Multi-stage large-scale multi-objective PMU optimization configuration method considering single-line fault

Abstract

The present invention relates to the field of power system monitoring and PMU optimization configuration. In order to reduce excessive observation redundancy under the premise of ensuring global observability, the present invention considers a single-line fault multi-stage large-scale multi-objective PMU optimization configuration method, obtains the topological structure of the distribution network, and constructs a distribution network system model; constructs a correlation matrix of the distribution network according to the topological structure of the distribution network and the zero injection node matrix; constructs a multi-objective synchronous phasor measurement unit PMU optimization configuration model of the distribution network; uses a large-scale multi-objective optimization algorithm to solve the multi-objective PMU optimization configuration model of the distribution network, and obtains the PMU optimal deployment plan set of the distribution network; uses a fuzzy decision-making method combining subjective and objective factors to select a flexible multi-stage PMU deployment plan from the optimal deployment plan set. The present invention is mainly used in power system monitoring occasions.

Description

Technical Field

[0001] The present invention relates to the fields of power system monitoring and PMU optimization configuration, and in particular to a multi-stage large-scale multi-objective PMU optimization configuration method considering single-line faults. Background Art

[0002] In response to the energy crisis and environmental protection pressure, more and more distributed power sources dominated by renewable energy are connected to the power system, but their intermittent and uncertain characteristics make the operation of the power system face severe challenges. Developing smart grids is an effective way to solve this problem.

[0003] The synchronized phasor measurement unit (PMU) with GPS as the time reference not only meets the spatial wide-area and temporal uniformity requirements of power system data acquisition and monitoring, but also can collect voltage and current amplitude information and phase angle information. It can realize real-time monitoring and analysis of the operating status of power systems in a wide area, and serve the real-time control and operation of power systems. In recent years, with the commercialization of 5G communication technology, its advantages of high stability and fast transmission speed have laid a solid foundation for the widespread use of PMU in power systems.

[0004] In order to monitor and control the entire distribution network in real time, the system must be globally observable. If PMUs are deployed at all nodes of the distribution network, all node voltages and branch currents are observable. However, due to the high deployment cost of PMUs and their ability to measure the voltage phasor of the installed node and the current phasor of the connected branches, it is unrealistic and unnecessary to deploy PMUs at all nodes of the network.

[0005] The optimal PMU deployment of the distribution network mainly considers the following four issues: (1) reducing the number of PMU deployments while ensuring the global observability of the system; (2) making the distribution network have a higher observability redundancy; (3) ensuring that the system does not lose global observability when a single-line failure occurs in the PMU; and (4) performing the optimal PMU deployment while considering the limitations on the number of PMU channels and communication facilities. Summary of the invention

[0006] In order to overcome the shortcomings of the prior art, the present invention aims to reduce excessive observation redundancy and achieve efficient PMU optimization configuration under the premise of ensuring global observability. To this end, the technical solution adopted by the present invention is to consider a single-line fault multi-stage large-scale multi-objective PMU optimization configuration method, obtain the topological structure of the distribution network, and construct a distribution network system model, including node and branch information in the distribution network; obtain the zero injection node position of the distribution network, and construct a zero injection node matrix;

[0007] According to the topological structure of the distribution network and the zero injection node matrix, the correlation matrix of the distribution network is constructed;

[0008] Construct a multi-objective PMU optimization configuration model for distribution networks, including:

[0009] Under the constraint condition of ensuring the global observability of the distribution system, the corresponding objective functions are constructed with the minimum PMU deployment cost, the maximum distribution system observation redundancy, the minimum probability of the distribution system losing global observability when a single PMU line fails, the minimum loss of a single PMU line failure, and the minimum standard deviation of the number of distribution system nodes observed as optimization goals.

[0010] A large-scale multi-objective optimization algorithm is used to solve the multi-objective PMU optimization configuration model of the distribution network to obtain the optimal PMU deployment solution set of the distribution network;

[0011] A fuzzy decision-making method combining subjective and objective factors is adopted to select a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set.

