CN112884608A - Power supply network black start partition scheme calculation method and calculation system - Google Patents

Power supply network black start partition scheme calculation method and calculation system Download PDF

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CN112884608A
CN112884608A CN202110267414.0A CN202110267414A CN112884608A CN 112884608 A CN112884608 A CN 112884608A CN 202110267414 A CN202110267414 A CN 202110267414A CN 112884608 A CN112884608 A CN 112884608A
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load
node
power supply
partition
nodes
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CN112884608B (en
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章海静
彭书涛
王建波
夏楠
邓俊
金吉良
刘瑶
郑天悦
李树芃
刘坤雄
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Shaanxi Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Shaanxi Electric Power Co Ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention discloses a power supply network black start partitioning scheme calculation method and a power supply network black start partitioning scheme calculation system. The analytical solution of the optimal partition scheme is directly obtained by solving a differential equation system, and manual selection of various schemes is not provided. The method is suitable for program implementation, and practical verification is carried out, so that a brand-new idea and method are provided for calculation of the black-start partition scheme.

Description

Power supply network black start partition scheme calculation method and calculation system
Technical Field
The invention belongs to the technical field of power grid partition calculation, and particularly relates to a power grid black-start partition scheme calculation method and a power grid black-start partition scheme calculation system.
Background
For a large system with a plurality of black start power supplies in the system, after a large power failure accident occurs, a reasonable partition scheme is helpful for coordinating and recovering all the systems in parallel so as to shorten the power recovery time of the whole system. The division of each partition should aim at minimizing inter-partition links and fully consider the rapid recovery of the power supply of one class of loads. At present, an integer linear programming model is mostly adopted in the existing partition division, and the model is solved for many times by constructing a 'cut' constraint and utilizing a high-efficiency solver CPLEX to obtain enough schemes for comparison, and finally, an optimal partition division scheme is selected. The disadvantages of this method are: the calculation process is relatively complex, the calculation time is long, and a set of solutions can be provided for manual selection instead of directly giving an optimal solution. From mathematical analysis, the optimal solution can be quickly and directly obtained by a method of solving a differential equation set, but a method of directly and quickly solving the optimal analytic solution by a form of solving the differential equation set without solving a plurality of partition schemes is lacked at present.
Disclosure of Invention
The invention provides a method and a system for calculating a black start partitioning scheme of a power supply network.
In order to achieve the above purpose, the method for calculating the black start partitioning scheme of the power supply network comprises the following steps:
constructing a minimum topological relation matrix of the load nodes and the black start power supply nodes, wherein elements in the relation matrix are minimum topological distances between each load node and the black start power supply nodes;
establishing a load node relation matrix table according to the incidence relation among the load nodes, wherein elements in the load node relation matrix table are used for representing the connection state between every two load nodes;
introducing variables for representing whether the load nodes are of a type of load and variables for representing whether the load nodes are adjustable loads;
constructing a partition range table, wherein elements in the partition range table are partition subordinate relation values of each black-start power supply node and each load node;
constructing an energy function by using elements in the minimum topological relation matrix of the constructed load nodes and black-start power supply nodes, elements in a load node relation matrix table, and introduced variables for representing whether the load nodes are a type of load and variables for representing whether the load nodes are adjustable loads;
and solving the established energy function to obtain each unit element value in the partition range table, and dividing the power supply partition according to each unit element value in the partition range table, wherein the load power supply node and the black start power supply node corresponding to the unit with the element value of 1 are divided into the same partition.
Further, the minimum topological relation matrix of the load nodes and the black-start power supply nodes is as follows:
w1 w2 … wj … wN
B1 d11 d12 … d1j … d1N
B2 d21 d22 … d2j … d2N
… … … … … … …
Bi di1 di2 … dij … diN
… … … … … … …
BM dM1 dM2 … dMj … dMN
wherein, w1～wNRepresenting the load node, B, in the system1～BMRepresenting M black-start power supply nodes, dijThe minimum topological distance between each load node and the black start power supply node is shown, N is the number of the load nodes, M is the number of the black start power supply nodes, i is the serial number of the black start power supply node, i is more than or equal to 1 and less than or equal to M, j is the serial number of the load nodes, and j is more than or equal to 1 and less than or equal to N.
