CN114123165A - Medium-voltage distribution network directed topology identification method based on directed adjacency matrix - Google Patents

Medium-voltage distribution network directed topology identification method based on directed adjacency matrix Download PDF

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CN114123165A
CN114123165A CN202111186939.8A CN202111186939A CN114123165A CN 114123165 A CN114123165 A CN 114123165A CN 202111186939 A CN202111186939 A CN 202111186939A CN 114123165 A CN114123165 A CN 114123165A
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directed
node
topology
power
distribution network
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茅东华
裘瑾怡
汪晓琴
裘卫星
王春雷
章立宗
陈涛涛
张锋明
王青青
赵健
王炜韬
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State Grid Zhejiang Electric Power Co Ltd Xinchang County Power Supply Co
Innovation And Entrepreneurship Center Of State Grid Zhejiang Electric Power Co ltd
Shanghai Electric Power University
Shaoxing Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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State Grid Zhejiang Electric Power Co Ltd Xinchang County Power Supply Co
Innovation And Entrepreneurship Center Of State Grid Zhejiang Electric Power Co ltd
Shanghai Electric Power University
Shaoxing Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention discloses a medium voltage distribution network directed topology identification method based on a directed adjacency matrix, which comprises the following steps: establishing a directed adjacency matrix of node voltages according to real-time voltage amplitude measurement data, and judging whether the topology changes; according to the power measurement data of a plurality of time sections, a node directed adjacency matrix is used as an optimization variable to construct a target function mathematical model of topology identification; linearizing a nonlinear constraint condition in the mathematical model of the objective function by adopting a large M method; inputting the active and reactive measurement data and the pseudo measurement data of the branches of the plurality of time sections into a linearized mathematical model, and obtaining the minimum weighted sum of squares of the residual errors to obtain the directed topology structure of the power distribution network. According to the method, through the linearization processing of the model, the topology identification can be well carried out by utilizing the pseudo quantity measurement and the limited quantity measurement of the power distribution network, the problem that the directed topology of the power distribution network cannot be accurately identified in the prior art is solved, and the method is simple and convenient and has high accuracy.

