demand of the corresponding section that is governed by a difference between the energy available in the corresponding section and the energy required by a load of the corresponding section. Furthermore, for each node of the plurality of nodes, an edge of the plurality of edges connecting the corresponding node of the plurality of nodes to an adjacent node of the plurality of nodes represents a connecting switch connecting the corresponding section to an adjacent section represented by the adjacent node. Furthermore, an edge has a property that imposes a constraint on the throughput of energy through a connecting switch in the direction of power flow to be less than or equal to the throughput of the connecting switch, which is determined by the type of the connecting switch and the state of the parent edge connecting the corresponding node to a parent node of the plurality of nodes.

[0029] A state of each node of the plurality of nodes defines an amount of net power demanded by a corresponding section of the distribution system. Upon collecting the graph-based representation of the distribution system, the processor of the control system is configured to determine a state of each of a plurality of edges of the graph-based representation that governs the power flow of the available energy by solving an optimization problem to optimize a cost function of characteristics of the plurality of nodes to optimize the planned outages taking into account the graph-based representation of the distribution system as a constraint. The processor then translates the determined state of each edge of the plurality of edges into a control command for a state of at least some switches of the distribution system and submits the control command to at least some switches of the distribution system to cause a change in the power flow of the available energy.

[0030] Some example embodiments also provide a method for controlling power flow of available energy in a power distribution system. The method includes collecting a graph-based representation of the power distribution system as a radial tree of a plurality of nodes connected by a plurality of edges. Each node of the plurality of nodes in the radial tree represents a section of the power distribution system that is isolated from other parts of the power distribution system by one or more switches when the one or more switches are in an open position. Furthermore, each node of the plurality of nodes has a characteristic of a power demand of the corresponding section that is governed by a difference between the energy available in the corresponding section and the energy required by the loads of the corresponding section. Furthermore, for each node of the plurality of nodes, an edge of the plurality of edges connecting the corresponding node of the plurality of nodes to an adjacent node of the plurality of nodes represents a connecting switch that connects the corresponding section to an adjacent section represented by the adjacent node. Furthermore, the edge has a property that limits a throughput of energy through the connecting switch in a direction of power flow to be equal to or less than a throughput of the connecting switch that is determined by a type of the connecting switch and a state of a parent edge connecting the corresponding node to a parent node of the plurality of nodes.

[0031] The state of each node of the plurality of nodes defines an amount of net power demanded by a corresponding section of the distribution system. The method then determines a state of each of a plurality of edges of the graph-based representation that governs the power flow of the available energy that solves an optimization problem to optimize a cost function of the characteristics of the plurality of nodes to optimize the planned outages taking into account the graph-based representation of the distribution system as a constraint. The method further includes converting the determined state of each edge of the plurality of edges into a control command for a state of at least some switches of the distribution system, and submitting the control command to at least some switches of the distribution system to cause a change in the power flow of the available energy.

[0032] Additionally or alternatively, some embodiments consider the evolution of outages during a hostile weather event. In these embodiments, in addition to managing outage rotations based on a static time horizon, the outage rotations are also generated in a time-rotating manner that reviews and updates the disaster situation throughout the duration of the disaster. This allows the outage rotation to adapt to changing conditions and create a better rotation scheme to take existing conditions into account.

[0033] In this regard, some example embodiments also provide methods for optimizing resilience enhancements in power distribution systems to enable more equitable outage rotation in the event of future extreme weather events. In addition to the above six objectives for outage impact mitigation and fairness, some embodiments also include minimizing maximum connected net load and average N-1 contingency duration of a feeder section, maximizing tie pickup capacity to size feeder sections for more effective load shedding and restoration, maximizing storage stored energy for power shortage and blackout scenarios, and maximizing stored energy release during black start events to optimize storage energy storage and dispatch for optimal utilization of storage capacity.

[0034] Additionally or alternatively, the minimization of operational costs is utilized to determine the optimal system configuration and storage usage to minimize the total cost of substation power supply, renewable generation wear costs, switch operation costs, load shedding costs, and storage charge / discharge wear costs. Investment cost minimization is also included to represent the budget constraint.

[0035] For example, some embodiments are based on the recognition that adding switches to a power distribution system, according to some embodiments, changes the configuration of the graph-based representation of the power distribution system. In addition, adding redundant switches, i.e., switches that are not normally needed, can increase the flexibility of the graph and benefit the optimization of power flows. As such, some embodiments add redundant switches, normally closed and normally open, to the power distribution system to increase such flexibility. For example, in some implementations, the power distribution system includes a radial path, where at least two switches in a normally closed state reduce the potential outage scope and duration, and at least one switch in a normally open state allows rerouting to other sources.

[0036] The resilience enhancement model of some embodiments balances the different benefits of placing additional switches and storage in strategic locations in the distribution system or ratings that meet system operational requirements under various operating scenarios including normal operation, power shortages, network failures, and black starts. The enhanced distribution system provides more flexibility for the distribution system to achieve more equitable outage rotations for the customers it serves.

[0037] The presently disclosed embodiments are further described with reference to the following drawings, in which: The drawings illustrated are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. [Brief description of the drawings]

[0038] [Figure 1A] 1 is a block diagram illustrating a method for controlling outage rotation in an electrical distribution system according to some example embodiments. [Figure 1B] FIG. 1 is a schematic diagram illustrating components and steps for controlling outage rotation in an electrical distribution system under extreme weather events, according to some example embodiments. [Figure 1C] FIG. 1 is a block diagram illustrating an outage rotation control system for an electrical distribution system under extreme weather events according to some example embodiments. [Diagram 2] FIG. 1 is a schematic diagram illustrating a power distribution system with tie switches and sectioning switches and renewable distributed generators according to some example embodiments. [Figure 3A] FIG. 1 is a schematic diagram illustrating the division of an electrical distribution system into a set of feeder sections that can be used for feeder isolation and restoration control, according to some example embodiments. [Figure 3B] FIG. 1 is a schematic diagram of a graph-based representation of an electrical distribution system according to some embodiments. [Figure 3C] FIG. 1 is a schematic diagram of a graph-based representation of an electrical distribution system according to some embodiments. [Figure 3D] FIG. 1 is a schematic diagram of a graph-based representation of an electrical distribution system according to some embodiments. [Figure 3E] FIG. 1 is a block diagram of a method for controlling power flow of available energy in a power distribution system according to some embodiments. [Figure 4A] FIG. 2 is a schematic diagram illustrating a forward generalized ReLU function used to represent objective satisfaction, according to some example embodiments; [Figure 4B] FIG. 1 is a schematic diagram illustrating a negative generalized ReLU function used to represent objective satisfaction, according to some example embodiments; [Diagram 5] FIG. 1 is a schematic diagram illustrating a graphical representation of the McCormick relaxation for continuous variable multiplication, according to some example embodiments. [Figure 6]FIG. 1 is a schematic diagram illustrating a sample power distribution system modified from an IEEE 123 node feeder with candidate switches and storage, according to some example embodiments. [Figure 7] FIG. 7 is a schematic diagram illustrating split fixed and flexible boundary sections of the sample power distribution system of FIG. 6 in accordance with some example embodiments. [Figure 8A] FIG. 7 is a schematic diagram illustrating an hourly power generation profile for a solar power plant of the sample system of FIG. 2 or FIG. 6 in accordance with some example embodiments. [Figure 8B] FIG. 7 is a schematic diagram illustrating an hourly power generation profile for a wind farm of the sample system of FIG. 2 or FIG. 6 in accordance with some example embodiments. [Figure 9A] FIG. 7 is a schematic diagram illustrating a typical hourly load profile for the load of the sample system of FIG. 2 or FIG. 6, in accordance with some example embodiments. [Figure 9B] FIG. 7 is a schematic diagram illustrating an hourly electricity price profile charged to the load of the sample system of FIG. 2 or FIG. 6 in accordance with some example embodiments. [Figure 10] FIG. 7 is a schematic diagram illustrating a predicted maximum power generation of a substation of the sample system of FIG. 2 or FIG. 6 in accordance with some example embodiments. [Figure 11] FIG. 3 is a schematic diagram illustrating an outage rotation schedule determined by optimizing the total lost energy for each portion of the sample system of FIG. 2 in accordance with some example embodiments. [Figure 12] FIG. 3 is a schematic diagram illustrating an outage rotation schedule determined by optimizing multiple objectives for both the system and customers for each portion of the sample system of FIG. 2 in accordance with some example embodiments. [Figure 13] FIG. 7 is a schematic diagram illustrating a power outage rotation schedule for the sample system of FIG. 6 with resilience enhancements for switches and storage in accordance with some example embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0039] Detailed Description Overview The present disclosure relates generally to power systems, and more specifically to outage rotation control in electrical distribution systems.