Further, element E in the load node relationship matrix tablejkThe values are as follows:
Figure BDA0002972754820000021
further, the variable vip is used for representing whether the load node is a class load or notjAnd a variable con for characterizing whether the load node is an adjustable loadjThe value is taken according to the following formula:
Figure BDA0002972754820000031
Figure BDA0002972754820000032
further, the partition range table is:
w1 w2 … wj … wN
B1 v11 v12 … … … v1N
B2 v21 v22 … … … v2N
… … … … … … …
Bi vi1 vi2 … vij … viN
… … … … … … …
BM vM1 … … vMj … vMN
wherein v isijPartition dependency values, v, for black start power node i and load node jijIs 0 or 1; each column in the partition range table has only one element of 1, and the others are 0; v. ofij When 1, it indicates the load node wjRow-in black start power node BiV. power supply section ofijWhen 0 denotes the load node wjNon-intrusive black start power node BiThe power supply partition of (1).
Further, the energy function is expressed as follows:
Figure BDA0002972754820000033
wherein E is an energy function value, E1-E5 are coefficients greater than 0, vijPartition dependency values, v, for black start power node i and load node jmnThe partition dependency values of a black start power source node M and a load node N are obtained, M is the serial number of the black start power source node, M is more than or equal to 1 and less than or equal to M, M is not less than i, N is the serial number of the load node, N is more than or equal to 1 and less than or equal to N, and N is not equal to j; ejnRepresenting the connection state of a load node j and a load node n; gamma rayiIs an intermediate variable, τiIs the intermediate variable(s) of the variable,
Figure BDA0002972754820000041
wjis the capacity of node j, siIs BiΔ is a scale factor;
Figure BDA0002972754820000042
αipower supply node B for black startiThe minimum force coefficient of (c).
A power supply network black start partition scheme computing system comprises a memory and a processor, wherein the memory is stored with a computer program capable of running on the processor, and the processor executes the computer program to realize the computing method.
Compared with the prior art, the invention has at least the following beneficial technical effects:
the invention provides a brand new energy function to achieve the aim of minimum inter-partition junctor, and describes the constraint conditions of minimum junctor, balance between adjustable load and black start power supply, quick power restoration of one class of load and the like by using a uniform analytic expression for the first time. Because the optimal partition scheme and the constraint conditions are simultaneously expressed by a uniform analytic expression, the partition scheme can be directly solved by solving a differential equation system. The process of solving the system of differential equations is itself a process of gradually reducing the energy function to a minimum value in the direction of the gradient. The energy function can be reduced to the lowest value by solving the differential equation, and the obtained solution is the analytic solution of the optimal partition scheme.
The design of the energy function is characterized in that the analytic expressions corresponding to all constraint terms in the energy function can be 0 only when the obtained solution is reasonable and feasible. The number of links is minimal, and the energy function is only guaranteed to be minimal when the obtained solution is reasonable and feasible. Therefore, the rationality of the solution can be guaranteed by the solution when the energy function obtained by solving the differential equation is the lowest, the connecting line can be minimized, and the decision can be conveniently and quickly made. The method is suitable for program implementation and is actually verified, the power grid and the most common IEEE-39 node system provided by the embodiment are actually calculated and verified, the iterative computation times reach the minimum value of the energy function within 200 times, at the moment, the constraint terms of the energy function are all 0, and the obtained solution is reasonable and the number of connecting lines is minimum. The invention provides a brand new thought and method for the calculation of the black start partitioning scheme.
The invention uniformly considers the constraint conditions of balancing between the adjustable load and the black start power supply, ensuring the quick recovery of power supply of the load and the like in the energy function. In order to rapidly solve the partition scheme, an analytic solution of the optimal partition scheme is directly solved by a method for solving a differential equation system, instead of providing manual selection of various schemes. The proposed method provides a new approach for the determination of black start partitioning schemes without the aid of other linear programming tools.