[0012] The method of constructing a correlation matrix of the power distribution network according to the topological structure of the power distribution network and the zero injection node matrix comprises:

[0013] A=merge(A′,Z)

[0014] Where A′ represents the original association matrix of the system, Z represents the zero injection node matrix of the system, and the function merge represents a merging rule: Considering that in the IEEE 9-node system, nodes 4, 7, and 9 are all zero injection nodes, if the voltages of two nodes among nodes 1, 5, and 6 are known, the KCL law can be applied at node 4 to estimate the voltage of the third node. Based on this conclusion, the zero injection node can be merged with any node connected to it, so node 4 is merged to node 1, node 7 to node 2, and node 9 to node 3;

[0015] The element a' of the original incidence matrix A' of the power distribution system ij Value: If node i is connected to node j, the value is 1, otherwise it is 0, and the diagonal elements are set to 1; the element z of the zero-injected node matrix Z i Value: If the node is a zero injection node, the value is 1, otherwise it is 0; The function of the merge function: merge the zero injection node with one of the nodes connected to it;

[0016] The association matrix A is obtained by merging all zero-injected nodes in A′, and its element a ij The value of a′ ij Same rules.

[0017] The objective function is constructed with the minimum deployment cost of PMU in the distribution network, which is as follows:

[0018]

[0019] stAX≥b

[0020] Where N represents the total number of nodes in the power distribution system; w i represents the cost of deploying PMU on node i; x i The state variable representing the configuration of PMU at the i-th node. When its value is 0, it indicates that PMU is not configured at the i-th node. When its value is 1, it indicates that PMU is configured at the i-th node. b represents a column vector with a length of N and all elements are 1.

[0021] The objective function is constructed based on the maximum observed redundancy of the distribution system, which is:

[0022]

[0023] Where S represents the set of nodes where PMU is deployed; d i Indicates the number of branches connected to node i.

[0024] The objective function is constructed by minimizing the probability of the distribution system losing global observability when a single-line PMU fails. Specifically, it is:

[0025]

[0026] Where, l represents the number of PMUs deployed in the power distribution system; c i It represents the state variable of the system when the PMU deployed at the i-th node fails. When its value is 1, it means that the system is still globally observable. When its value is 0, it means that the system is not globally observable.

[0027] The objective function is constructed with the minimum loss of PMU single-line fault, specifically:

[0028]

[0029] Among them, D ij It means that when the PMU deployed at the i-th node fails, the state variable of the j-th node, when its value is 1, indicates that the j-th node is still observable, and when its value is 0, indicates that the j-th node is unobservable.

[0030] The objective function is constructed by minimizing the standard deviation of the number of observations of the distribution system nodes, specifically:

[0031]

[0032] Among them, i It represents the number of times the i-th node is observed, as shown in the following formula:

[0033]

[0034] The large-scale multi-objective optimization algorithm is used to solve the multi-objective PMU optimization deployment model of the distribution network to obtain the optimal PMU deployment solution set of the distribution network, including:

[0035] According to the topological structure of the distribution network and the zero-injection node matrix, after constructing the association matrix of the distribution network, n deployment schemes are generated as the initial population, where the number and location of PMU deployments in each deployment scheme are random, and whether the n deployment schemes all meet the conditions for making the system in a globally observable state is determined, and the schemes that do not meet the conditions are updated to deployment schemes that meet the conditions;

[0036] Import the updated n deployment schemes and the cost of deploying PMUs on each node into the objective function, solve the objective function values ​​of these deployment schemes and select the dominant individuals according to the screening conditions of the large-scale multi-objective optimization algorithm;

[0037] The dominant individuals are used as parents to simulate binary crossover or mutation to generate offspring and the offspring are updated to a deployment scheme that satisfies the constraints; the parents and offspring are merged into one population and the dominant individuals are selected as the parents of the next iteration according to the screening conditions of the large-scale multi-objective optimization algorithm;

[0038] After gmax iterations, the dominant individuals selected by the large-scale multi-objective optimization algorithm will be used as the optimal deployment solution set of PMUs in the distribution network.