[0040] The present disclosure is presented to control outage rotation of a power distribution system when a shortage of power from the main grid occurs. Various embodiments consider one scenario or a combination of two scenarios for outage rotation control. The first scenario is to determine a fair rotation scheme under a given system configuration. This scenario controls the power system during planned outages to achieve fairness to all users with a given placement of switches and storage in the power system. The second scenario is to enhance the power system to achieve a fairer outage rotation. The second scenario is to design a cost-effective scheme to place additional automatic switches and storage in the system to allow for a fair outage rotation.

[0041] "Outage" as used herein may mean any scenario in which power supply to a consumer area is cut off or falls below a threshold level. Some possible reasons behind an outage may include reduced power availability, increased load, sudden reduction in load on supply due to hostile events such as weather events, etc. Outage rotation is a control measure for altering power flow throughout the distribution system and therefore requires controlling one or more electricity producing and distribution infrastructures in the distribution system. From an operational perspective, outage rotation or rotating load shedding aims to optimize the load distribution on sources and transmission lines while ensuring optimal power demand fulfillment. Implementation of planned outages may include effective load separation, source rerouting, and provision for local resource backup.

[0042] In these regards, it is of utmost importance to realize an effective outage rotation strategy that is fit for purpose related to outage rotation. The technical significance associated with effective outage rotation schemes can be understood from the fact that these strategies help in effectively handling the available power when required, such as during load and production mismatch or extreme weather events. While during such hostile events, the interruption or reduction of power supply to one or more geographical areas may be required, at the same time, the generation of electricity will not be synchronously stopped or reduced. Therefore, these strategies also help in avoiding the breakdown of transmission equipment by effectively routing the energy from the production end to the consumption end during extreme events.

[0043] Towards these ends, some example embodiments provide a method for controlling outage rotation. FIG. 1A is a block diagram illustrating one such method for controlling outage rotation in an electrical distribution system, according to an embodiment of the present disclosure. In some example embodiments, the method may be initiated upon detection of a hostile event, such as an extreme weather-related event. Computer program instructions for method 100A may be stored in a memory and executed by a processing circuit upon detection of such a hostile event or alarm. Detection of the hostile event may indicate the initiation of an outage event occurring to the electrical distribution system.

[0044] Step 125 includes method 100A receiving, via a communication network, a forecasted evolution trajectory of the substation generation shortfall, a forecasted profile of the load demand, renewable generation, and current storage state, and a switch status for an outage event to occur, using interface 153. Interface 153 may receive the trajectory for the substation generation shortfall from one or more substations or distribution systems. Interface 153 may receive forecasted profiles of the load demand and renewable generation from one or more loads and renewable generators, current storage state from one or more battery energy storage systems, and switch status from one or more switch devices associated with the distribution system.

[0045] Step 130 includes the method 100 of dividing the distribution system into feeder sections according to switch locations using a hardware processor 155, and simplifying the system into a connected network by modeling the sections as nodes and the switches as links. To that end, a graph-based structure of the distribution system can be obtained, for example, from a database storage.

[0046] In step 132 of FIG. 1A, the hardware processor 155 can build an internal / external power balance model to relate section energization status and loading to switch status and storage charging / discharging.

[0047] Step 134 uses hardware processor 155 to formulate an optimization of switch operation schedules and storage operation schedules along a rolling scheduling horizon to mitigate the impact of power outages with fair power outage rotation.

[0048] Step 136 uses a hardware processor 155 to solve the nonlinear optimization model by a linear transformation using a directed feasible region.

[0049] 1A, the method 100 includes using a computing device 157 to transmit, via a communication network, commands for switching, discharging, or charging storage, scheduled at an optimal solution for each period within the rolling scheduling range. When step 140 is completed, control returns to step 125, and steps 125-140 are repeated for the next rolling range if any rolling ranges remain that require the planned outage to be optimized. If there is no next rolling range, the method 100A ends.

[0050] FIG. 1B is a schematic diagram illustrating components and steps for controlling outage rotation in an electrical distribution system during an extreme weather event according to an embodiment of the present disclosure.

[0051] 1B may include a hardware processor 155 in communication with the input interface 139, the memory 137, the interface 153, and the computing device 157. The computing device 157 may be connected to a set of switches 110 installed in the power distribution system 115. The power distribution system may have a set of energy storage 145 to reduce power outage loss energy and perform black start of the power distribution system 115. The power outage rotation control system implemented using the method 100B may control the set of switches 110 and storage 145, and may send and receive information. It is contemplated that the hardware processor 155 may include two or more hardware processors depending on the requirements of a particular application. Of course, other components may be incorporated into the method 100, including input interfaces, output interfaces, and transceivers.

[0052] Continuing with reference to FIG. 1B, an embodiment of method 100B includes receiving 165 using interface 153 over a communications network a forecasted evolution trajectory of substation generation deficit, a forecasted profile of load demand, renewable generation, and current storage status, as well as switch status for an occurring power outage event.

[0053] Step 170 of method 100B includes using hardware processor 155 to divide the power distribution system into feeder sections according to the locations of switches, and simplifying the system into a connected network by modeling the sections as nodes and the switches as links.

[0054] Step 172 involves building an internal / external power balance model to relate section energization status and loading to switch status and storage charging and discharging.

[0055] Step 174 includes mitigating the impact of outages with fair outage rotation by formulating the optimization of switch operation schedules and storage operation schedules along a rolling scheduling horizon. Planned or rotating outages are systematic, temporary outages that help balance the supply and demand of electricity in a power system. Typically, power system operators call for planned outages and implement temporary outages one area at a time to limit the duration of outages in each area. In these situations, outage rotation is based on rules that are accepted for a particular distribution system. However, rule-based outage rotation is often not optimal for a particular type of outage or for a particular consumer of the distribution system.

