An active power distribution network fault recovery method based on a fusion multi-agent architecture

Abstract

The application discloses a kind of active distribution network fault recovery methods of fusion multi-agent architecture, including sequentially connected input unit, topological partition unit, fault recovery unit and output unit;Input unit obtains distribution network frame data, distribution network node data, mobile energy storage vehicle's distributed resource data and PMU measurement data;Topological partition unit establishes active distribution network network topology relationship according to the data characteristics provided by input unit and PMU optimization configuration, and carries out two-stage network partition to active distribution network;Fault recovery unit constructs group fault repair power recovery model with power outage economic loss, repair time and positive and negative sequence current deviation value index comprehensive optimization as target, realizes the real-time optimization of fault repair;The output unit is the optimal fault repair power recovery strategy of output entire fault cycle.The application can output optimal emergency repair strategy in entire fault cycle.

Description

Technical Field

[0001] This invention relates to an active distribution network fault recovery method with a converged multi-agent architecture for emergency power restoration in the field of distribution network emergency repair. Background Technology

[0002] The safe and stable operation of the power grid currently faces numerous challenges. On the one hand, the source, grid, and load structures of the new power system have undergone significant changes. Factors such as the dominance of new energy sources, high levels of power electronics, and high cyber-physical integration are continuously increasing the complexity of the power grid structure and operation modes. There is an urgent need to introduce synchronous phasor measurement devices (PMUs) with real-time performance, high precision, synchronization, and comprehensive data to overcome the problems commonly found in conventional measurement devices in traditional power grids, such as long acquisition cycles, asynchronous measurements, and weak dynamics. This would enhance the new power grid's ability to dynamically perceive the high-density real-time operating status and security situation factors caused by source-load uncertainties. On the other hand, with the increasing severity of climate change and the international situation, the frequency of unconventional events such as extreme natural disasters and deliberate attacks is gradually increasing. The external environment for power grid operation is deteriorating, easily inducing power equipment accidents and power system disasters, and increasing the risk of cascading fault propagation. Therefore, it is necessary to accelerate the implementation of major measures to improve the emergency recovery capabilities of the distribution network, thereby ensuring the power safety of my country's power grid and its users.

[0003] A search of existing literature and patents revealed that, among the existing literature, Pan Gaofeng, Wang Xinghua, Peng Xiangang, et al., published "Research on Power Grid Reactive Power Partitioning and Dominant Node Selection Method Based on Community Structure Theory" in "Power System Protection and Control" (2013, 41(22):32-37), which proposes a power system network topology partitioning model based on edge similarity weights based on the community structure partitioning algorithm principle in complex network theory, and introduces a community structure modular index to dynamically evaluate the reactive power balance status of each partition of the power grid. Li Dahu, Yuan Zhijun, He Jun, et al., published "Power Grid Operation Risk Situation Awareness Method for Typhoon Weather" in "High Voltage Engineering" (2021, 47(07):2301-2311), which uses equipment failure probability models, power grid time-varying risk propagation models, and optimal DC power flow models to quantitatively evaluate the real-time and future operation risk status of power grid operation status elements from both probability and consequence perspectives. Tian Shuxin, Li Kunpeng, Wei Shurong, et al., published "A Method for Security Situation Awareness of Distribution Network Based on Synchronous Phasor Measurement Device" in the Proceedings of the Chinese Society for Electrical Engineering (2021, 41(02): 617-632). This method constructs a hierarchical model of the distribution network topology based on the node matrix and variable adjacency matrix configured by the distribution network PMU, and then forms a multi-layer synchronous parallel sensing method integrating LSTM, enabling prediction and early warning of the security operation status of the distribution network under normal operation and fault disturbances. Li Hengxuan, Sun Haishun, et al., published "Multi-Agent Fault Self-Recovery System for Distribution Network with Distributed Power Sources" in the Proceedings of the Chinese Society for Electrical Engineering (2012, 32(04): 49-56). This method treats the bus as a kind of agent, and establishes a fully distributed multi-agent system to transmit and coordinate distributed information after a fault occurs, thereby achieving global recovery of the lost power load. Xu Yan, Zhang Hui, Ma Tianxiang, et al., published "Coordination and Optimization Strategy for Emergency Recovery and Repair of Distribution Networks with Distributed Generation" (2021, 45(22):38-46) in *Automation of Electric Power Systems*. They constructed a discrete probability model of distributed generation (DG) output and proposed an active coordination and optimization strategy for emergency recovery and repair of distribution network faults that considers the uncertainty of DG output, which improved the utilization rate of DG to a certain extent. He Jun, Yu Hua, Deng Changhong, et al., published "Power Supply Guarantee Strategy for Key Area Power Grids Based on Situational Awareness under Extreme Weather" (2022, 48(4):1277-1285) in *High Voltage Engineering*. This paper utilizes DG output prediction, energy storage, and electric vehicle power station charging and discharging prediction to deeply perceive the source and load of the power grid in key areas. It then establishes a power supply recovery strategy that considers the cost of load power supply guarantee and the cost of load loss, promoting the power grid to repair and restore power in a favorable direction.Among existing patents, the authorized invention patent "An Optimization Algorithm for Active Distribution Network Load Fault Recovery Strategy" by Xie Hua, Xu Yin, and Wang Yifan of Beijing Jiaotong University constructs a multi-period load fault recovery strategy optimization model and dynamically adjusts the load recovery scheme using the acquired real-time information. The authorized invention patent "A Method for a Unified Active Distribution Network Fault Recovery Model Considering Reconfiguration and Islanding Simultaneously" by Tang Yida, Gu Wei of Southeast University, and Sheng Wanxing of China Electric Power Research Institute Co., Ltd., constructs a unified mathematical model that includes power flow constraints, "virtual power flow" connectivity constraints, and consideration of reconfiguration and islanding based on the acquisition of power grid fault information and distribution network information, thereby formulating fault recovery operation strategies covering more possibilities. The authorized invention patent of Yang Lijun, Cao Yujie, Zhang Zizhen, et al. from Yanshan University, entitled "An Active Distribution Network Fault Recovery Strategy Considering Internal and External Game Theory," establishes a fault recovery model considering both internal and external game theory based on the principle of balancing the interests of supply and demand during the recovery process. It transforms the fault recovery problem into a game problem among multiple recovery schemes, using evaluation indicators such as network loss and minimum node voltage values ​​to determine the optimal fault recovery scheme. While the above literature and patents study fault recovery methods from different perspectives, they do not comprehensively consider the combined effects of real-time random disturbances of distributed resources and cluster faults under extreme events on active distribution network fault emergency recovery schemes. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an active distribution network fault recovery method that integrates a multi-agent architecture. This method is an active distribution network group fault recovery method that deeply mines the real-time measurement and information processing capabilities of the PMU, thereby outputting the optimal emergency repair strategy throughout the entire fault cycle.

[0005] One technical solution to achieve the above objective is: an active distribution network fault recovery method integrating a multi-agent architecture, comprising an input unit, a topology partitioning unit, a fault recovery unit, and an output unit connected in sequence;

[0006] The input unit acquires distribution network structure data, distribution network node data, distributed resource data including mobile energy storage vehicles, and PMU measurement data. The PMU measurement data refers to the measured values ​​of voltage phasors, current phasors, power, positive sequence current, and negative sequence current of distributed power sources and loads obtained by high-density sampling of PMUs.

[0007] The topology partitioning unit establishes the active distribution network topology based on the data characteristics provided by the input unit and the PMU optimization configuration, using the graph duality theory in graph theory. Then, it performs two-stage network partitioning of the active distribution network based on the hybrid search algorithm and PMU partitioning support.

[0008] The fault recovery unit proposes a PMU multi-agent communication architecture based on network partitioning to construct a group fault emergency repair power supply model with the goal of comprehensively optimizing the indicators of power outage economic loss, repair time and positive and negative sequence current deviation, thereby realizing real-time optimization of fault repair.

[0009] The output unit outputs the optimal fault repair and power restoration strategy for the entire fault cycle.

[0010] Furthermore, the topology partitioning unit consists of a PMU optimization configuration subunit, a network partitioning initial screening subunit, and a network partitioning fine screening subunit. The PMU optimization configuration subunit combines the active distribution network topology diagram with the known limited PMU configurations, and uses a graph ordering system centered on the PMU configuration nodes to establish a radial network structure diagram of the active distribution network. Assuming that the total number of network nodes is n when the active distribution network is operating normally, and there are m PMUs configured, the network is partitioned based on the nodes of the configured PMUs. At the same time, a tree and a degree function are introduced. The degree function of the tree is defined as d(V), which represents the degree of vertex V. If d(V) = 0, the node is an isolated node; if d(V) = 1, the node is a leaf node; if d(V) > 1, the node is a branch node.

