Reliability evaluation method and system for flexible interconnected distribution network considering fault recovery

Abstract

The method and system for reliability evaluation of flexible interconnected distribution network considering fault recovery comprise: constructing a multi-device collaborative recovery optimization model, the constraint conditions comprising a topology constraint and a power flow constraint based on an improved virtual flow method; converting the nonlinear constraint into a linear one; generating a fault scene by using sequential Monte Carlo simulation for sampling, recording the current fault occurrence time, calculating the average equivalent output of the wind-photovoltaic joint output scene corresponding to the fault occurrence time as the upper limit of the wind-photovoltaic DG output, improving the original power flow constraint based on the upper limit of the wind-photovoltaic DG output, and adopting the improved multi-device collaborative recovery optimization model for optimal fault recovery; and if the simulation time exceeds the simulation time limit, calculating the node reliability index and the FIDN reliability index. The present application can effectively improve the system reliability, smooth the new energy fluctuation and share the risk brought by SOP fault.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, and more specifically, relates to a method and system for reliability assessment of flexible interconnected distribution networks that takes fault recovery into account. Background Technology

[0002] Flexible interconnected distribution networks, centered on flexible power electronic devices, utilize equipment such as smart soft switches (Soft OpenPoint, SOP) to achieve flexible interconnection and dynamic power regulation between multiple feeders and regions. This breaks through the limitations of the traditional radial operation of distribution networks, enabling flexible optimization of power flow distribution, alleviating line congestion, and promoting the consumption of renewable energy, providing a new technological path for improving the reliability of distribution networks. Among these, the smart soft switch, as the core hub equipment of the flexible interconnected distribution network, directly determines the regulation effect and system reliability level of the flexible interconnection. Meanwhile, the Modular Multi-level Converter (MMC) port, as a core component of the SOP, is a crucial prerequisite for ensuring the SOP's fault response and power regulation capabilities. Exploring multi-port flexible interconnection technology to achieve unified flexible connections between multiple feeders, thereby enabling seamless switching of multiple converter operating modes under fault scenarios, is an important development direction for flexible interconnection technology.

[0003] However, the reliability assessment of flexible interconnected distribution networks faces challenges from multi-dimensional uncertainties, further exacerbating the difficulty and complexity of the assessment. On the one hand, the uncertainty of wind and solar power output leads to random fluctuations in the power supply on the source side of the distribution network, making it difficult to accurately predict the scope of fault impact. On the other hand, the MMC port of the SOP has a significant degree of fault uncertainty. The hybrid MMC consists of a large number of half-bridge sub-modules (HBSM) and full-bridge sub-modules (FBSM). There is a reliability correlation among the sub-modules (SM), and their failure rate is not constant but dynamically changes with operating time due to factors such as redundancy configuration and lifespan depletion. Failure of the MMC port will directly lead to the loss of SOP control capability, thereby affecting fault recovery efficiency and even expanding the scope of power outage.

[0004] Fault recovery, as an effective means to improve the reliability of distribution networks, directly determines the outage time, outage range, and economic losses. In flexible interconnected distribution networks, the fault recovery capability of a single device is limited and cannot cope with complex fault scenarios caused by multi-dimensional uncertainties. Therefore, collaborative fault recovery of multiple flexible resource devices becomes an inevitable choice. Distributed generators (DG), energy storage systems (ESS), and other devices operating in conjunction with standard operating procedures (SOPs) can fully leverage the advantages of each device: ESS can smooth out fluctuations in renewable energy output and provide emergency power support; DG can quickly respond to fault demands and supplement power resources; and SOPs can realize cross-feeder power transfer and optimize the allocation of fault recovery resources. Through the collaborative output of multiple devices, outage time and outage load can be minimized, fault recovery efficiency can be improved, and the continuity of power supply in the distribution network can be guaranteed. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for reliability assessment of flexible interconnected distribution networks that considers fault recovery.

[0006] The present invention adopts the following technical solution.

[0007] The first aspect of this invention proposes a reliability assessment method for flexible interconnected distribution networks considering fault recovery, comprising: A multi-device collaborative recovery optimization model considering SOP failures is constructed with the maximum load recovery amount as the objective function. The constraints of the multi-device collaborative recovery optimization model include topology constraints and power flow constraints based on the improved virtual flow method. The nonlinear constraints in the multi-device collaborative recovery optimization model are transformed into linear constraints using mixed-integer second-order cone programming. Sampling is performed using sequential Monte Carlo simulation to generate fault scenarios for feeders and four-terminal SOPs. For the currently generated fault scenario, the time of the current fault occurrence is recorded. The average equivalent output during the fault period is calculated by combining the wind power-solar power output scenario corresponding to the time of the fault occurrence, which serves as the upper limit of the wind power-solar power output. Based on the upper limit of the wind power-solar power output, the original power flow constraints are improved to obtain a modified multi-device collaborative recovery optimization model. The modified multi-device collaborative recovery optimization model is used for optimal fault recovery. After recovery, update the fault status, which includes the simulation time. If the simulation time exceeds the simulation time limit, calculate the node reliability index and FIDN reliability index based on the current fault status. Otherwise, repeat the above steps starting from the fault scenario of generating the feeder and four-terminal SOP.

[0008] Preferably, the topological constraints based on the improved virtual flow method are as follows: Construct a virtual network for the target FIDN. When the SOP has load transfer capability and the node connected to the MMC port at the faulty feeder becomes a balanced node, the corresponding node is considered an additional virtual power node. The topology constraints include: the operational status of a faulty branch is 0; for a non-faulty branch, if either of the two nodes of the branch is the parent node of the other node, the operational status of the corresponding branch is 1, otherwise it is 0; for all actual power supply nodes, the energized status of the node is 1; for all load nodes, there is at most one parent node, and when a parent node exists, the energized status of the node is 1. For all load nodes, the sum of the energization state of node i and the virtual power flow from node i to other nodes in all branches containing node i is equal to the state variable of whether node i is powered by an actual power source or a virtual power source, plus the sum of the virtual power flow from other nodes to node i in all branches containing node i. Furthermore, for all branches, the virtual power flow from node i to other nodes in the branch is greater than or equal to the energized state of node i multiplied by a negative set coefficient, and less than or equal to the energized state of node i multiplied by a set coefficient. The sum of the operational status of all branches equals the sum of the energized status of all load nodes and actual power nodes minus the sum of the energized status of all CDG nodes, minus the working status of the virtual power supply of the node connected to the MMC port at the fault feeder, and minus 1. For all load nodes and actual power supply nodes, the state variable of whether node i is powered by an actual power supply or a virtual power supply is greater than or equal to 0 and less than or equal to the working state of the virtual power supply corresponding to node i multiplied by a set coefficient.

[0009] Preferably, the operating state of the virtual power supply is as follows: If node i is an actual power supply node, then the working state of the virtual power supply is multiplied by 1; When the MMC port is fault-free, the fault status of the MMC end is 1; otherwise, it is 0. If node i is the node connected to the SOP, then if the fault status of the MMC port connected to node i is 1, and except for node... If the sum of the fault states of the MMC ports connected to all ports of the SOP is greater than or equal to 1, then the working state of the virtual power supply is 1; otherwise, it is 0. If node i is a CDG node, then the working state of the virtual power supply is greater than or equal to the product of the fault feeder state and the power-on state of node i, and less than or equal to the product of the fault feeder state and the power-on state of node i plus 1 and the difference between the fault feeder state and the fault feeder state. When a FIDN fault occurs at a node When the feeder is in a faulty feeder state, the status is 1; otherwise, it is 0.

