CN112884608B - Power supply network black start partition scheme calculation method and system - Google Patents
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Abstract
The invention discloses a method and a system for calculating a black start partition scheme of a power supply network. The analytical solution of the optimal partition scheme is directly obtained by a method for solving the differential equation set, and the manual selection of multiple schemes is not provided. The method is suitable for program implementation, actual verification is carried out, and a brand new thought and method are provided for the calculation of the black start partition scheme.
Description
Technical Field
The invention belongs to the technical field of power grid partition calculation, and particularly relates to a power supply network black start partition scheme calculation method and a power supply network black start partition scheme calculation system.
Background
For a large system with a plurality of black start power supplies in the system, after a blackout accident occurs, a reasonable partition scheme is beneficial to the coordination and parallel recovery of each system so as to shorten the recovery power supply time of the whole system. The partitioning of each partition should be aimed at minimizing inter-partition links and fully taking into account the rapid restoration of power to a class of loads. At present, the existing partition division mostly adopts an integer linear programming model, and the model is solved for many times by constructing a cutting constraint and utilizing an efficient solver CPLEX so as to obtain enough schemes for comparison, and finally, the optimal partition division scheme is selected. The disadvantages of this approach are: the calculation process is relatively complex, the calculation time is long, and a group of solutions can be provided for manual selection instead of directly giving the optimal scheme. The method for quickly and directly obtaining the optimal solution through solving the differential equation set is not needed to obtain a plurality of partition schemes, but the method for quickly and directly obtaining the optimal solution through solving the differential equation set mode is not available at present.
Disclosure of Invention
The invention provides a method and a system for calculating a black start partition scheme of a power supply network, which directly calculate an analytic solution of an optimal partition scheme by solving a differential equation set, rather than providing manual selection of multiple schemes.
In order to achieve the above purpose, the method for calculating the black start partition 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 the load nodes and the black start power supply nodes;
according to the association relation among the load nodes, a load node relation matrix table is established, and elements in the load node relation matrix table are used for representing the connection state between every two load nodes;
introducing a variable for representing whether the load node is a type of load and a variable for representing whether the load node is an adjustable load;
constructing a partition range table, wherein elements in the partition range table are partition membership values of each black start power supply node and each load node;
constructing an energy function by utilizing elements in a constructed minimum topological relation matrix of the load nodes and the black start power supply nodes, elements in a load node relation matrix table, and introduced variables used for representing whether the load nodes are of a type of load and variables used for representing whether the load nodes are adjustable loads;
and solving the established energy function to obtain element values of all units in the partition range table, dividing power supply partitions according to the element values of all units in the partition range table, and dividing load power supply nodes and black start power supply nodes corresponding to the units with the element values of 1 into the same partition.
Further, the minimum topological relation matrix of the load node and the black start power supply node is as follows:
| w 1 | w 2 | … | w j | … | w N | |
| B 1 | d 11 | d 12 | … | d 1j | … | d 1N |
| B 2 | d 21 | d 22 | … | d 2j | … | d 2N |
| … | … | … | … | … | … | … |
| B i | d i1 | d i2 | … | d ij | … | d iN |
| … | … | … | … | … | … | … |
| B M | d M1 | d M2 | … | d Mj | … | d MN |
wherein w is 1 ～w N Representing load nodes, B in a system 1 ～B M Represents M black start power supply nodes d ij For the minimum topological distance between each load node and the black start power supply node, 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 1-1 and is less than or equal to M, j is the serial number of the load nodes, and j is 1-1 and is less than or equal to N.
Further, element E in the load node relation matrix table jk The values are as follows:
further, a variable vip for characterizing whether a load node is a class of loads j And a variable con for characterizing whether the load node is an adjustable load j The values were taken according to the following:
further, the partition scope table is:
| w 1 | w 2 | … | wj | … | w N | |
| B 1 | v 11 | v 12 | … | … | … | v 1N |
| B 2 | v 21 | v 22 | … | … | … | v 2N |
| … | … | … | … | … | … | … |
| B i | v i1 | v i2 | … | v ij | … | v iN |
| … | … | … | … | … | … | … |
| B M | v M1 | … | … | v Mj | … | v MN |
wherein v is ij Power supply node i and negative for black startPartition membership value, v, of load node j ij 0 or 1; each column in the partition range table has only one element of 1 and the others of 0; v ij When=1, the load node w is represented j Scribing black start power node B i Power supply partition of v ij When=0, the load node w is represented j Node B of starting power without black i Is provided.