[0011] Furthermore, the network partitioning initial screening subunit uses a search algorithm to perform a first-stage traversal screening of the network structure, the specific steps of which are as follows:

[0012] Step 1: Network simplification. After obtaining the network topology and PMU deployment information in the PMU optimization configuration subunit, select a PMU node j as the root node. This node is the configuration PMU node.

[0013] Meanwhile, we define criterion 1: the node is a configured PMU node; criterion 2: d(V) = 0; criterion 3: d(V) > 1; any node in the network is retained if it satisfies one of these criteria; otherwise, the node is removed, and finally, the simplified tree of the distribution network is obtained.

[0014] Step 2: Perform a global BFS, using the known PMU-configured node as the root node. Expand outwards using a breadth-first search algorithm to find the second-level and third-level root nodes. If the secondary root node d(V) of the current node is 1, jump to step 3; if d(V) > 1, continue the current search; if d(V) = 0, stop the search of the current branch.

[0015] Step 3: Local DFS. After completing one breadth-first search, perform a local depth-first search on each leaf branch where the secondary root node is located. When a node with d(V) > 1 is found, jump back to step 2. If a node with d(V) = 1 is found, continue the current search. If a node with d(V) = 0 is found, stop the search of the current branch.

[0016] Step 4: Determine if the search is complete. For the current root node, the search stops when the degree function value of all nodes found at the same level is 0.

[0017] Step 5: Initially screen the partitions where nodes are located. For any node, if there are no other PMUs on the unique topology connection between the node and the current node j, then the node may belong to the PMU partition where node j is located, and it is regarded as a node to be partitioned; otherwise, the node must not belong to the PMU partition where node j is located.

[0018] Step 6: Select the next node j to configure PMU and repeat the above process, where j = j + 1, j = 1, 2, ..., m; until the recursive loop of all j is completed, output the first stage partition screening results of the entire network.

[0019] Furthermore, the network partitioning fine screening subunit uses the PMU partitioning support index to refine the initial network partitioning results, forming a reasonable active distribution network partitioning optimization scheme. The specific method is as follows:

[0020] First, we can obtain the following from the linear Newton-Lafferty power flow model:

[0021]

[0022] By setting ΔP = 0 and ΔQ = 0 respectively, we can simplify to obtain the sensitivity matrix of voltage amplitude-reactive power and the sensitivity matrix of voltage phase angle-active power. Furthermore, we can define the reactive and active electrical distances at nodes i and j as follows:

[0023]

[0024] In the formula,

[0025] In order to comprehensively utilize the various situational factors provided by PMU measurements, the reactive electrical distance D ij and active electrical distance B ij By performing a weighted summation, the comprehensive electrical distance H between nodes i and j is obtained. ij for:

[0026] H ij =kD ij +(1-k)B ij

[0027] In the formula, k and 1-k correspond to the weight values ​​of reactive electrical distance and active electrical distance, respectively;

[0028] Comprehensive electrical distance H ijThe larger the value, the stronger the coupling between nodes i and j, and the closer the connection. The goal of network partitioning is to make the electrical quantities between nodes within the same partition closely connected and have a strong coupling, i.e., a larger overall electrical distance. In contrast, between partitions, the electrical quantities between different nodes are sparsely connected and have a weak coupling, i.e., a smaller overall electrical distance.

[0029] Secondly, let the partition where a node j with a PMU configuration is located be A. k Furthermore, each partition has exactly one node configured with a PMU; based on this PMU deployment principle, the comprehensive electrical distance H ij The larger the value, the closer the electrical connection between node i and node j configured with the PMU, and therefore node i belongs to A. k The greater the support of the partition, the more likely node i belongs to A. k Support α i (A k The size of the integral electrical distance H ij Proportional;

[0030] Given α i (A k ) and H ij Functional relation

[0031]

[0032] To ensure that the support level is proportional to the corresponding comprehensive electrical distance, the above formula can be derived to satisfy the following conditions: Condition 1, 0 < α0 < 1; Condition 2, Condition 3,

[0033] It can be seen from condition 1 and condition 2 that if H ij =0, then α i (A k When the total electrical distance is 0, node i is at a distance of 0 from A. k The partition's support is 0, meaning node i does not belong to A at all. k Partitioning; and as can be seen from condition 3, when the comprehensive electrical distance is infinite, node i is paired with A k The partition support is maximized, and node i belongs entirely to A. k Partitioning;

[0034] The function can be defined as:

[0035]

[0036] In the formula, r, β, and τ are correlation coefficients, with r taking the value of 0.5 and β and τ taking the value of 1.

[0037] This allows us to calculate the support level of all nodes i in the system for nodes j in partition k that are configured with PMUs, and then perform data normalization on this support.

[0038]

[0039] The support levels of each node to each PMU node in the system given by the above formula are arranged in descending order, and the node to be partitioned is assigned to the partition corresponding to the maximum support. The loop is iterated until all nodes in the system are traversed, thereby determining the partition to which each node belongs.

[0040] Furthermore, the fault recovery unit includes a PMU multi-agent architecture sub-unit, a positive and negative sequence current deviation value sub-unit, and a multi-fault emergency repair optimization model sub-unit.

[0041] Furthermore, the PMU multi-agent architecture subunit utilizes a multi-functional PMU information transmission communication architecture, using the PMU as a proxy for each network partition to achieve real-time reporting and decision-making of fault information. Addressing the inconsistency between the time scale of PMU high-frequency sampling data and the time scale of fault recovery low-frequency data, this method uses a weighted summation method to fuse PMU high-frequency sampling data into low-frequency information during the fault recovery low-frequency interval t to t+1. The specific formula is as follows:

[0042]

[0043] In the formula, η is the number of high-frequency data points included in a low-frequency time interval; B(j,λ) is the weighting function; z uj The data consists of high-frequency sampling data from a PMU with multiple variables; λ is an undetermined parameter that determines the approximate shape of the weighting function; if λ = 0, it indicates an equal-weighted form; if λ < 0, it indicates that z is smaller. uj Obtain a larger weight; if λ>0, it indicates a larger z. uj To gain a larger weight;

[0044] After processing the data using the above formula, a power curve containing source load measurement information can be obtained, and a time-varying model of source load power can then be constructed:

[0045]

[0046] In the formula, F i (t) represents the power value of node i in time period t; f i (x) is the curve function of the DG or load at node i.

[0047] Furthermore, the positive and negative sequence current deviation value subunit, based on the information provided by the PMU information acquisition agent and switch agent in the PMU-MAS, utilizes the PMU device of the active distribution network partition to perform real-time measurement of the positive and negative sequence currents within the partition for three power frequency cycles after the fault occurs, and calculates the positive and negative sequence current deviation value to characterize the fault state repair effect. The specific method is as follows:

[0048]

[0049] In the formula, Y i It is the positive-sequence admittance of node i before the fault; I PMU,i1 It is the measured value of the positive sequence current injected into node i provided by the PMU information acquisition agent; I PMU,i2 It is the measured value of the negative sequence current injected into node i provided by the PMU information acquisition agent; U′ f,i 、Y′ f,i These are the voltage value of node i and the positive sequence node admittance after the fault occurs, respectively; n is the total number of faulty lines or adjacent nodes corresponding to fault point k.

[0050] Furthermore, the multi-fault emergency repair optimization model subunit, combined with fixed energy storage, mobile energy storage, and PMU information acquisition agent, establishes an active distribution network cluster fault emergency repair optimization model with the objective of minimizing the comprehensive economic loss corresponding to the power outage economic loss, repair time, and positive and negative sequence current deviation values. The specific method is as follows:

[0051] First, the objective function of the active distribution network multi-fault emergency repair optimization model is formed;

[0052] f=min(f1(X)+λ1f2(X)+λ2f3(X))

[0053]

[0054] f2(X) = max{T1 T2 ... T N}

[0055]

[0056]

[0057] In the formula, X = (x1, x2, ... x m) represents the repair sequence of the faulty nodes; m represents the total number of faulty nodes; f1(X), f2(X), and f3(X) represent the economic loss caused by the power outage, the maximum repair time, and the positive and negative sequence current deviation, respectively; λ1 and λ2 represent the economic loss per unit time and the economic loss corresponding to the unit positive and negative sequence current deviation. To ensure that the optimized repair results can restore system power supply as quickly as possible and ensure the overall network operation status of the partitioned PMU is satisfactory, λ1 and λ2 can be taken as large values; p is the electricity price; i is the fault repair sequence; T(x i ) is the faulty node x i The duration of the fault; j represents the importance of different fault nodes; ω j For weights; L j (x i ) and L′ j (x i ) is the fault number x i The power loss of uncontrollable loads with importance level j and the power provided by distributed resources; N is the number of repair teams; T i It is the time spent by the emergency repair team i from the start to the end of the repair; t k t is the time taken to repair the kth fault; k-1→k t is the travel time for repair team i to move from the (k-1)th fault point to the kth fault point. 0→1 It is the travel time from the starting point to the first point of failure for the emergency repair team;

[0058] Then, the constraints are determined, specifically including:

[0059] Constraint 1: Energy storage charging and discharging constraints.