[0010] Preferably, if the SOP is a four-terminal SOP, the operating state of the corresponding virtual power supply is linearized by introducing auxiliary variables, specifically: If at least one of the MMC ports other than the MMC port connected to the FIDN fault feeder is working normally, the auxiliary variable is set to 1; otherwise, the auxiliary variable is set to 0. If node i is a node connected to a four-terminal SOP, then the working state of the virtual power supply is less than or equal to the auxiliary variable, and greater than or equal to the fault state of the MMC port connected to node i plus the auxiliary variable minus 1.

[0011] Preferably, the average equivalent output during the fault period is calculated based on the wind-solar combined output scenario corresponding to the fault occurrence time, and is used as the upper limit of the wind-solar DG output, specifically: The probability of occurrence of various wind-solar combined output scenarios set for different seasons was statistically analyzed; Determine the season in which the fault occurred, and based on the probability of occurrence of each wind-solar power combined output scenario, randomly select one wind-solar power combined output scenario through the cumulative probability interval to obtain the daily wind-solar power combined output time-series curve for the corresponding wind-solar power combined output scenario; identify the fault occurrence time and fault end time in the daily wind-solar power combined output time-series curve, and extract the output sequence of each wind-solar power combined DG in the distribution network from the fault occurrence time to the fault end time; the upper limit of the output of the corresponding wind-solar power combined DG is equal to the rated capacity of the corresponding wind-solar power combined DG divided by the total number of sampling points in the output sequence multiplied by the sum of the outputs of all sampling points in the output sequence.

[0012] Preferably, the original power flow constraint is improved based on the upper limit of wind power-solar power generation (DG), specifically as follows: The improved power flow constraint is as follows: node The injected active power equals the sum of the active power output from the corresponding MMC port, the active charging and discharging power of the ESS, the active power output of the CDG, and the output of the wind-solar DG, minus the node power. The product of the active load and the load shedding variable at the node, when a fault occurs, If the load is not removed, the load removal variable is 1; if it is removed, it is 0. node The injected reactive power equals the sum of the reactive power output from the corresponding MMC port, the reactive power charging and discharging power of the ESS, and the reactive power output of the CDG, minus the node's reactive power. The product of reactive load and load shedding variable; Furthermore, the wind power-photovoltaic DG output of node i is less than or equal to the upper limit of the wind power-photovoltaic DG output multiplied by the corresponding node's power-on status; The improved power flow constraints are also transformed into linear constraints through mixed-integer second-order cone programming.

[0013] Preferably, the fault status is updated, specifically as follows: Fault status includes fault operating time, node fault count, node fault accumulation time, and simulation time. Record the fault time of the faulty line. and repair time Update the fault operation time to the original fault operation time plus the fault time. ; For each load node, update the node fault count to the original node fault count plus 1 and the difference between the count and the power supply status of the corresponding load node; then add 1 to the difference between the count and the power supply status of the corresponding load node and the repair time. Multiply the sum of the switching times by the sum of the switching times, add the product of the power supply status of the corresponding load node and the switching time to get the sum; update the node fault accumulation time to the original node fault accumulation time plus the sum. Update the simulation time to the original simulation time plus the failure time. Repair time and switch switching time.

[0014] Preferably, the node reliability index and FIDN reliability index are calculated based on the current fault state, specifically as follows: Node reliability metrics include the expected outage rate and expected outage time of nodes; FIDN reliability metrics include the system average outage frequency, the system average outage time, and the system's expected annual power shortage. The expected power outage rate of a node is obtained by dividing the node fault count by the fault operating time. The expected power outage time of a node is obtained by dividing the cumulative time of node failure by the simulation time limit. The sum of the expected outage rates of all load nodes and the number of users at the corresponding load nodes is divided by the sum of the number of users at all load nodes to obtain the system average outage frequency. The sum of the expected outage rates of all load nodes and the number of users at the corresponding load nodes is divided by the sum of the number of users at all load nodes to obtain the system average outage time. For each load level, the expected power shortage at that load level is obtained by multiplying the outage power of all load nodes, the load factor of the corresponding load level, and the rated load. The expected power shortage at that load level is then multiplied by the duration of the corresponding load level and divided by the total number of hours in a year to obtain the annual expected power shortage at that load level. The annual expected power shortages at all load levels are then summed to obtain the system's annual expected power shortage. A second aspect of this invention proposes a reliability assessment system for flexible interconnected distribution networks considering fault recovery, based on the method described in the first aspect of this invention. This system includes a model building module, a linear transformation module, and a reliability calculation module, specifically: Model building module: used to construct a multi-device collaborative recovery optimization model that takes into account SOP failures with the objective function of maximizing load recovery amount. The constraints of the multi-device collaborative recovery optimization model include topology constraints and power flow constraints based on the improved virtual flow method. Linear transformation module: used to transform nonlinear constraints in the multi-device collaborative recovery optimization model into linear constraints through mixed-integer second-order cone programming; The reliability calculation module is used to sample and generate fault scenarios for feeders and four-terminal SOPs using sequential Monte Carlo simulation. For the currently generated fault scenario, it records the time of the fault occurrence and calculates the average equivalent output during the fault period based on the wind-solar combined output scenario corresponding to the fault occurrence time. This average equivalent output is used as the upper limit of the wind-solar DG output. Based on the upper limit of the wind-solar DG output, the original power flow constraints are improved to obtain a modified multi-device collaborative recovery optimization model. The modified multi-device collaborative recovery optimization model is used for optimal fault recovery. After recovery, the fault status is updated. The fault status includes the simulation time. If the simulation time exceeds the simulation time limit, the expected value of the node's outage rate and the expected value of the outage time are used as the node reliability index. The FIDN reliability index is calculated based on the node reliability index. Otherwise, the above steps are repeated starting from the generation of the fault scenario for feeders and four-terminal SOPs.

[0015] A third aspect of the invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor performing steps using the reliability assessment method for flexible interconnected distribution networks considering fault recovery as described in the first aspect of the invention.

[0016] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, uses the steps of the reliability assessment method for flexible interconnected distribution networks considering fault recovery as described in the first aspect of the present invention.

