CN114896745A - Multi-stage large-scale multi-objective PMU (phasor measurement Unit) optimal configuration method considering single-line fault - Google Patents

Multi-stage large-scale multi-objective PMU (phasor measurement Unit) optimal configuration method considering single-line fault Download PDF

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CN114896745A
CN114896745A CN202210489490.0A CN202210489490A CN114896745A CN 114896745 A CN114896745 A CN 114896745A CN 202210489490 A CN202210489490 A CN 202210489490A CN 114896745 A CN114896745 A CN 114896745A
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曹斌
闫彦龙
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Abstract

The invention relates to the field of power system monitoring and PMU optimal configuration, aiming at reducing overhigh observation redundancy on the premise of ensuring the overall observability, the invention considers a single-line fault multi-stage large-scale multi-target PMU optimal configuration method, obtains a topological structure of a power distribution network and constructs a power distribution network system model; constructing an incidence matrix of the power distribution network according to the topological structure of the power distribution network and the zero injection node matrix; constructing a multi-target synchronous Phasor Measurement Unit (PMU) optimal configuration model of a power distribution network; solving a multi-target PMU optimal configuration model of the power distribution network by adopting a large-scale multi-target optimization algorithm to obtain an optimal PMU deployment scheme set of the power distribution network; and selecting a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set by adopting a fuzzy decision method combining subjectivity and objectivity. The invention is mainly applied to the monitoring occasions of the power system.

Description

Multi-stage large-scale multi-objective PMU (phasor measurement Unit) optimal configuration method considering single-line fault
Technical Field
The invention relates to the field of monitoring of a power system and optimal configuration of PMUs, in particular to a multi-stage large-scale multi-objective PMU optimal configuration method considering single-line faults.
Background
In order to deal with the energy crisis and the environmental protection pressure, more and more renewable energy-dominated distributed power sources are connected into the power system, but the intermittent and uncertain characteristics make the operation of the power system face serious challenges. Developing a smart grid is an effective way to solve this problem.
The synchronous Phasor Measurement Unit (PMU) taking the GPS as a time reference not only meets the requirements of space wide area and time identity of data acquisition and monitoring of a power system, but also can acquire amplitude information and phase angle information of voltage and current. The real-time monitoring and analysis of the running state of the electric power system with wide regions can be realized, and the real-time control and running service of the electric power system can be realized. In recent years, with the commercialization of 5G communication technology, the advantages of high stability and high transmission speed lay a solid foundation for the wide use of PMUs in power systems.
To monitor and control the entire distribution network in real time, the system must be globally observable. If all nodes of the distribution network have PMUs deployed, all node voltages and branch currents are observable. However, since the PMU is expensive to deploy and can measure the voltage phasor of the installation node and the current phasor of the connected branches, it is not practical and necessary to deploy PMUs on all nodes of the network.
The optimal PMU deployment for a power distribution network mainly takes into account the following four issues: (1) reducing the deployment quantity of PMUs on the premise of ensuring that the system is globally observable; (2) enabling a distribution network to have higher observable redundancy; (3) when the PMU has a single-wire fault, the system is ensured not to lose the global observability; (4) optimal PMU deployment is made taking into account PMU channel number limitations as well as communication facility limitations.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to reduce overhigh observation redundancy and realize efficient PMU optimal configuration on the premise of ensuring the global observability, and the technical scheme adopted by the invention is to consider a single-line fault multi-stage large-scale multi-target PMU optimal configuration method, obtain the topological structure of a power distribution network and construct a power distribution network system model which comprises node and branch information in the power distribution network; acquiring a zero injection node position of a power distribution network, and constructing a zero injection node matrix;
constructing an incidence matrix of the power distribution network according to the topological structure of the power distribution network and the zero injection node matrix;
the method for constructing the optimal configuration model of the multi-target synchronous phasor measurement unit PMU of the power distribution network comprises the following steps:
under the constraint condition of ensuring the global observability of the power distribution system, constructing corresponding objective functions respectively by taking the minimum PMU deployment cost, the maximum observed redundancy of the power distribution system, the minimum probability of losing the global observability of the power distribution system when a PMU single-line fault occurs, the minimum PMU single-line fault loss and the minimum standard deviation of the observed number of nodes of the power distribution system as optimization targets;
solving a multi-target PMU optimal configuration model of the power distribution network by adopting a large-scale multi-target optimization algorithm to obtain an optimal PMU deployment scheme set of the power distribution network;
and selecting a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set by adopting a fuzzy decision method combining subjectivity and objectivity.