[0060]

[0061] In the formula, P i c.max P i d.max These represent the upper limits for charging and discharging energy stored at node i; These are 0-1 type variables, representing the flag bits for energy storage charging and discharging at node i during time period t.

[0062] Constraint 2, Constraints related to mobile energy storage systems:

[0063] The spatiotemporal transfer characteristics of mobile energy storage system dispatch are as follows:

[0064]

[0065] In the formula, L ij (t) represents the status flag of the mobile energy storage system during the journey from station i to station j, when L ijWhen (t) = 1, it means that at time t, the mobile energy storage system is on its way from station i to station j; otherwise, L ij (t) = 0 indicates that it is not present; tr ij The formula represents the time taken to move from station i to station j; T is the total scheduling time; and S is the set of stations. The above formula constrains the relationship between the mobile energy storage system and the stations during its movement.

[0066] The charge and discharge characteristics of the mobile energy storage system are as follows:

[0067]

[0068] In the formula, These represent the charging and discharging flags of MESS at station i at time t, and are 0-1 type variables; This indicates the maximum charging power and maximum discharging power of MESS;

[0069] Constraint 3, Topological Constraint:

[0070] After the fault is repaired, the distribution network topology, excluding DG, must meet the following requirements:

[0071] g k ∈G k

[0072] In the formula, g k This refers to the current operating structure of the power distribution network; G k It is the collection of all radial structures in a power distribution network;

[0073] Constraint 4, Branch Flow Constraint:

[0074] Establish a Distflow power flow model suitable for radial distribution networks:

[0075]

[0076]

[0077]

[0078]

[0079] In the formula, ψ(i) represents the set of end nodes of the branch with node i as the first node; π(i) represents the set of beginning nodes of the branch with node i as the last node; R ki X ki These represent the resistance and reactance values ​​of branch ki, respectively; I ki (t) represents the current flowing through branch ki at time t; P i (t), Q i(t) represents the active power and reactive power injected by node i at time t, respectively; P Load.i (t), Q Load.i (t) represents the active power and reactive power of the load at node i at time t, respectively; P DG.i (t), Q DG.i (t) represents the active power and reactive power output by the distributed power source port connected to node i at time t; and These are the charging active power, discharging active power, charging reactive power, and discharging reactive power of MESS, respectively. and These are the active power for charging, active power for discharging, reactive power for charging, and reactive power for discharging of stationary energy storage, respectively.

[0080] Constraint 5, Safe Operation Constraint:

[0081]

[0082] In the formula, U i,t Operating voltage; I ij,t This is the operating current; and U i,t These represent the upper and lower limits of the voltage at node i during time period t, respectively. This represents the upper limit of the current in branch ij during time period t;

[0083] Constraint 6, Power Constraint within the Island:

[0084]

[0085] In the formula, D is the set of nodes within the island; n is the number of nodes within the island; P DG,t It is the output value of the distributed power source in time period t; L i,t It represents the load of node i within the island during time period t;

[0086] Constraint 7, Emergency Repair Resource Constraints:

[0087] χ≤Ω

[0088] In the formula, χ represents the resources consumed during emergency repair of a certain fault; Ω represents the total amount of resources provided for this emergency repair task.

[0089] Finally, in the emergency power restoration model, since the power flow constraints are nonlinear, the model belongs to a mixed-integer nonlinear programming problem, which is difficult for the solver to solve directly. To address this, a second-order cone relaxation method is used to enable the solver to solve the problem. The specific method is as follows:

[0090] use and Replace the quadratic terms in the Distflow power flow constraints and safety constraints:

[0091]

[0092] Constraints 4 and 5 then transform into the following form:

[0093]

[0094]

[0095]

[0096]

[0097] After the above processing, the calculation formulas for power and voltage / current are still non-convex. Using a second-order cone relaxation technique, they are transformed into the following second-order cone form:

[0098]

[0099] After coneification, the mixed-integer nonlinear programming model has been transformed into a mixed-integer second-order cone programming model, which is then processed using the solver CPLEX.

[0100] Furthermore, the output unit refers to the application of the established multi-fault repair model to solve for emergency repair and power restoration schemes for clustered faults under extreme events, and the use of the PMU multi-agent architecture to provide real-time updates to the repair teams and distributed resources throughout the fault cycle.

[0101] The present invention provides an active distribution network fault recovery method integrating a multi-agent architecture. After a sudden new fault occurs, the repair scheme of the PMU multi-agent system is updated, enabling the team to achieve dynamic repair during the emergency repair process, improving repair efficiency, shortening the overall repair time, reducing the economic losses caused by load outages, and enhancing the power supply reliability of the power grid. Attached Figure Description

[0102] Figure 1 This is a flowchart illustrating an active distribution network fault recovery method integrating a multi-agent architecture according to the present invention.

[0103] Figure 2 PMU multi-agent architecture diagram;

[0104] Figure 3 This is the topology of the PG&E69 active distribution network system;

[0105] Figure 4 The positive and negative sequence current deviation values ​​of each node at the instant the fault occurs;

[0106] Figure 5This is a structural diagram of a sudden new fault in the PG&E69 active distribution network system. Detailed Implementation

[0107] To better understand the technical solution of the present invention, detailed descriptions are provided below through specific embodiments:

[0108] This invention discloses an active distribution network fault recovery method integrating a multi-agent architecture. First, a topology traversal search is performed on the active distribution network with configured PMUs, and a two-stage network partitioning model of the active distribution network is established using PMU partition support that integrates comprehensive electrical distance. Then, an ADN cluster fault scenario under extreme events is set up, and a PMU multi-agent communication architecture is constructed. Finally, a fault emergency repair and power restoration model considering the PMU multi-agent architecture is established, forming an emergency repair and power restoration strategy with the comprehensive optimization of power outage economic losses, repair time, and positive and negative sequence current deviation values ​​as its objectives. This achieves real-time repair optimization and dynamic adjustment of active distribution network fault recovery.

[0109] Please see Figure 1 The flowchart of the active distribution network fault recovery method with integrated multi-agent architecture of the present invention is shown in the figure.

[0110] like Figure 1 As shown, an active distribution network fault recovery method integrating a multi-agent architecture includes an input unit 1, a topology partitioning unit 2, a fault recovery unit 3, and an output unit 4 connected in sequence.

[0111] The input unit 1 acquires data such as distribution network structure data, distribution network node data, distributed resource data including mobile energy storage vehicles, and PMU measurement data. The PMU measurement data refers to the measured values ​​of distributed power source and load voltage phasors, current phasors, power, positive sequence current, and negative sequence current obtained by high-density sampling using PMU.

[0112] The topology partitioning unit 2 establishes the active distribution network topology relationship based on the data characteristics and PMU optimization configuration provided by the input unit 1 and the graph duality theory in graph theory. Then, it performs two-stage network partitioning of the active distribution network based on the hybrid search algorithm and PMU partition support.

[0113] The fault recovery unit 3 proposes a PMU multi-agent communication architecture based on network partitioning to construct a group fault emergency repair power supply model with the goal of comprehensively optimizing the indicators of power outage economic loss, repair time and positive and negative sequence current deviation, thereby realizing real-time optimization of fault repair.

[0114] The output unit 4 outputs the optimal fault repair and power restoration strategy for the entire fault cycle.

[0115] The input unit 1 refers to the active distribution network branch data, node power load power data, status data of distributed resources such as mobile energy storage vehicles, and the measured values ​​of distributed power source and load voltage phasors, current phasors, power, positive sequence current, and negative sequence current obtained by high-density sampling using PMU.

[0116] The topology partitioning unit 2 comprises a PMU optimization configuration subunit 21, a network partition initial screening subunit 22, and a network partition fine screening subunit 23.

[0117] The PMU optimization configuration subunit 21 combines the active distribution network topology diagram with known limited PMU configurations, and uses graph order pairs centered on PMU configuration nodes to establish a radial network structure diagram of the active distribution network.

