CN110222966B - Distribution network distributed state estimation-oriented synchronous phasor measurement configuration partitioning method - Google Patents
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Abstract
A distribution network distributed state estimation-oriented synchronous phasor measurement configuration partitioning method comprises the following steps: for a selected power distribution system, acquiring a topological connection relation of a power distribution network, constructing an adjacent matrix A, and setting the number M of sub-regions; establishing a synchronous phasor measurement configuration partition model facing to the distributed state estimation of the power distribution network; solving a synchronous phasor measurement configuration partition model facing the distribution network distributed state estimation through a genetic algorithm; and outputting the obtained synchronous phasor measurement configuration partition scheme oriented to the distribution network distributed state estimation. The invention ensures connectivity of the subareas by using a method of selecting the central node first and then gradually expanding outwards, takes the minimum difference of the number of the nodes among the subareas as a target function and solves the problem through a genetic algorithm, thereby ensuring the minimum difference of the number of the nodes among the subareas and ensuring the similar state estimation time of different areas, thereby reducing the waiting time of adjacent area communication and ensuring the real-time property of distributed state estimation.
Description
Technical Field
The invention relates to a power distribution network partitioning method. In particular to a distribution network distributed state estimation oriented synchronous phasor measurement configuration partitioning method.
Background
With the enlargement of the scale of a power distribution system, a large number of distributed power sources are accessed and users participate widely, the communication burden of the traditional centralized state estimation is gradually increased, the dimension of a state variable is high, the overall solving time is long, and the requirement of real-time analysis and control of the power distribution network is difficult to meet. In order to reduce communication burden and increase computation speed, distributed state estimation is becoming an effective solution to the problem. The premise of state estimation convergence is that the system is considerable, and the existing power distribution network cannot meet the integral observability due to the fact that the data acquisition points are multiple, the distribution is wide, the coverage of monitoring points is not comprehensive, and the configuration is unreasonable. In addition, most of the measurement used for state estimation comes from a data acquisition and monitoring control System (SCADA) and an advanced measurement system (AMI), and not only is the data itself low in precision, poor in synchronism and long in acquisition period, but also the measurement and state variables are in a nonlinear relation, and iterative solution needs to be performed through algorithms such as a weighted least square method, and even if distributed state estimation is adopted, the accuracy and the real-time performance of system state solution are difficult to guarantee.
Due to the introduction of the synchronous phasor measurement device, the operation monitoring level of the power distribution network is greatly improved. Compared with the traditional measuring device, the synchronous phasor measuring device can synchronously acquire the measurement information of the node voltage phasor, the branch current phasor and the system frequency, is high in uploading speed, effectively solves the problems of poor measurement data quality, low synchronism and long acquisition period of the traditional power distribution system, improves the calculation speed and accuracy of applications such as model parameter verification, state estimation, system protection and operation control, and is an important link for the technical development of the intelligent power distribution network. Particularly, in the application of state estimation, the voltage and current phasor measurement acquired by the synchronous phasor measurement device is in a linear relation with the state variable of the system, so that the calculation time is greatly reduced, and the real-time analysis and control of the power distribution system are guaranteed.
If all the measurement data adopted in the distributed state estimation come from the synchronous phasor measurement device, the rapidity of state variable solving can be ensured, the communication burden can be reduced, and the accuracy and the instantaneity of the estimation result can be ensured due to strong data synchronism and high uploading frequency. However, before configuring the synchronous phasor measurement apparatus, the partitioning of the power distribution network needs to be completed. The existing power distribution network distributed state estimation partitioning method mainly comprises the following steps: and manually completing the partition of the power distribution network based on the topological structure and the geographical position partition, the existing measurement partition and the distributed state estimation partition principle. Partitioning is difficult to ensure that the number of nodes in each partition is similar based on a topological structure and a geographic position; the method is based on the fact that the partition cannot be completed when the measurement configuration of the power distribution network is insufficient or configuration information cannot be obtained by the existing measurement partition, and the partition effect is related to the setting of relevant parameters, so that the method is not suitable for the situation that synchronous phasor measurement is configured after the partition is performed; the optimal partitioning scheme is difficult to obtain after the power distribution network partitioning is completed manually. Therefore, finding an optimization method which is not based on existing measurement and meets the principle of distributed state estimation to complete power distribution network partitioning, enabling the number of nodes between each region to be similar and enabling adjacent regions to have only one overlapped node is a prerequisite condition for configuring a synchronous phasor measurement device to enable each sub-network to be completely observable so as to achieve distributed state estimation.
Disclosure of Invention
The invention aims to solve the technical problem of providing a synchronous phasor measurement configuration partitioning method for distributed state estimation of a power distribution network, which can reduce the waiting time of adjacent area communication and ensure the real-time property of the distributed state estimation.
The technical scheme adopted by the invention is as follows: a distribution network distributed state estimation-oriented synchronous phasor measurement configuration partitioning method comprises the following steps:
1) For a selected power distribution system, acquiring a topological connection relation of a power distribution network, constructing an adjacent matrix A, and setting the number M of sub-regions;
2) Establishing a synchronous phasor measurement configuration partition model facing to the distributed state estimation of the power distribution network;
3) Solving the synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation in the step 2) through a genetic algorithm;
4) And outputting the obtained synchronous phasor measurement configuration partition scheme oriented to the distribution network distributed state estimation.