[0056] Therefore, it is an objective of some embodiments to provide a method for controlling a power distribution system suitable for optimizing the outage rotation principle. In other words, it is an objective of some embodiments to replace rule-based outage rotation with optimization-based outage rotation. However, optimization-based techniques require power flow analysis of large-scale power distribution systems and suffer from the curse of dimensionality problem. Therefore, it is not surprising that, to the best of available knowledge, optimization-based techniques have not been adopted to control outage rotation in power distribution system operations.

[0057] Step 176 involves solving the nonlinear optimization model by a linear transformation using the oriented feasible region.

[0058] Step 180 of method 100B includes using computing device 157 to transmit, via a communications network, commands for opening / closing a switch, discharging, or charging storage, scheduled at the optimal solution for each period within the rolling scheduling range.

[0059] These steps can be performed iteratively over a rolling scheduling horizon: for each run, the preconditions for the most recent run are considered in evaluating the objective function.

[0060] FIG. 1C is a block diagram illustrating an outage rotation control system 100C for an electrical distribution system under extreme weather events according to some embodiments.

[0061] The power outage rotation control system 100C includes a human-machine interface (HMI) 167 connectable to a keyboard 11 and a pointing device / media 12, a processor 155, a storage device 154, a memory 137, a network interface controller (NIC) 163 connectable to a network 51 including a local area network and an Internet network, a display interface 161 connected to a display device 141, an input interface 139 connectable to an input device 35, and a printer interface 133 connectable to a printing device 131.

[0062] The outage rotation control 100C can receive electrical signals 195 indicative of status or measurements of switchable devices or energy storage disposed in the power distribution system 115 via a network 51 connected to the NIC 163. The network 51 is connected to an external system 101 that can provide control signals to measurement devices in the power distribution system 115 to perform remote control of the measurement devices. Additionally, the outage rotation control system 100C can provide control status data (signals) to the external system 101 via the network 51 so that the external system 101 can control switching operations provided in the power distribution system 115. Additionally, the outage rotation control system 100C can be controlled from the external system 101 by receiving control data (signals) of the outage rotation control via the network 51.

[0063] The storage device 154 includes existing conditions and predicted system parameters 154A for the power distribution system 115 and an outage rotation control program module 154B. The input device / media 35 may include a module that reads a program stored on a computer readable media recording medium (not shown).

[0064] To control outage rotation in the power distribution system 115, the outage rotation control system 100C may receive status data for the power distribution system 115 from measurement devices included in the power distribution system 115.

[0065] According to some embodiments of the present invention, the power distribution system 115 may include a set of switchable devices, a set of renewable generators, and a set of energy storage structures. The outage rotation control system 100C receives forecasted power generation, load demand profile, and measured storage state via the network 51 (communication network) using the interface 153 of FIG. 1A and FIG. 1B. The memory 137 can load a computer executable program stored in the storage device 154, which includes existing conditions (such as cumulative outage hours or duration), forecast data profile 154A of load demand, renewable power generation or substation power supply, and an outage rotation control program (module) 154B configured to control outage rotation in the power distribution system 115. At least one processor 155 connected to the memory 137 and the interface 153 is used to execute the outage rotation control program 154B loaded from the storage device 154. For example, the outage rotation control program 154B, when executed by the processor 155, causes the processor 155 to receive power shortage updates and current equipment or storage status from measurements 195, and the processor 155 determines whether a power shortage will be caused on the power distribution system 115 by comparing the available power provided through the substation with local load demand, renewable generation, and storage levels. If a power shortage is identified, the outage rotation program 154B further requests the processor 155 to provide a predicted data profile from storage 154, and then, through connection tracing and power balancing, the program 154B determines an outage rotation scheme by identifying switches 110 to isolate the determined feeder sections by disconnecting them from access to all sources of power, and also determines a storage dispatch scheme by identifying storage 145 adjusted to charge or discharge to adjust the power balance of each feeder section along with the predicted renewable generation.The processor 155 then outputs a switch operation and storage dispatch schedule for the power distribution system 115, which indicates which switches 110 are to operate in what type of operation and by what time period, and also details the charge / discharge status and controlled charge rate level of each storage 145 in the power distribution system. Additionally, the interface (NIC) 163 can receive measured signals and power shortage event updates (not shown) 195 from the power distribution system 115 over the network 51 at every pre-configured time period.

[0066] In some cases, an instruction to start / execute power outage rotation control may be sent to the power outage rotation control system 100C using the keyboard 11, or sent from the external system 101 via the network 51.

[0067] Automatic Isolation and Restoration of Electric Distribution Systems The distribution system isolates a portion of an energized section by automatically operating switches installed in the section and restores the load demand by using local renewable energy and storage when isolated and external power input from adjacent sections when re-energized in the system through corresponding operation of switches along the path from the substation to the section. Each substation may include several feeders.

[0068] FIG. 2 illustrates an exemplary power distribution system 200, modified from the IEEE 123 node test feeder operating at a nominal voltage of 4.16 kV, operating in accordance with some embodiments. As shown in FIG. 2, a main grid 201 supplies power to the power distribution system 200 through substations. The substations distribute the power to customers through feeders. In FIG. 2, the system 200 includes two substations SUB-I and SUB-II. Substation SUB-I includes three feeders FDR-I, FDR-II, and FDR-III, and SUB-II includes feeder FDR-IV, feeder FDR-V, and feeder FDR-VI.

[0069] A feeder, such as any of Feeder FDR-I to FDR-VI, may include a set of loads, a local renewable generator, and a battery energy storage system. Each feeder may be equipped with several normally closed sectioning switches (including one circuit breaker at the feeder head) that allow the feeder to be divided into a set of energized sections. A feeder may connect with other feeders through normally open tie switches installed at the borders of adjacent feeders.

[0070] Continuing with reference to FIG. 2, exemplary system 200 has three solar power plants installed at nodes 13, 76, 101 with a capacity of 20 kW per phase, and wind power plants 47 and 57 with a capacity of 20 kW per phase. The system has six feeders fed at nodes 150, 195, 251, 350, 451 and 610, seven tie switches on 13-152, 18-135, 23-235, 158-105, 160-60, 72-672, and 94-54, and eleven sectioning switches (including six circuit breakers) on 150-149, 195-95, 251-250, 350-300, 451-450, 610-61, 7-178, 447-44, 97-197, 867-86, and 151-300. Taking FDR-1 as an example, one circuit breaker is installed at branch 150-149, a sectioning switch at branch 7-178, and three tie switches at 13-152, 18-135 and 23-235, connecting to FDR-VI, FDR-IV and FDR-III respectively.

[0071] During power shortage from the power system, the power system operator needs to adjust the operation status of sectioning and tie switches to cut off power supply to some feeder sections to realize a new balance between power supply and demand. The goal of outage rotation is to determine the optimal switch operation scheme to dynamically rebalance power supply and demand along the power shortage range to meet the diverse or even competing needs of the system and customers. Due to the large space of switch operation combinations and the complex operation adjustment along the power shortage range, the outage rotation problem is currently difficult to model and solve as an optimization problem, but is usually determined by using heuristic methods instead. The optimality of the solution is one of the main challenges faced by heuristic rule-based methods when dealing with practical systems. Another concern is that the current practice mainly considers the system demands, such as minimizing energy losses, but ignores the interests of customers.