Furthermore, the first term of the energy function is 0 only under one condition, namely the sum of the numerical values of each column in the partition range table is 1, namely only one unit in each column of the partition range table is 1, and the rest are 0, so that each load node is ensured to be powered by a black start power supply; in the second term constraint of the energy function, the capacity of the black-start power supply node i is greater than the total amount of a class of loads in the power supply area
Figure BDA0002972754820000051
If the value is 0, otherwise, the value is 1, and the power supply power balance of the power supply area is ensured;
Figure BDA0002972754820000052
it can be found that the capacity of the black-start power supply node i is less than the total amount of adjustable load in its supply area
Figure BDA0002972754820000053
Is 0, otherwise is 1; the third item can restrict the adjustable load capacity of each subarea to be larger than the output force of the black start power supply; the fourth item restricts the loss caused by power supply of each load node as small as possible; the fifth item ensures that the nodes of each zone are wired to the black start power supply node of that zone.
Drawings
FIG. 1 is a structural view of a power supply network of embodiment 1;
FIG. 2 is a graph of the results of the black start partition calculation in example 1;
FIG. 3 is a first partition result graph obtained by traversal according to example 1;
FIG. 4 is a diagram of a second partitioning result obtained by traversal in the embodiment 1;
FIG. 5 is a graph of the result of the third partition in example 1 obtained by traversal.
Fig. 6 is a structure diagram of a power supply network of embodiment 2;
FIG. 7 is a graph of the results of the example 2 black start partition calculations;
FIG. 8 is a graph of the first partition result of example 2 obtained by traversal;
FIG. 9 is a diagram of a second partitioning result obtained by traversal in the embodiment 2;
fig. 10 is a schematic diagram of a power supply network black start partitioning scheme computing system.
Detailed Description
In order to make the objects and technical solutions of the present invention clearer and easier to understand. The present invention will be described in further detail with reference to the following drawings and examples, wherein the specific examples are provided for illustrative purposes only and are not intended to limit the present invention.
In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implying any number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified. In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Referring to fig. 1, a power supply network black start partition scheme calculation method includes the following steps:
the method comprises the following steps: the minimum topological relation matrix of the load node-black start power supply shown in the table 1 is constructed
TABLE 1 topological relationship matrix
w1 w2 … wj … wN
B1 d11 d12 … d1j … d1N
B2 d21 d22 … d2j … d2N
… … … … … … …
Bi di1 di2 … dij … diN
… … … … … … …
BM dM1 dM2 … dMj … dMN
In Table 1, w1～wNFor the load nodes in the system, B1～BMThe number of the power nodes capable of being started in black is M, and the power nodes are referred to as black-start power nodes in the following text, wherein N is the number of load nodes, M is the number of the black-start power nodes, i is the serial number of the black-start power nodes, i is more than or equal to 1 and less than or equal to M, j is the serial number of the load nodes, and j is more than or equal to 1 and less than or equal to N. For each unit in Table 1 dijAnd (4) showing. dijThe minimum topological distance from the black-start power source node i to the load node j is defined as the minimum power supply path of the black-start power source node i connected to the load j in an extensive search mode.
Step two: establishing a load node relation matrix table as shown in table 2 according to the incidence relation of each load node, wherein each unit in the table 2 uses EjkAnd (4) showing.
TABLE 2 node relationship matrix
w1 w2 … wk … wN
w1 E11 E12 … E1k … E1N
w2 E21 E22 … E1k … E2N
… … … … … … …
wj Ej1 Ej2 … Ejk … EjN
… … … … … … …
wN EN1 EN2 … ENk … ENN
EjkRepresenting the connection state of a load node j and a load node k, wherein k is the serial number of the load node, k is more than or equal to 1 and less than or equal to N, EjkThe mathematical description of (a) is:
Figure BDA0002972754820000071
step three: introducing variable vipjAnd variable conjDefined as shown in formula (2) and formula (3), respectively:
Figure BDA0002972754820000072
Figure BDA0002972754820000073
step four: with B1～BMIndicating that the power nodes can be black-started, a partition range table is constructed as shown in table 3.
TABLE 3 partition Range Table
w1 w2 … wj … wN
B1 v11 v12 … … … v1N
B2 v21 v22 … … … v2N
… … … … … … …
Bi vi1 vi2 … vij … viN
… … … … … … …
BM vM1 … … vMj … vMN
vijThe unit value v of (i, j) in Table 3ijA partition dependency value v of the power supply partition in which the black start power supply node i is positioned and the load node jijTaking the value of 0 or 1. In Table 3, only one element in each column is 1, and the others are 0, i.e., the sum of the elements in each column is 1. v. ofijWhen 1, it indicates the load node wjRow-in black start power node BiV. power supply section ofijWhen 0 denotes the load node wjNon-intrusive black start power node BiThe power supply partition of (1).