[0017] The beneficial effects of this invention are as follows: Compared with the prior art, this invention establishes a MISOCP fault recovery model and FIDN reliability assessment method based on an improved virtual flow method, taking into account the uncertainty of SOP failures and the coordination of multiple flexible resource devices. Furthermore, considering wind power-solar uncertainty, it designs an average equivalent output method for the fault period, proposing a comprehensive FIDN reliability assessment method that considers the multi-dimensional uncertainties of wind power, solar power output, and SOP failures, as well as fault recovery. Analysis and comparison of system reliability indicators show that the intermittency of wind power-solar power output and the randomness of SOP failures jointly increase the difficulty of distribution network fault recovery, while the coordinated output of multiple types of flexible resources can effectively improve system reliability, mitigate renewable energy fluctuations, and share the risks brought by SOP failures. The multi-dimensional uncertainty coupling reliability assessment method proposed in this invention can achieve quantitative assessment of FIDN reliability under different resource configuration scenarios, providing a method and approach for resource planning and fault recovery scheduling of distribution networks with flexible interconnection of renewable energy. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of a flexible interconnected distribution network with four-terminal SOPs; Figure 2 A flowchart for FIDN reliability assessment considering SOP failure uncertainty and multi-device collaborative recovery; Figure 3 Flowchart for calculating average equivalent output during the fault period; Figure 4 A flowchart for FIDN reliability assessment considering wind power-solar power output, SOP failure uncertainty, and coordinated recovery; Figure 5 This represents a typical daily wind power output scenario across all four seasons after reductions. Figure 5 (a) is a typical daily wind power output scenario in spring after reduction; Figure 5 (b) is a typical summer day wind power output scenario after reduction; Figure 5 (c) is a typical daily wind power output scenario in autumn after reduction; Figure 5 (d) is a typical daily wind power output scenario in winter after reduction; Figure 6 This represents a typical daily photovoltaic power output scenario across all four seasons after reductions. Figure 6 (a) A typical daily photovoltaic power output scenario in spring after reduction; Figure 6 (b) A typical daily photovoltaic output scenario in summer after reduction; Figure 6 (c) is a typical daily photovoltaic power output scenario in autumn after reduction; Figure 6 (d) is a typical daily photovoltaic output scenario in winter after reduction; Figure 7 A schematic diagram of the improved 37-node system; Figure 8 The curves showing the changes in EENS and SAIDI under different DG capacities; Figure 8 (a) shows the variation curves of EENS under different DG capacities; Figure 8 (b) shows the variation curves of SAIDI under different DG capacities. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0020] Embodiment 1 of the present invention proposes a reliability assessment method and system for flexible interconnected distribution networks considering fault recovery, specifically as follows: 1. Multi-device collaborative recovery optimization model considering SOP failures 1.1 Four-terminal SOP fault model and control mode This embodiment takes a four-terminal SOP as an example, assuming that the capacity and structure of the MMC of each port are the same, and that the power distribution system only considers a single fault.

[0021] (1) Single MMC and dual MMC faults: When a single or dual port fault occurs in a four-terminal SOP, the faulty port is isolated, and the remaining ports are functioning normally. If the feeder where the fault occurs happens to be connected to the faulty MMC, the faulty feeder cannot transfer the load through the SOP; if the feeder where the fault occurs is connected to a normal MMC, at least one normal MMC port among the remaining ports can work together to transfer the load and help restore power supply.

[0022] (2) Three-MMC fault: The four-terminal SOP is in STATCOM mode, and all three faulty MMC ports are blocked and isolated, with the only normal port providing reactive power support. The faulty feeder cannot be restored to power supply through SOP transfer.

[0023] (3) Four MMC failures: If all four MMCs fail at the same time, the entire SOP equipment will be taken out of operation. All MMCs will be locked and isolated. At this time, the SOP will also be unable to transfer the load.

[0024] In summary, a four-terminal SOP (Standard Operating Procedure) has the capability to transfer load only when the feeder where the distribution network fault is located is connected to a normal MMC (Medium-terminal Control) port and at least one of the remaining MMC ports is functioning normally; otherwise, the interrupted load can only be restored through other means. Compared with traditional tie lines and B2B type two-terminal SOPs, this increases the number of feeders that can provide transfer support after a fault, thereby reducing the power outage time at load nodes.

[0025] When FIDN is running normally, none of the nodes connected to the MMC port are unbalanced nodes. At this time, one of the MMC ports is running in unbalanced mode. The mode controls the voltage of the DC bus, while the remaining MMC ports are in PQ mode to control active and reactive power.

[0026] When a fault occurs at a point in the FIDN, if the four-terminal SOP has load transfer capability, the MMC port connected to the feeder where the fault occurred switches to Vf control mode to act as a voltage source and provide stable voltage to the power-loss load. The node where this MMC port is located becomes the balancing node, and the other normal MMC ports operate in... The mode can be either PQ mode or PQ mode to control the DC bus voltage and active and reactive power respectively.

[0027] 1.2 Objective function of multi-device collaborative recovery optimization model considering SOP failure The decision variables of the multi-device collaborative recovery optimization model considering SOP failure include: four-terminal SOP, controllable distributed generator (CDG), output of photovoltaic-storage DG, output of ESS, branch on / off status; node energized status; whether the load is disconnected; branch power flow; voltage and current squares; distributed generator output; SOP power; SOP operating status; ESS output and charging / discharging status.

[0028] The objective function for load transfer and recovery optimization in a flexible interconnected distribution network with four-terminal standard operating procedures (SOPs) after each fault occurs is as follows: For maximum load recovery: (1) In the formula: For nodes Active load at location; Represents a node The value indicates whether the load has been removed. If it has not been removed, the value is 1; if it has been removed, the value is 0.

[0029] 1.3 Constraints of the Multi-device Collaborative Recovery Optimization Model Considering SOP Failure 1) Topological constraints based on the improved virtual flow method At all times during operation, the FIDN should always maintain a radial configuration. After a distribution network fault occurs, multiple devices, including four-terminal SOPs, CDGs, photovoltaic-storage DGs, and ESSs, work together to recover from the fault. Among them, the four-terminal SOPs flexibly interconnect feeders, which may form a ring network. Therefore, this embodiment proposes an improved virtual flow method for FIDN to set radial and connectivity constraints. First, a virtual network of the target FIDN is established, and the node load is set to 1 (the total node load = 1 in the virtual network is a mathematical calculation; in the actual system, the power supply / load nodes are still strictly distinguished by physical definition). When the SOP has load transfer capability, and the node connected to the MMC port at the faulty feeder becomes a balanced node, this node is considered an additional virtual power supply node.

[0030] (2) (3) (4) (5) (6) (7) (8) (9) (10) In the formula: branch road The operational status is set as follows: 1 if connected, 0 if disconnected. Represents a node Is it a node? If the parent node is a valid parent node, set the value to 1; otherwise, set the value to 0. For nodes The energized state is 1 if energized and 0 otherwise. branch road The virtual current flow is a continuous variable; branch road The virtual trend; For nodes Whether it is powered by an actual power source (substation) or a virtual power source, the value is 1 if yes, and 0 otherwise; This indicates the working status of the virtual power supply; it is 1 if the power supply is working and 0 otherwise. The operating status of the virtual power supply of the node connected to the MMC port at the faulty feeder. The node connected to the MMC port at the faulty feeder; For the set of all branches; For the set of faulty branches; For the set of all load nodes; This is the set of actual power supply nodes (substation nodes); The set of nodes connected to CDG; The coefficient is set to be a sufficiently large positive real number.

[0031] Equation (2) is used to constrain a single branch to have only a one-way parent-child relationship, thus avoiding the formation of a loop network; Equation (4) indicates that the node Power can be supplied when there is at least one parent node; Equation (6) is the virtual power flow balance constraint that all load nodes in the virtual network must satisfy; Equation (8) is the virtual power flow of the branch. and branch state variables The coupling constraint is that the virtual power flow is allowed to flow through the branch only when the branch is connected; Equation (9) is the coupling constraint between the number of branches and the node state. The number of connected branches is the number of energized nodes minus the number of working virtual power sources and the number of actual power sources (substations); Equation (10) indicates that the connected nodes can only be powered by the virtual power source when the virtual power source is in working state.