[0072] Some embodiments replace the structural model of the power distribution system with a meta-structure of different dimensions, and replace the power flow model with an internal power balancing model of the meta-structure to optimize the power flow analysis in the system. The purpose of such a replacement is to provide a new optimization space suitable for power flow analysis, which allows to reduce the computational burden and reduce the possibility of the curse of dimensionality in the optimization problem in controlling the power distribution system. That is, to avoid direct modeling of the large-scale power flow, which causes the curse of dimensionality problem, for system optimization, some embodiments first divide the power distribution system into a set of feeder sections separated by switchable devices that are normally open or normally closed, and then simplify the power distribution system into a connected network by modeling the feeder sections as its nodes and the switches as its links. The power flow model of the system is replaced with an internal power balance model that balances the local generation and load of each section when it is isolated, and an external power balance model that adjusts the power exchange with adjacent sections through the switches when it is energized. Using the small-scale power flow calculation, it can be confirmed whether there is a power flow violation in any of the feeder sections. If a violation is found, it can be eliminated by adjusting / reducing the switch power flow limit according to the sensitivity of the violation to power injection at the switch. The energized status of each feeder section can be determined by the state of the switches present on the path between the section and the available substations / feeders. In some implementations, the energy lost due to isolation of the section is determined based on local renewable generation, storage dispatch, and load demand.

[0073] As such, some embodiments use a graph-based representation of the structure of the power distribution system. Each node of the graph is a section of the power system, e.g., a feeder section, separated from other sections of the power system by a switch. The switches may be of different types, such as normally closed or normally open switches. Some example embodiments model the switch with a binary variable representing its open / closed status and a set of continuous variables representing the amount of current / power flowing through the switch. The variables may be subject to a set of thresholds for the maximum current / power allowed to flow through the switch. In some example embodiments, the thresholds may be configurable to represent operational requirements.

[0074] FIG. 3A is a schematic diagram illustrating the division of a distribution system into a set of feeder sections that can be used for feeder isolation and restoration control, according to some embodiments. Switches in open status (e.g., 13-152) and closed status (e.g., 150-149) are represented by unfilled and filled rectangles, respectively. Solid lines represent buses, and solid lines between two buses represent distribution lines. Feeder heads at buses are represented as filled vertical / horizontal rectangles. As shown in FIG. 3A, the system can be divided into a set of energized sections according to the open / closed status of switches in the distribution system. For example, based on the current switch status, feeder FDR-1 has two energized sections SECT-I-1 and SECT-I-2, and feeder FDR-III has only one energized section SECT-III-1. If a section is isolated from the system due to a fault or rotation requirement, the entire load in the section is lost, minus the portion that is met by the local renewable generators and battery energy storage system.

[0075] 3B is a schematic diagram of a graph-based representation 399b of the structure of a power distribution system according to some embodiments. In this drawing, the main system 300b (similar to the main system 201 in FIG. 2) is represented as a rectangle. Substations SUB-I 310b, feeder heads 320b, or feeder sections are represented as ellipses. Switches are represented as solid lines when closed (such as switch 178-7) and dotted lines when open (such as 18-135).

[0076] The graph-based representation of the power distribution system is a radial tree of a plurality of nodes, such as nodes 310b, 320b, 330b, and 340b, connected by a plurality of edges, such as 305b, 315b, 325b, and 335b. Each node of the plurality of nodes represents a section of the power distribution system, isolated from other parts of the power distribution system by one or more switches when the one or more switches are in an open position. For example, node 330b can represent section SECT-I-1 of FIG. 3A, and node 340b can represent section SECT-I-2. Each node of the plurality of nodes has a characteristic of the power demand of the corresponding section, which is governed by the difference between the energy required by the loads of the corresponding section and the energy available in the corresponding section from one or a combination of local energy generators and local energy storage. For example, the section may include loads that require energy and generators that generate energy. The difference between the local demand of the section and the local production in the section is a characteristic of the node that represents the section.

[0077] Similarly, each edge of the multiple edges connecting a node to an adjacent node represents a switch connecting the section represented by the node to the adjacent section represented by the adjacent node. For example, edge 335b can represent switch 178-7 in FIG. 3A connecting sections SECT-II-2 and SECT-II-1. Edges have properties that impose constraints on the throughput of energy through the switch in the direction of power flow.

[0078] In particular, the graph-based representation 399b is a radial tree distribution of the input energy 300b. A radial tree is a way of displaying a tree structure (e.g., a tree data structure) in a radial outward manner. As such, edges are directional and can be bidirectional, such as edge 345b, which forms a loop if closed, or unidirectional, such as edges 305b or 315b.

[0079] Switches connect the power flow between each feeder section and other sections of the distribution system. Thus, switches are represented as edges connecting nodes of a graph-based representation. A characteristic of a node is its power demand (fixed or time-varying), while a characteristic of an edge is the potential throughput of delivering power through the switch. In some example embodiments, the graph is a radial tree starting from a root node representing a source feeding the distribution system, such as the main power system 300b. Thus, the throughput of a switch connecting a node to its children is the minimum of the throughput of the switch, as determined by its type, and the throughput of the edge leading to the node, which determines the maximum flow of energy the switch can receive. Note that edges are directional, and a pair of nodes can be connected by an edge in one or both directions with different throughputs.

[0080] Consider this graph-based representation and note that the state of the entire distribution system can be represented as a function of the state of the switches that pass or block the flow of energy. Thus, the effects of the internal complexities of different elements of the distribution system, such as the individual demands of different loads, power storage, generation, types, and costs of production of power, can be reduced (or aggregated) or simply ignored by optimization.

[0081] In addition, this graph-based representation is advantageous for power generation shortages caused by disasters, which may be reflected in the properties of the nodes and edges. The graph is a radial tree that spreads outward, i.e., radiates, from the root node, so that each node is connected to the root node through one or more radial paths. When at least one edge on a path leading to a node is deleted or opened, this entire path is blocked. The deletion of edges may be intentional or unintentional, i.e., controlled or uncontrolled. For example, unintentional deletion may occur due to hostile events such as natural disasters and / or unexpected events. Intentional deletion may occur due to optimization of power distribution in case of energy shortages. This intentional deletion may be achieved by opening a switch.

[0082] Thus, the configuration of the radial tree can be changed in case of natural disasters and / or unexpected events. However, if there is an edge on this tree, it is considered that the edge can pass energy, taking into account its throughput, which can be changed by natural events and / or as a result of optimization. Whether a switch should pass energy or not depends on the state of the switch and the corresponding state of the edge.

[0083] 3C is an example schematic diagram of a graph-based representation 399c of the structure of an electric power distribution system affected by an example adversarial event 300c, according to some embodiments. In this case, some conductors of the distribution line of the feeder section represented by node 340b are cut, and thus node 340b is removed from the representation. Other examples include changes in the properties of nodes due to damage to local energy generators, such as storage at a power plant.

[0084] As illustrated by the principle of Figure 3C, in some embodiments, the control system stores a nominal graph-based representation of the distribution system and updates the nominal graph-based representation of the distribution system based on the type of adversarial event to collect the graph-based representation of the distribution system. For example, the nominal graph-based representation of the distribution system may be the graph of Figure 3B, and the graph-based representation of Figure 3C is an updated graph caused by a situation in which the energy available to the distribution system is less than the required energy due to the adversarial event.