Step five: an energy function represented by the formula (4) is constructed.
Figure BDA0002972754820000081
Wherein E is an energy function value, E1-E5 are coefficients greater than 0, vmnThe partition relation value of a black start power source node M and a load node N is shown, M is the serial number of the black start power source node, M is more than or equal to 1 and less than or equal to M, M is not less than i, N is the serial number of the load node, N is more than or equal to 1 and less than or equal to N, and N is not less than j. EjnTo indicate the connection state of the load node j and the load node n. Gamma rayiIs an intermediate variable, τiIs the intermediate variable(s) of the variable,
Figure BDA0002972754820000082
wjis the capacity of node j, siIs BiAnd Δ is a scale factor, and may be 0.01 or less.
Figure BDA0002972754820000083
αiPower supply node B for black startiThe minimum force coefficient of (c).
The first term of the energy function is 0 only in one case, namely the sum of the numerical values of each column in table 3 is 1, namely only one unit of each column in table 3 is 1, and the rest are 0, so that each load node is ensured to be powered by a black start power supply. In the second term constraint of the energy function, the capacity of the black-start power supply node i is greater than the total amount of a class of loads in the power supply area
Figure BDA0002972754820000084
And if the value is 0, otherwise, the value is 1, and the power supply power balance of the power supply area is ensured.
Figure BDA0002972754820000085
It can be found that the capacity of the black-start power supply node i is less than the total amount of adjustable load in its supply area
Figure BDA0002972754820000086
Is 0, otherwise is 1. The third term can restrict the adjustable load of each partitionThe charge is larger than the output of the black start power supply. The fourth term constrains the losses incurred when powering each load node to be as small as possible. The fifth item ensures that the nodes of each zone are wired to the black start power supply node of that zone.
Step six: solving formula (4) using formula (5)
Figure BDA0002972754820000091
Wherein u isijTo solve for vijThe solving method of the intermediate variable (2) is shown in the formula (6).
Step seven: from equations (4) and (5), the dynamic equation for equation (4) can be solved as follows:
Figure BDA0002972754820000092
wherein u isvFor the normalization coefficient, it may be taken as 0.01 or less. Solving the formula (6) by using an Eulerian method, calculating an energy function value E according to the formula (4) after each iterative solution, and stopping iterative calculation when the E is not reduced any more. According to vijThe power supply partition, v, of each black start power supply node can be determinedijWhen 1, it indicates the load node wjRow-in black start power node BiV. power supply section ofijWhen 0 denotes the load node wjNon-intrusive black start power node BiThe power supply partition of (1). E does not terminate the iteration when it is decreasing for each element v in Table 3ijAnd the element value and the corresponding energy function E are minimum, the tie line of each partition is also minimum, and the partition is divided into the optimal partition.
Referring to fig. 10, a power supply network black-start partitioning scheme calculation system includes a memory and a processor, the memory stores a computer program that can be executed on the processor, and the processor executes the computer program to implement the power supply network black-start partitioning scheme calculation method.
Example 1
The invention will be described in detail with reference to specific examples, a power supply network of which is shown in FIG. 1, w2And w7Is a type of load, w4And w6For adjustable loading, w1、w3、w5Is a non-categorical and non-adjustable load, B1And B2For the black start power supply, the grid parameters are shown in table 4.
TABLE 4 Power grid parameter Table
w1 w2 w3 w4 w5 w6 w7 B1 B2 α1 α2
Capacity/size (MW) 60 50 75 40 55 40 80 70 90 0.3 0.3
The method comprises the following steps: firstly, a node-black start power supply minimum topology relation matrix shown in table 5 is constructed
TABLE 5 topological relationship matrix
w1 w2 w3 w4 w5 w6 w7
B1 1 1 2 3 3 2 4
B 2 3 3 2 1 1 2 1
Step two: establishing a load node relation matrix table as shown in table 6 according to the incidence relation of each node, wherein each unit in the table uses EjkAnd (4) showing.