The constructing of the incidence matrix of the power distribution network according to the topology structure and the zero injection node matrix of the power distribution network includes:
A＝merge(A′,Z)
wherein, A' represents the original incidence 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 IEEE9 node system, nodes 4, 7, and 9 are all zero injection nodes, if the voltages of two of nodes 1, 5, and 6 are known, the KCL law can be applied to estimate the voltage of the third node at node 4, and based on this conclusion, the zero injection node can be merged with any node connected to it, merging node 4 to node 1, node 7 to node 2, and node 9 to node 3;
element a ' of primary correlation matrix A ' of the power distribution system ' ij Taking values: if the node i is connected with the node j, the value is 1, otherwise, the value is 0, and the diagonal element is defined as 1; what is needed isElement Z of the zero injection node matrix Z i Taking values: if the node is a zero injection node, the value is 1, otherwise, the value is 0; the function merge is: merging the zero injection node with one of the nodes connected to it;
the incidence matrix A is obtained by combining all zero injection nodes by A', and the element a of the incidence matrix A ij Value and a' ij The rules are the same.
The method comprises the following steps of constructing a target function with least PMU deployment cost of a power distribution network, specifically:
Figure BDA0003631024250000021
s.t.AX≥b
wherein N represents the total number of nodes in the power distribution system; w is a i Represents the cost of deploying PMUs on node i; x is the number of i When the value of the state variable which represents that the ith node configures the PMU is 0, the state variable which represents that the ith node does not configure the PMU, and when the value of the state variable which represents that the ith node configures the PMU is 1, the state variable which represents that the ith node configures the PMU is present; b represents a column vector of length N and all elements 1.
The method for observing the maximum construction target function of the redundancy by using the power distribution system specifically comprises the following steps:
Figure BDA0003631024250000022
wherein S represents a node set for deploying PMU; d i Indicating the number of branches connected to node i.
The method comprises the following steps of constructing an objective function with the minimum probability that a power distribution system loses global observability when a PMU single-line fault occurs, specifically:
Figure BDA0003631024250000023
wherein l represents the number of PMUs deployed by the power distribution system; c. C i The system state variable is represented when PMU deployed at the ith node fails, when the value of the system state variable is 1, the system is still globally observable, and the value of the system state variable is representedA value of 0 indicates that the system is not fully observable.
Constructing an objective function with the minimum single-line fault loss of the PMU, specifically:
Figure BDA0003631024250000024
wherein D is ij When a PMU deployed at an ith node fails, a state variable of the jth node indicates that the jth node is still observable when the value of the state variable is 1, and indicates that the jth node is not observable when the value of the state variable is 0.
The method comprises the following steps of constructing a target function by using the minimum standard deviation of observed numbers of nodes of a power distribution system, and specifically comprises the following steps:
Figure BDA0003631024250000031
wherein o is i Represents the number of times the ith node is observed, as shown in the following formula:
Figure BDA0003631024250000032
the method for solving the multi-target PMU optimized deployment model of the power distribution network by adopting the large-scale multi-target optimization algorithm to obtain the PMU optimal deployment scheme set of the power distribution network comprises the following steps:
according to a topological structure and a zero injection node matrix of a power distribution network, after an incidence matrix of the power distribution network is constructed, n deployment schemes are generated as an initial population, wherein the PMU deployment quantity and the position of each deployment scheme are random, whether the n deployment schemes all meet the condition that a system is in a global observable state or not is judged, and the schemes which do not meet the condition are updated into the deployment schemes which meet the condition;
leading the updated n deployment schemes and the cost of deploying PMUs by each node into the objective function, solving each objective function value of the deployment schemes, and selecting out a dominant individual according to the screening condition of the large-scale multi-objective optimization algorithm;
performing simulated binary crossing or mutation on the dominant individual as a parent to generate a child and updating the child into a deployment scheme meeting constraint conditions; combining the parent and the offspring into a population, and selecting the dominant individual as the parent of the next iteration according to the screening condition of the large-scale multi-objective optimization algorithm;
after the gmax iterations, the dominant individuals screened out by the large-scale multi-objective optimization algorithm are used as an optimal PMU deployment scheme set of the power distribution network.