[0085] 3D is an exemplary schematic diagram of a graph-based representation 399d of a distribution system structure according to some embodiments. This example shows a graph-based representation of a potential distribution system structure to be determined to reduce a particular cost function or to satisfy some particular constraints. In this figure, a normally closed switch 340b3 between 18-21 is determined to be installed to split the original feeder section SECT-I-2 into two sections SECT-I-2-1, 340b1 and SECT-I-2-2, 340b2 to reduce maximum section energy loss. Various operations and planning measures of the distribution system can be determined using the graph-based representation by specifying the properties, states, and / or constraints of the nodes and edges.

[0086] For example, in some embodiments, the constraints defined by the graph-based representation include one or a combination of the following: the possibility of power exchange between nodes, constraints on the direction of power flow of each edge, constraints on the throughput of power flow at each edge, a power balance between the power flowing into each non-isolated node and the power flowing out of each non-isolated node, and radial constraints on the radial paths formed by the edges. Additionally or alternatively, the characteristics of the edges impose constraints such that the throughput of energy through a switch in the direction of power flow is less than or equal to the throughput of the switch, as determined by its type and the state of the parent edge connecting the node to the parent node, and the state of each node determines the amount of power flowing through the corresponding switch.

[0087] Thus, the graph-based representation of the power distribution system according to some embodiments allows for formulating an optimization problem using the following principle: optimizing a cost function of the properties of the nodes as a function of the states of the edges, given a radial tree of the graph that defines the node and edge relationships and properties as constraints. In particular, the graph-based representation of the grid meta-structure is distinguishable to enable a variety of optimization techniques.

[0088] 3E illustrates a block diagram of a method 300e performed by a control system for controlling the flow of available energy in a power distribution system, according to some embodiments. The control system includes a processor and a memory having instructions stored thereon that, when executed by the processor, cause the control system to perform steps of the method 300e.

[0089] The method 300e collects 310e a graph-based representation 315e of the power distribution system as a radial tree of nodes connected by edges. As described in connection with Figures 3B-3D, each node of the plurality of nodes represents a section of the power distribution system that is isolated from other parts of the power distribution system by one or more switches when the one or more switches are in an open position. Each edge of the plurality of edges connecting a node to an adjacent node represents a switch connecting the section represented by the node to the adjacent section represented by the adjacent node, each node of the plurality of nodes has a characteristic of the power demand of the corresponding section that is governed by the difference between the energy required by the loads of the corresponding section and the energy available in the corresponding section from one or a combination of local energy generators and local energy storage, and the edge has a characteristic that constrains the throughput of energy through the switch in the direction of power flow.

[0090] The method 300e solves 320e an optimization problem to determine states 325e of each of a plurality of edges of the graph-based representation 315e that govern the power flow of the available energy, and optimizes a cost function of the characteristics of a plurality of nodes, taking into account the graph-based representation of the power distribution system as constraints. The constraints may include connection relationships between the nodes and edges, and technological operating models and limitations associated with the nodes and edges.

[0091] Next, the method 300e converts (330e) the determined state 325e of each edge of the plurality of edges into a control command 335e for a state of at least some of the switches of the power distribution system and submits (340e) the control command 335e to the at least some of the switches of the power distribution system to cause a change in the power flow of the available energy.

[0092] The optimized edge state can be translated into a control command based on the edge state and the current state of the switch. For example, if the state of the switch is normally open and the control command is also "open switch", then such a control command may or may not be sent. However, if the state of the switch is normally open and the control command is "close switch", then such a control command is sent.

[0093] Alternatively, the method 300e solves 320e an optimization problem to determine a combination of a state 325e of each of the plurality of edges and a property of each of the plurality of nodes of the graph-based representation 315e that governs the power flow of the available energy that optimizes a cost function of the states of the plurality of edges and the properties of the plurality of nodes taking into account the graph-based representation of the distribution system as constraints. The method 300e then converts 330e the determined state 325e of each of the plurality of edges and the properties of each of the plurality of nodes into control commands 335e for the states of at least some switches and the properties of at least some nodes of the distribution system and submits 340e the control commands 335e to the at least some switches and some nodes of the distribution system to cause a change in the power flow of the available energy.

[0094] Different embodiments use different methods to optimize the state of the edges of the graph. For example, to allow for fair outage rotation considering various interests, some embodiments balance one or a combination of objectives by modeling the outage rotation as a multi-objective optimization problem, including minimizing lost energy and minimizing switch operations representing the needs of the power system, minimizing section outage duration and minimizing section outage frequency representing customer demands, minimizing the difference in outage frequency between feeder sections, and minimizing the difference in outage frequency between feeder sections to achieve the goal of fair outage rotation.

[0095] Illustrative embodiment: Fair outage rotation given system configuration Problem formulation The disclosed method is designed to achieve fair outage rotation among different sections of the system while maximally maintaining system balance, so that the impact of power shortages is shared equally among customers. The method utilizes both graph topology analysis and mixed integer linear programming to determine the outage rotation scheme.

[0096] The system is first divided into a set of feeder sections by opening all the switches, and each full connected area is formed as a feeder section. Then, by modeling each section as a node and each switch as a link, a connected network is generated that represents the topological structure of the power distribution system, and the corresponding connection relationships between the sections, feeders, and substations can be established through the analysis of the network connectivity. As shown in Figure 2 or Figure 3B, the power distribution can be considered as a configurable tree, where the main system is the root, the first hierarchical overhead links connect the main system to the substations, the second hierarchical real / overhead links connect the substations to the feeders, and each feeder forms a branch of the tree. Through switch operations, the tree branches can be interrupted or reconfigured while leaving the radial tree configuration.

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[0099] In addition, T cis the time horizon of the power shortage event even if the rotation is performed without adapting to the outage evolution, i.e., the static rotation scheduling method is adopted. In the case of the rolling rotation method, the existing conditions such as the previous outage duration and number for each feeder section before the new rolling scheduling horizon is started are included in evaluating each objective function. The static method is used when an accurate prediction is obtained for the power shortage evolution process, otherwise the rolling horizon method is used and the existing conditions are taken into account in triggering the new solution.

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[0102] Blackout rotation is subject to technical constraints necessitated by device characteristics, power flow, system radial operation, and power shortage conditions.

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[0109] By combining multiple objective optimization problems into one objective problem by using a satisfaction function, they can be combined or combined into a single objective problem by describing the satisfaction of each objective task and defining a new objective task that seeks the maximum of the weighted sum of the satisfaction or minimum satisfaction. Typically, the satisfaction function is a nonlinear function such as a sigmoid function. For computational simplicity, a generalized modified linear activation function (ReLU) is used instead to describe the satisfaction of the required objective. ReLU is generalized with a configurable non-zero gradient and a capped output to 1, as shown in FIG. 4A or FIG. 4B. Thus, FIG. 4A is a schematic diagram of a positive generalized ReLU function used to represent the objective satisfaction according to some example embodiments, and FIG. 4B is a schematic diagram of a negative generalized ReLU function used to represent the objective satisfaction according to some example embodiments.

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[0112] Model Transformation and Solution The model formulated above is a nonlinear optimization problem with mixed binary and continuous variables and logical operations. We propose a directed feasible region based method as well as an undirected feasible region method to convert the nonlinear optimization model to a mixed integer linear programming problem (MILP). This method converts the nonlinear operation to a linear operation while also avoiding infeasible solutions, such as when dealing with conflicting or unreasonable objective tolerances.