[0039] The method adopts a fuzzy decision-making method combining subjective and objective factors to select a flexible multi-stage PMU deployment plan from the optimal deployment plan set, including: firstly determining the subjective weight coefficient of each objective function by means of a hierarchical analysis method, then determining the objective weight coefficient of each objective function by means of an entropy weight method, and finally superimposing the weight coefficients of the two and applying them to the PMU optimal deployment plan set obtained by a large-scale multi-objective optimization algorithm, thereby selecting a flexible multi-stage PMU deployment plan.

[0040] The characteristics and beneficial effects of the present invention are:

[0041] Under the premise of ensuring that the power distribution network has global observability, the present invention seeks a deployment scheme that uses the least possible PMU deployment cost to achieve the largest possible system observable redundancy, the smallest possible PMU single-line failure loss, the most uniform system redundancy, and the smallest possible probability that the system is not globally observable due to a PMU single-line failure. Combined with the fuzzy decision method, a flexible multi-stage deployment scheme that can change with the PMU deployment cost is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the process of the present invention.

[0043] Figure 2 This is the topological structure diagram of the IEEE 9-node distribution system without zero injection node merging.

[0044] Figure 3 This is the topological structure diagram of the IEEE 9-node distribution system after zero-injection node merging. DETAILED DESCRIPTION

[0045] In the technical solution that does not consider the single-line failure of PMU, some nodes can only be observed once, and the loss of this observation value will cause the network to lose global observability. In the technical solution that considers the single-line failure of PMU, a single node will be observed at least twice, which will cause a surge in the cost of deploying PMUs and form excessive observation redundancy in the distribution network. In order to solve this problem, the present invention transforms the single-line failure of PMU from a constraint condition to an objective function, and proposes a multi-stage large-scale multi-objective PMU optimization configuration method that considers the loss of single-line failure.

[0046] A multi-stage large-scale multi-objective PMU optimization configuration method considering single-line fault loss, including:

[0047] Obtain the topological structure of the distribution network and construct a distribution network system model, including node and branch information in the distribution network; obtain the zero injection node position of the distribution network and construct a zero injection node matrix;

[0048] According to the topological structure of the distribution network and the zero injection node matrix, the correlation matrix of the distribution network is constructed;

[0049] Construct a multi-objective PMU optimization configuration model for the distribution network, including:

[0050] Under the constraint condition of ensuring the global observability of the distribution system, corresponding objective functions are constructed with the minimum PMU deployment cost, the maximum system observation redundancy, the minimum probability of the system losing global observability when a single PMU line fails, the minimum PMU single-line failure loss, and the minimum standard deviation of the number of system node observations as optimization goals.

[0051] A large-scale multi-objective optimization algorithm is used to solve the multi-objective PMU optimization configuration model of the distribution network, and the optimal PMU deployment solution set of the distribution network is obtained.

[0052] A fuzzy decision-making method combining subjective and objective factors is adopted to select a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set.

[0053] Furthermore, constructing the association matrix of the distribution network according to the topological structure of the distribution network and the zero injection node matrix includes:

[0054] A=merge(A′,Z)

[0055] Among them, A′ represents the original association matrix of the system, Z represents the zero injection node matrix of the system, and the function merge represents a merging rule: considering Figure 2 In the IEEE 9-node system shown, nodes 4, 7, and 9 are all zero injection nodes. If the voltages of two nodes among nodes 1, 5, and 6 are known, the KCL law can be applied at node 4 to estimate the voltage of the third node. Based on this conclusion, the zero injection node can be merged with any node connected to it. The system after merging node 4 to node 1, node 7 to node 2, and node 9 to node 3 is as follows Figure 3 As shown;

[0056] The element a' of the original incidence matrix A' of the system ij Value: If node i is connected to node j, the value is 1, otherwise it is 0, and the diagonal elements are set to 1; the element z of the zero-injected node matrix Z i Value: If the node is a zero injection node, the value is 1, otherwise it is 0; The function of the merge function: merge the zero injection node with one of the nodes connected to it;

[0057] The association matrix A is obtained by merging all zero-injected nodes in A′, and its element a ij The value of a′ ij Same rules.