[0118] Graphs help provide isomorphic mappings for engineering systems, and graph duality theory can be used to effectively solve partitioning problems. Generally, elements in graph theory can be mapped one-to-one with elements in a distribution network, clarifying complex networks. A graph can be defined by an ordered pair G = (V, E), where V represents the set of vertices and E represents the set of edges, with each edge defined by its two endpoints. For the PMU partitioning problem, a simple graph without self-loops and multiple edges is used. Due to the high cost of PMUs, existing distribution networks often only have a limited number of PMUs installed. Assuming that the active distribution network has n total nodes and m PMUs configured during normal operation, the network can be partitioned starting from the nodes with configured PMUs.

[0119] To accurately represent the radial structure of a power distribution network and its internal topological relationships, trees and degree functions are introduced based on graph theory. A tree is a uniquely connected path between any two nodes and is a graph that does not contain any loops. The degree function of a tree is defined as d(V), representing the degree of vertex V. If d(V) = 0, the node is an isolated node; if d(V) = 1, the node is a leaf node; if d(V) > 1, the node is a branch node.

[0120] The network partitioning initial screening subunit 22 employs a hybrid search algorithm combining "overall breadth-first search (BFS)" and "local depth-first search (DFS)" to perform the first stage of traversal screening of the network structure. This method avoids the large memory consumption caused by blind search and can quickly find all solutions. The specific steps are as follows:

[0121] Step 1: Network simplification. After obtaining the network topology and PMU deployment information in the PMU optimization configuration subunit, select a PMU node j as the root node. This node is the configuration PMU node.

[0122] Meanwhile, we define criterion 1: the node is a configured PMU node; criterion 2: d(V) = 0; criterion 3: d(V) > 1; any node in the network is retained if it satisfies one of these criteria; otherwise, the node is removed, and finally, the simplified tree of the distribution network is obtained.

[0123] Step 2: Perform a global BFS, using the known PMU-configured node as the root node. Expand outwards using the breadth-first search algorithm to find the second-level and third-level root nodes. If the secondary root node d(V) of the current node is 1, jump to step 3; if d(V) > 1, continue the current search; if d(V) = 0, stop the search of the current branch.

[0124] Step 3: Local DFS. After completing one breadth-first search, perform a local depth-first search on each leaf branch where the secondary root node is located. When a node with d(V) > 1 is found, jump back to step 2. If a node with d(V) = 1 is found, continue the current search. If a node with d(V) = 0 is found, stop the search of the current branch.

[0125] Step 4: Determine if the search is complete. For the current root node, the search stops when the degree function value of all nodes found at the same level is 0.

[0126] Step 5: Initially screen the partitions where nodes are located. For any node, if there are no other PMUs on the unique topology connection between the node and the current node j, then the node may belong to the PMU partition where node j is located, and it is regarded as a node to be partitioned; otherwise, the node must not belong to the PMU partition where node j is located.

[0127] Step 6: Select the next node j to configure PMU and repeat the above process, where j = j + 1, j = 1, 2, ..., m; until the recursive loop of all j is completed, output the first stage partition screening results of the entire network.

[0128] The network partitioning fine screening subunit 23 uses the PMU partitioning support index to refine the initial screening results of the network partitioning, forming a reasonable active distribution network partitioning optimization scheme.

[0129] Based on the initial screening results of network partitioning, a comprehensive electrical distance can be defined, and the partition support of the node to be partitioned to the configured PMU node can be calculated, thereby realizing the final area allocation of each node in the second stage.

[0130] First, we can obtain the following from the linear Newton-Lafferty power flow model:

[0131]

[0132] By setting ΔP = 0 and ΔQ = 0 respectively, we can simplify to obtain the sensitivity matrix of voltage amplitude-reactive power and the sensitivity matrix of voltage phase angle-active power. Furthermore, we can define the reactive and active electrical distances at nodes i and j as follows:

[0133]

[0134] In the formula,

[0135] In order to comprehensively utilize the various situational factors provided by PMU measurements, the reactive electrical distance D ij and active electrical distance B ij By performing a weighted summation, the comprehensive electrical distance H between nodes i and j is obtained. ij for:

[0136] H ij =kD ij +(1-k)B ij

[0137] In the formula, k and 1-k correspond to the weight values ​​of reactive electrical distance and active electrical distance, respectively;

[0138] Comprehensive electrical distance H ij The larger the value, the stronger the coupling between nodes i and j, and the closer the connection. The goal of network partitioning is to make the electrical quantities between nodes within the same partition closely connected and have a strong coupling, i.e., a larger overall electrical distance. In contrast, between partitions, the electrical quantities between different nodes are sparsely connected and have a weak coupling, i.e., a smaller overall electrical distance.

[0139] Secondly, let the partition where a node j with a PMU configuration is located be A. k Furthermore, each partition has exactly one node configured with a PMU; based on this PMU deployment principle, the comprehensive electrical distance H ij The larger the value, the closer the electrical connection between node i and node j configured with the PMU, and thus node i belongs to A. k The greater the support of the partition, the more likely node i belongs to A. k Support α i (A k The size of the integral electrical distance H ij Proportional;

[0140] Given α i (A k ) and H ij Functional relation

[0141]

[0142] To ensure that the support level is proportional to the corresponding comprehensive electrical distance, the above formula can be derived to satisfy the following conditions: Condition 1, 0 < α0 < 1; Condition 2, Condition 3,

[0143] It can be seen from condition 1 and condition 2 that if H ij =0, then α i (A k When the total electrical distance is 0, node i is at a distance of 0 from A. k The partition's support is 0, meaning node i does not belong to A at all. k Partitioning; and as can be seen from condition 3, when the comprehensive electrical distance is infinite, node i is paired with A k The partition support is maximized, and node i belongs entirely to A. k Partitioning;

[0144] The function can be defined as:

[0145]

[0146] In the formula, r, β, and τ are correlation coefficients, where r > 0, and β and τ are generally small integers. In this invention, r is 0.5, and β and τ are 1.

[0147] This allows us to calculate the support level of all nodes i in the system for nodes j in partition k that are configured with PMUs, and then perform data normalization on this support.

[0148]

[0149] The support levels of each node to each PMU node in the system given by the above formula are arranged in descending order, and the node to be partitioned is assigned to the partition corresponding to the maximum support. The loop is iterated until all nodes in the system are traversed, thereby determining the partition to which each node belongs.

[0150] Therefore, the second-stage partitioning is based on the initial screening and narrowing of the traversal space in the first-stage partitioning. It allocates nodes in the sub-regions of the distribution network according to the tightness of the electrical coupling relationship between nodes. This helps to reduce the time for acquiring real-time status elements of the distribution network, improves computational efficiency, and provides a physical topology basis for subsequent parallel partitioning computation.

[0151] The fault recovery unit 3 includes a PMU multi-agent architecture subunit 31, a positive and negative sequence current deviation value subunit 32, and a multi-fault emergency repair optimization model subunit 33.

[0152] The PMU multi-agent architecture subunit 31 utilizes a multi-functional PMU information transmission communication architecture, using the PMU as an agent for each network partition to achieve real-time reporting and decision-making of fault information.

[0153] Multi-Agent Systems (MAS) possess autonomy, collaboration, and parallel computing capabilities, enabling agents to coordinate and solve the entire problem. After configuring PMU devices and partitioning the network, operational status can be quickly collected, understood, and predicted, with real-time dynamic capture of source load information. A PMU-MAS based on PMU information collection and partitioning uses PMU devices as information agents in each network partition, processing information matched by each agent partition at the device layer. The communication architecture between agents is as follows: Figure 2 As shown.

[0154] The PMU-MAS architecture can be divided into four layers, from top to bottom: the information layer, the decision layer, the coordination layer, and the equipment layer. The equipment layer includes DG agents, energy storage agents, load agents, and their connected bus and line switch agents, reflecting the operational status of each device. The coordination layer includes PMU partition agents and emergency repair team agents. The PMU partition agents collect network topology partition information and information from each agent in the equipment layer within each partition; the emergency repair team agents receive emergency power restoration strategies from the dispatch center. The decision layer, based on data from the coordination and information layers, allows the dispatch center to quickly formulate reasonable and effective emergency power restoration plans. The information layer utilizes PMUs and other hybrid measurement devices to collect and store information on the historical, current, and predicted status of all network devices.

[0155] When extreme events cause widespread failures, the various agents at the equipment layer cooperate to quickly report the failure information at the disaster site to the dispatch center through the PMU partition agent and the PMU information collection agent. The dispatch center will then formulate a repair and recovery plan based on the failure information reported by the PMU and available resources. If new changes occur during the repair process, the dispatch center will issue real-time updated repair strategies to the repair teams based on the new changes uploaded by the PMU information collection agent and the partition agent.