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[0119] Using the above method, the power outage rotation problem can be converted into a MILP problem and solved using commercially available software. The resulting switch status settings and storage operations are then converted into a set of feasible switching sequences, taking into account the switch characteristics and the detailed charging and discharging schedule of the energy storage system.

[0120] It should be noted that if the forecast of the power shortage event is likely to be very accurate, a static range method can be used to determine the outage rotation plan through a one-shot solution of the model formulated above. Otherwise, the outage rotation plan may be determined by using a rolling range method, where each new solution is determined over a portion of the entire range of the power shortage by considering the existing conditions for the current range portion.

[0121] Illustrative embodiment: Strengthening the power grid for more equitable outage rotation For distribution systems with fixed system configurations, their ability to achieve fairness in outage rotation is limited due to the fixed settings of feeder sections and fixed placement of storage. Fairer outage rotation can be achieved by embedding outage rotation considerations into the system resilience enhancement process. Enhancement considerations in this disclosure include the addition of sectioning switches (i.e., normally closed switches), tie switches (i.e., normally open switches), and battery energy storage systems (BESSs).

[0122] Assuming that the location and ratings of each candidate switch and storage are known, the goal of the power distribution system is to determine the optimal cost-effective combination of switches and storage to meet the diverse requirements from the system and customer satisfaction, subject to technical and financial constraints arising from normal operation, network failures, power shortages, black starts, and financial viability.

[0123] To this end, some embodiments include adding redundant switches that are normally closed or open. In this way, the configuration of the graph-based representation of the power system is changed, adding flexibility to the optimization. As a result, in some embodiments, the power distribution system includes a radial path, where at least two normally closed switches are directly connected on the radial path to allow for dividing the radial path into smaller sections, and at least one normally open switch radial path to allow for rerouting to an alternative power source. Having at least two normally closed switches in a string only makes sense due to the principles employed by the embodiments. Additionally or alternatively, some embodiments improve the flexibility of the optimization by optimizing the location of the redundant switches.

[0124] 6 is a schematic diagram illustrating a sample distribution system modified from an IEEE 123 node feeder with candidate switches and storage according to some example embodiments. This example has five candidate storages planned to be added at nodes 7, 36, 58, 72, 105 with a capacity of 500 kWh / 50 kW per phase. In addition, there are also four sectionalized switches planned to be added to the system on branches 13-138, 57-576, 72-726, 78-788, and 47-479.

[0125] FIG. 7 is a schematic diagram illustrating split fixed boundary sections and flexible boundary sections of the sample distribution system shown in FIG. 6 according to some example embodiments. A fixed boundary section refers to a feeder section whose boundaries all switches are existing installed switches, such as SECT-II-1. In contrast, a flexible boundary section refers to a section whose boundaries include at least one switch whose installation status is to be determined, such as SECT-I-2-1 and SECT-I-2-2. Thus, if the installation status of a switch in a flexible boundary section is not installed, this section is fused as a whole with the adjacent flexible boundary section to be used for isolation and restoration. For example, if switch on 18-138 is determined to be not installed, flexible boundary sections SECT-I-2-1 and SECT-I-2-2 are fused together as the minimum isolation section. Otherwise, it can be considered as an independent section to be isolated or restored.

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[0130] The objectives of section connection load and average N-1 contingency duration are used to reduce the size of the section to be separated and the expected failure duration. According to the given position of the switch to be determined for installation, a set of candidate sections can be generated first, and then a final section can be generated by fusing adjacent candidate sections based on the determined installation status. For a section, if one of the switches is not an existing switch, i.e., its installation status needs to be determined, this section is called a flexible boundary section. If its installation status is determined to be true, this candidate section becomes a fixed boundary section after installation. If the installation status is false, this section is merged with the adjacent section and separated as one fixed boundary section.

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[0140] Another objective for evaluating the ability of a candidate storage is to meet the needs of a black start by discharging to its connected sections. Black start in this specification refers to a power outage scenario in which the entire distribution system loses power supply from the main grid.

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[0146] Constraints for optimization include radial operating requirements, power balance and power flow requirements, switch capacity limits and storage energy balance requirements, as well as constraints specified for the operating scenario.

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[0148] This set of relationships between the construction and operation of the switch to verify a normally closed switch is treated as a closed link, and a normally open switch, if not installed, is treated as an open link.

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[0159] The above method can also be transformed into a standard MILP to be solved using the directed feasible region method. The solution of the transformed model provides an optimal placement scheme for switches and storage. Through the realization of the determined placement scheme for placing switches and storage at the determined locations with the determined ratings, a power distribution system with a fairer outage rotation function can be realized.

[0160] Working Example One illustrative application of the presented method can be demonstrated by using the sample system shown in Figures 2 and 6. The power shortage scenario is that 50% generating capacity of the main grid is lost in 24 hours.

[0161] The predicted hourly power generation profiles for the solar and wind power plants are shown in Figures 8A and 8B. A typical hourly load profile and corresponding price profile are shown in Figures 9A and 9B. The predicted maximum power generation of two substations in the sample system under a power shortage scenario is shown in Figure 10.

[0162] Power outage rotation with fixed system configuration Figure 2 is used to generate an outage rotation scheme with a fixed system configuration. First, an outage rotation scheme, Plan I, is generated using only the loss energy objectives commonly used by distribution systems. The determined scheme and its evaluated attributes are listed in Tables I-1, I-2, and I-3 below.

[0163] [Table 1]

[0164] As shown in Table I-1 and Table I-3, the loss energy of this plan is 22.64 MWh and the number of switch operations is 2. The outage schedule is listed in Table I-2 and shown in Figure 11. As shown in Figure 11, feeders FDR-II and FDR-VI experienced a 24-hour outage. All other feeders maintained normal power supply throughout the shortage period.

[0165] Clearly, the scheme presented in Plan I does not produce a fair rotation among all customers. As shown in Figure 11 and Table I-2, some customers experience longer outages lasting 24 hours. Meanwhile, there are customers who do not experience any outages at all. This causes a significant bias in service to the customers.

[0166] Then, another outage rotation scheme, Plan II, is determined using all the objectives related to both customer and system benefits. The determined scheme and its evaluated attributes are listed in Tables II-1, II-2 and II-3.

[0167] Compared to Plan I, the energy losses in Plan II increased slightly by 14.62%, reaching 25.95 MWh, and a higher number of switching operations was required, i.e. 26 times instead of 2 in Plan I. However, customers / consumers experienced shorter outages and a fairer outage rotation. The maximum outage duration was reduced by 50.0%, from 24 hours to 12 hours, and the maximum outage time difference was reduced by 75%, to 3 hours instead of 24 hours in Plan I.

[0168] The outage rotation schedule is shown in Figure 12. As shown in the figure, the outages rotate among six different parts, and only a three hour difference in outages is observed between different parts of the system.

[0169] [Table 2]

[0170] Power outage rotation with resilience-enhancing system configuration Some illustrative but non-limiting test scenarios are now described. The proposed model can be tested using a sample system with enhanced resilience, shown in Figure 6. Assume there are five candidate storages at nodes 7, 36, 58, 105, 72 with a capacity of 500 kWh / 50 kW per phase, and five candidate normally closed switches at branches 47-479, 13-138, 57-576, 78-788, and 72-726. The test scenarios include one normal scenario and one power shortage scenario, where 50% generating capacity of the main grid is lost during a 24-hour period.