[0058] Furthermore, the objective function is constructed with the minimum deployment cost of PMU in the distribution network, which is:

[0059]

[0060] stAX≥b

[0061] Where N represents the total number of nodes in the power distribution system; w i represents the cost of deploying PMU on node i; x i The state variable representing the configuration of PMU at the i-th node. When its value is 0, it indicates that PMU is not configured at the i-th node. When its value is 1, it indicates that PMU is configured at the i-th node. b represents a column vector with a length of N and all elements are 1.

[0062] Furthermore, the objective function is constructed with the maximum system observation redundancy, specifically:

[0063]

[0064] Where S represents the set of nodes where PMU is deployed; d i Indicates the number of branches connected to node i.

[0065] Furthermore, the objective function is constructed with the minimum probability of the system losing global observability when a single-line fault occurs in the PMU, specifically:

[0066]

[0067] Where, l represents the number of PMUs deployed in the power distribution system; c i It represents the state variable of the system when the PMU deployed at the i-th node fails. When its value is 1, it means that the system is still globally observable. When its value is 0, it means that the system is not globally observable.

[0068] Furthermore, the objective function is constructed with the minimum loss of PMU single-line fault, which is:

[0069]

[0070] Among them, D ij It means that when the PMU deployed at the i-th node fails, the state variable of the j-th node, when its value is 1, indicates that the j-th node is still observable, and when its value is 0, indicates that the j-th node is unobservable.

[0071] Furthermore, the objective function is constructed with the minimum standard deviation of the number of observations of system nodes, specifically:

[0072]

[0073] Among them, i It represents the number of times the i-th node is observed, as shown in the following formula:

[0074]

[0075] Furthermore, the large-scale multi-objective optimization algorithm is used to solve the multi-objective PMU optimization deployment model of the distribution network to obtain the optimal PMU deployment solution set of the distribution network, including:

[0076] According to the topological structure of the distribution network and the zero-injection node matrix, after constructing the association matrix of the distribution network, n deployment schemes are generated as the initial population, in which the number and location of PMU deployments in each deployment scheme are random. It is determined whether the n deployment schemes all meet the requirement of making the system globally observable and the schemes that do not meet the conditions are updated to deployment schemes that meet the conditions.

[0077] The updated n deployment schemes and the cost of deploying PMUs at each node are imported into the objective function, the objective function values ​​of these deployment schemes are solved, and the dominant individuals are selected according to the screening conditions of the large-scale multi-objective optimization algorithm.

[0078] The dominant individuals are used as parents to simulate binary crossover or mutation to generate offspring and update the offspring to a deployment scheme that satisfies the constraints. The parents and offspring are merged into one population and the dominant individuals are selected as the parents of the next iteration according to the screening conditions of the large-scale multi-objective optimization algorithm.

[0079] After gmax iterations, the dominant individuals selected by the large-scale multi-objective optimization algorithm will be used as the optimal deployment solution set of PMUs in the distribution network.

[0080] Furthermore, a fuzzy decision-making method combining subjective and objective factors is adopted to select a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set, including:

[0081] First, the subjective weight coefficient of each objective function is determined by the hierarchical analysis method, and then the objective weight coefficient of each objective function is determined by the entropy weight method. Finally, the weight coefficients of the two are superimposed and applied to the PMU optimal deployment plan set obtained by the large-scale multi-objective optimization algorithm, so as to select a flexible multi-stage PMU deployment plan.