TABLE 6 node relationship matrix
w1 w2 w3 w4 w5 w6 w7
w1 0 0 0 0 0 1 0
w2 0 0 1 0 0 0 0
w3 0 1 0 1 0 0 0
w4 0 0 1 0 0 0 0
w5 0 0 0 0 0 1 1
w 6 1 0 0 0 1 0 0
w7 0 0 0 0 1 0 0
Step three: introducing variable vipjAnd conj，w2And w7Is a type of load, w4And w6Is an adjustable load.
Figure BDA0002972754820000101
Step four: a partition range table as shown in table 7 was constructed.
TABLE 7 partition Range Table
w1 w2 w3 w4 w5 w6 w7
B1 v11 v12 v13 v14 v15 v16 v17
B2 v21 v22 v23 v24 v25 v26 v27
In Table 7, vijTaking the value of 0 or 1. In Table 7, only one element in each column is 1, and the others are 0, i.e., the sum of the elements in each column is 1. v. ofijWhen 1, it indicates the load node wjStrike-in black start power supply BiV. power supply section ofijWhen 0 denotes the load node wjNon-strike-in black start power supply BiThe power supply partition of (1). A cell of 1 indicates that the corresponding column node is assigned to the partition in which the corresponding row black start power supply is located.
Step five: an energy function shown in formula (1) is constructed.
Figure BDA0002972754820000111
Wherein, E1-1000, E2-200, E3-200, E4-20.0, and E5-80.0.
Figure BDA0002972754820000112
siIs BiAnd Δ is a scale factor, and may be 0.01 or less.
Figure BDA0002972754820000113
Step six: solving formula (1) using formula (2)
Figure BDA0002972754820000114
Wherein v isijTable 7 for meaning synchronization; u. ofijTo solve for vijThe solving method of the intermediate variable (2) is shown in the formula (3).
Step seven: from equations (1), (2), the dynamic equation for equation (1) can be solved as follows:
Figure BDA0002972754820000121
wherein u isv0.01 or less. Solving the formula (3) by using an Eulerian method, calculating an energy function value E according to the formula (1) after each iterative solution, and stopping iterative calculation when the E is not reduced any more. From the calculated vijAnd obtaining each black start power supply partition table 8.
TABLE 8 partition Range Table
w1 w2 w3 w4 w5 w6 w7
B1 1 1 1 0 0 1 0
B2 0 0 0 1 1 0 1
The partition map obtained from Table 8 is shown in FIG. 2, i.e., black start power supply B1Load node w1Load node w2Load node w3And load node w6Is the same partition, black start power supply B2Load node w4Load node w5And load node w7Are the same partition.
Other partition schemes can be searched in a traversal mode, as shown in fig. 3-5, the number of the connection lines of the partition scheme shown in fig. 3 is 4, which is more than the partition scheme obtained by the method of the present invention, and the requirement of ensuring power supply to a class of loads is not satisfied. The number of the partitioning scheme links shown in fig. 4 is 4, which is more than the partitioning scheme obtained by the present invention. The number of the partition scheme connecting lines shown in fig. 5 is 2, which is the same as the partition scheme connecting lines obtained by the invention, but does not satisfy the constraint condition that the adjustable load is larger than the minimum output of the black-start power supply. As can be seen from a comparison of fig. 2 to 5, the partition scheme calculated by the present invention is due to other partition schemes.
The verification is as follows:
example 2
In the following, the detailed description of the present invention is made by referring to specific examples, an IEEE-39 node grid is shown in fig. 6, nodes 12 and 17 are a class of loads, the adjustable loads are numbered (7,20,21,23,24,25,28,31,34,35), the node 30 and the node 33 are black-start power supplies B1 and B2, both sets α are 0.3, and grid parameters are shown in table 9.