The number M of the subregions in the step 1) is as follows:
wherein N represents the total node number of the power distribution system to be partitioned,
representing number->
And rounding down.
The distribution network distributed state estimation-oriented synchronous phasor measurement configuration partition model in the step 2) takes the minimum difference of the number of nodes among the sub-partitions as a target function, and the mathematical expression is as follows:
wherein N is i Indicates the number of nodes included in the sub-region i.
The step 3) comprises the following steps:
(3.1) setting the length of the chromosome of an individual in a genetic algorithm to be equal to the number M of sub-regions, setting a value set of genes on the chromosome to be a set omega formed by all nodes of a power distribution system, wherein omega = {1, 2.., N }, N represents the total number of the nodes of the power distribution system to be partitioned, randomly generating an initial population, setting an evolutionary algebra d =1, and setting a cross probability p C Genetic probability p M And a maximum evolution algebra D;
(3.2) obtaining an initial center node through chromosomes of individuals in a group, partitioning the power distribution network by using a center expansion partitioning method, and further calculating the fitness of the individuals;
(3.3) acting a selection operator on the population, and reserving the individual with the highest fitness;
(3.4) acting the crossover operator and the mutation operator on the selected population to generate a next generation, wherein the evolution algebra d = d +1;
(3.5) if the evolution algebra D is less than D, entering the step (3.2), otherwise, entering the step (3.6);
and (3.6) outputting the individual with the highest fitness as an optimal solution.
The method for center-expanded partition in step (3.2) comprises:
(3.2.1) setting all the nodes not to be partitioned, randomly acquiring M nodes as initial central nodes, and marking the initial central nodes as partitioned nodes;
(3.2.2) the number of expansion times k =0, updating the sub-region set corresponding to the initial central node according to the initial central node and constructing a partition matrix E k The number of expansion times k = k +1; wherein the partition matrix E k Is a matrix of dimension M × N, for
l and i respectively represent a node number and a sub-region number, and if the node l is in the sub-region i, E k Ith row and ith column element E k，i，l =1, otherwise E k，i，l Is 0, set of subregions Γ l The middle element is the number of the subregion to which the node l belongs, if the node l is in the subregion i, i belongs to the gamma l ；
(3.2.3) setting a partition matrix E 'to be adjusted after the k expansion' k ＝E k-1 A and A are adjacent matrixes, and a partition matrix E 'to be adjusted' k All the non-zero elements in the sub-area are set to be 1, i =1, j =2, and i and j are the numbers of the sub-areas;
(3.2.4) if j > M, i = i +1, j = i +1, and entering the (3.2.5) th step, and otherwise, entering the (3.2.6) th step;
(3.2.5) if i = M, entering the (3.2.8) step, otherwise, entering the (3.2.6) step;
(3.2.6) obtaining a set Λ of overlapping nodes of the sub-region i and the sub-region j i，j If the node set is overlapped i，j If the current is an empty set, j = j +1, and the step (3.2.4) is carried out, otherwise, the step (3.2.7) is carried out;
(3.2.7) if overlapping node set Λ i，j In the method, only two nodes are provided, and the two nodes are partitioned nodes, the two nodes are respectively used as the shared boundary nodes of the sub-regions i and j, and the comparison is maximumSelecting a boundary node by taking the minimum difference as a target according to the difference between the number of the area nodes and the minimum number of the area nodes, and adjusting a to-be-adjusted partition matrix E 'by taking a node in the pre-expansion sub-area i as a boundary if the differences are the same' k Updating a sub-region set corresponding to the boundary node, wherein j = j +1, and entering the (3.2.4) th step;
(3.2.8) set the set of all partitioned nodes to Ω 1 To a
If i ∈ Γ l Then the partition matrix E 'is to be adjusted' k Line i of l element E' k，i，l =1, otherwise E' k，i，l ＝0；
(3.2.9) set the set of all non-partitioned overlapping nodes to Ω 2 To for
If the overlapped subareas have boundaries, dividing the node l into the subarea with the minimum node number, if the subarea with the minimum node number has a plurality of subareas, dividing the node l into the subarea with the minimum serial number, and adjusting the subarea matrix E 'to be adjusted' k Updating the sub-region set corresponding to the node l;
(3.2.10) assuming that i =1, j =2, i and j are both sub-region numbers;
(3.2.11) if j > M, i = i +1, j = i +1, and entering the (3.2.12) th step, and otherwise entering the (3.2.13) th step;
(3.2.12) if i = M, entering the (3.2.15) step, otherwise, entering the (3.2.13) step;
(3.2.13) obtaining the set Λ of overlapping nodes of the sub-regions i and j i，j If the node set is overlapped i，j If the current is an empty set, j = j +1, and the step (3.2.11) is entered, otherwise, the step (3.2.14) is entered;
(3.2.14) if overlapping node set Λ i，j The node is not partitioned, and the sub-region i and the sub-region j are overlapped for the first time, the node is used as a boundary node shared by the sub-region i and the sub-region j, and a partition matrix E 'to be adjusted is adjusted' k Updating the pairs of edge nodesThe corresponding subregion set, j = j +1, enters the step (3.2.11);
(3.2.15) setting the adjusted partition matrix E k ＝E′ k If E is k ＝E k-1 Entering the step (3.2.16), otherwise, E k The node contained in the node list is marked as a partitioned node, the expansion times k = k +1, and the step (3.2.3) is carried out;
(3.2.16) according to partition matrix E k And outputting a partition result.