The method for selecting a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set by adopting a fuzzy decision method combining subjectivity and objectivity comprises the following steps: firstly, subjective weight coefficients of each target function are determined through an analytic hierarchy process, then objective weight coefficients of each target function are determined through an entropy weight method, and finally the weight coefficients of the objective weight coefficients and the objective weight coefficients are overlapped and applied to a PMU optimal deployment scheme set obtained through a large-scale multi-target optimization algorithm, so that a flexible multi-stage PMU deployment scheme is selected.
The invention has the characteristics and beneficial effects that:
on the premise of ensuring that the distribution network has global observability, the invention searches for a deployment scheme which uses the PMU deployment cost as less as possible to realize that the observable redundancy of the system is as large as possible, the PMU single-line fault loss is as small as possible, the system redundancy is as uniform as possible, and the system has the possibility of incomplete observability due to the PMU single-line fault and is as small as possible. And a flexible multi-stage deployment scheme which can change along with the deployment cost of the PMU is obtained by combining a fuzzy decision method.
Description of the drawings:
FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a topology diagram of an IEEE9 node power distribution system without zero injection node merging.
Fig. 3 is a topology diagram of an IEEE9 node power distribution system with zero injection node merging.
Detailed Description
In the technical scheme without considering PMU single-wire fault, some nodes can be observed only once, and the loss of the observed value causes the loss of global observability of the network. In the solution considering PMU single wire fault, a single node will be observed at least twice, which may lead to a surge in costs for PMU deployment and may create too high observation redundancy in the distribution network. In order to solve the problem, the invention converts the single-line fault of the PMU from a constraint condition to an objective function, and provides a multi-stage large-scale multi-objective PMU optimal configuration method considering the single-line fault loss.
A multi-stage large-scale multi-objective PMU optimal configuration method considering single line fault loss comprises the following steps:
acquiring a topological structure of a power distribution network, and constructing a power distribution network system model, wherein the power distribution network system model comprises node and branch information in the power distribution network; acquiring a zero injection node position of a power distribution network, and constructing a zero injection node matrix;
constructing an incidence matrix of the power distribution network according to the topological structure of the power distribution network and the zero injection node matrix;
the method for constructing the multi-target PMU optimal configuration model of the power distribution network comprises the following steps:
under the constraint condition of ensuring the global observability of the power distribution system, corresponding objective functions are respectively constructed by taking the minimum PMU deployment cost, the maximum system observation redundancy, the minimum probability of losing the global observability of the system when the PMU single line fails, the minimum PMU single line failure loss and the minimum standard deviation of the observed number of system nodes as optimization objectives.
And solving the multi-target PMU optimal configuration model of the power distribution network by adopting a large-scale multi-target optimization algorithm to obtain an optimal PMU deployment scheme set of the power distribution network.
A fuzzy decision method combining subjectivity and objectivity is adopted to select a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set.
Further, the constructing a correlation matrix of the power distribution network according to the topology of the power distribution network and the zero injection node matrix includes:
A＝merge(A′,Z)
wherein, A' represents the original incidence matrix of the system, Z represents the zero injection node matrix of the system, and the function merge represents a merging rule: consider that in the IEEE9 node system shown in fig. 2, the 4, 7, and 9 nodes are all zero injection nodes. If the voltages of two of nodes 1, 5, 6 are known, the voltage of the third node can be estimated at node 4 using KCL law. Based on this conclusion, the zero injection node can be merged with any node connected to it. The system after node 4 is merged to node 1, node 7 to node 2, and node 9 to node 3 is shown in fig. 3;
element a ' of the primary correlation matrix A ' of the system ' ij Taking values: if the node i is connected with the node j, the value is 1, otherwise, the value is 0, and the diagonal element is defined as 1; element Z of the zero injection node matrix Z i Taking values: if the node is a zero injection node, the value is 1, otherwise, the value is 0; the function merge: merging the zero injection node with one of the nodes connected to it;
the incidence matrix A is obtained by combining all zero injection nodes by A', and the element a of the incidence matrix A ij Value and a' ij The rules are the same.