Further, the energy function expression is as follows:
wherein E is the energy function value, E1-E5 are coefficients greater than 0, v ij For the partition membership value, v, of black start power supply node i and load node j mn The partition dependency value of the black start power supply node M and the load node N is that M is the serial number of the black start power supply node, M is not less than 1 and not more than M, M is not less than i, N is the serial number of the load node, N is not less than 1 and not more than N, and N is not less than j; e (E) jn To represent the connection state of load node j and load node n; gamma ray i As intermediate variable τ i As an intermediate variable, the number of the variables,w j for the capacity, s, of node j i Is B i Delta is the proportional amplification factor; />α i Power node B for black start i Is used for the minimum output coefficient of the motor.
The power supply network black start partition scheme computing system comprises a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, and the computing method is realized when the processor executes the computer program.
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 interconnection lines among partitions, and uses a unified analysis type to describe constraint conditions of minimum interconnection lines, balance between adjustable load and black start power supply, guarantee that a type of load is quickly restored to power supply, and the like for the first time. Because the optimal partition scheme and the constraint condition are simultaneously represented by a unified analytical formula, the partition scheme can be directly obtained by a method for solving a differential equation set. The process of solving the differential equation set is itself a process of gradually decreasing the energy function to the minimum value in the gradient direction. The energy function can be reduced to the minimum value by solving the differential equation, and the obtained solution is the analysis solution of the optimal partition scheme.
The energy function design of the invention is characterized in that the analytic expression corresponding to each constraint term in the energy function can be 0 only when the obtained solution is reasonable and feasible. And the minimum connecting lines are adopted, and the minimum energy function can be ensured only when the obtained solution is reasonable and feasible. Therefore, the solution when the energy function obtained by solving the differential equation is the lowest can ensure the rationality of the solution, and can also minimize the connecting line at the same time, thereby being convenient and quick to make decisions. The method is suitable for program implementation, actual verification is carried out, actual calculation verification is carried out on the power grid provided by the embodiment and the most common IEEE-39 node system, the iterative calculation times reach the minimum value of the energy function within 200 times, at the moment, constraint items of the energy function are all 0, and the obtained solution is reasonable and the connecting line is minimum. The invention provides a brand new thought and method for the calculation of the black start partition scheme.
The invention uniformly considers the constraint conditions of balancing the adjustable load and the black start power supply, ensuring that the load is quickly recovered to be powered and the like in the energy function. In order to quickly obtain the partition scheme, it is proposed to directly obtain the analytic solution of the optimal partition scheme by a method of solving the differential equation set, instead of providing manual selection of multiple schemes. The proposed method provides a new method for determination of a black start partition scheme without the aid of other linear programming tools.
Further, the first term of the energy function is only 0 in one case, i.e. the sum of the values of each column in the partition range table is 1, i.e. there is only one single column in the partition range tableThe element is 1, the rest are 0, and each load node is guaranteed to be provided with a black start power supply for supplying power; in the second constraint of the energy function, when the capacity of the black start power supply node i is larger than the total load of one type in the power supply areaIf the power is 0, otherwise, the power is 1, so that the power supply balance of the power supply area is ensured; />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 +.>0, otherwise 1; the third item can restrict the adjustable load of each partition to be larger than the output force of the black start power supply; the fourth constraint is that the loss caused by power supply of each load node is as small as possible; the fifth item ensures that the nodes of each region are wired to the black start power supply node of that region.
Drawings
Fig. 1 is a diagram of the power supply network structure of embodiment 1;
FIG. 2 is a graph showing the results of the black start partition calculation in example 1;
FIG. 3 is a graph of the first partitioning results of example 1 obtained by traversal;
FIG. 4 is a graph of the second partitioning results of example 1 obtained by traversal;
FIG. 5 is a graph of the third partitioning results of example 1 obtained by traversal.
Fig. 6 is a diagram of the power supply network structure of embodiment 2;
FIG. 7 is a graph showing the result of the black start partition calculation in example 2;
FIG. 8 is a graph of the first partitioning results of example 2 obtained by traversal;
FIG. 9 is a graph of the second partitioning results of example 2 obtained by traversal;
fig. 10 is a schematic diagram of a power supply network black start partition scheme computing system.
Detailed Description
In order to make the purpose and technical scheme of the invention clearer and easier to understand. The present invention will now be described in further detail with reference to the drawings and examples, which are given for the purpose of illustration only and are not intended to limit the invention thereto.