[0156] In this invention, the PMU acts as a proxy, acquiring source load output power measurements at 20ms sampling intervals. To address the inconsistency between the time scale of the PMU's high-frequency sampling data and the time scale of the fault recovery low-frequency data, this invention fuses the PMU's high-frequency sampling data into low-frequency information using a weighted summation method during the fault recovery low-frequency interval from t to t+1. The specific formula is as follows:

[0157]

[0158] In the formula, η is the number of high-frequency data points included in a low-frequency time interval; B(j,λ) is the weighting function; z uj The data consists of high-frequency sampling data from a PMU with multiple variables; λ is an undetermined parameter that determines the approximate shape of the weighting function; if λ = 0, it indicates an equal-weighted form; if λ < 0, it indicates that z is smaller. ujObtain a larger weight; if λ>0, it indicates a larger z. uj To gain a larger weight;

[0159] After processing the data using the above formula, a power curve containing source load measurement information can be obtained, and a time-varying model of source load power can then be constructed:

[0160]

[0161] In the formula, F i (t) represents the power value of node i in time period t; f i (x) is the curve function of the DG or load at node i.

[0162] The positive and negative sequence current deviation value subunit 32, based on information provided by the PMU information acquisition agent and switch agent in the PMU-MAS, utilizes the PMU device of the active distribution network partition to measure the positive and negative sequence currents in the partition for three power frequency cycles after a fault occurs in real time, and calculates the positive and negative sequence current deviation values ​​to characterize the fault state repair effect. Cluster faults under extreme events mainly include single-phase-to-ground short circuits, two-phase short circuits, two-phase-to-ground short circuits, three-phase short circuits, and longitudinal asymmetric faults. According to composite sequence network theory, when these faults occur in the system, their fault currents all contain positive sequence components. Among them, when different asymmetric faults occur, their fault currents all contain negative sequence components. Therefore, based on the ADN network partitioning model, the PMU partition agent can be used to monitor fault status elements, including positive sequence currents, within the region.

[0163] Fault monitoring for PMU partition agents can be divided into two categories:

[0164] (1) The first type is that the node or adjacent node is configured with a PMU, and when a single fault occurs, the observable value can be guaranteed by direct measurement or derivation of pseudo-measurement value by the PMU.

[0165] (2) The second type is that neither the node nor its adjacent nodes are configured with PMU. When a single failure occurs, some nodes are not observable.

[0166] For the first type of monitoring situation, the positive and negative sequence currents at the fault location or adjacent nodes can be directly observed. The measured values ​​deviate significantly from the currents obtained from the admittance matrix of the nodes after the fault. For the second type of monitoring situation, if the fault occurs on a line in an unobservable area, the voltage amplitude at the unobservable nodes at both ends of the line will be significantly reduced. However, since it is unobservable, the voltage amplitude before the fault can be used to approximate the calculation of the positive and negative sequence currents.

[0167] In summary, to measure the severity of a fault condition, the positive and negative sequence current deviation index is defined as the sum of the absolute value of the difference between the PMU measurement or pseudo-measurement of the positive sequence current injected into the node and the node injected current derived from the node voltage equation, and the PMU measurement or pseudo-measurement of the negative sequence current injected into the node. Based on the information provided by the PMU information acquisition agent and switch agent in the PMU-MAS, the PMU devices in the active distribution network section are used to measure the positive and negative sequence currents in the section for three power frequency cycles after a fault occurs in real time. Under the above two monitoring conditions, the positive and negative sequence current deviation value for the corresponding fault k is calculated.

[0168]

[0169] In the formula, Y i It is the positive-sequence admittance of node i before the fault; I PMU,i1 It is the measured value of the positive sequence current injected into node i provided by the PMU information acquisition agent; I PMU,i2 It is the measured value of the negative sequence current injected into node i provided by the PMU information acquisition agent; U′ f,i 、Y′ f,i These are the voltage value of node i and the positive sequence node admittance after the fault occurs, respectively; n is the total number of faulty lines or adjacent nodes corresponding to fault point k.

[0170] The multi-fault emergency repair optimization model subunit 33 is an active distribution network group fault emergency repair optimization model that combines fixed energy storage, mobile energy storage and PMU information acquisition agent to establish the comprehensive economic loss corresponding to the indicators of power outage economic loss, repair time and positive and negative sequence current deviation value as the objective.

[0171] In multi-fault emergency repair, due to the distance between faults, the different power levels of each lost load, and the varying importance of each load, multi-fault emergency repair is a multi-objective, multi-constraint optimization problem with the repair sequence as the control variable. To simplify the model solution and analysis, it is assumed that each dispatched team can independently complete the repair work when a fault occurs, and that each fault can be successfully repaired; the next fault can only be repaired after the repair work of one fault is completed; and the team's work efficiency remains constant throughout the entire repair process.

[0172] Generally, the optimization goals for emergency repairs can be divided into two aspects: firstly, reducing economic losses from power outages by prioritizing repairs of areas with larger power losses and higher importance; secondly, reducing repair time by prioritizing the path with the shortest overall repair completion time. To account for the impact of changes in network topology and situational observability during repairs, a positive and negative sequence current deviation index is added to the optimization objective. This leverages the source-load dynamic sensing capabilities of the PMUs within each zone and the PMU-MAS to formulate emergency repair and power restoration strategies for the fault set. The resulting objective function for the active distribution network multi-fault repair optimization model is as follows:

[0173] First, in the problem of multi-fault emergency repair, since there is a certain distance between each fault, the power of each power-loss load is different, and the importance of each load is also different, multi-fault emergency repair is a multi-objective and multi-constraint optimization problem with the repair sequence as the control variable.

[0174] f=min(f1(X)+λ1f2(X)+λ2f3(X))

[0175]

[0176] f2(X) = max{T1 T2 ... T N}

[0177]

[0178]

[0179] In the formula, X = (x1, x2, ... x m ) represents the repair sequence of the faulty nodes; m represents the total number of faulty nodes; f1(X), f2(X), and f3(X) represent the economic loss caused by the power outage, the maximum repair time, and the positive and negative sequence current deviation, respectively; λ1 and λ2 represent the economic loss per unit time and the economic loss corresponding to the unit positive and negative sequence current deviation. To ensure that the optimized repair results can restore system power supply as quickly as possible and ensure the overall network operation status of the partitioned PMU is satisfactory, λ1 and λ2 can be taken as large values; p is the electricity price; i is the fault repair sequence; T(x i ) is the faulty node x i The duration of the fault; j represents the importance of different fault nodes; ω j For weights; L j (x i ) and L′ j (x i ) is the fault number x i The power loss of uncontrollable loads with importance level j and the power provided by distributed resources; N is the number of repair teams; T i This is the time spent by the emergency repair team from the start to the end of the repair operation.k t is the time taken to repair the kth fault; k-1→k t is the travel time for repair team i to move from the (k-1)th fault point to the kth fault point. 0→1 It is the travel time from the starting position to the first fault location for the emergency repair team.

[0180] Then, the constraints are determined, specifically including:

[0181] Constraint 1: Energy storage charging and discharging constraints. Since the output of distributed generation is closely related to the weather, the output of DG may decrease significantly during a certain period of failure when the weather changes. This further illustrates the necessity of introducing an Energy Storage System (ESS) in the event of a power outage in the distribution network.

[0182]

[0183] In the formula, P i c.max P i d.max These represent the upper limits for charging and discharging energy stored at node i; These are 0-1 type variables, representing the flag bits for energy storage charging and discharging at node i during time period t.

[0184] Constraint 2: Utilization of Mobile Energy Storage Systems. The spatial mobility of Mobile Energy Storage Systems (MESS) allows them to appear at nodes in dire need of power support, restoring power to more loads while ensuring power supply to critical loads.

[0185] The spatiotemporal transfer characteristics of mobile energy storage system dispatch are as follows:

[0186]

[0187] In the formula, L ij (t) represents the status flag of the mobile energy storage system during the journey from station i to station j, when L ij When (t) = 1, it means that at time t, the mobile energy storage system is on its way from station i to station j; otherwise, L ij (t) = 0 indicates that it is not present; tr ij The formula represents the time taken to move from station i to station j; T is the total scheduling time; and S is the set of stations. The above formula constrains the relationship between the mobile energy storage system and the stations during its movement.