Further, an objective function is constructed with the least deployment cost of the power distribution network PMU, specifically:
Figure BDA0003631024250000041
s.t.AX≥b
wherein N represents the total number of nodes in the power distribution system; w is a i Represents the cost of deploying PMUs on node i; x is the number of i When the value of the state variable which represents that the ith node configures the PMU is 0, the state variable which represents that the ith node does not configure the PMU, and when the value of the state variable which represents that the ith node configures the PMU is 1, the state variable which represents that the ith node configures the PMU is present; b represents a column vector of length N and all elements 1.
Further, a system observation redundancy maximum construction objective function is specifically as follows:
Figure BDA0003631024250000051
wherein S represents a node set for deploying PMU; d i Indicating the number of branches connected to node i.
Further, the method includes that an objective function is constructed with the smallest probability that a system loses global observability when a PMU single-line fault occurs, and specifically includes:
Figure BDA0003631024250000052
wherein l represents the number of PMUs deployed by the power distribution system; c. C i The system state variable is used for representing the state variable of the system when the PMU deployed at the ith node fails, when the value of the system state variable is 1, the system is still globally observable, and when the value of the system state variable is 0, the system is not fully locally observable.
Further, an objective function is constructed with a PMU single-wire fault loss minimum, specifically:
Figure BDA0003631024250000053
wherein D is ij When a PMU deployed at an ith node fails, a state variable of the jth node indicates that the jth node is still observable when the value of the state variable is 1, and indicates that the jth node is not observable when the value of the state variable is 0.
Further, constructing an objective function with the minimum standard deviation of the observed number of the system nodes, specifically:
Figure BDA0003631024250000054
wherein o is i Represents the number of times the ith node is observed, as shown in the following formula:
Figure BDA0003631024250000055
further, the solving of the multi-objective PMU optimized deployment model of the power distribution network by using the large-scale multi-objective optimization algorithm to obtain an optimal PMU deployment scheme set of the power distribution network includes:
according to the topological structure of the power distribution network and the zero injection node matrix, after the incidence matrix of the power distribution network is constructed, n deployment schemes are generated to serve as an initial population, wherein the PMU deployment quantity and the PMU deployment position of each deployment scheme are random. And judging whether the n deployment schemes all meet the requirement of enabling the system to be in a global observable state and updating the scheme which does not meet the condition into the deployment scheme which meets the condition.
And importing the updated n deployment schemes and the cost for deploying the PMU by each node into the objective function, solving each objective function value of the deployment schemes, and selecting the dominant individual according to the screening conditions of the large-scale multi-objective optimization algorithm.
And performing simulated binary crossing or mutation on the dominant individual as a parent to generate a child and updating the child into a deployment scheme meeting the constraint condition. And combining the parent and the offspring into a population, and selecting the dominant individual as the parent of the next iteration according to the screening condition of the large-scale multi-objective optimization algorithm.
After the gmax iterations, the dominant individuals screened out by the large-scale multi-objective optimization algorithm are used as an optimal PMU deployment scheme set of the power distribution network.
Further, the method for selecting a flexible multi-stage PMU deployment scenario from an optimal deployment scenario set by using a fuzzy decision method combining subjective and objective includes:
the method comprises the steps of firstly determining a subjective weight coefficient of each target function through an analytic hierarchy process, then determining an objective weight coefficient of each target function through an entropy weight method, and finally superposing the weight coefficients and applying the superposed weight coefficients to a PMU optimal deployment scheme set obtained through a large-scale multi-target optimization algorithm, so that a flexible multi-stage PMU deployment scheme is selected.