TABLE 9 electric network parameter table
Figure BDA0002972754820000131
The method comprises the following steps: firstly, a node-black start power supply minimum topology relation matrix shown in a table 10 is constructed (after the load point number is deleted, the black start power supply number is sequentially sequenced according to the original order, and the load point number in the subsequent step is the same)
TABLE 10 topological relationship matrix
w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13
B1 2 1 2 3 4 5 6 5 4 7 6 7 5
B2 7 6 6 5 6 7 8 7 8 6 8 6 5
w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26
B1 4 5 6 4 3 6 7 6 7 8 6 2 3
B2 4 3 2 3 4 1 2 3 4 5 3 7 5
w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37
B1 5 4 5 6 7 8 8 8 3 5 3
B2 4 6 7 8 7 3 5 5 7 7 9
Step two: based on the association relationship of each node, a load node relationship matrix table is established as shown in Table 11, wherein each unit in the table uses EjkAnd (4) showing.
TABLE 11 node relationship matrix
Figure BDA0002972754820000141
Step three: introducing variable vipjAnd conj。
Figure BDA0002972754820000142
Figure BDA0002972754820000151
Step four: a partition range table as shown in table 12 was constructed.
TABLE 12 partition Range Table
w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13
B1 v1,1 v1,2 v1,3 v1,4 v1,5 v1,1 v1,2 v1,8 v1,9 v1,10 v1,11 v1,12 v1,13
B2 v2,1 v2,2 v2,3 v2,4 v2,5 v2,1 v2,2 v2,8 v2,9 v2,10 v2,11 v2,12 v2,13
w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26
B1 v1,14 v1,15 v1,16 v1,17 v1,18 v1,19 v1,20 v1,21 v1,22 v1,23 v1,24 v1,25 v1,26
B2 v2,14 v2,15 v2,16 v2,17 v2,18 v2,19 v2,20 v2,21 v2,22 v2,23 v2,24 v2,25 v2,26
w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37
B1 v1,27 v1,28 v1,29 v1,30 v1,31 v1,32 v1,33 v1,34 v1,35 v1,36 v1,37
B2 v2,27 v2,28 v2,29 v2,30 v2,31 v2,32 v2,33 v2,34 v2,35 v2,36 v2,37
In Table 12, vijTaking the value of 0 or 1. In Table 7, only one element in each column is 1, and the others are 0, i.e., the sum of the elements in each column is 1. v. ofijWhen 1, it indicates the load node wjStrike-in black start power supply BiV. power supply section ofijWhen 0 denotes the load node wjNon-strike-in black start power supply BiThe power supply partition of (1). A cell of 1 indicates that the corresponding column node is assigned to the partition in which the corresponding row black start power supply is located.
Step five: an energy function represented by the formula (4) is constructed.
Figure BDA0002972754820000161
Wherein, E1-1000, E2-200, E3-200, E4-20.0, and E5-80.0.
Figure BDA0002972754820000162
siIs BiAnd Δ is a scale factor, and may be 0.01 or less.
Figure BDA0002972754820000163
Step six: solving formula (4) using formula (5)
Figure BDA0002972754820000164
Wherein v isijThe meaning synchronization table 12; u. ofijTo solve for vijThe solving method of the intermediate variable (2) is shown in the formula (6).
Step seven: from equations (4) and (5), the dynamic equation for equation (4) can be solved as follows:
Figure BDA0002972754820000165
wherein u isv0.01 or less. Solving the formula (6) by using an Eulerian method, calculating an energy function value E according to the formula (3) after each iterative solution, and stopping iterative calculation when the value E is not reduced. From the calculated vijA black start power supply partition table 13 is obtained.