Description

Medium-voltage distribution network directed topology identification method based on directed adjacency matrix
Technical Field
The invention belongs to the technical field of power distribution of a power system, and particularly relates to a directed topology identification method of a power distribution network.
Background
The power distribution network is usually designed in a closed loop mode and operates in an open loop mode, radiation is kept during normal operation, when faults occur or optimal control is carried out, the section switch and the connection line act, the topological structure of the power distribution network is changed, and the trend direction of partial branches is changed. Under the current distribution automation level, part of section switches in a power distribution network are not provided with distribution automation terminals, and after the switches act, the remote signaling and remote measuring functions do not exist, so that the report needs to be manually checked, the network topology stored in the system cannot be updated in time, and the safe and economic operation of the power distribution network is influenced.
The topology identification method of the existing power distribution network is roughly divided into a data driving method, a linear programming method and the like. The data-driven approach requires the distribution network to be equipped with costly PMUs and to provide a large amount of historical data such as voltage magnitude phase angle, which is difficult to obtain in a practical distribution network. The linear programming method avoids the problem that voltage phase angle data are difficult to obtain, but only undirected topology can be obtained, namely the trend direction on the topology is unknown, and misoperation and refusal of the relay protection device are easily caused. Therefore, a directed topology recognition tool is urgently needed to be developed, and the reliable identification of the directed topology of the power distribution network is realized by utilizing the limited measurement information of the power distribution network.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a medium-voltage distribution network directed topology identification method based on a directed adjacency matrix, so as to realize the reliable identification of the directed topology of the distribution network.
In order to solve the technical problems, the invention adopts the following technical scheme:
a directed topology identification method for a medium-voltage distribution network based on a directed adjacency matrix comprises the following steps:
establishing a directed adjacency matrix of node voltages according to real-time voltage amplitude measurement data, and judging whether the topology changes;
according to the power measurement data of a plurality of time sections, a node directed adjacency matrix is used as an optimization variable to construct a target function mathematical model of topology identification;
linearizing a nonlinear constraint condition in the mathematical model of the objective function by adopting a large M method;
inputting the active and reactive measurement data and the pseudo measurement data of the branches of the plurality of time sections into a linearized mathematical model, and obtaining the minimum weighted sum of squares of the residual errors to obtain the directed topology structure of the power distribution network.
Preferably, the detection index for judging the topology change is as follows:
Figure BDA0003299636890000021
Figure BDA0003299636890000022
wherein V is a node voltage adjacency matrix, C is a node directed adjacency matrix, C (i, j) ═ 1 indicates that a node i is connected with a node j, and power flows from i to j; v (i, j) takes a value equal to the voltage amplitude of node i minus the voltage amplitude of node j, K being 20;
and updating the value in the node voltage adjacent matrix in real time according to the measurement data, and judging that the topology is changed when a negative value appears in the node voltage adjacent matrix.
Preferably, the objective function mathematical model for constructing topology identification by using the node directed adjacency matrix as an optimization variable is as follows:
an objective function:
Figure BDA0003299636890000023
wherein T is the number of measured cross sections; pr (Pr) oftIs the weight of the tth measured section;
Figure BDA0003299636890000024
sLj,t、
Figure BDA0003299636890000025
and Sij,tMeasured and estimated values of node injected power and line through power, including active power sum, respectively, for the tth sectionReactive power; w represents a measurement weight, including a node injection power measurement weight and a branch power measurement weight;
constraint conditions are as follows:
Figure BDA0003299636890000026
Figure BDA0003299636890000027
Figure BDA0003299636890000028
Figure BDA0003299636890000031
Ct∈{0,1}
Figure BDA0003299636890000032
wherein the content of the first and second substances,
Figure BDA0003299636890000033
and
Figure BDA0003299636890000034
measuring value matrixes respectively representing active power and reactive power of branches of the tth measuring section; ptAnd QtAn estimated value matrix respectively representing the active power and the reactive power of the branch of the tth measuring section;
Figure BDA0003299636890000035
and
Figure BDA0003299636890000036
respectively representing the active and passive measured value matrixes injected into the nodes of the t-th measuring section; ctIndicating the presence of time tTo the adjacency matrix; e represents the error matrix of each measured quantity; row denotes the row and column of the matrix,
Figure BDA0003299636890000037
hadamard product, N, of a representation matrixnodeAnd NrootRepresenting the total number of nodes and the number of source nodes of the power distribution system, respectively.
According to the technical scheme, through the linearization processing of the model, the topology identification can be well carried out by utilizing the pseudo-quantity measurement and the limited quantity measurement of the power distribution network, the problem that the directed topology of the power distribution network cannot be accurately identified in the prior art is solved, and the method is simple and convenient and has high accuracy.
The following detailed description and the accompanying drawings are included to provide a further understanding of the invention.
Drawings
The invention is further described with reference to the accompanying drawings and the detailed description below:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a simulation system;
FIG. 3 is a diagram of a single time slice topology identification result;
fig. 4 is a schematic diagram of the recognition result of the multi-time discontinuous surface topology.
Detailed Description
The technical solutions of the embodiments of the present invention are explained and illustrated below with reference to the drawings of the embodiments of the present invention, but the following embodiments are only preferred embodiments of the present invention, and not all embodiments. Based on the embodiments in the implementation, other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present invention.
The technology of the invention is based on the existing limited measurement data of the power distribution network, and adopts a linear programming method to identify the directed topology of the medium-voltage power distribution network.