[0032] Virtual power supply working status To improve the core variables of the virtual flow method, detailed definitions are required. For nodes connected to the four-terminal SOP, the definition of this variable, as described in 1.1, needs to be tailored to both FIDN faults and SOP device port faults; for nodes connected to the CDG, Similarly, the definition needs to be based on the fault condition of FIDN and the location of CDG. The specific definitions and constraints are as follows: (11) (12) (13) (14) In the formula: , They are nodes , The status variable of the connected MMC port is 1 if the MMC port is fault-free and 0 if it is faulty. Indicates whether the FIDN fault occurred at the node. If it is the feeder, take 1; otherwise, take 0. It is a set of actual power source (substation) nodes; This is the set of nodes containing all ports of the SOP. To remove nodes All ports of the SOP are located on the node; The set of all nodes connected to CDG.

[0033] For equation (12) of the four-terminal SOP, an auxiliary variable is introduced. Linearization is performed to obtain the relevant constraints: (15) (16) (17) (18) (19) In the formula: Auxiliary variables.

[0034] Equations (15) to (16) are for The value of is restricted and defined to indicate whether at least one of the MMC ports other than the MMC port connected to the FIDN fault feeder is working normally. If so, it is 1; otherwise, it is 0. Equations (17) to (19) ensure that the node at the connection between the fault feeder and the SOP becomes a virtual power source only when the feeder where the FIDN fault is located is connected to the normal MMC port and at least one of the other MMC ports is working normally.

[0035] 2) Operational constraints of the four-terminal SOP When a four-terminal flexible soft switch is put into operation, power loss must be taken into account, while satisfying its own power balance constraints and the capacity constraints of each port: (20) (twenty one) (twenty two) In the formula: For MMC ports; Total number of MMC ports; For MMC port Output active power; For MMC port The output reactive power; For MMC port Active power loss; For MMC port Capacity constraints; For MMC port The power loss coefficient.

[0036] 3) Output and constraints of distributed power sources For distributed generation (DG) with photovoltaic (PV) output, a combined PV and energy storage (ESS) power generation model is adopted to obtain a multi-state output model for DG. Then, a backward scenario reduction technique is used to obtain the final multiple output scenarios and probabilities for the PV-ESS DG.

[0037] Controllable distributed power sources such as micro gas turbines or diesel generators are characterized by high flexibility, rapid start-up, and stable operation. They can quickly respond to load changes and facilitate fault recovery after a FIDN failure. The operating constraints that CDGs need to meet are as follows: (twenty three) (twenty four) In the formula: , They are nodes The active and reactive power outputs of CDG; , They are nodes The maximum active and reactive power output of CDG.

[0038] 4) Operational constraints of energy storage devices An ESS (Emerging Power Supply) can be rapidly deployed after a FIDN (Fixed Grid Network) failure, releasing stored energy quickly to reduce outage time and provide temporary power support for critical equipment and loads, thereby improving system power supply continuity and reliability. During normal distribution network operation, the ESS stores energy to prepare for the next failure. During charging and discharging, the ESS's SOC (State of Charge) should always be maintained within permissible limits.

[0039] (25) (26) (27) (28) (29) (30) (31) (32) (33) In the formula: , They are nodes The active charging and discharging power of the ESS; , , , They are nodes The maximum and minimum active charging and discharging power of the ESS; , They are nodes The reactive charging and discharging power of the ESS; , , , They are nodes The maximum and minimum reactive charging and discharging power of the ESS; For nodes The value is 1 if the energy storage is in a charging state, and 0 otherwise. For nodes The value is 1 if the stored energy is being discharged, and 0 otherwise. For nodes The remaining energy of the ESS; For nodes The capacity of the ESS; This represents the change in the remaining capacity of the ESS after one complete charge-discharge cycle. , They are nodes The maximum and minimum values ​​of the ESS charge level; , They are nodes The charging and discharging efficiency of the ESS; , These represent the fault-free operating time and fault repair time of the faulty line, respectively. This is the set of all ESS connection nodes.

[0040] Equations (25) to (28) ensure that the charging and discharging power of the ESS does not exceed the limit; Equation (29) restricts the ESS to charge and discharge only when the connected node is powered on, and it will only be in one of the states; Equations (30) to (32) are constraints on the remaining capacity of the ESS to avoid deep charging and discharging.

[0041] 5) FIDN power flow constraints In the fault recovery process of flexible interconnected distribution networks, whether in normal operation, fault isolation, or recovery phases, the optimized coordinated output of multiple devices (ESS, distributed generation, and flexible interconnection device four-terminal SOP) must strictly meet power flow constraints. These constraints include power balance, voltage range, and line capacity. Power flow constraints based on the Disflow model ensure that the system remains stable and safe during dynamic adjustments.

[0042] (34) (35) (36) (37) (38) (39) (40) (41) In the formula: , They are nodes Injected active and reactive power; , For the line The active and reactive power transmitted; , For the line The active and reactive power transmitted; , They are nodes The active charging and discharging power and reactive charging and discharging power of the ESS are positive values ​​for the corresponding charging power and negative values ​​for the corresponding discharging power. For nodes reactive load; in equation (36) Let node i be the MMC port connected to node i. Output active power; , For the line Resistance and reactance; , For nodes The active and reactive power outputs of the photovoltaic-storage DG; , For the flow through the line The current and its permissible upper limit; , , For nodes , The voltage and reference value.

[0043] 1.4 Model Processing and FIDN Reliability Assessment Procedure 1.4.1 Linearization of the Optimization Model Because the aforementioned constraints include quadratic and integer terms, conventional algorithms and intelligent optimization algorithms struggle to reach the global optimum and suffer from low computational efficiency. Mixed-integer second-order cone programming (MISOCP) combines the features of MIP and second-order cone programming (SOCP), effectively addressing this problem. Through equivalent substitution, the Big M method, and second-order cone relaxation (SOCR), nonlinear constraints can be transformed into linear constraints, thus converting the original problem into a mixed-integer second-order cone programming model, facilitating the use of commercial solvers to obtain the optimal solution of the objective function.

[0044] 1) Equivalent substitution and the Big M method The power flow constraint equations (34)~(35) and (38)~(40) can be linearized using only equivalent substitution and the Big M method. Auxiliary variables of current and voltage are introduced. , The terms that replace the squares of current and voltage: (42) (43) Combining the Big M method, the power flow constraints (34)~(35) and (38)~(40) can be transformed into the following forms: (44) (45) (46) (47) (48) (49) (50) (51) 2) Second-order cone relaxation Equation (41) cannot be completely linearized using equivalent transformations. Further SOCR processing is required to obtain the standard second-order cone form of equation (41) as follows: (52) Since the domain of the variables in equations (20) and (22) is non-convex, second-order cone relaxation is also required. The transformed constraints are: (53) (54) In summary, the FIDN fault recovery MISOCP model, which considers both four-terminal SOP faults and multi-device collaborative recovery, is as follows:

[0045]

[0046] 1.4.2 FIDN Reliability Assessment Based on SMCS and MISOCP Without considering the uncertainty of wind power-solar power output, as shown in the figure... Figure 2 The method utilizes sequential Monte Carlo simulation for sampling to generate fault scenarios for the feeder and four-terminal SOP, comprehensively capturing fault conditions. For specific fault scenarios, a multi-device MISOCP model is used for optimal fault recovery, and finally, reliability indicators are calculated. This method effectively handles the time-varying nature of SOP failure rates and comprehensively considers the output of recovery resources.