[0082] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0083] PMU is an important part of smart grid. The data section synchronization error of PMU based on GPS unified timing is only 100-1000 nanoseconds, which is much smaller than the SCADA system with a maximum data section synchronization error of about 5 seconds. It can provide better support for real-time monitoring and control of the distribution network. If PMU is deployed at each node of the distribution network, the system can be globally observable; however, the high cost and high communication conditions of PMU limit its widespread deployment, and even if PMU is not deployed at all nodes, the system can be globally observable, so it is not necessary to deploy PMU at all nodes. At the same time, the application of Kirchhoff's law and Ohm's law at zero injection nodes can also significantly reduce the number of PMUs required in the system:

[0084] (1) The node where the PMU is deployed is directly observable, and the node voltage and branch current connected to the node are also observable; (2) When the voltage phasor at both ends of the branch is known, the current phasor of the branch can be indirectly observed; (3) For a zero injection node with N branches, when the current phasors of its N-1 branches are known, the current phasor of the Nth branch can be calculated; (4) If the observability of a zero injection node is unknown, but the nodes connected to it are all observable, then the node is indirectly observable.

[0085] For zero injection nodes, through the application of KCL law and Ohm's law, they can be merged into any node connected to it, thereby reducing the number of PMUs deployed to achieve global observability of the distribution system.

[0086] The idea of ​​the present invention is: since the power grid enterprise may not be able to deploy a sufficient number of PMUs at one time to meet the constraints of the distribution system under the single-line PMU failure to ensure the global observability of the system, this constraint condition is converted into an objective function. Under the premise of ensuring the global observability of the system, a deployment scheme is sought with the lowest possible PMU deployment cost, the largest possible system observable redundancy, the smallest possible PMU single-line failure loss, the most uniform system redundancy, and the smallest possible probability that the system is not globally observable due to the single-line PMU failure. Combined with the fuzzy decision-making method, a flexible multi-stage deployment scheme that can change with the PMU deployment cost is obtained.

[0087] See also Figure 1 The present invention provides a multi-stage large-scale multi-objective PMU optimization configuration method considering single-line fault loss, comprising the following steps:

[0088] Construction of S1 distribution network model

[0089] The topological structure of the distribution network is obtained, and a distribution network system model is constructed, including node and branch information in the distribution network; the position of the zero injection node of the distribution network is obtained, and a zero injection node matrix is ​​constructed; the nodes include transformers, loads, and distributed power sources in the distribution network; the branch information refers to the starting node number of each branch in the distribution network.

[0090] Merging of S2 zero injection nodes and construction of system node association matrix

[0091] According to the distribution network system model and the zero injection node matrix, all zero injection nodes are merged to construct the node association matrix of the system.

[0092]

[0093] The parameter n represents the number of nodes after merging, and its value should be equal to the total number of nodes in the distribution network minus the number of zero injection nodes. ij The value is 1, otherwise it is 0, and the diagonal elements are set to 1.

[0094] Construction of multi-objective PMU optimization configuration model for S3 distribution network

[0095] S3.1 Construction of objective function

[0096] Under the constraint condition of ensuring the global observability of the distribution system, corresponding objective functions are constructed with the minimum PMU deployment cost, the maximum system observation redundancy, the minimum probability of the system losing global observability when a single PMU line fails, the minimum PMU single-line failure loss, and the minimum standard deviation of the number of system node observations as optimization goals.

[0097] (1) The optimization goal is to minimize the cost of PMU deployment in the distribution network:

[0098] The topology of the power distribution network is complex. The cost of configuring PMUs at different nodes is different, and the global observability of the system can be achieved without configuring PMUs at all nodes. Therefore, PMU placement has become an important economic optimization problem. Its objective function is:

[0099]

[0100] Where N represents the total number of nodes in the power distribution system; w i represents the cost of deploying PMU on node i; x i The state variable indicating whether the ith node is configured with a PMU. When its value is 0, it indicates that the ith node is not configured with a PMU. When its value is 1, it indicates that the ith node is configured with a PMU.