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The PMU is an important component of the smart power grid, the synchronous error of the data section acquired by the PMU based on GPS unified time service is only 100 plus 1000 nanoseconds, and is much smaller than that of an SCADA system which acquires the data section synchronous error for about 5 seconds at most, so that better support can be provided for real-time monitoring and control of a power distribution network. If a PMU is deployed on each node of the distribution network, the system can realize global observation; however, the high cost and high communication conditions of PMUs limit their wide deployment and system global observability can be achieved even if PMUs are not deployed on all nodes, so it is not necessary to deploy PMUs on all nodes. Meanwhile, the application of kirchhoff's law and ohm's law to the zero injection node can also significantly reduce the number of PMUs required in the system:
(1) the node where the PMU is deployed can be directly observed, and the voltage and the branch current of the node connected to the node can also be observed; (2) when the voltage phasors at two ends of the branch circuit are known, the current phasor of the branch circuit can be indirectly observed; (3) for a zero injection node with N branches, when the current phasors of N-1 branches are known, the current phasor of the Nth branch can be calculated; (4) a zero injection node is indirectly observable if its observability is unknown, but the nodes to which it is connected are all observable.
For the zero injection node, the KCL law and the ohm law can be combined on any node connected with the zero injection node through application of the KCL law and the ohm law, so that the PMU deployment number required for realizing the overall observability of the power distribution system is reduced.
The idea of the invention is as follows: because a power grid enterprise may not deploy enough PMUs at one time to meet the requirement that a power distribution system guarantees the global observability of the system under the constraint condition of single-line PMU fault, the constraint condition is converted into a target function, and on the premise of guaranteeing the global observability of the system, a deployment scheme is searched for, wherein the deployment cost of the PMUs is as low as possible, the observable redundancy of the system is as large as possible, the PMU single-line fault loss is as small as possible, the system redundancy is as uniform as possible, and the probability that the system is not fully considerable due to the PMU single-line fault is as small as possible. And a flexible multi-stage deployment scheme which can change along with the deployment cost of the PMU is obtained by combining a fuzzy decision method.
Referring to fig. 1, the multi-stage large-scale multi-objective PMU optimal configuration method considering single-line fault loss provided by the invention includes the following steps:
construction of S1 distribution network model
Acquiring a topological structure of a power distribution network, and constructing a power distribution network system model, wherein the power distribution network system model comprises node and branch information in the power distribution network; acquiring a zero injection node position of a power distribution network, and constructing a zero injection node matrix; the nodes comprise transformers, loads, distributed power supplies and the like in a power distribution network; the branch information assigns the initial node number of each branch in the electric network.
S2 combination of zero injection nodes and construction of system node incidence matrix
And combining all the zero injection nodes according to the distribution network system model and the zero injection node matrix to construct a node incidence matrix of the system.
Figure BDA0003631024250000061
Where the parameter n represents the number of nodes after merging, the value of which should be equal to the total number of nodes in the distribution network minus the number of zero injection nodes. If node i is connected to node j then a ij The value is 1, otherwise 0, and the diagonal element is defined as 1.
S3 construction of multi-target PMU (phasor measurement Unit) optimal configuration model of power distribution network
S3.1 construction of an objective function
Under the constraint condition of ensuring the global observability of the power distribution system, corresponding objective functions are respectively constructed by taking the minimum PMU deployment cost, the maximum system observation redundancy, the minimum probability of losing the global observability of the system when the PMU single line fails, the minimum PMU single line failure loss and the minimum standard deviation of the observed number of system nodes as optimization objectives.
(1) The method takes the minimum PMU deployment cost of the power distribution network as an optimization target:
the topological structure of the power distribution network is complicated, the cost for configuring PMUs by different nodes is different, and the system can be observed globally without configuring PMUs on all nodes, so that PMU placement becomes an important economic optimization problem. The objective function is:
Figure BDA0003631024250000071
wherein N represents the total number of nodes in the power distribution system; w is a i Represents the cost of deploying PMUs on node i; x is the number of i And when the value of the state variable which represents that the ith node configures the PMU is 0, the state variable which represents that the ith node does not configure the PMU, and when the value of the state variable which represents that the ith node configures the PMU is 1, the state variable which represents that the ith node configures the PMU is provided.
(2) The maximum of the system observation redundancy is an optimization target:
the system observation redundancy is the ratio of the number of independent measurements to the number of state variables in the system, and can improve the reliability of the system to a certain extent. Its objective function can be expressed as:
Figure BDA0003631024250000072
wherein S represents a node set for deploying PMU; d is a radical of i Indicating the number of branches connected to node i.