[0047] Since reliability index calculations are based on specific load node failure scenarios, it is necessary to first analyze the load node recovery process. After a FIDN failure occurs, the circuit breaker at the substation outgoing line trips instantaneously, cutting off power to the faulty feeder and causing all load nodes on that feeder to lose power. Subsequently, the first disconnecting switch upstream of the fault opens, isolating the fault and forming a fault isolation zone. After isolation, the circuit breaker recloses, restoring power to the non-faulty areas through network reconstruction. All nodes except the load nodes within the isolation zone regain power. Therefore, nodes in the non-faulty area are affected by "switching-only interruptions," achieving fault isolation and power restoration through the actions of circuit breakers and switches; load nodes in the isolation zone, however, require the disconnecting switch to close after the distribution network fault is fully repaired before power can be restored, thus being affected by "repair-and-switching interruptions." Due to the presence of multiple recovery devices in the FIDN, load nodes can be further divided into three categories based on the degree of impact from the fault: 1) Load nodes in non-faulty areas are affected by "interruption-only switching", and the power outage time is the corresponding switch switching time.

[0048] The load nodes in the fault isolation zone can be divided into recoverable and unrecoverable nodes.

[0049] 2) The recoverable node benefits from the presence of multiple recovery devices, allowing it to regain power before the FIDN fault is completely resolved. Since the recovery devices selected in this embodiment all have rapid response capabilities, their operation time is negligible, and the power outage time is approximately the same as the switch switching time.

[0050] 3) Unrecoverable nodes can only be restored to power after the FIDN fault has been completely cleared. Affected by the "repair and switching interruption", the power outage time is the fault repair time and the switch switching time.

[0051] Based on the above classification of load nodes after a fault, the algorithm flow proposed in this embodiment is as follows: Step 1: Establishing a reliability model.

[0052] Step 2: Obtain network topology and device data. Read the FIDN topology structure; obtain key device data such as CDG capacity, optical storage DG output scenario, and ESS capacity.

[0053] Step 3: Initialization: Set simulation time limit ,initial .

[0054] Step 4: FIDN Fault Scenario Generation. Sequential Monte Carlo simulation sampling is used to calculate the Time To Fault (TTF) and Time To Repair (TTR) for each line. The line with the smallest TTF is identified as the faulty line, and its fault time is recorded. and repair time Random sampling was used to obtain the fault status of all MMCs at the four-terminal SOP.

[0055] Step 5: Fault Matching. Perform fault matching between the FIDN and the four-terminal SOP according to Section 1.1 of this embodiment to determine whether the SOP has load transfer capability.

[0056] Step 6: Fault Recovery Optimization. After a FIDN failure, under the fault recovery MISOCP model established in this embodiment, multiple devices coordinate their output to help the load in the power outage area regain power. If the SOP has a transfer capability, the device will instantly activate to transfer the load using the flexible interconnection between feeders; the CDG, PV-Storage DG, and ESS can all respond quickly with output. Note: PV-Storage DG and ESS can only output power when they have an electrical connection with the main grid.

[0057] Step 7: Load Point Fault Status Recording. Accumulate this information after each FIDN fault optimization. Until trouble-free operating time In the middle, for all load nodes According to its power supply status Update fault counter That is, superposition To Node Fault Counter Middle; superposition Node Failure Time Accumulator Among them This refers to the switch switching time. In this embodiment, ← represents a variable update operation, that is, assigning the value on the right to the variable on the left. The update rules are as follows: (55) (56) (57) Step 8: Simulate time limit judgment. Accumulated to simulation time In the middle, determine whether the simulation time limit has been exceeded. If the limit is exceeded, return to step 4; otherwise, end the simulation and proceed to step 9.

[0058] Step 9: Calculate node reliability metrics and FIDN reliability metrics. Load Nodes Expected power outage rate Expected power outage time The formulas for calculating the system average outage frequency (SAIFI), system average outage duration (SAIDI), and system annual expected energy not supplied (EENS) are as follows: (58) (59) (60) (61) (62) In the formula: For load nodes Number of users at the location; The load level is used to indicate the load condition. For load level The duration; For load level The load factor represents the load level. The load ratio under; It is a set of load levels; For the set of load nodes, Load Node k Power outage capacity, For load nodes k The rated load.

[0059] Step 10: Calculation complete, statistical analysis of the calculation results.

[0060] 2. FIDN Fault Recovery Model Considering Wind-Solar Output Uncertainty 2.1 Average equivalent output during the fault period This embodiment employs a distributed wind-solar combined output scenario with seasonal variations and a 15-minute time resolution to characterize the uncertainty and temporal volatility of renewable energy output. During the sequential Monte Carlo simulation, the timing and duration of system faults are random, and the fault recovery period may span multiple 15-minute output sampling points. Since fault durations are typically short, wind and solar output fluctuate only slightly within a short timeframe. To reduce the computational load of the Monte Carlo simulation and achieve a balance between computational accuracy and simulation efficiency, the average equivalent output during the fault period is adopted. This approximation method has a negligible impact on reliability statistics, effectively reflecting the temporal volatility characteristics of renewable energy output while avoiding the massive computational burden of multi-period rolling optimization, thus significantly improving simulation efficiency. The specific steps are as follows: like Figure 3 As shown, Step 1: Determine the time of the fault occurrence. The season in question. Considering that power distribution network fault simulation often involves multi-year cyclical scenarios, the simulation time can exceed the range of hours in a single year. First, the arbitrary simulation time is calculated by taking the remainder of equation (63). Mapped to cumulative hours per year Assuming a year has 365 days, the total number of hours in a single year is 8760 hours. Further, the time of the fault occurrence is determined according to equation (64). The season is determined according to the Gregorian calendar: March to May is spring, June to August is summer, September to November is autumn, and December to February is winter.

[0061] (63) (64) In the formula: The code represents the season: 1 for spring, 2 for summer, 3 for autumn, and 4 for winter.

[0062] Step 2: Randomly select a typical day scene. Encode by season. Based on this, the probabilities of four scenarios corresponding to the season are extracted as shown in Table 1. Based on the statistical probability distribution of typical sunrise power-making scenarios in this season, the typical sunrise scenario number of this season is randomly selected using the cumulative probability interval matching method. Obtain the corresponding complete typical day's wind power-photovoltaic combined time-series output curve.

[0063] Step 3: Locate the intraday time period in which the first and last moments of the fault recovery occur. Based on... and Locate the time of fault occurrence in the corresponding typical daily wind-solar combined power output curve. and the time of fault termination The time period numbers are respectively and Considering the intraday variation in the combined wind and solar power output on a typical day, this embodiment divides a 24-hour day into 96 consecutive time periods in 15-minute increments, with 00:00-00:15 being the first time period, 00:15-00:30 being the second time period, ..., 23:45-00:00 being the 96th time period.

[0064] Step 4: Extract the wind power-solar DG output sequence. Based on... and Extract all wind-solar DG outputs covered during the fault recovery phase to obtain the wind-solar DG output sequence. ,in For the first The per-unit value of wind power-solar DG output for each coverage period.