Referring to fig. 1, a specific process of identifying a directional topology of a distribution network by using a directional adjacency matrix-based medium-voltage distribution network directional topology identification method includes the following steps:
s1: acquiring real-time measurement data of the voltage amplitude of the measurable node by using an intelligent measurement terminal;
s2: topology change detection index: updating elements in the node voltage adjacency matrix by using the measured node voltage amplitude data, and judging whether the topology changes;
s3: after the topology changes, an intelligent measurement terminal is used for collecting measurement data of a plurality of time sections, wherein the measurement data comprises active power and reactive power of known branches in the topology, injected active power and reactive power of nodes, and load pseudo-quantity measurement data;
s4: taking elements in the node directed adjacency matrixes as optimization variables, constructing an optimization model of directed topology recognition of the power distribution network, and giving flow constraint and radial constraint conditions of the model;
s5: linearizing a nonlinear term of a constraint condition in the topology identification model by adopting a large M method;
s6: and inputting the obtained multi-section measurement data into a linearized model to obtain the directed topology structure of the power distribution network.
In step S2, the topology change detection index is specifically:
Figure BDA0003299636890000041
Figure BDA0003299636890000042
where V is the node voltage adjacency matrix and C is the node directed adjacency matrix. C (i, j) ═ 1 indicates that node i and node j are connected, and power flows from i to j; v (i, j) is equal to the voltage amplitude of node i minus the voltage amplitude of node j, K is a large positive number, and is generally selected to be 20.
And updating the value in the node voltage adjacent matrix in real time according to the measurement data, and judging that the topology is changed when a negative value appears in the node voltage adjacent matrix.
In step S4, the directed topology identification model of the medium voltage distribution network specifically includes:
an objective function:
Figure BDA0003299636890000043
wherein T is the number of measured cross sections; pr (Pr) oftThe weight of the tth measured section is calculated according to a principal component analysis method;
Figure BDA0003299636890000044
sLj,t，
Figure BDA0003299636890000045
and Sij,tRespectively representing a measured value and an estimated value of node injection power and line flowing power of a t section, firstly setting an initial value of the estimated value to be 95% -105% of the measured value, and then inputting the estimated value which is a result output by a target function in the last iteration process and comprises active power and reactive power; and w represents a measurement weight, which comprises a node injection power measurement weight and a branch power measurement weight, wherein the measurement weight is calculated according to a principal component analysis method. It can be understood that the most likely topology corresponding to a part of the known branch powers is found out among all possible operating topologies.
The constraint conditions include power flow constraint and radial constraint:
and (3) power flow constraint:
Figure BDA0003299636890000051
Figure BDA0003299636890000052
Figure BDA0003299636890000053
Figure BDA0003299636890000054
radial constraint:
Ct∈{0,1}
Figure BDA0003299636890000055
wherein the content of the first and second substances,
Figure BDA0003299636890000056
and
Figure BDA0003299636890000057
measuring value matrixes respectively representing active power and reactive power of branches of the tth measuring section; ptAnd QtAn estimated value matrix respectively representing the active power and the reactive power of the branch of the tth measuring section;
Figure BDA0003299636890000058
and
Figure BDA0003299636890000059
respectively representing the active and passive measured value matrixes injected into the nodes of the t-th measuring section; ctA directed adjacency matrix representing time t; e represents the error matrix of each measured quantity; row denotes the row and column of the matrix,
Figure BDA00032996368900000510
representing the hadamard product of the matrix. N is a radical ofnodeAnd NrootRepresenting the total number of nodes and the number of source nodes of the power distribution system, respectively. It will be understood by those skilled in the art that the master node is the connection point of the components in the power distribution system and the source node is the node in the power distribution system that has no voltage.
Step S5, linearizing the nonlinear constraint condition by using a large M method:
-Ct·M≤Pt≤Ct·M
-Ct·M≤Qt≤Ct·M
where M is an arbitrarily large positive number.
Because the constraint condition contains a term for multiplying a 0-1 variable representing the switch state and a continuous variable representing the branch power, the constraint condition belongs to nonlinear constraint, the two inequalities are introduced, the nonlinear constraint is converted into linear constraint, and the solution of a model is facilitated.
Obtaining a linearized distribution network directed topology identification model:
Figure BDA0003299636890000061
Figure BDA0003299636890000062
Figure BDA0003299636890000063
Figure BDA0003299636890000064
Figure BDA0003299636890000065
Ct∈{0,1}
Figure BDA0003299636890000066
step S6 specifically includes:
and (4) inputting the power measurement quantity and the load pseudo quantity of each branch of the power distribution network in real time, which are obtained in the step (S3), into a directed topology identification model of the power distribution network to obtain a directed adjacency matrix C and a directed topology structure of the power distribution network.
The above method was tested on a simulation test system as shown in fig. 2. Specifically, 100 times of simulation is performed on MATLAB, and the accuracy of topology identification is defined as follows:
Figure BDA0003299636890000067
wherein N represents the number of topology identifications, NCIndicating the number of correct identifications.
And (3) changing a network topological structure: and (3) opening the branches 2-19 and closing the branches 66-22, and performing topology identification by considering different measurement errors and measurement section numbers, wherein the obtained topology identification result is shown in fig. 3 and 4.
Therefore, according to the results, the specific implementation method solves the problem that the prior art cannot accurately identify the directed topology of the power distribution network, and is simple and convenient and high in accuracy.
While the invention has been described with reference to specific embodiments thereof, it will be understood by those skilled in the art that the invention is not limited thereto, and may be embodied in many different forms without departing from the spirit and scope of the invention as set forth in the following claims. Any modification which does not depart from the functional and structural principles of the present invention is intended to be included within the scope of the claims.