In the description of the present invention, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more. In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
Referring to fig. 1, a method for calculating a black start partition scheme of a power supply network includes the following steps:
step one: constructing a minimum topology relation matrix of the load node and the black start power supply shown in table 1
TABLE 1 topological relation matrix
| w 1 | w 2 | … | w j | … | wN | |
| B 1 | d 11 | d 12 | … | d 1j | … | d 1N |
| B 2 | d 21 | d 22 | … | d 2j | … | d 2N |
| … | … | … | … | … | … | … |
| B i | d i1 | d i2 | … | d ij | … | d iN |
| … | … | … | … | … | … | … |
| B M | d M1 | d M2 | … | d Mj | … | d MN |
In Table 1, w 1 ～w N B, which is a load node in the system 1 ～B M The power supply is characterized by being M power supply nodes which can be started in black, wherein N is the number of load nodes, M is the number of the black start power supply nodes, i is more than or equal to 1 and less than or equal to M, j is the number of the load nodes, and j is more than or equal to 1 and less than or equal to N. The units shown in Table 1 are d ij And (3) representing. d, d ij The minimum topological distance from the black start power supply node i to the load node j is the minimum power supply path of the black start power supply node i connected to the load j in a breadth search mode.
Step two: according to the association relation of each load node, establishingThe load node relation matrix table shown in Table 2 is E for each cell in Table 2 jk And (3) representing.
TABLE 2 node relationship matrix
| w 1 | w 2 | … | w k | … | w N | |
| w 1 | E 11 | E 12 | … | E 1k | … | E 1N |
| w 2 | E 21 | E 22 | … | E 1k | … | E 2N |
| … | … | … | … | … | … | … |
| w j | E j1 | E j2 | … | E jk | … | E jN |
| … | … | … | … | … | … | … |
| w N | E N1 | E N2 | … | E Nk | … | E NN |
E jk Representing the connection state of a load node j and a load node k, wherein k is the serial number of the load node, and k is more than or equal to 1 and less than or equal to N and E jk Is described mathematically as:
step three: introduction of variable vip j And variable con j The definitions are shown in the formula (2) and the formula (3) respectively:
step four: with B 1 ～B M It is indicated that the power supply node can be black-started, and the partition range table shown in table 3 is constructed.
TABLE 3 partition Range Table
| w 1 | w 2 | … | wj | … | w N | |
| B 1 | v 11 | v 12 | … | … | … | v 1N |
| B 2 | v 21 | v 22 | … | … | … | v 2N |
| … | … | … | … | … | … | … |
| B i | v i1 | v i2 | … | v ij | … | v iN |
| … | … | … | … | … | … | … |
| B M | v M1 | … | … | v Mj | … | v MN |
v ij The (i, j) cell value v in Table 3 ij For the partition subordinate relation value v of the power supply partition where the black start power supply node i is located and the load node j ij And the value is 0 or 1. Each column in table 3 has only one element of 1 and the others of 0, i.e. the sum of the elements of each column is 1.v ij When=1, the load node w is represented j Scribing black start power node B i Power supply partition of v ij When=0, the load node w is represented j Node B of starting power without black i Is provided.
Step five: an energy function shown in formula (4) is constructed.
Wherein E is the energy function value, E1-E5 are coefficients greater than 0, v mn The partition relation value of the black start power supply node M and the load node N is that M is the serial number of the black start power supply node, M is not less than 1 and not more than M, M is not less than i, N is the serial number of the load node, N is not less than 1 and not more than N, and N is not less than j. E (E) jn To represent the connection state of load node j and load node n. Gamma ray i As intermediate variable τ i As an intermediate variable, the number of the variables,w j for the capacity, s, of node j i Is B i Delta is a proportional amplification factor, and is preferably 0.01 or less. />α i Power node B for black start i Is used for the minimum output coefficient of the motor.
The first term of the energy function is only 0 in one case, namely the sum of the values of each column in the table 3 is 1, namely only one unit in each column in the table 3 is 1, and the rest is 0, so that each load node is ensured to be supplied with power by a black start power supply. In the second constraint of the energy function, when the capacity of the black start power supply node i is larger than the total load of one type in the power supply areaAnd if the power is 0, otherwise, the power is 1, and the power supply balance of the power supply area is ensured. />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 +.>0, otherwise 1. The third term may then restrict the adjustable load amount of each partition to be greater than the black start power out force. The fourth constraint is that the loss incurred when powering the various load nodes is as small as possible. The fifth item ensures that the nodes of each region are wired to the black start power supply node of that region.