[0065] Step 5: Calculate the upper limit of the average equivalent output of wind-solar DG during the fault recovery period. .based on According to equation (65), the upper limit of the equivalent constant output of wind power-photovoltaic DG during the entire fault recovery period is obtained. In each fault recovery optimization, the actual grid-connected output of wind-solar DG ranges from 0 to this equivalent upper limit. Optimize between them.

[0066] (65) In the formula: This refers to the rated capacity of wind power-photovoltaic DG.

[0067] By using the average equivalent output during the fault period as described above, the overall level of renewable energy output during the fault period can be reflected, avoiding random errors caused by single-point values. Furthermore, it eliminates the need to perform multi-period rolling optimization during each fault recovery. While ensuring the accuracy of reliability statistics, it significantly reduces the computational load of large-scale SMCS iterations, thereby significantly improving simulation efficiency.

[0068] 2.2 Fault Recovery Model Correction Considering Uncertainty in Wind Power-Solar Power Output The average equivalent output of wind power-solar DG during the FIDN fault recovery period is determined based on the aforementioned average equivalent output method during the fault period. Subsequently, only a small-scale modification needs to be made to the FIDN fault recovery MISOCP model mentioned above in this embodiment, which considers the four-terminal SOP fault and the multi-device collaborative recovery, to achieve the goal of simultaneously taking into account the uncertainty of wind power-solar power output and the uncertainty of SOP fault.

[0069] In scenario-based distribution network fault recovery, the time-series output curves of wind-solar-hydrogen (DG) power generation under various scenarios represent its maximum available output. The actual grid-connected power is determined by the optimization model between 0 and this upper limit. This study considers this upper limit to be the proposed maximum available output. When the grid cannot fully absorb the load, wind and solar power curtailment is permitted to meet system security constraints. Therefore, this embodiment adds the following operational constraints that wind-solar DG must satisfy to the aforementioned fault recovery MISOCP model: (66) In the formula: For nodes Active power output of wind power-solar DG; For nodes The average equivalent output of wind power-solar DG; It is the set of distribution network nodes connected to wind power-photovoltaic DG.

[0070] Meanwhile, since this embodiment incorporates wind-solar distributed generation (DG) to account for the uncertainty of wind-solar power output, the aforementioned solar-storage DG is correspondingly discarded. Therefore, the original FIDN power flow constraints need to be modified accordingly: (67) (68) The improved power flow constraints are also transformed into linear constraints through mixed-integer second-order cone programming; In summary, the FIDN fault recovery MISOCP model, which takes into account the uncertainties of wind power-solar power output, the uncertainties of four-terminal SOP failures, and the collaborative recovery of multiple devices, is as follows:

[0071]

[0072] 2.3 FIDN Reliability Assessment Process Considering Multi-Dimensional Uncertainties and Fault Recovery The FIDN reliability assessment process proposed in this embodiment, which considers the uncertainty of wind power-solar power output, SOP failure uncertainty, and failure recovery, is as follows: Figure 4 As shown.

[0073] 2.4 Case Analysis 2.4.1 Results of Generating and Reducing Wind Power-Photovoltaic Combined Output Scenarios The generation and reduction were performed using actual operating conditions of a power grid in my country. The system has a total installed capacity of 40270MW, with 3010MW of renewable energy installed capacity, of which wind power and photovoltaic (PV) capacity are approximately 2:3. The year is divided into four seasons: spring, summer, autumn, and winter. Based on the wind-PV joint output function, 300 wind power and PV output scenarios considering the correlation between wind and PV output are generated for each season. K-means clustering algorithm is then used to reduce the number of scenarios, ultimately resulting in 16 typical output scenarios (4 for each season). The reduced scenario diagram is shown below. Figure 5 and Figure 6 As shown ( Figure 5 and Figure 6 (a), (b), (c), and (d) correspond to spring, summer, autumn, and winter, respectively. The probability of each scenario is shown in Table 1.

[0074] Table 1. Probability of occurrence of each typical power output scenario

[0075] 2.4.2 Example Introduction Using the obtained wind-solar combined output scenarios as the data basis for wind-solar DG, an improved 37-bus system is adopted, such as... Figure 7 As shown, the method proposed in this embodiment is verified and analyzed.

[0076] The original 37-node system simulation consisted of 4 feeders, including 1 substation node and 36 load nodes, with a base voltage of 13.2 kV and an operating voltage range of 0.95~1.05 pu. The failure rate of all branches was set to 0.1 / (km·a). Load randomness was established through three load levels, represented by the percentage of peak load, with proportions of 70%, 83%, and 100%, respectively, and each load level lasting for 2000h, 5760h, and 1000h per year, respectively.

[0077] For the port MMC of the SOP, without considering redundancy, each bridge arm is configured with 22 sub-modules, with a 1:1 ratio of half-bridge to full-bridge sub-modules. Both half-bridge and full-bridge have one redundant sub-module. The efficiency is 0.06. Four-terminal SOPs are connected to four feeders to achieve flexible interconnection between feeders. The access points are nodes 11, 15, 25, and 35. The MMC port loss factor is 0.02, and the capacity is 3MW for each. Further, CDG or wind-PV DG with a capacity of 3MW are connected at nodes 5, 22, and 30. An ESS with a capacity of 6MWh is connected at node 8. The maximum charge / discharge power is 2MW, the maximum reactive power compensation power is 2MVar, the charge / discharge efficiency is 0.9, the initial SOC is 0.3, and the upper and lower limits of SOC are 0.9 and 0.1, respectively.

[0078] 2.4.3 Reliability Index Analysis for Different Device Access Scenarios with and without SOP Failure To verify the effectiveness of the proposed algorithm, the following six sets of different recovery device access scenarios were designed for comparative analysis of reliability indicators, specifically set as follows: Scenario 1: Baseline solution for resource recovery without flexibility; Scenario 2: Only SOPs participate in fault recovery; Scenario 3: SOP and CDG participate in fault recovery; Scenario 4: SOP and wind-solar DG participate in fault recovery; Scenario 5: SOP, CDG, and ESS participate in fault recovery; Scenario 6: SOP, wind power-solar DG, and ESS participate in fault recovery.

[0079] Under the ideal scenario of not considering SOP failures, i.e. assuming that the SOP always maintains normal operating condition, the reliability assessment results are shown in Table 2: Table 2 System reliability indicators under different recovery device access scenarios without considering SOP failures

[0080] The reliability assessment results, considering SOP failures, are shown in Table 3: Table 3 System reliability indicators considering different recovery device access scenarios for SOP failures

[0081] Analyzing the trends of EENS and SAIDI in Tables 2 and 3 respectively, it is clear that the gradual integration and coordinated output of flexible recovery resources have a step-by-step optimization effect on FIDN reliability. Scenario 1, as the baseline scheme without flexible recovery resources, shows the highest levels of both EENS and SAIDI. This is because traditional distribution networks lack active recovery mechanisms; after a fault, loads can only wait for power restoration from the upstream grid, resulting in a large outage area, long duration, and poor reliability. However, when SOPs participate in fault recovery, both indicators in Scenario 2 show a significant decrease compared to Scenario 1. This indicates that SOPs, through cross-feeder power sharing and reconfiguring the post-fault network topology, can effectively reduce the outage area and shorten load outage time, improving the distribution network's fault recovery capability and reliability. Further integration of CDG or wind-PV DG on top of SOPs further optimizes reliability compared to Scenario 2, and Scenario 3's indicators are better than Scenario 4's. This difference stems from the difference in output characteristics between traditional controllable DG and renewable energy DG. CDG (Constant Current Generation) output is stable and controllable, providing continuous and predictable power support for outage loads after a fault. In contrast, wind and solar DG output fluctuates due to natural conditions, making its fault recovery support capability relatively unstable. When an ESS (Emergency Safe Grid) is further integrated into the SOP+CDG and SOP+Wind-PV DG configurations, the distribution network reliability indicators reach the optimal level for each corresponding combination, fully demonstrating the ESS's role in smoothing fluctuations and regulating peak and valley loads. For scenario 5, the ESS can work in conjunction with the CDG to further supplement power regulation and shorten fault recovery time. For scenario 6, the ESS can effectively smooth out fluctuations in wind and solar power output, transforming intermittent renewable energy output into stable fault recovery resources, effectively compensating for the reliability shortcomings caused by the uncertainty of wind-PV DG output. Overall, the more complete the combination and configuration of flexible recovery resources, the stronger the distribution network's fault recovery capability and the higher its reliability level.