Claims (3)

1. A directed topology identification method for a medium-voltage distribution network based on a directed adjacency matrix is characterized by comprising the following steps:
establishing a directed adjacency matrix of node voltages according to real-time voltage amplitude measurement data, and judging whether the topology changes;
according to the power measurement data of a plurality of time sections, a node directed adjacency matrix is used as an optimization variable to construct a target function mathematical model of topology identification;
linearizing a nonlinear constraint condition in the mathematical model of the objective function by adopting a large M method;
inputting the active and reactive measurement data and the pseudo measurement data of the branches of the plurality of time sections into a linearized mathematical model, and obtaining the minimum weighted sum of squares of the residual errors to obtain the directed topology structure of the power distribution network.
2. The directed topology identification method for the medium voltage distribution network based on the directed adjacency matrix according to claim 1, characterized in that: the detection indexes for judging the topology change are as follows:
Figure FDA0003299636880000011
Figure FDA0003299636880000012
wherein V is a node voltage adjacency matrix, C is a node directed adjacency matrix, C (i, j) ═ 1 indicates that a node i is connected with a node j, and power flows from i to j; v (i, j) takes a value equal to the voltage amplitude of node i minus the voltage amplitude of node j, K being 20;
and updating the value in the node voltage adjacent matrix in real time according to the measurement data, and judging that the topology is changed when a negative value appears in the node voltage adjacent matrix.
3. The directed topology identification method for the medium voltage distribution network based on the directed adjacency matrix according to claim 2, characterized in that: the method comprises the following steps of (1) constructing a mathematical model of an objective function of topology identification by taking a node directed adjacency matrix as an optimization variable:
an objective function:
Figure FDA0003299636880000013
wherein T is the number of measured cross sections; pr (Pr) oftIs the weight of the tth measured section;
Figure FDA0003299636880000014
sLj,t、
Figure FDA0003299636880000015
and Sij,tRespectively representing measured values and estimated values of node injection power and line flowing power of the t section, including active power and reactive power; w represents a measurement weight, including a node injection power measurement weight and a branch power measurement weight;
constraint conditions are as follows:
Figure FDA0003299636880000021
Figure FDA0003299636880000022
Figure FDA0003299636880000023
Figure FDA0003299636880000024
Ct∈{0,1}
Figure FDA0003299636880000025
wherein the content of the first and second substances,
Figure FDA0003299636880000026
and
Figure FDA0003299636880000027
measuring value matrixes respectively representing active power and reactive power of branches of the tth measuring section; ptAnd QtAn estimated value matrix respectively representing the active power and the reactive power of the branch of the tth measuring section;
Figure FDA0003299636880000028
and
Figure FDA0003299636880000029
respectively representing the active and passive measured value matrixes injected into the nodes of the t-th measuring section; ctA directed adjacency matrix representing time t; e represents the error matrix of each measured quantity; row denotes the row and column of the matrix,
Figure FDA00032996368800000210
hadamard product, N, of a representation matrixnodeAnd NrootRepresenting the total number of nodes and the number of source nodes of the power distribution system, respectively.
CN202111186939.8A 2021-10-12 2021-10-12 Medium-voltage distribution network directed topology identification method based on directed adjacency matrix Pending CN114123165A (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104600699A (en) * 2015-01-27 2015-05-06 清华大学 Power distribution network structure estimation method based on mixed integer quadratic programming model
CN111313405A (en) * 2020-02-29 2020-06-19 上海电力大学 Medium-voltage distribution network topology identification method based on multiple measurement sections

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104600699A (en) * 2015-01-27 2015-05-06 清华大学 Power distribution network structure estimation method based on mixed integer quadratic programming model
CN111313405A (en) * 2020-02-29 2020-06-19 上海电力大学 Medium-voltage distribution network topology identification method based on multiple measurement sections

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
许栋梁: "基于有向邻接矩阵的配电网拓扑检测与识别", 《电力系统保护与控制》, pages 76 - 85 *

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