(3) The method takes the minimum probability that the system loses global observability when a PMU single-wire fault occurs as an optimization target:
in order to improve the observability of a power distribution system under the condition of a PMU single-line fault and simultaneously measure the economy of the power distribution system, the constraint condition that the system keeps global observability under the PMU single-line fault is converted into an objective function:
Figure BDA0003631024250000073
wherein l represents the number of PMUs deployed by the power distribution system; c. C i The system state variable is used for representing the state variable of the system when the PMU deployed at the ith node fails, when the value of the system state variable is 1, the system is still globally observable, and when the value of the system state variable is 0, the system is not fully locally observable.
(4) The PMU single line fault loss is minimized as an optimization target:
if the power distribution system cannot maintain global observability at each PMU single line fault, then the observability loss for each PMU single line fault needs to be calculated. If the PMU single-line fault causes the system to lose global observability, the average number of unobservable nodes caused by the PMU single-line fault is used as a loss index, and the objective function can be expressed as follows:
Figure BDA0003631024250000074
wherein D is ij When a PMU deployed at the ith node fails, a state variable of the jth node with a value of 1 indicates that the jth node is still observable, and a value of 0 indicates that the jth node is not observable.
(5) And (3) taking the minimum standard deviation of the observed number of the system nodes as an optimization target:
as the ability of the power distribution system to withstand PMU single line faults increases, very high redundancy may be produced in some parts of the system and very low redundancy in other parts. The invention introduces the standard deviation of the observed number of all nodes in the system to avoid the occurrence of the situation of redundancy unbalance. The objective function is:
Figure BDA0003631024250000081
wherein o is i Represents the number of times the ith node is observed, as shown in the following formula:
Figure BDA0003631024250000082
s3.2 construction of constraints
The invention aims to solve the optimal PMU deployment scheme by taking the minimum PMU deployment cost, the maximum system observation redundancy, the minimum probability of losing the global observability of the system when the PMU single line fails, the minimum PMU single line fault loss and the minimum standard deviation of the observed number of system nodes as optimization targets under the constraint condition of ensuring the global observability of the power distribution system. The constraint formula is as follows:
AX≥b
where A is the correlation matrix of the system, X ═ X 1 ,x 2 ,...,x n ] T ，x i When the value of the state variable which represents that the ith node configures the PMU is 0, the state variable which represents that the ith node does not configure the PMU, and when the value of the state variable which represents that the ith node configures the PMU is 1, the state variable which represents that the ith node configures the PMU is present; b represents a column vector of length N and all elements 1.
Solving of S4 multi-objective optimization problem
By adopting a large-scale multi-objective optimization algorithm, such as NSGA3, MOEAD, Two _ Arch2 and the like, a large-scale multi-objective PMU optimization model considering single-line fault loss can be solved.
S5, a flexible multi-stage deployment scheme which can change with PMU deployment cost is selected from the optimal deployment scheme set by adopting a fuzzy decision method. The subjective weight coefficient and the objective weight coefficient are combined to obtain the weight coefficient of the fuzzy decision method.
S5.1 determination of subjective weighting coefficients
The subjective weight coefficient can be directly given by an expert with abundant experience, or given by adopting schemes such as an AHP analytic hierarchy process and the like. The subjective weighting factor is denoted as W j Wherein j is 1, 2.
S5.2 determination of the Objective weighting coefficients
The decision making process is limited by psychological factors and empirical knowledge of the decision maker, so the invention adds an objective weight coefficient to counteract the influence. The entropy weight method is an objective weighting method, and in the specific use process, the entropy weight of each index is calculated by using the information entropy according to the dispersion degree of data of each index, and then certain correction is carried out on the entropy weight according to each index, so that objective index weight is obtained.
1) Establishing a decision matrix Y n×m Wherein n is the number of the schemes in the optimal deployment scheme set, m is the number of the objective functions, and y ij Namely the objective function value of the jth objective function of the ith scheme.