[0171] Using the above optimization model, a final solution was obtained in which all candidate storages were determined to be installed and for the switches, switches on 78-788 were selected as being installed.

[0172] Based on this resilience enhancement system, outage rotation schemes are generated for the same power shortage scenarios used above. The determined schemes and their evaluated attributes are listed in Tables III-1, III-2 and III-3.

[0173] In Plan III, the lost energy is much less, 20.60 MWh, compared to Plans I and II, and the switch operates a reasonable number of times, i.e., 13 times. The reduction in lost energy is due to the use of storage discharge and the reduction in the maximum connected load due to the installation of additional switches. The maximum outage duration difference is 12 hours and the maximum number of outages is 2. This plan shows a better fairness of rotation compared to Plan I. As in Plan II, the maximum outage duration difference is only 3 hours and the maximum number of outages difference is 1, but the switch operations are much less.

[0174] [Table 3]

[0175] Figure 13 shows the outage rotation schedule given by Plan III, which rotates between six parts of the system, each part including a set of sections separated by switches.

[0176] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. It is contemplated that various changes may be made to the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0177] Specific details are given in the following description for a thorough understanding of the embodiments. However, those skilled in the art will understand that the embodiments can be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments in unnecessary detail. In other examples, well-known processes, structures, and techniques may be shown without unnecessary detail so as not to obscure the embodiments. Furthermore, like reference numbers and names in the various drawings refer to like elements. Also, individual embodiments may be described as a process that is shown as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe operations as a sequential process, many of the operations may be performed in parallel or simultaneously. In addition, the order of operations may be permuted. A process may be terminated when its operations are completed, but may have additional steps not discussed or included in the diagram. Furthermore, not all operations in any process specifically described may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. If a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or to the main function.

[0178] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, manually or automatically. The manual or automated implementation may be performed or at least assisted through a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments for performing the necessary tasks may be stored on a machine-readable medium. A processor may perform the necessary tasks. The various methods or processes outlined herein may be coded as software executable on one or more processors using any one of a variety of operating systems or platforms. In addition, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and may be compiled as executable machine language code or intermediate code that runs on a framework or virtual machine. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0179] The embodiments of the present disclosure may be implemented as a method, an example of which is provided. The acts performed as part of the method may be ordered in any suitable manner. Thus, the embodiments may be configured to perform acts in different orders than described, including performing some acts simultaneously, even though they are shown in the illustrative embodiments as a series of acts. Furthermore, the use of order terms such as "first," "second," and the like to modify elements of the claims does not in itself imply a priority, precedence, or order of one element of the claim relative to another element, or a chronological order in which the actions of a method are performed, but is merely used as a label to distinguish one element of a claim having a particular name from another element having the same name (apart from the use of order terms) to distinguish elements of the claims. Although the present disclosure has been described with several preferred embodiments, it should be understood that various other adaptations and modifications can be made within the spirit and scope of the disclosure. It is therefore an aspect of the following claims to cover all such variations and modifications that fall within the true spirit and scope of the disclosure.

Claims

1. A control system for controlling the power flow of available energy in a power distribution system, the control system comprising a processor and a memory storing instructions, wherein when an instruction is executed by the processor, the control system... The command performs the task of collecting a graph-based representation of the power distribution system as a radial tree consisting of multiple nodes connected by multiple edges, each node of the multiple nodes representing a section of the power distribution system, the section being separated from the rest of the power distribution system by one or more switches when one or more switches are in the open position, each edge of the multiple nodes connecting a node to an adjacent node representing a switch connecting the section represented by the node to an adjacent section represented by the adjacent node, each node of the multiple nodes having the power demand characteristics of the corresponding section, the power demand characteristics being governed by the difference between the energy required from the load of the corresponding section and the energy available within the corresponding section from one or a combination of local energy generators and local energy storage, and the edge having the characteristic of restricting the throughput of energy through the switch in the direction of power flow, and the command further commands the control system, By solving the optimization problem, the system optimizes the cost function of the characteristics of the plurality of nodes, taking into account the graph-based representation of the power distribution system as a constraint, and determines the state of each edge among the plurality of edges of the graph-based representation that governs the power flow of the available energy. The cost function includes different components directed towards different objectives of the optimization problem, such that the optimization problem becomes a multi-objective optimization. The aforementioned different objectives are to minimize the total system energy loss, the total number of system switch operations, the maximum system section separation duration, the maximum system section separation frequency, the maximum difference in separation duration between any two feeder sections, and the maximum difference in separation frequency between any two feeder sections, wherein the objectives are defined for a set of consecutive time steps, and at least some of the edges have different statuses in different time steps, and the instruction further enables the control system to Converting the determined state of each of the aforementioned multiple edges into a control command for the state of at least some switches in the power distribution system, By submitting the control command to at least some switches in the power distribution system, a change is caused in the power flow of the available energy. A control system that controls the power flow of available energy in the power distribution system based on the submitted control command.

2. The control system according to claim 1, wherein the constraints defined by the graph-based representation include one or a combination of the following: the possibility of power exchange between the nodes, constraints on the direction of the power flow at each edge, constraints on the throughput of the power flow at each edge, a power balance between the power flowing into each unseparated node and the power flowing out of each node, and radial constraints on radial paths formed by a plurality of edges.

3. The control system according to claim 1, wherein the energy available to the power distribution system is less than the required energy due to an adversarial event, and the control system updates the nominal graph-based representation of the power distribution system based on the type of the adversarial event to collect the graph-based representation of the power distribution system.

4. The control system according to claim 1, wherein the optimized state of the edge is converted into the control command based on the state of the edge and the current state of the switch.

5. The control system according to claim 1, wherein the characteristics of the edge are constrained such that the throughput of energy passing through the switch in the direction of the power flow is less than or equal to the throughput of the switch, which is determined by the type of switch and the state of the parent edge connecting the node to the parent node, and the state of each node determines the amount of power flowing through the corresponding switch.

6. The control system according to claim 1, wherein the control system converts the multi-objective optimization to a single-objective optimization by defining its objective as maximizing the sum of a first item defined as a weighted sum of satisfaction levels for all of the multiple objectives and a second item defined as the minimum weighted satisfaction level among all of the multiple objectives.

7. The control system according to claim 6, wherein the degree of satisfaction of each objective is defined using a generalized normalized linear unit (ReLU) action function, which is generalized by defining the gradient in the positive or negative direction by the minimum and maximum objective values, with an upper threshold of 1.

0.

8. The control system according to claim 1, wherein the optimization problem is a nonlinear optimization problem using a mixture of binary and continuous variables and logical operations, and is solved using a nonlinear solver.

9. The control system according to claim 1, wherein the optimization problem is converted into a mixed-integer linear programming (MILP) problem and solved using a MILP solver.

10. The control system according to claim 9, wherein the optimization problem is extended by replacing each generalized ReLu function, binary operation, and logical operation with an auxiliary optimization problem described by a linear objective function constrained by a set of linearly feasible boundaries.

11. The control system according to claim 1, wherein the optimization problem is solved by a machine learning solution using a physical information neural network (PINN), the machine learning solution solves the optimization problem by training the PINN to minimize a loss function including the cost function and a penalty for constraint violation, the inputs of the PINN being a set of adversarial events defined considering a graph-based representation, and the outputs being a set of corresponding switch statuses at each time step.