Step six: solving (4) by using (5)
Wherein u is ij To solve for v ij The solution method is shown as the formula (6).
Step seven: from equations (4), (5), the dynamic equation solving equation (4) is:
wherein u is v For the normalization coefficient, 0.01 or less is preferable. Solving the formula (6) by using an Euler method, calculating an energy function value E according to the formula (4) after each iteration solution, and terminating the iteration calculation when E is not reduced. According to v ij Power supply partition of each black start power supply node can be determined, v ij When=1, the load node w is represented j Scribing black start power node B i Power supply partition of v ij When=0, the load node w is represented j Node B of starting power without black i Is provided. E terminating each cell v in Table 3 obtained by iterating without decreasing ij The element value, the corresponding energy function E is minimum, the connecting lines of all the subareas are minimum, and the subareas are divided into optimal subareas.
Referring to fig. 10, a power supply network black start partition scheme computing system includes a memory and a processor, where the memory stores a computer program that can run on the processor, and when the processor executes the computer program, the power supply network black start partition scheme computing method is implemented.
Example 1
The invention will be described in detail with reference to specific examples, in which a power supply network is shown in FIG. 1, w 2 And w 7 Is a kind of load, w 4 And w 6 For adjustable load, w 1 、w 3 、w 5 Is of a non-class and is not adjustable in load, B 1 And B 2 For a black start power supply, the grid parameters are shown in table 4.
Table 4 grid parameter table
| w 1 | w 2 | w 3 | w 4 | w 5 | w 6 | w 7 | B 1 | B 2 | α 1 | α 2 | |
| Capacity/size (MW) | 60 | 50 | 75 | 40 | 55 | 40 | 80 | 70 | 90 | 0.3 | 0.3 |
Step one: first, a node-black start power supply minimum topological relation matrix shown in Table 5 is constructed
TABLE 5 topological relation matrix
| w 1 | w 2 | w 3 | w 4 | w 5 | w 6 | w 7 | |
| B 1 | 1 | 1 | 2 | 3 | 3 | 2 | 4 |
| B 2 | 3 | 3 | 2 | 1 | 1 | 2 | 1 |
Step two: according to the association relation of each node, a load node relation matrix table shown in table 6 is established, and each unit in the table is E jk And (3) representing.
TABLE 6 node relationship matrix
| w 1 | w 2 | w 3 | w 4 | w 5 | w 6 | w 7 | |
| w 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| w 2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| w 3 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
| w 4 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| w 5 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| w 6 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| w 7 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
Step three: introduction of variable vip j And con j ，w 2 And w 7 Is a kind of load, w 4 And w 6 Is an adjustable load.
Step four: a partition scope table is constructed as shown in table 7.
TABLE 7 partition Range Table
| w 1 | w 2 | w 3 | w 4 | w 5 | w 6 | w 7 | |
| B 1 | v 11 | v 12 | v 13 | v 14 | v 15 | v 16 | v 17 |
| B 2 | v 21 | v 22 | v 23 | v 24 | v 25 | v 26 | v 27 |
In Table 7, v ij And the value is 0 or 1. Each column in table 7 has only one element of 1 and the others of 0, i.e. the sum of the elements of each column is 1.v ij When=1, the load node w is represented j Drawing in black start power supply B i Power supply partition of v ij When=0, the load node w is represented j Does not draw in black start power supply B i Is provided. The cell of 1 indicates that the corresponding column node is assigned to the partition where the corresponding row black start power supply is located.
Step five: an energy function shown in formula (1) is constructed.
Wherein e1=1000, e2=200, e3=200, e4=20.0, e5=80.0.s i Is B i Delta is a proportional amplification factor, and is preferably 0.01 or less. />
Step six: solving the equation (1) using the equation (2)
Wherein v is ij Meaning synchronization table 7 of (2); u (u) ij To solve for v ij The solution method is shown as the formula (3).
Step seven: from equations (1), (2), the dynamic equation solving equation (1) is:
wherein u is v =0.01 or less. Solving the solution (3) by using an Euler method, wherein after each iteration solution, the solution is neededThe energy function value E is calculated according to equation (1), and the iterative calculation is terminated when E is no longer decreasing. According to the calculated v ij Each black start power supply partition table 8 is available.