2) Converting the decision matrix Y into a target relative advantage matrix F:
Figure BDA0003631024250000091
3) calculating the entropy value of the j index:
Figure BDA0003631024250000092
wherein the content of the first and second substances,
Figure BDA0003631024250000093
and when f ij When equal to 0, f ij /f j ＝0。
4) Calculating the entropy weight of the jth index:
Figure BDA0003631024250000094
example (b):
firstly, topology information of a power distribution network is imported, a power distribution network system model is constructed, the power distribution network system model comprises the initial node numbers and the zero injection node positions of all branches in the power distribution network, and then all the zero injection nodes are combined according to the rule of S2 and a system incidence matrix A is constructed. And then randomly generating n deployment schemes which are used as initial populations of the large-scale multi-objective optimization algorithm and updating all the deployment schemes into qualified individuals according to the constraint conditions in S3.2. And importing the PMU installation positions of the n deployment schemes and the PMU installation cost into 5 objective functions of S3.1, solving the objective function values of the deployment schemes by using a large-scale multi-objective optimization algorithm, and selecting elite individuals according to an elite selection strategy to perform crossing or variation to generate filial generations for next iteration. It is worth noting that the child generated at each iteration must satisfy the S3.2 constraint. After the maximum iteration number is reached, the large-scale multi-objective optimization algorithm outputs an optimal deployment solution set, and solutions in the solution set are all non-dominant.
And taking the optimal deployment solution set generated in the step S4 as an input of the step S5, determining a subjective weight coefficient W according to a rule of S5.1, determining an objective weight coefficient W 'according to a rule of S5.2, and combining the subjective weight coefficient W and the objective weight coefficient W' to obtain a final weight coefficient. Finally, a flexible multi-stage deployment scheme which can change along with PMU deployment cost is selected from the optimal deployment solution set generated by the large-scale multi-objective optimization algorithm through the fuzzy decision method.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (7)

1. A multi-stage large-scale multi-objective PMU optimal configuration method considering single-line faults is characterized by comprising the steps of obtaining a topological structure of a power distribution network, and constructing a power distribution network system model, wherein the power distribution network system model comprises node and branch information in the power distribution network; acquiring a zero injection node position of a power distribution network, and constructing a zero injection node matrix;
constructing an incidence matrix of the power distribution network according to the topological structure of the power distribution network and the zero injection node matrix;
the method for constructing the optimal configuration model of the multi-target synchronous phasor measurement unit PMU of the power distribution network comprises the following steps:
under the constraint condition of ensuring the global observability of the power distribution system, constructing corresponding objective functions respectively by taking the minimum PMU deployment cost, the maximum observed redundancy of the power distribution system, the minimum probability of losing the global observability of the power distribution system when a PMU single-line fault occurs, the minimum PMU single-line fault loss and the minimum standard deviation of the observed number of nodes of the power distribution system as optimization targets;
solving a multi-target PMU optimal configuration model of the power distribution network by adopting a large-scale multi-target optimization algorithm to obtain an optimal PMU deployment scheme set of the power distribution network;
and selecting a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set by adopting a fuzzy decision method combining subjectivity and objectivity.
2. The multi-stage large-scale multi-objective PMU optimal configuration method for considering single-line faults according to claim 1, wherein the constructing of the incidence matrix of the distribution network according to the topology structure and the zero-injection node matrix of the distribution network comprises the following steps:
A＝merge(A′,Z)
wherein, A' represents the original incidence 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 IEEE9 node system, nodes 4, 7, and 9 are all zero injection nodes, if the voltages of two of nodes 1, 5, and 6 are known, the KCL law can be applied to estimate the voltage of the third node at node 4, and based on this conclusion, the zero injection node can be merged with any node connected to it, merging node 4 to node 1, node 7 to node 2, and node 9 to node 3;
element a ' of primary correlation matrix A ' of the power distribution system ' ij Taking values: if the node i is connected with the node j, the value is 1, otherwise, the value is 0, and the diagonal element is defined as 1; element Z of the zero injection node matrix Z i Taking values: if the node is a zero injection node, the value is 1, otherwise, the value is 0; the function merge is: merging the zero injection node with one of the nodes connected to it;
the incidence matrix A is obtained by combining all zero injection nodes by A', and the element a of the incidence matrix A ij Value and a' ij The rules are the same.