[0188] The charge and discharge characteristics of the mobile energy storage system are as follows:

[0189]

[0190] In the formula, These represent the charging and discharging flags of MESS at station i at time t, and are 0-1 type variables; This indicates the maximum charging power and maximum discharging power of MESS;

[0191] Constraint 3, Topological Constraint:

[0192] After the fault is repaired, the distribution network topology, excluding DG, must meet the following requirements:

[0193] g k ∈G k

[0194] In the formula, g k This refers to the current operating structure of the power distribution network; G k It is the collection of all radial structures in a power distribution network;

[0195] Constraint 4, Branch Flow Constraint:

[0196] Establish a Distflow power flow model suitable for radial distribution networks:

[0197]

[0198]

[0199]

[0200]

[0201] In the formula, ψ(i) represents the set of end nodes of the branch with node i as the first node; π(i) represents the set of beginning nodes of the branch with node i as the last node; R ki X ki These represent the resistance and reactance values ​​of branch ki, respectively; I ki (t) represents the current flowing through branch ki at time t; P i (t), Q i (t) represents the active power and reactive power injected by node i at time t, respectively; P Load.i (t), Q Load.i (t) represents the active power and reactive power of the load at node i at time t, respectively; P DG.i (t), Q DG.i (t) represents the active power and reactive power output by the distributed power source port connected to node i at time t; and These are the charging active power, discharging active power, charging reactive power, and discharging reactive power of MESS, respectively. and These are the active power for charging, active power for discharging, reactive power for charging, and reactive power for discharging of stationary energy storage, respectively.

[0202] Constraint 5, Safe Operation Constraint:

[0203]

[0204] In the formula, U i,t Operating voltage; I ij,t This is the operating current; and U i,t These represent the upper and lower limits of the voltage at node i during time period t, respectively. This represents the upper limit of the current in branch ij during time period t;

[0205] Constraint 6, Power Constraint within the Island:

[0206]

[0207] In the formula, D is the set of nodes within the island; n is the number of nodes within the island; P DG,t It is the output value of the distributed power source in time period t; L i,t It represents the load of node i within the island during time period t;

[0208] Constraint 7, Emergency Repair Resource Constraints:

[0209] χ≤Ω

[0210] In the formula, χ represents the resources consumed during emergency repair of a certain fault; Ω represents the total amount of resources provided for this emergency repair task.

[0211] Finally, in the emergency power restoration model, since the power flow constraints are nonlinear, the model belongs to a mixed-integer nonlinear programming problem, which is difficult for the solver to solve directly. To address this, a second-order cone relaxation method is used to enable the solver to solve the problem. The specific method is as follows:

[0212] use and Replace the quadratic terms in the Distflow power flow constraints and safety constraints:

[0213]

[0214] Constraints 4 and 5 then transform into the following form:

[0215]

[0216]

[0217]

[0218]

[0219] After the above processing, the calculation formulas for power and voltage / current are still non-convex. Using a second-order cone relaxation technique, they are transformed into the following second-order cone form:

[0220]

[0221] After coneification, the mixed-integer nonlinear programming model has been transformed into a mixed-integer second-order cone programming model, which is then processed using the solver CPLEX.

[0222] The output unit 4 refers to the application of the established multi-fault repair model to solve for emergency repair and power restoration schemes for clustered faults under extreme events, and the use of the PMU multi-agent architecture to give real-time instructions to the repair teams and distributed resources throughout the fault cycle on the repair strategy. Specific Implementation

[0224] This example uses a test system of an urban medium-voltage distribution network, represented by a PG&E69 network containing distributed generation sources. The topology is shown below. Figure 3 As shown in Table 1, taking the deployment of 7, 12, and 24 PMUs in the PG&E69 system as examples, the improved PG&E69 network is divided into two stages for network partitioning. First, using a hybrid search method, the network partitioning preliminary screening sub-unit is applied to perform preliminary screening of the active distribution network network partitioning, and the results are shown in Table 1.

[0225] Table 1 Initial Screening of PG&E69 Network Partitions

[0226]

[0227]

[0228] Based on the initial screening results of network partitioning, 7, 12, and 24 PMUs were configured at different locations in the PG&E69 network, respectively. The network partitioning fine screening subunit was then applied to perform a second-stage partitioning of the PG&E69 network with different numbers of PMUs. Table 2 shows the solution time of the two-stage partitioning method in the PG&E69 network.

[0229] Table 2 Solution time of the two-stage partitioning method in PG&E69 network

[0230]

[0231] As shown in Tables 1 and 2, as the number of PMUs increases, the number of network partitions also increases accordingly. Parallel computing can continuously shorten the partitioning time. However, the increased number of partitions leads to a significant reduction in the initial screening range of each node, reducing the number of loop iterations. Consequently, the solution time of the two-stage network partitioning method under different schemes with 7, 12, and 24 PMUs is limited.

[0232] (1) Analysis of clustered failures

[0233] Assuming extreme weather occurs at 8:00 AM, resulting in 8 faults in the distribution network, the specific load loss levels are shown in Table 3. The weighting coefficients for Level 1, Level 2, and Level 3 loads are set to 100, 10, and 1, respectively. The types of load loss are shown in Table 4, with industrial, commercial, and residential electricity prices at 0.6 yuan / kWh, 0.92 yuan / kWh, and 0.57 yuan / kWh, respectively. The distributed generation (DG) connections in the network are shown in Table 5. Furthermore, the feeder connected at node 26 can be considered equivalent to a virtual distributed generation (DG) with a capacity of 100kW. An energy storage battery is connected at node 47, with a charging / discharging limit of 200kW. Eight nodes in the distribution network have MESS charging / discharging stations, with the maximum charging / discharging power of the two MESS units being 200kW and 100kW, respectively. The status information for DG, loads, stationary energy storage, and mobile energy storage is transmitted and uploaded by the PMU multi-agent system.

[0234] Table 3 Load Levels of Power Loss Loads

[0235]

[0236]

[0237] Table 4 Load Types of Power Loss Loads

[0238]

[0239] Table 5 Distributed Power Generation Parameters

[0240]

[0241] Assume the power company has two emergency repair teams, T1 and T2, with repair efficiency coefficients of 1.2 and 1 respectively; and two mobile energy storage vehicles, M1 and M2, with the same working efficiency. The starting position of both the repair teams and the energy storage vehicles is at node 1. The estimated repair time for each fault (based on the repair efficiency of T2) is shown in Table 6. Each time interval is 15 minutes, and the interval between each two fault points for both the repair teams and the energy storage vehicles is 15 minutes.

[0242] Table 6 Estimated Repair Time for Each Fault Point

[0243]

[0244] Configure 7 PMUs and create corresponding network partitions for 8 fault occurrence times in the PG&E69 system. After configuring the PMUs and partitioning the network in the PG&E69, proceed as follows: Figure 3Fault scenario setup. For the partition information at the moment multiple faults occur, the real-time acquisition of positive and negative sequence currents by PMU devices in each partition of the PMU multi-agent system is used. Combined with the judgment of the PMU partition agent monitoring type of each fault area and the calculation formula for positive and negative sequence current deviation, the fault lines or connected nodes corresponding to different faults at the moment of fault occurrence are obtained, as shown in Table 7. The normalized values ​​of the positive and negative sequence current deviations corresponding to each node are as follows: Figure 4 As shown.

[0245] Table 7. Faulted lines or fault points at the moment the fault occurs.

[0246]

[0247] Considering the participation of MESS in emergency repair scheduling and the scenario of dynamic load changes, the fault sequence and repair time of the two emergency repair teams are obtained, as shown in Tables 8 and 9. The dispatch path of MESS is determined based on matching the capacity of the lost power load and the importance of the load, as shown in Table 10. The values ​​in parentheses are the charging and discharging times of the MESS.

[0248] Table 8 Repair Plan for T1 Fault in Emergency Repair Team

[0249]

[0250] Table 9 Repair Plan for T2 Fault in Emergency Repair Team

[0251]

[0252]

[0253] Table 10 Dispatch Paths for Mobile Energy Storage M1 and M2

[0254]

[0255] As shown in Tables 8-10, team T1 exited dispatching after completing the repair work at fault point 8 at 15:20; team T2 exited dispatching after completing the repair work at fault point 1 at 16:12. Furthermore, during the entire repair process for fault points 1 and 8, since the feeder and DG provided ample power, the time-varying islanding demand was always less than the power supply from the feeder and DG; therefore, MESS did not provide charging power at the corresponding sites.

[0256] To comprehensively analyze the impact of MESS scheduling and load time-varying characteristics on the economic losses of emergency repairs, this example sets up four scenarios for comparison. Case 1 represents the recovery method without considering load dynamics or MESS participation in scheduling; Case 2 represents the recovery method considering only load time-varying characteristics; Case 3 represents the recovery method considering only MESS participation in scheduling; and Case 4 represents the recovery method considering both load time-varying characteristics and MESS participation in scheduling. The economic losses from load outages and the total target economic losses under different scenarios are calculated, and the results are shown in Table 11.