TABLE 8 partition Range Table
| w 1 | w 2 | w 3 | w 4 | w 5 | w 6 | w 7 | |
| B 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
| B 2 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
The graph of the available areas from Table 8 is shown in FIG. 2, namely, black start power supply B 1 Load node w 1 Load node w 2 Load node w 3 Load node w 6 For the same partition, the black start power supply B 2 Load node w 4 Load node w 5 Load node w 7 Is the same partition.
Other partition schemes can be searched in a traversing mode, as shown in fig. 3-5, the number of the partition scheme connecting lines shown in fig. 3 is 4, and the number of the partition scheme connecting lines is more than that of the partition scheme obtained by the method of the invention, and the requirements for guaranteeing power supply to one type of load are not met. The partition scheme tie lines shown in fig. 4 are 4, which are more than the partition scheme obtained by the invention. The partitioning scheme connecting lines shown in fig. 5 are 2, which are the same as the partitioning scheme connecting lines obtained by the invention, but do not meet the constraint condition that the adjustable load is larger than the minimum output of the black start power supply. As can be seen by comparing fig. 2 to 5, the partitioning scheme calculated by the present invention is due to other partitioning schemes.
The verification is as follows:
example 2
The invention will be described in detail below with reference to specific examples, wherein an IEEE-39 node power grid is shown in FIG. 6, nodes 12 and 17 are of a type of load, the adjustable load number is (7,20,21,23,24,25,28,31,34,35), the nodes 30 and 33 are black start power supplies B1 and B2, the two sets alpha are both 0.3, and the power grid parameters are shown in Table 9.
Table 9 grid parameter table
Step one: firstly, constructing a node-black start power supply minimum topological relation matrix shown in a table 10 (load point numbers are the same as the load point numbers in the following steps after deleting the black start power supply numbers and sequencing in sequence according to the original sequence)
Table 10 topology relation 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: according to the association relation of each node, a load node relation matrix table shown in table 11 is established, and each unit in the table is E jk And (3) representing.
Table 11 node relationship matrix
Step three: introduction of variable vip j And con j 。
Step four: a partition scope table is constructed as shown in table 12.
TABLE 12 partition Range Table
| w1 | w2 | w3 | w4 | w5 | w6 | w7 | w8 | w9 | w10 | w11 | w12 | w13 | |
| B1 | v 1,1 | v 1,2 | v 1,3 | v 1,4 | v 1,5 | v 1,1 | v 1,2 | v 1,8 | v 1,9 | v 1,10 | v 1,11 | v 1,12 | v 1,13 |
| B2 | v 2,1 | v 2,2 | v 2,3 | v 2,4 | v 2,5 | v 2,1 | v 2,2 | v 2,8 | v 2,9 | v 2,10 | v 2,11 | v 2,12 | v 2,13 |
| w14 | w15 | w16 | w17 | w18 | w19 | w20 | w21 | w22 | w23 | w24 | w25 | w26 | |
| B1 | v 1,14 | v 1,15 | v 1,16 | v 1,17 | v 1,18 | v 1,19 | v 1,20 | v 1,21 | v 1,22 | v 1,23 | v 1,24 | v 1,25 | v 1,26 |
| B2 | v 2,14 | v 2,15 | v 2,16 | v 2,17 | v 2,18 | v 2,19 | v 2,20 | v 2,21 | v 2,22 | v 2,23 | v 2,24 | v 2,25 | v 2,26 |
| w27 | w28 | w29 | w30 | w31 | w32 | w33 | w34 | w35 | w36 | w37 | |||
| B1 | v 1,27 | v 1,28 | v 1,29 | v 1,30 | v 1,31 | v 1,32 | v 1,33 | v 1,34 | v 1,35 | v 1,36 | v 1,37 | ||
| B2 | v 2,27 | v 2,28 | v 2,29 | v 2,30 | v 2,31 | v 2,32 | v 2,33 | v 2,34 | v 2,35 | v 2,36 | v 2,37 |
In Table 12, v ij And the value is 0 or 1. Each column in table 7 has only one element of 1 and the others of 0, i.e. the sum of the elements of each column is 1.v ij When=1, the load node w is represented j Drawing in black start power supply B i Power supply partition of v ij When=0, the load node w is represented j Does not draw in black start power supply B i Is provided. The cell of 1 indicates that the corresponding column node is assigned to the partition where the corresponding row black start power supply is located.