Table 13 partition range table
w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13
B1 1 1 1 1 1 1 1 1 1 0 0 0 0
B2 0 0 0 0 0 0 0 0 0 1 1 1 1
w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26
B1 0 0 0 0 1 0 0 0 0 0 0 1 0
B2 1 1 1 1 0 1 1 1 1 1 1 0 1
w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37
B1 0 0 0 1 0 0 0 0 1 0 1
B2 1 1 1 0 1 1 1 1 0 1 0
The partition map obtained from table 13 is shown in fig. 7, and the number of links is 4. Other partitioning schemes with few links can be searched in a traversal mode, as shown in fig. 8 and 9, the number of the partitioning scheme links in fig. 8 and 9 is 5, which is more than the partitioning scheme calculated by the present invention. The partition scheme calculated by the present invention is due to other partition schemes.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (7)

1. A power supply network black start partition scheme calculation method is characterized by comprising the following steps:
constructing a minimum topological relation matrix of the load nodes and the black start power supply nodes, wherein elements in the relation matrix are minimum topological distances between each load node and the black start power supply nodes;
establishing a load node relation matrix table according to the incidence relation among the load nodes, wherein elements in the load node relation matrix table are used for representing the connection state between every two load nodes;
introducing variables for representing whether the load nodes are of a type of load and variables for representing whether the load nodes are adjustable loads;
constructing a partition range table, wherein elements in the partition range table are partition subordinate relation values of each black-start power supply node and each load node;
constructing an energy function by using elements in the minimum topological relation matrix of the constructed load nodes and black-start power supply nodes, elements in a load node relation matrix table, and introduced variables for representing whether the load nodes are a type of load and variables for representing whether the load nodes are adjustable loads;
and solving the established energy function to obtain each unit element value in the partition range table, and dividing the power supply partition according to each unit element value in the partition range table, wherein the load power supply node and the black start power supply node corresponding to the unit with the element value of 1 are divided into the same partition.
2. A power supply network black-start partitioning scheme calculation method according to claim 1, wherein the minimum topological relation matrix of the load nodes and the black-start power supply nodes is as follows:
w1 w2 … wj … wN B1 d11 d12 … d1j … d1N B2 d21 d22 … d2j … d2N … … … … … … … Bi di1 di2 … dij … diN … … … … … … … BM dM1 dM2 … dMj … dMN
wherein, w1～wNRepresenting the load node, B, in the system1～BMRepresenting M black-start power supply nodes, dijThe minimum topological distance between each load node and the black start power supply node is shown, N is the number of the load nodes, M is the number of the black start power supply nodes, i is the serial number of the black start power supply node, i is more than or equal to 1 and less than or equal to M, j is the serial number of the load nodes, and j is more than or equal to 1 and less than or equal to N.
3. A power supply network black start partitioning scheme calculation method as claimed in claim 1, wherein element E in the load node relation matrix tablejkThe values are as follows:
Figure FDA0002972754810000021
4. a power supply network black start partitioning scheme calculation method as claimed in claim 1, wherein said variable vip for characterizing whether a load node is a class of load or not is a variable vip for characterizing whether a load node is a class of load or notjAnd a variable con for characterizing whether the load node is an adjustable loadjThe value is taken according to the following formula:
Figure FDA0002972754810000022
Figure FDA0002972754810000023
5. a power supply network black start partitioning scheme calculation method as claimed in claim 1, wherein said partitioning range table is:
w1 w2 … wj … wN B1 v11 v12 … … … v1N B2 v21 v22 … … … v2N … … … … … … … Bi vi1 vi2 … vij … viN … … … … … … … BM vM1 … … vMj … vMN
wherein v isijPartition dependency values, v, for black start power node i and load node jijIs 0 or 1; each column in the partition range table has only one element of 1, and the others are 0; v. ofijWhen 1, it indicates the load node wjRow-in black start power node BiV. power supply section ofijWhen 0 denotes the load node wjNon-intrusive black start power node BiThe power supply partition of (1).
6. A power supply network black start partitioning scheme calculation method as claimed in claim 1, wherein said energy function expression is as follows:
Figure FDA0002972754810000031
wherein E is an energy function value, E1-E5 are coefficients greater than 0, vijPartition dependency values, v, for black start power node i and load node jmnThe partition dependency values of a black start power source node M and a load node N are obtained, M is the serial number of the black start power source node, M is more than or equal to 1 and less than or equal to M, M is not less than i, N is the serial number of the load node, N is more than or equal to 1 and less than or equal to N, and N is not equal to j; ejnRepresenting the connection state of a load node j and a load node n; gamma rayiIs an intermediate variable, τiIs the intermediate variable(s) of the variable,
Figure FDA0002972754810000032
wjis the capacity of node j, siIs BiΔ is a scale factor;
Figure FDA0002972754810000033
αipower supply node B for black startiThe minimum force coefficient of (c).
7. A power supply network black start partitioning scheme computing system comprising a memory and a processor, the memory having stored thereon a computer program operable on the processor, the processor when executing the computer program implementing the method of any one of claims 1 to 6.
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