12. The control system according to claim 1, wherein the control of the power flow of the distribution system is performed on a given graph-based representation of adversarial events occurring on the distribution system, the adversarial events affect one or a combination of the following: power available from the main grid, switch on / off status, switch throughput, and the amount or status of storage or generation or line segments within the section.

13. The control system according to claim 1, wherein the section of the power distribution system is formed by opening all switches, and each connection area is designed as a section of the power distribution system, and the section includes a set of buses connected to a renewable generator, an electrical energy storage system, a load, and line segments connected between the buses.

14. The control system according to claim 1, wherein the control of the power flow of the power distribution system is performed over a range of static time covering all time steps throughout the entire duration of the adversarial event, or in a time rotation scheme that reconsiders and updates node and edge statuses throughout the entire duration of the adversarial event.

15. The control system according to claim 1, wherein the section within the power distribution system is divided into two or more sections by adding one or more surplus normally closed switches, the arrangement of the surplus switches is determined by minimizing a plurality of cost functions, the plurality of cost functions including at least two of minimizing the annual cost of the switches, minimizing the maximum connected net load between the sections connected by the surplus switches, the maximum average N-1 contingency duration of the sections connected by the surplus switches, minimizing the expected operating cost for all reasonable normal operating conditions of the power distribution system, minimizing the total expected energy loss for reasonable adversarial events, minimizing the total expected number of switch operations for reasonable adversarial events, minimizing the expected maximum section separation duration for reasonable adversarial events, minimizing the expected maximum section separation frequency for reasonable adversarial events, minimizing the expected maximum difference in separation duration between any two feeder sections for reasonable adversarial events, and minimizing the expected maximum difference in separation frequency between any two feeder sections for reasonable adversarial events.

16. The control system according to claim 1, wherein a normally open switch is added between two radial paths to create a surplus loop that operates radially, the arrangement of the surplus switch is determined by minimizing a plurality of cost functions, the plurality of cost functions including at least two of minimizing the annual cost of the switch, minimizing the maximum pickup net load by the surplus switch which is negative, minimizing the expected operating cost for all reasonable normal operating conditions of the system, minimizing the total expected energy loss for reasonable adversarial events, minimizing the total expected number of switch operations for reasonable adversarial events, minimizing the expected maximum section separation duration for reasonable adversarial events, minimizing the expected maximum section separation frequency for reasonable adversarial events, minimizing the expected maximum difference in separation duration between any two feeder sections for reasonable adversarial events, and minimizing the expected maximum difference in separation frequency between any two feeder sections for reasonable adversarial events.

17. A control system according to claim 1, wherein a surplus energy storage system is added to the distribution system at a location determined by minimizing a plurality of cost functions, the plurality of cost functions comprising at least two of the following: minimizing the annual cost of storage; minimizing the discharge capacity from the storage which is negative; minimizing the expected operating cost for all reasonable normal operating conditions of the system; minimizing the total expected energy loss for reasonable adversarial events; minimizing the total expected number of switch operations for reasonable adversarial events; minimizing the expected maximum section separation duration for reasonable adversarial events; minimizing the expected maximum section separation frequency for reasonable adversarial events; minimizing the expected maximum difference in separation duration between any two feeder sections for reasonable adversarial events; and minimizing the expected maximum difference in separation frequency between any two feeder sections for reasonable adversarial events.

18. The control system according to claim 1, wherein the power distribution system includes a radial path, at least two normally closed switches directly connected on the radial path allow the radial path to be divided into smaller sections, and at least one normally open switch allows the radial path to be rerouted to an alternative power source.

19. A control system for controlling the power flow of available energy in a power distribution system, the control system comprising a processor and a memory storing instructions, wherein when an instruction is executed by the processor, the control system The command performs the task of collecting a graph-based representation of the power distribution system as a radial tree consisting of multiple nodes connected by multiple edges, each node of the multiple nodes representing a section of the power distribution system, the section being separated from the rest of the power distribution system by one or more switches when one or more switches are in the open position, each edge of the multiple nodes connecting a node to an adjacent node representing a switch connecting the section represented by the node to an adjacent section represented by the adjacent node, each node of the multiple nodes having the power demand characteristics of the corresponding section, the power demand characteristics being governed by the difference between the energy required from the load of the corresponding section and the energy available within the corresponding section from one or a combination of local energy generators and local energy storage, and the edge having the characteristic of restricting the throughput of energy through the switch in the direction of power flow, and the command further commands the control system, By solving the optimization problem, the system optimizes the cost function of the characteristics of the plurality of nodes, taking into account the graph-based representation of the power distribution system as a constraint, and determines the state of each edge among the plurality of edges of the graph-based representation that governs the power flow of the available energy. The cost function includes different components directed towards different objectives of the optimization problem, such that the optimization problem becomes a multi-objective optimization. The control system converts the multi-objective optimization into a single-objective optimization by defining its objective as maximizing the sum of a first item defined as a weighted sum of satisfaction levels for all of the multiple objectives, and a second item defined as the minimum weighted satisfaction level among all of the multiple objectives. The degree of satisfaction of each objective is defined using a generalized normalized linear unit (ReLU) action function, which is generalized by defining the gradient in the positive or negative direction by the minimum and maximum objective values, with an upper threshold of 1.0, and the instruction further enables the control system to Converting the determined state of each of the aforementioned multiple edges into a control command for the state of at least some switches in the power distribution system, By submitting the control command to at least some switches in the power distribution system, a change is caused in the power flow of the available energy. A control system that controls the power flow of available energy in the power distribution system based on the submitted control command.

20. A control system for controlling the power flow of available energy in a power distribution system, the control system comprising a processor and a memory storing instructions, wherein when an instruction is executed by the processor, the control system The command performs the task of collecting a graph-based representation of the power distribution system as a radial tree consisting of multiple nodes connected by multiple edges, each node of the multiple nodes representing a section of the power distribution system, the section being separated from the rest of the power distribution system by one or more switches when one or more switches are in the open position, each edge of the multiple nodes connecting a node to an adjacent node representing a switch connecting the section represented by the node to an adjacent section represented by the adjacent node, each node of the multiple nodes having the power demand characteristics of the corresponding section, the power demand characteristics being governed by the difference between the energy required from the load of the corresponding section and the energy available within the corresponding section from one or a combination of local energy generators and local energy storage, and the edge having the characteristic of restricting the throughput of energy through the switch in the direction of power flow, and the command further commands the control system, By solving the optimization problem, the system optimizes the cost function of the characteristics of the plurality of nodes, taking into account the graph-based representation of the power distribution system as a constraint, and determines the state of each edge among the plurality of edges of the graph-based representation that governs the power flow of the available energy. The aforementioned optimization problem is transformed into a mixed-integer linear programming (MILP) problem and solved using a MILP solver. The optimization problem is extended by replacing each of the generalized normalized linear unit (ReLU) functions, binary operations, and logical operations with an auxiliary optimization problem described by a linear objective function constrained by a set of linearly feasible boundaries, and the instruction further extends to the control system, Converting the determined state of each of the aforementioned multiple edges into a control command for the state of at least some switches in the power distribution system, By submitting the control command to at least some switches in the power distribution system, a change is caused in the power flow of the available energy. A control system that controls the power flow of available energy in the power distribution system based on the submitted control command.

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