[0257] Table 11 Comparison of economic losses in different fault repair scenarios

[0258]

[0259] Comparing cases 2 and 4, it can be seen that increasing MESS dispatch resources during emergency repairs can significantly reduce the economic losses and total losses from load outages. Comparing cases 3 and 4, it can be seen that the time-varying nature of the load will affect the economic losses of emergency repairs. In case 3, which does not consider the time-varying nature of the load, the economic losses in case 3 are slightly smaller because the demand of each load in the distribution network is at a low level at the time of the fault.

[0260] (2) Analysis of sudden new faults

[0261] Suppose that at 10:00 AM, two new faults suddenly occur in the distribution network, at fault points 9 and 10. The distribution network structure at this time is as follows: Figure 5 As shown in the table. When a new fault occurs, if the multi-agent system based on real-time fault acquisition by the PMU partition is not invoked, the team will carry out fault repair according to the original plan. The new fault will be repaired after the aforementioned faults are repaired. However, fault recovery usually takes a certain amount of time. Therefore, during the repair process, the fluctuation of load and distributed energy, and the impact of repairing and connecting each fault point to the grid on the active distribution network may cause real-time changes in the positive and negative sequence current deviation values ​​at the fault point. The PMU multi-agent system can utilize the real-time sensing capabilities of the partition PMU device for switch agents, load agents, and DG agents to dynamically sense the changes in positive and negative sequence current deviation values ​​caused by source-load fluctuations and grid connection impact scenarios, and update them in real time. If the control center invokes the real-time fault information collected by the PMU partition, the control center will make real-time dynamic adjustments to the repair plan based on the existing repair resources and team capabilities to obtain the optimal solution. The two repair plans are shown in Tables 12 and 13, respectively.

[0262] Table 12. Repair solutions for PMU multi-agent information not being updated after a sudden new fault.

[0263]

[0264] Table 13 Repair plan for updating PMU multi-agent information after a sudden new fault.

[0265]

[0266] As shown in Tables 12 and 13, when team T1 was repairing fault point 5 and team T2 was repairing fault point 3, new fault points 9 and 10 appeared. If teams T1 and T2 repaired the fault points according to their original repair strategies, they would repair the new fault points last. If the topology information is updated in real time based on the PMU, the control center agent will update and adjust the repair strategies of the team agents in real time. In fact, since the distribution network is radial, the appearance of fault point 9 makes it meaningless to repair fault point 6 before repairing fault point 9. Only after fault point 9 is repaired can the loads connected to 6 be guaranteed to have their power restored. The same applies to fault point 10.

[0267] In summary, the repair scheme for updating the PMU multi-agent system after a sudden new fault enables the team to perform dynamic repairs during the emergency repair process, improving repair efficiency, shortening the overall repair time, reducing the economic losses caused by load outages, and enhancing the power supply reliability of the power grid.

[0268] Those skilled in the art should recognize that the above embodiments are merely illustrative of the present invention and are not intended to limit the present invention. Any variations or modifications to the above embodiments that are within the spirit and essence of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A method for active distribution network fault recovery integrating a multi-agent architecture, characterized in that: It includes an input unit, a topology partitioning unit, a fault recovery unit, and an output unit connected in sequence; The input unit acquires distribution network structure data, distribution network node data, distributed resource data including mobile energy storage vehicles, and PMU measurement data. The PMU measurement data refers to the measured values ​​of voltage phasors, current phasors, power, positive sequence current, and negative sequence current of distributed power sources and loads obtained by high-density sampling of PMUs. The topology partitioning unit establishes the active distribution network topology based on the data characteristics provided by the input unit and the PMU optimization configuration, using the graph duality theory in graph theory. Then, it performs two-stage network partitioning of the active distribution network based on the hybrid search algorithm and PMU partitioning support. The fault recovery unit proposes a PMU multi-agent communication architecture based on network partitioning to construct a group fault emergency repair power supply model with the goal of comprehensively optimizing the indicators of power outage economic loss, repair time and positive and negative sequence current deviation, thereby realizing real-time optimization of fault repair. The output unit outputs the optimal fault repair and power restoration strategy for the entire fault cycle. The topology partitioning unit consists of a PMU optimization configuration subunit, a network partitioning initial screening subunit, and a network partitioning fine screening subunit. The PMU optimization configuration subunit combines the active distribution network topology diagram with the known limited PMU configurations and uses graph order pairs centered on PMU configuration nodes to establish a radial network structure diagram of the active distribution network. Assuming an active distribution network operates normally, the total number of nodes is n, and m PMUs are configured. The network is partitioned based on the nodes with configured PMUs. A tree structure and a degree function are introduced. The degree function of the tree is defined as d(V), representing the degree of vertex V. If d(V) = 0, the node is an isolated node; if d(V) = 1, the node is a leaf node; if d(V) > 1, the node is a branch node. The network partitioning fine screening subunit uses the PMU partitioning support index to refine the initial screening results of the network partitions, forming a reasonable active distribution network partitioning optimization scheme. The specific method is as follows: First, we can obtain the following from the linear Newton-Lafferty power flow model: By setting ΔP = 0 and ΔQ = 0 respectively, we can simplify to obtain the sensitivity matrix of voltage amplitude-reactive power and the sensitivity matrix of voltage phase angle-active power. Furthermore, we can define the reactive and active electrical distances at nodes i and j as follows: In the formula, In order to comprehensively utilize the various situational factors provided by PMU measurements, the reactive electrical distance D ij and active electrical distance B ij By performing a weighted summation, the comprehensive electrical distance H between nodes i and j is obtained. ij for: H ij =kD ij +(1-k)B ij In the formula, k and 1-k correspond to the weight values ​​of reactive electrical distance and active electrical distance, respectively; Comprehensive electrical distance H ij The larger the value, the stronger the coupling between nodes i and j, and the closer the connection. The goal of network partitioning is to make the electrical quantities between nodes within the same partition closely connected and have a strong coupling, i.e., a larger overall electrical distance. In contrast, between partitions, the electrical quantities between different nodes are sparsely connected and have a weak coupling, i.e., a smaller overall electrical distance. Secondly, let the partition where a node j with a PMU configuration is located be A. k Furthermore, each partition has exactly one node configured with a PMU; based on this PMU deployment principle, the comprehensive electrical distance H ij The larger the value, the closer the electrical connection between node i and node j configured with the PMU, and therefore node i belongs to A. k The greater the support of the partition, the more likely node i belongs to A. k Support α i (A k The size of the integral electrical distance H ij Proportional; Given α i (A k ) and H ij Functional relation To ensure that the support level is proportional to the corresponding comprehensive electrical distance, the above formula can be derived to satisfy the following conditions: Condition 1, 0 < α0 < 1; Condition 2, Condition 3, It can be seen from condition 1 and condition 2 that if H ij =0, then α i (A k When the total electrical distance is 0, node i is at a distance of 0 from A. k The partition's support is 0, meaning node i does not belong to A at all. k Partitioning; and as can be seen from condition 3, when the comprehensive electrical distance is infinite, node i is paired with A k The partition support is maximized, and node i belongs entirely to A. k Partitioning; The function can be defined as: In the formula, r, β, and τ are correlation coefficients, with r taking the value of 0.5 and β and τ taking the value of 1. This allows us to calculate the support level of all nodes i in the system for nodes j in partition k that are configured with PMUs, and then perform data normalization on this support. The support levels of each node to each PMU node in the system given by the above formula are arranged in descending order, and the node to be partitioned is assigned to the partition corresponding to the maximum support. The loop is iterated until all nodes in the system are traversed, thereby determining the partition to which each node belongs.

2. The active distribution network fault recovery method with integrated multi-agent architecture according to claim 1, characterized in that: The network partitioning initial screening subunit uses a search algorithm to perform the first-stage traversal screening of the network structure. The specific steps are as follows: Step 1: Network simplification. After obtaining the network topology and PMU deployment information in the PMU optimization configuration subunit, select a PMU node j as the root node. This node is the configuration PMU node. Simultaneously define criterion 1: the node is a configured PMU node; criterion 2: d(V) = 0; Criterion: d(V)>1; any node in the network is retained if it satisfies one of the principles; otherwise, the node is removed, and finally the simplified tree of the distribution network is obtained. Step 2: Perform a global BFS, using the known PMU-configured node as the root node. Expand outwards using a breadth-first search algorithm to find the second-level and third-level root nodes. If the secondary root node d(V) of the current node is 1, jump to step 3; if d(V) > 1, continue the current search; if d(V) = 0, stop the search of the current branch. Step 3: Local DFS. After completing one breadth-first search, perform a local depth-first search on each leaf branch where the secondary root node is located. When a node with d(V) > 1 is found, jump back to step 2. If a node with d(V) = 1 is found, continue the current search. If a node with d(V) = 0 is found, stop the search of the current branch. Step 4: Determine if the search is complete. For the current root node, the search stops when the degree function value of all nodes found at the same level is 0. Step 5: Initially screen the partitions where nodes are located. For any node, if there are no other PMUs on the unique topology connection between the node and the current node j, then the node may belong to the PMU partition where node j is located, and it is regarded as a node to be partitioned; otherwise, the node must not belong to the PMU partition where node j is located. Step 6: Select the next node j to configure PMU and repeat the above process, where j = j + 1, j = 1, 2, ..., m; until the recursive loop of all j is completed, output the first stage partition screening results of the entire network.