[0082] A comparative analysis of the reliability assessment results in Tables 2 and 3 reveals that SOP port failures directly lead to varying degrees of reduction in distribution network reliability across different scenarios. This indicates that the SOP, as the core equipment for FIDN fault recovery, has a significant impact on the overall reliability of FIDN due to its own fault status. Therefore, the possibility of SOP failure must be fully considered in FIDN reliability planning and analysis. However, with the gradual integration of DG and ESS, FIDN reliability has effectively recovered. This demonstrates that the combined configuration and coordinated output of multiple types of recovery resources can effectively mitigate risks and enhance the fault tolerance and anti-interference capabilities of the distribution network fault recovery system.

[0083] In summary, improving the reliability of distribution network fault recovery is not simply a matter of adding up single resources, but rather requires constructing a multi-source collaborative fault recovery system to ensure that the distribution network has sufficient fault recovery capabilities and robustness, thereby achieving optimal reliability improvement. Furthermore, given the high penetration of new energy sources, the combined configuration of Standard Operating Procedures (SOP), wind-solar distributed generation (DG), and Safe Storage Systems (ESS) can serve as a preferred solution for distribution network fault recovery resource planning, ensuring the reliability level of the distribution network while achieving new energy consumption.

[0084] 2.4.4 Quantitative Relationship Analysis between Wind Power-Photovoltaic / Controllable DG Capacity and FIDN Reliability To further analyze the impact of DG capacity on FIDN reliability, scenarios 3, 4, and 6 were selected to plot the variation curves of EENS and SAIDI under different DG capacities, as shown below. Figure 8 (a) Figure 8 As shown in (b), the parameter settings of other devices remain unchanged.

[0085] Depend on Figure 8 (a) Figure 8 (b) It can be seen that as the DG capacity gradually increases from 1MW to 10MW, the EENS and SAIDI of the three resource allocation schemes all show a continuous downward trend, and the rate of decline shows a clear marginal decreasing characteristic. In the capacity range of 1~5MW, the EENS of Scenario 3 drops rapidly from 35.345MWh / a to 27.541MWh / a, a decrease of 22.1%, while the EENS decreases of Scenario 4 and Scenario 6 are 3.5% and 2.4%, respectively. The change pattern of the SAIDI index is highly consistent with that of EENS. As the DG capacity increases to 10MW, the SAIDI of Scenario 3 drops from 0.693h / a to 0.463h / a, a decrease of 33.2%, while the SAIDI decreases of Scenario 4 and Scenario 6 are only 9.3% and 6.5%, respectively. This indicates that large-capacity CDG can provide sufficient and certain power support to the outage area after a fault through stable and controllable power output, thereby significantly reducing the power shortage and shortening the average outage duration, and significantly improving the reliability of FIDN. In contrast, wind-solar DG is constrained by natural conditions, and its output is intermittent and fluctuating. Its effect on improving EENS is weaker than that of CDG, and its effect on improving outage duration is limited.

[0086] As capacity increases further, the EENS reduction in Scenario 3 narrows, and the optimization effect of further capacity expansion on EENS tends to plateau. This indicates that excessive capacity expansion not only fails to achieve efficient reliability improvement but may also lead to resource redundancy and waste. Meanwhile, the EENS and SAIDI in Scenario 4 remain between those in Scenario 3 and Scenario 6. This is because, under the same capacity conditions, CDG improves the reliability of FIDN power supply better than wind-solar DG. ESS can suppress wind-solar power output fluctuations through charge and discharge levels, transforming intermittent renewable energy output into more stable fault recovery resources, compensating for the shortcomings caused by the output fluctuations of wind-solar DG, and improving the fault recovery capability and power supply reliability level of distribution networks containing distributed renewable energy.

[0087] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0088] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0089] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0090] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A reliability assessment method for flexible interconnected distribution networks considering fault recovery, characterized in that, include: A multi-device collaborative recovery optimization model considering SOP failures is constructed with the maximum load recovery amount as the objective function. The constraints of the multi-device collaborative recovery optimization model include topology constraints and power flow constraints based on the improved virtual flow method. The nonlinear constraints in the multi-device collaborative recovery optimization model are transformed into linear constraints through mixed integer second-order cone programming. Sampling is performed using sequential Monte Carlo simulation to generate fault scenarios for feeders and four-terminal SOPs. For the currently generated fault scenario, the time of the current fault occurrence is recorded. The average equivalent output during the fault period is calculated by combining the wind power-solar power output scenario corresponding to the time of the fault occurrence, which serves as the upper limit of the wind power-solar power output. Based on the upper limit of the wind power-solar power output, the original power flow constraints are improved to obtain a modified multi-device collaborative recovery optimization model. The modified multi-device collaborative recovery optimization model is used for optimal fault recovery. After recovery, update the fault status, which includes the simulation time. If the simulation time exceeds the simulation time limit, calculate the node reliability index and FIDN reliability index based on the current fault status. Otherwise, repeat the above steps starting from the fault scenario of generating the feeder and four-terminal SOP.

2. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 1, characterized in that: The topological constraints based on the improved virtual flow method are as follows: Construct a virtual network for the target FIDN. When the SOP has load transfer capability and the node connected to the MMC port at the faulty feeder becomes a balanced node, the corresponding node is considered an additional virtual power node. The topology constraints include: the operational status of a faulty branch is 0; for a non-faulty branch, if either of the two nodes of the branch is the parent node of the other node, the operational status of the corresponding branch is 1, otherwise it is 0; for all actual power supply nodes, the energized status of the node is 1; for all load nodes, there is at most one parent node, and when a parent node exists, the energized status of the node is 1. For all load nodes, the sum of the energization state of node i and the virtual power flow from node i to other nodes in all branches containing node i is equal to the state variable of whether node i is powered by an actual power source or a virtual power source, plus the sum of the virtual power flow from other nodes to node i in all branches containing node i. Furthermore, for all branches, the virtual power flow from node i to other nodes in the branch is greater than or equal to the energized state of node i multiplied by a negative set coefficient, and less than or equal to the energized state of node i multiplied by a set coefficient. The sum of the operational status of all branches equals the sum of the energized status of all load nodes and actual power nodes minus the sum of the energized status of all CDG nodes, minus the working status of the virtual power supply of the node connected to the MMC port at the fault feeder, and minus 1. For all load nodes and actual power supply nodes, the state variable of whether node i is powered by an actual power supply or a virtual power supply is greater than or equal to 0 and less than or equal to the working state of the virtual power supply corresponding to node i multiplied by a set coefficient.

3. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 2, characterized in that: The specific operating state of the virtual power supply is as follows: If node i is an actual power supply node, then the working state of the virtual power supply is multiplied by 1; When the MMC port is fault-free, the fault status of the MMC end is 1; otherwise, it is 0. If node i is the node connected to the SOP, then if the fault status of the MMC port connected to node i is 1, and except for node... If the sum of the fault states of the MMC ports connected to all ports of the SOP is greater than or equal to 1, then the working state of the virtual power supply is 1; otherwise, it is 0. If node i is a CDG node, then the working state of the virtual power supply is greater than or equal to the product of the fault feeder state and the power-on state of node i, and less than or equal to the product of the fault feeder state and the power-on state of node i plus 1 and the difference between the fault feeder state and the fault feeder state. When a FIDN failure occurs at a node When the feeder is in a faulty feeder state, the status is 1; otherwise, it is 0.

4. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 3, characterized in that: If the SOP is a four-terminal SOP, the operating state of the corresponding virtual power supply is linearized by introducing auxiliary variables, specifically: If at least one of the MMC ports other than the MMC port connected to the FIDN fault feeder is working normally, the auxiliary variable is set to 1; otherwise, the auxiliary variable is set to 0. If node i is a node connected to a four-terminal SOP, then the working state of the virtual power supply is less than or equal to the auxiliary variable, and greater than or equal to the fault state of the MMC port connected to node i plus the auxiliary variable minus 1.

5. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 1, characterized in that: The average equivalent output during the fault period is calculated based on the wind-solar combined output scenario corresponding to the time of the fault, and is used as the upper limit of the wind-solar DG output. Specifically: The probability of occurrence of various wind-solar combined output scenarios set for different seasons was statistically analyzed; Determine the season in which the fault occurred, and based on the probability of occurrence of each wind-solar power combined output scenario, randomly select one wind-solar power combined output scenario through the cumulative probability interval to obtain the daily wind-solar power combined output time-series curve for the corresponding wind-solar power combined output scenario; identify the fault occurrence time and fault end time in the daily wind-solar power combined output time-series curve, and extract the output sequence of each wind-solar power combined DG in the distribution network from the fault occurrence time to the fault end time; the upper limit of the output of the corresponding wind-solar power combined DG is equal to the rated capacity of the corresponding wind-solar power combined DG divided by the total number of sampling points in the output sequence multiplied by the sum of the outputs of all sampling points in the output sequence.

6. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 5, characterized in that: The original power flow constraint is improved based on the upper limit of wind-solar DG output, specifically as follows: The improved power flow constraint is as follows: node The injected active power equals the sum of the active power output from the corresponding MMC port, the active charging and discharging power of the ESS, the active power output of the CDG, and the output of the wind-solar DG, minus the node power. The product of the active load and the load shedding variable at the node, when a fault occurs, If the load is not removed, the load removal variable is 1; if it is removed, it is 0. node The injected reactive power equals the sum of the reactive power output from the corresponding MMC port, the reactive power charging and discharging power of the ESS, and the reactive power output of the CDG, minus the node's reactive power. The product of reactive load and load shedding variable; Furthermore, the wind power-photovoltaic DG output of node i is less than or equal to the upper limit of the wind power-photovoltaic DG output multiplied by the corresponding node's power-on status; The improved power flow constraints are also transformed into linear constraints through mixed-integer second-order cone programming.

7. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 1, characterized in that: Update the fault status as follows: Fault status includes fault operating time, node fault count, node fault accumulation time, and simulation time. Record the fault time of the faulty line. and repair time Update the fault operation time to the original fault operation time plus the fault time. ; For each load node, update the node fault count to the original node fault count plus 1 and the difference between the count and the power supply status of the corresponding load node; then add 1 to the difference between the count and the power supply status of the corresponding load node and the repair time. Multiply the sum of the switching times by the sum of the switching times, add the product of the power supply status of the corresponding load node and the switching time to get the sum; update the node fault accumulation time to the original node fault accumulation time plus the sum. Update the simulation time to the original simulation time plus the failure time. Repair time and switch switching time.

8. The reliability assessment method for flexible interconnected distribution networks considering fault recovery according to claim 7, characterized in that: Based on the current fault state, calculate the node reliability index and the FIDN reliability index, specifically: Node reliability metrics include the expected outage rate and expected outage time of nodes; FIDN reliability metrics include the system average outage frequency, the system average outage time, and the system's expected annual power shortage. The expected power outage rate of a node is obtained by dividing the node fault count by the fault operating time. The expected power outage time of a node is obtained by dividing the cumulative time of node failure by the simulation time limit. The sum of the expected outage rates of all load nodes and the number of users at the corresponding load nodes, divided by the sum of the number of users at all load nodes, is used as the system average outage frequency. The sum of the expected outage rates of all load nodes and the number of users at the corresponding load nodes is divided by the sum of the number of users at all load nodes to obtain the system average outage time. For each load level, the expected power shortage at the corresponding load level is obtained by superimposing the outage power of all load nodes, the load factor of the corresponding load level, and the rated load. The expected power shortage at the corresponding load level is calculated by multiplying the expected power shortage at the corresponding load level by the duration of the corresponding load level and then dividing by the total number of hours in a year. The annual expected power shortage at the corresponding load level is obtained by superimposing the annual expected power shortage at all load levels.

9. A reliability assessment system for flexible interconnected distribution networks considering fault recovery based on the method of any one of claims 1-8, comprising a model building module, a linear transformation module, and a reliability calculation module, characterized in that: Model building module: used to construct a multi-device collaborative recovery optimization model that takes into account SOP failures with the objective function of maximizing load recovery amount. The constraints of the multi-device collaborative recovery optimization model include topology constraints and power flow constraints based on the improved virtual flow method. Linear transformation module: used to transform nonlinear constraints in the multi-device collaborative recovery optimization model into linear constraints through mixed-integer second-order cone programming; Reliability calculation module: Used to sample using sequential Monte Carlo simulation to generate fault scenarios for feeders and four-terminal SOPs. For the currently generated fault scenario, the current fault occurrence time is recorded. Combined with the wind-solar power output scenario corresponding to the fault occurrence time, the average equivalent output during the fault period is calculated as the upper limit of the wind-solar DG output. Based on the upper limit of the wind-solar DG output, the original power flow constraints are improved to obtain the modified multi-device collaborative recovery optimization model. The modified multi-device collaborative recovery optimization model is used for optimal fault recovery. After recovery, update the fault status, which includes the simulation time. If the simulation time exceeds the simulation time limit, use the expected value of the node's outage rate and the expected value of the outage time as the node reliability index, and calculate the FIDN reliability index based on the node reliability index. Otherwise, repeat the above steps starting from the fault scenario of generating the feeder and four-terminal SOP.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: The processor performs the steps of using the reliability assessment method for flexible interconnected distribution networks that takes into account fault recovery as described in any one of claims 1 to 8.

11. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed by a processor, uses the steps of the reliability assessment method for flexible interconnected distribution networks considering fault recovery as described in any one of claims 1 to 8.

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