Step five: an energy function shown in formula (4) is constructed.
Wherein e1=1000, e2=200, e3=200, e4=20.0, e5=80.0.s i Is B i Delta is a proportional amplification factor, and is preferably 0.01 or less. />
Step six: solving (4) by using (5)
Wherein v is ij Meaning synchronization table 12 of (c); u (u) ij To solve for v ij The solution method is shown as the formula (6).
Step seven: from equations (4), (5), the dynamic equation solving equation (4) is:
wherein u is v =0.01 or less. Solving the formula (6) by using an Euler method, calculating an energy function value E according to the formula (3) after each iteration solution, and terminating the iteration calculation when E is not reduced. According to the calculated v ij Each black start power supply partition table 13 is available.
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 graph of the available sections of table 13 is shown in fig. 7, with 4 links. Other partition schemes with fewer connecting lines can be searched in a traversing mode, as shown in fig. 8 and 9, and the connecting lines of the partition schemes in fig. 8 and 9 are 5, which is more than the partition scheme calculated by the invention. The partitioning scheme calculated by the present invention is due to other partitioning schemes.
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (7)
1. The method for calculating the black start partition scheme of the power supply network is characterized by comprising the following steps of:
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 the load nodes and the black start power supply nodes;
according to the association relation among the load nodes, a load node relation matrix table is established, and elements in the load node relation matrix table are used for representing the connection state between every two load nodes;
introducing a variable for representing whether the load node is a type of load and a variable for representing whether the load node is an adjustable load;
constructing a partition range table, wherein elements in the partition range table are partition membership values of each black start power supply node and each load node;
constructing an energy function by utilizing elements in a constructed minimum topological relation matrix of the load nodes and the black start power supply nodes, elements in a load node relation matrix table, and introduced variables used for representing whether the load nodes are of a type of load and variables used for representing whether the load nodes are adjustable loads;
and solving the established energy function to obtain element values of all units in the partition range table, dividing power supply partitions according to the element values of all units in the partition range table, and dividing load power supply nodes and black start power supply nodes corresponding to the units with the element values of 1 into the same partition.
2. The method for calculating a black-start partition scheme of a power supply network according to claim 1, wherein a minimum topological relation matrix of load nodes and black-start power supply nodes is as follows:
wherein w is 1 ～w N Representing load nodes, B in a system 1 ～B M Represents M black start power supply nodes d ij For the minimum topological distance between each load node and the black start power supply node, N is the number of the load nodes, M is the number of the black start power supply nodes, and i is the serial number of the black start power supply nodesAnd i is more than or equal to 1 and less than or equal to M, j is the serial number of the load node, and j is more than or equal to 1 and less than or equal to N.
3. The method for calculating a black start partition scheme for a power supply network according to claim 1, wherein element E in the load node relation matrix table jk The values are as follows:
4. the method for calculating a black start partition scheme of a power supply network according to claim 1, wherein the variable vip is used for representing whether the load node is a type of load j And a variable con for characterizing whether the load node is an adjustable load j The values were taken according to the following:
5. the method for calculating a black start partition scheme of a power supply network according to claim 1, wherein the partition range table is:
wherein v is ij For the partition membership value, v, of black start power supply node i and load node j ij 0 or 1; each column in the partition range table has only one element of 1 and the others of 0; v ij When=1, the load node w is represented j Scribing black start power node B i Power supply partition of v ij When=0, the load node w is represented j Node B of starting power without black i Is provided.
6. The method for calculating a black start partition scheme of a power supply network according to claim 1, wherein the energy function expression is as follows:
wherein E is the energy function value, E1-E5 are coefficients greater than 0, v ij For the partition membership value, v, of black start power supply node i and load node j mn The partition dependency value of the black start power supply node M and the load node N is that M is the serial number of the black start power supply node, M is not less than 1 and not more than M, M is not less than i, N is the serial number of the load node, N is not less than 1 and not more than N, and N is not less than j; e (E) jn To represent the connection state of load node j and load node n; gamma ray i As intermediate variable τ i As an intermediate variable, the number of the variables,w j for the capacity, s, of node j i Is B i Delta is the proportional amplification factor; />α i Power node B for black start i Is used for the minimum output coefficient of the motor.
7. A power supply network black start partition scheme computing system comprising a memory and a processor, the memory having stored thereon a computer program executable on the processor, the processor implementing the method of any of claims 1-6 when executing the computer program.
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