3. The active distribution network fault recovery method integrating a multi-agent architecture according to claim 1, characterized in that, The fault recovery unit includes a PMU multi-agent architecture sub-unit, a positive and negative sequence current deviation value sub-unit, and a multi-fault emergency repair optimization model sub-unit.

4. The active distribution network fault recovery method with integrated multi-agent architecture according to claim 3, characterized in that, The PMU multi-agent architecture subunit utilizes a multi-functional PMU information transmission communication architecture, using the PMU as a proxy for each network partition to achieve real-time reporting and decision-making of fault information. Addressing the inconsistency between the time scale of PMU high-frequency sampling data and the time scale of fault recovery low-frequency data, this method uses a weighted summation method to fuse PMU high-frequency sampling data into low-frequency information during the fault recovery low-frequency interval t to t+1. The specific formula is as follows: In the formula, η is the number of high-frequency data points included in a low-frequency time interval; B(j,λ) is the weighting function; z uj The data consists of high-frequency sampling data from a PMU with multiple variables; λ is an undetermined parameter that determines the approximate shape of the weighting function; if λ = 0, it indicates an equal-weighted form; if λ < 0, it indicates that z is smaller. uj Obtain a larger weight; if λ>0, it indicates a larger z. uj To gain a larger weight; After processing the data using the above formula, a power curve containing source load measurement information can be obtained, and a time-varying model of source load power can then be constructed: In the formula, F i (t) represents the power value of node i in time period t; f i (x) is the curve function of the DG or load at node i.

5. The active distribution network fault recovery method integrating a multi-agent architecture according to claim 3, characterized in that, The positive and negative sequence current deviation value subunit, based on the information provided by the PMU information acquisition agent and switch agent in PMU-MAS, uses the PMU device of the active distribution network partition to measure the positive and negative sequence currents in the partition for three power frequency cycles after the fault occurs in real time, and calculates the positive and negative sequence current deviation value to characterize the fault state repair effect. The specific method is as follows: In the formula, Y i It is the positive-sequence admittance of node i before the fault; I PMU,i1 It is the measured value of the positive sequence current injected into node i provided by the PMU information acquisition agent; I PMU,i2 It is the measured value of the negative sequence current injected into node i provided by the PMU information acquisition agent; U′ f,i 、Y′ f,i These are the voltage value of node i and the positive sequence node admittance after the fault occurs, respectively; n is the total number of faulty lines or adjacent nodes corresponding to fault point k.

6. The active distribution network fault recovery method with integrated multi-agent architecture according to claim 3, characterized in that, The multi-fault emergency repair optimization model subunit combines fixed energy storage, mobile energy storage, and PMU information acquisition agent to establish an active distribution network cluster fault emergency repair optimization model with the objective of minimizing the comprehensive economic loss corresponding to the power outage economic loss, repair time, and positive and negative sequence current deviation values. The specific method is as follows: First, the objective function of the active distribution network multi-fault emergency repair optimization model is formed; f=min(f1(X)+λ1f2(X)+λ2f3(X)) f2(X)=max{T1 T2...T N } In the formula, X = (x1, x2, ... x m ) represents the repair sequence of the faulty nodes; m represents the total number of faulty nodes; f1(X), f2(X), and f3(X) represent the economic loss caused by the power outage, the maximum repair time, and the positive and negative sequence current deviation, respectively; λ1 and λ2 represent the economic loss per unit time and the economic loss corresponding to the unit positive and negative sequence current deviation. In order to ensure that the repair optimization results can restore the system power supply as soon as possible and ensure the overall network operation status of the partitioned PMU as soon as possible, λ1 and λ2 can be taken as large values; p represents the electricity price. i represents the fault repair sequence; T(x) i ) is the faulty node x i The duration of the fault; j represents the importance of different fault nodes; ω j For weights; L j (x i ) and L′ j (x i ) is the fault number x i The power loss of uncontrollable loads with importance level j and the power provided by distributed resources; N is the number of repair teams; T i It is the time spent by the emergency repair team from the start to the end of the emergency repair; t k t is the time taken to repair the kth fault; k-1→k t is the travel time for repair team i to move from the (k-1)th fault point to the kth fault point. 0→1 It is the travel time from the starting point to the first point of failure for the emergency repair team; Then, the constraints are determined, specifically including: Constraint 1: Energy storage charging and discharging constraints. In the formula, P i c.max P i d.max These represent the upper limits for charging and discharging energy stored at node i; These are 0-1 type variables, representing the flag bits for energy storage charging and discharging at node i during time period t. Constraint 2, Constraints related to mobile energy storage systems: The spatiotemporal transfer characteristics of mobile energy storage system dispatch are as follows: In the formula, L ij (t) represents the status flag of the mobile energy storage system during the journey from station i to station j, when L ij When (t) = 1, it means that at time t, the mobile energy storage system is on its way from station i to station j; otherwise, L ij (t) = 0 indicates that it is not present; tr ij The formula represents the time taken to move from station i to station j; T is the total scheduling time; and S is the set of stations. The above formula constrains the relationship between the mobile energy storage system and the stations during its movement. The charge and discharge characteristics of the mobile energy storage system are as follows: In the formula, These represent the charging and discharging flags of MESS at station i at time t, and are 0-1 type variables; This indicates the maximum charging power and maximum discharging power of MESS; Constraint 3, Topological Constraint: After the fault is repaired, the distribution network topology, excluding DG, must meet the following requirements: g k ∈G k In the formula, g k This refers to the current operating structure of the power distribution network; G k It is the collection of all radial structures in a power distribution network; Constraint 4, Branch Flow Constraint: Establish a Distflow power flow model suitable for radial distribution networks: In the formula, ψ(i) represents the set of end nodes of the branch with node i as the first node; π(i) represents the set of beginning nodes of the branch with node i as the last node; R ki X ki These represent the resistance and reactance values ​​of branch ki, respectively; I ki (t) represents the current flowing through branch ki at time t; P i (t), Q i (t) represents the active power and reactive power injected by node i at time t, respectively; P Load.i (t), Q Load.i (t) represents the active power and reactive power of the load at node i at time t, respectively; P DG.i (t), Q DG.i (t) represents the active power and reactive power output by the distributed power source port connected to node i at time t; and These are the charging active power, discharging active power, charging reactive power, and discharging reactive power of MESS, respectively. and These are the active power for charging, active power for discharging, reactive power for charging, and reactive power for discharging of stationary energy storage, respectively. Constraint 5, Safe Operation Constraint: In the formula, U i,t Operating voltage; I ij,t This is the operating current; and U i,t These represent the upper and lower limits of the voltage at node i during time period t, respectively. This represents the upper limit of the current in branch ij during time period t; Constraint 6, Power Constraint within the Island: In the formula, D is the set of nodes within the island; n is the number of nodes within the island; P DG,t It is the output value of the distributed power source in time period t; L i,t It represents the load of node i within the island during time period t; Constraint 7, Emergency Repair Resource Constraints: χ≤Ω In the formula, χ represents the resources consumed during emergency repair of a certain fault; Ω represents the total amount of resources provided for this emergency repair task. Finally, in the emergency power restoration model, since the power flow constraints are nonlinear, the model belongs to a mixed-integer nonlinear programming problem, which is difficult for the solver to solve directly. To address this, a second-order cone relaxation method is used to enable the solver to solve the problem. The specific method is as follows: use and Replace the quadratic terms in the Distflow power flow constraints and safety constraints: Constraints 4 and 5 then transform into the following form: After the above processing, the calculation formulas for power and voltage / current are still non-convex. Using a second-order cone relaxation technique, they are transformed into the following second-order cone form: After coneification, the mixed-integer nonlinear programming model has been transformed into a mixed-integer second-order cone programming model, which is then processed using the solver CPLEX.

7. The active distribution network fault recovery method integrating a multi-agent architecture according to claim 1, characterized in that, The output unit refers to the application of the established multi-fault repair model to solve for emergency repair and power restoration schemes for clustered faults under extreme events, and to use the PMU multi-agent architecture to give real-time instructions on the repair team and distributed resources throughout the fault cycle to update the repair strategy.

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