[0101] (2) Taking the maximum system observation redundancy as the optimization goal:

[0102] System observation redundancy is the ratio of the number of independent measurements in the system to the number of state variables, which can improve the reliability of the system to a certain extent. Its objective function can be expressed as:

[0103]

[0104] Where S represents the set of nodes where PMU is deployed; d i Indicates the number of branches connected to node i.

[0105] (3) The optimization goal is to minimize the probability of the system losing global observability when a single PMU line fails:

[0106] In order to improve the observability of the power distribution system under the condition of a single-line fault of the PMU while measuring its economic efficiency, the present invention converts the constraint condition that the system maintains global observability under the condition of a single-line fault of the PMU into an objective function:

[0107]

[0108] Where, l represents the number of PMUs deployed in the power distribution system; c iIt represents the state variable of the system when the PMU deployed at the i-th node fails. When its value is 1, it means that the system is still globally observable. When its value is 0, it means that the system is not globally observable.

[0109] (4) The optimization goal is to minimize the loss caused by a single-line failure of the PMU:

[0110] If the distribution system cannot maintain global observability every time a single PMU line fails, it is necessary to calculate the observability loss of each single PMU line failure. If a single PMU line failure causes the system to lose global observability, the average number of unobservable nodes caused by the single PMU line failure is used as the loss indicator, and its objective function can be expressed as:

[0111]

[0112] Among them, D ij It means that when the PMU deployed at the i-th node fails, the state variable of the j-th node, when its value is 1, indicates that the j-th node is still observable, and when its value is 0, indicates that the j-th node is unobservable.

[0113] (5) The optimization goal is to minimize the standard deviation of the number of observed nodes in the system:

[0114] As the power distribution system's ability to resist single-line failure of the PMU increases, very high redundancy may be generated in some parts of the system, while very low redundancy may be generated in other parts. The present invention introduces the standard deviation of the number of observations of all nodes in the system to avoid the occurrence of redundancy imbalance. Its objective function is:

[0115]

[0116] Among them, i It represents the number of times the i-th node is observed, as shown in the following formula:

[0117]

[0118] S3.2 Construction of constraints

[0119] The purpose of this invention is to solve the optimal deployment scheme of PMU under the constraint condition of ensuring the global observability of the power distribution system, with the minimum PMU deployment cost, the maximum system observation redundancy, the minimum probability of the system losing global observability when a single-line PMU fails, the minimum loss of a single-line PMU failure, and the minimum standard deviation of the number of observed system nodes as the optimization objectives. The constraint formula is as follows:

[0120] AX ≥ b

[0121] Where A is the system's incidence matrix, X = [x1, x2, ..., x n ]T , x i The state variable representing the configuration of PMU at the i-th node. When its value is 0, it indicates that PMU is not configured at the i-th node. When its value is 1, it indicates that PMU is configured at the i-th node. b represents a column vector with a length of N and all elements are 1.

[0122] Solution of S4 multi-objective optimization problem

[0123] By using large-scale multi-objective optimization algorithms, such as NSGA3, MOEAD, Two_Arch2, etc., a large-scale multi-objective PMU optimization model considering single-line fault losses can be solved.

[0124] S5 uses a fuzzy decision method to select a flexible, multi-stage deployment plan from the optimal deployment plan set that can vary with the PMU deployment cost. Combining the subjective weight coefficient with the objective weight coefficient, the weight coefficient of the fuzzy decision method can be obtained.

[0125] S5.1 Determination of subjective weight coefficient

[0126] The subjective weight coefficient can be directly given by experienced experts, or by using AHP and other schemes. The subjective weight coefficient is denoted as W j , where j = 1, 2, ..., 5.

[0127] S5.2 Determination of objective weight coefficients

[0128] The decision-making process is limited by the decision-maker's psychological factors and experience knowledge, so the present invention adds an objective weight coefficient to offset this influence. The entropy weight method is an objective weighting method. In the specific use process, the entropy weight of each indicator is calculated based on the dispersion of the data of each indicator using information entropy, and then the entropy weight is corrected according to each indicator to obtain a more objective indicator weight.