3. The multi-stage large-scale multi-objective PMU optimal configuration method considering single-line faults according to claim 1, characterized in that an objective function is constructed with least deployment cost of PMUs of a power distribution network, and specifically comprises the following steps:
Figure FDA0003631024240000011
s.t.AX≥b
wherein N represents the total number of nodes in the power distribution system; w is a i Represents the cost of deploying PMUs on node i; x is the number of i When the value of the state variable which represents the configuration PMU of the ith node is 0, the state variable represents that the ith node does not haveWhen the value of the configuration PMU is 1, the configuration PMU is present at the ith node; b represents a column vector of length N and all elements 1.
4. The multi-stage large-scale multi-objective PMU optimal configuration method considering single-line faults as recited in claim 1, characterized in that a power distribution system is used for observing a redundancy maximum construction objective function, and specifically comprises the following steps:
Figure FDA0003631024240000021
wherein S represents a node set for deploying PMU; d is a radical of i Indicating the number of branches connected to node i.
The method comprises the following steps of constructing an objective function with the minimum probability that a power distribution system loses global observability when a PMU single-line fault occurs, specifically:
Figure FDA0003631024240000022
wherein l represents the number of PMUs deployed by the power distribution system; c. C i The system state variable is used for representing the state variable of the system when the PMU deployed at the ith node fails, when the value of the system state variable is 1, the system is still globally observable, and when the value of the system state variable is 0, the system is not fully locally observable.
5. The multi-stage large-scale multi-objective PMU optimal configuration method considering single-line faults according to claim 1, characterized in that an objective function is constructed with the PMU single-line fault loss minimum, and specifically comprises:
Figure FDA0003631024240000023
wherein D is ij When a PMU deployed at an ith node fails, a state variable of the jth node indicates that the jth node is still observable when the value of the state variable is 1, and indicates that the jth node is not observable when the value of the state variable is 0.
The method comprises the following steps of constructing a target function by using the minimum standard deviation of observed numbers of nodes of a power distribution system, and specifically comprises the following steps:
Figure FDA0003631024240000024
Figure FDA0003631024240000025
wherein o is i Indicating the number of times the ith node was observed.
6. The method according to claim 1, wherein the obtaining the optimal PMU deployment scenario set of the power distribution network by solving the multi-objective PMU deployment model of the power distribution network using the large-scale multi-objective optimization algorithm includes:
according to a topological structure and a zero injection node matrix of a power distribution network, after an incidence matrix of the power distribution network is constructed, n deployment schemes are generated as an initial population, wherein the PMU deployment quantity and the position of each deployment scheme are random, whether the n deployment schemes all meet the condition that a system is in a global observable state or not is judged, and the schemes which do not meet the condition are updated into the deployment schemes which meet the condition;
leading the updated n deployment schemes and the cost of deploying PMUs by each node into the objective function, solving each objective function value of the deployment schemes, and selecting out a dominant individual according to the screening condition of the large-scale multi-objective optimization algorithm;
performing simulated binary crossing or mutation on the dominant individual as a parent to generate a child and updating the child into a deployment scheme meeting constraint conditions; combining the parent and the offspring into a population, and selecting the dominant individual as the parent of the next iteration according to the screening condition of the large-scale multi-objective optimization algorithm;
after the gmax iterations, the dominant individuals screened out by the large-scale multi-objective optimization algorithm are used as an optimal PMU deployment scheme set of the power distribution network.
7. The multi-stage large-scale multi-objective PMU optimization configuration method for considering single-line faults according to claim 1, characterized in that the method for selecting a flexible multi-stage PMU deployment scheme from the optimal deployment scheme set by using a fuzzy decision method combining subjectivity and objectivity comprises the following steps: firstly, subjective weight coefficients of each target function are determined through an analytic hierarchy process, then objective weight coefficients of each target function are determined through an entropy weight method, and finally the weight coefficients of the objective weight coefficients and the objective weight coefficients are overlapped and applied to a PMU optimal deployment scheme set obtained through a large-scale multi-target optimization algorithm, so that a flexible multi-stage PMU deployment scheme is selected.
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CN115693668A (en) * 2023-01-05 2023-02-03 国网上海市电力公司 Power distribution network PMU multi-objective optimization point distribution method based on entropy weight ideality sorting
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CN115693668A (en) * 2023-01-05 2023-02-03 国网上海市电力公司 Power distribution network PMU multi-objective optimization point distribution method based on entropy weight ideality sorting
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