[0129] 1) Establish decision matrix Y n×m , where n is the number of solutions in the optimal deployment solution set, m is the number of objective functions, and y ij That is, the objective function value of the jth objective function of the ith solution.

[0130] 2) Convert the decision matrix Y into the target relative advantage matrix F:

[0131]

[0132] 3) Calculate the entropy value of the jth indicator:

[0133]

[0134] in, And when fij = 0, f ij / f j =0.

[0135] 4) Calculate the entropy weight of the jth indicator:

[0136]

[0137] Example:

[0138] First, the topological information of the distribution network is imported, and the distribution network system model is constructed, including the starting node number of each branch in the distribution network and the position of the zero injection node. Then, all the zero injection nodes are merged according to the rules of S2 and the system association matrix A is constructed. Then, n deployment schemes are randomly generated and all of them are updated to qualified individuals according to the constraints in S3.2. These n deployment schemes will be used as the initial population of the large-scale multi-objective optimization algorithm. The PMU installation positions and their PMU installation costs of these n deployment schemes are imported into the five objective functions of S3.1. The large-scale multi-objective optimization algorithm is used to solve the objective function values ​​of these deployment schemes and select elite individuals according to their elite selection strategy for crossover or mutation to generate offspring for the next iteration. It is worth noting that the offspring generated in each iteration must meet the constraints of S3.2. After reaching the maximum number of iterations, the large-scale multi-objective optimization algorithm will output an optimal deployment solution set, and the solutions in this solution set are all non-dominated.

[0139] The optimal deployment solution set generated by S4 is used as the input of S5, and the subjective weight coefficient W is determined according to the rules of S5.1, and the objective weight coefficient W′ is determined according to the rules of S5.2, and then the two are combined as the final weight coefficient. Finally, a flexible multi-stage deployment plan that can change with the PMU deployment cost can be selected from the optimal deployment solution set generated by the large-scale multi-objective optimization algorithm through this fuzzy decision-making method.

[0140] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed in the present invention should be covered within the protection scope of the present invention.

Claims

1. A multi-stage, large-scale, multi-objective PMU optimization configuration method considering single-line faults, characterized in that: Obtain the topological structure of the distribution network and build a distribution network system model, including node and branch information in the distribution network; Obtain the zero injection node positions of the distribution network and construct a zero injection node matrix; According to the topological structure of the distribution network and the zero injection node matrix, the correlation matrix of the distribution network is constructed; Construct a multi-objective PMU optimization configuration model for distribution networks, including: Under the constraint condition of ensuring the global observability of the distribution system, the corresponding objective functions are constructed with the minimum PMU deployment cost, the maximum distribution system observation redundancy, the minimum probability of the distribution system losing global observability when a single PMU line fails, the minimum PMU single-line failure loss, and the minimum standard deviation of the number of distribution system node observations as optimization goals. A large-scale multi-objective optimization algorithm is used to solve the multi-objective PMU optimization configuration model of the distribution network to obtain the optimal PMU deployment solution set of the distribution network. The specific steps are as follows: According to the topological structure of the distribution network and the zero-injection node matrix, after constructing the association matrix of the distribution network, n deployment schemes are generated as the initial population, where the number and location of PMU deployments in each deployment scheme are random, and whether the n deployment schemes all meet the conditions for making the system in a globally observable state is determined, and the schemes that do not meet the conditions are updated to deployment schemes that meet the conditions; Import the updated n deployment schemes and the cost of deploying PMUs on each node into the objective function, solve the objective function values ​​of these deployment schemes and select the dominant individuals according to the screening conditions of the large-scale multi-objective optimization algorithm; The dominant individuals are used as parents to simulate binary crossover or mutation to generate offspring and the offspring are updated to a deployment scheme that satisfies the constraints; the parents and offspring are merged into one population and the dominant individuals are selected as the parents of the next iteration according to the screening conditions of the large-scale multi-objective optimization algorithm; After gmax iterations, the dominant individuals selected by the large-scale multi-objective optimization algorithm will be used as the optimal deployment solution set of PMUs in the distribution network; A fuzzy decision-making method combining subjective and objective factors is adopted to select a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set.

2. The multi-stage, large-scale, multi-objective PMU optimization configuration method considering single-line faults as claimed in claim 1 is characterized in that: The method of constructing a correlation matrix of the power distribution network according to the topological structure of the power distribution network and the zero injection node matrix comprises: A=merge(A′,Z) Where A′ represents the original association matrix of the system, Z represents the zero injection node matrix of the system, and the function merge represents a merging rule: Considering that in the IEEE 9-node system, nodes 4, 7, and 9 are all zero injection nodes, if the voltages of two nodes among nodes 1, 5, and 6 are known, the KCL law can be applied at node 4 to estimate the voltage of the third node. Based on this conclusion, the zero injection node can be merged with any node connected to it, so node 4 is merged to node 1, node 7 to node 2, and node 9 to node 3; The element a of the original incidence matrix A′ of the power distribution system i ' j Value: If node i is connected to node j, the value is 1, otherwise it is 0, and the diagonal elements are set to 1; the element z of the zero-injected node matrix Z i Value: If the node is a zero injection node, the value is 1, otherwise it is 0; The function of the merge function: merge the zero injection node with one of the nodes connected to it; The association matrix A is obtained by merging all zero-injected nodes in A′, and its element a ij Value and a i ' j Same rules.

3. The multi-stage, large-scale, multi-objective PMU optimization configuration method considering single-line faults as claimed in claim 1 is characterized in that: The objective function is constructed with the minimum deployment cost of PMU in the distribution network, which is as follows: stAX≥b Where N represents the total number of nodes in the power distribution system; w i represents the cost of deploying PMU on node i; x i The state variable representing the configuration of PMU at the i-th node. When its value is 0, it indicates that PMU is not configured at the i-th node. When its value is 1, it indicates that PMU is configured at the i-th node. b represents a column vector with a length of N and all elements are 1.

4. The multi-stage, large-scale, multi-objective PMU optimization configuration method considering single-line faults as claimed in claim 1 is characterized in that: The objective function is constructed based on the maximum observed redundancy of the distribution system, which is: Where S represents the set of nodes where PMU is deployed; d i represents the number of branches connected to node i; The objective function is constructed by minimizing the probability of the distribution system losing global observability when a single-line PMU fails. Specifically, it is: Where, l represents the number of PMUs deployed in the power distribution system; c i It represents the state variable of the system when the PMU deployed at the i-th node fails. When its value is 1, it means that the system is still globally observable. When its value is 0, it means that the system is not globally observable.

5. The multi-stage, large-scale, multi-objective PMU optimization configuration method considering single-line faults as claimed in claim 1 is characterized in that: The objective function is constructed with the minimum loss of PMU single-line fault, specifically: Among them, D ij It means that when the PMU deployed at the i-th node fails, the state variable of the j-th node, when its value is 1, indicates that the j-th node is still observable, and when its value is 0, indicates that the j-th node is unobservable; The objective function is constructed by minimizing the standard deviation of the number of observations of the distribution system nodes, specifically: Among them, i Indicates the number of times the i-th node is observed.

6. The multi-stage, large-scale, multi-objective PMU optimization configuration method considering single-line faults as claimed in claim 1 is characterized in that: The method adopts a fuzzy decision-making method combining subjective and objective factors to select a flexible multi-stage PMU deployment plan from the optimal deployment plan set, including: firstly determining the subjective weight coefficient of each objective function by means of a hierarchical analysis method, then determining the objective weight coefficient of each objective function by means of an entropy weight method, and finally superimposing the weight coefficients of the two and applying them to the PMU optimal deployment plan set obtained by a large-scale multi-objective optimization algorithm, thereby selecting a flexible multi-stage PMU deployment plan.

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