The synchronous phasor measurement configuration partitioning method for the distributed state estimation of the power distribution network ensures connectivity of sub-regions by using a method of selecting a central node first and then gradually expanding outwards, takes the minimum difference of the number of nodes among the sub-regions as a target function and solves the target function through a genetic algorithm, ensures the minimum difference of the number of nodes among the regions, ensures that state estimation time of different regions is close, reduces the waiting time of communication of adjacent regions and ensures the real-time property of the distributed state estimation.
Drawings
FIG. 1 is a flow chart of a method for partitioning a synchronous phasor measurement configuration for distributed state estimation of a power distribution network according to the present invention;
FIG. 2 is an IEEE 33 node calculation diagram;
FIG. 3 is a graph of the PG & E69 node calculation;
FIG. 4 is an IEEE 33 node example partitioning result;
FIG. 5 is the PG & E69 node example partitioning results.
Detailed Description
The following describes the partition method for the measurement configuration of the synchronous phasor for the distributed state estimation of the power distribution network in detail with reference to the embodiments and the drawings.
As shown in fig. 1, the method for partitioning a synchronized phasor measurement configuration for distributed state estimation of a power distribution network according to the present invention includes the following steps:
1) For a selected power distribution system, acquiring a topological connection relation of a power distribution network, constructing an adjacent matrix A, and setting the number M of sub-regions, wherein the number M of the sub-regions is as follows:
wherein N represents the total node number of the power distribution system to be partitioned,
means number->
And rounding down.
2) Establishing a synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation, wherein the synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation takes the minimum node number difference among sub-regions as a target function, and the mathematical expression is as follows:
wherein N is i Indicates the number of nodes included in the sub-region i.
3) Solving the synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation in the step 2) through a genetic algorithm; the method comprises the following steps:
(3.1) setting the chromosome length of an individual in a genetic algorithm to be equal to the number M of subregions, setting a value set of genes on the chromosome to be a set omega formed by all nodes of a power distribution system, wherein omega = {1, 2.., N }, and N represents the total number of the nodes of the power distribution system to be partitioned, randomly generating an initial population, setting an evolution algebra d =1, and setting a cross probability p C Genetic probability p M And a maximum evolution algebra D;
(3.2) obtaining an initial center node through chromosomes of individuals in a group, partitioning the power distribution network by using a center expansion partitioning method, and further calculating the fitness of the individuals; the center expansion partition method comprises the following steps:
(3.2.1) setting all the nodes not to be partitioned, randomly acquiring M nodes as initial central nodes, and marking the initial central nodes as partitioned nodes;
(3.2.2) the number of expansion times k =0, updating the sub-region set corresponding to the initial central node according to the initial central node and constructing a partition matrix E k The number of expansion times k = k +1; wherein the partition matrix E k Is a matrix of dimension M × N, for
l and i respectively represent a node number and a sub-region number, and if the node l is in the sub-region i, E k Row i and column l element E of k，i，l =1, otherwise E k，i，l Is 0, the set of sub-regions Γ l The middle element is the number of the subregion to which the node l belongs, if the node l is in the subregion i, i belongs to the gamma l ；
(3.2.3) setting a partition matrix E 'to be adjusted after the k expansion' k ＝E k-1 A and A are adjacent matrixes, and a partition matrix E 'to be adjusted' k All the non-zero elements in the list are set to be 1, i =1, j =2, and i and j are all subarea numbers;
(3.2.4) if j > M, i = i +1, j = i +1, and the step (3.2.5) is entered, otherwise, the step (3.2.6) is entered;
(3.2.5) if i = M, entering the (3.2.8) th step, otherwise, entering the (3.2.6) th step;
(3.2.6) obtaining the overlapping node set Lambda of the sub-regions i and j i，j If the node set is overlapped i，j If the current is an empty set, j = j +1, and the step (3.2.4) is carried out, otherwise, the step (3.2.7) is carried out;
(3.2.7) if overlapping node set Λ i，j If there are only two nodes in the partition matrix E ' and the two nodes are all partitioned nodes, the two nodes are respectively used as shared boundary nodes of the sub-area i and the sub-area j, the difference between the maximum area node number and the minimum area node number is compared, the boundary node is selected by taking the minimum difference as a target, and if the differences are the same, the node in the sub-area i before expansion is taken as a boundary, and the partition matrix E ' to be adjusted is adjusted ' k Updating a sub-region set corresponding to the boundary node, wherein j = j +1, and entering the (3.2.4) step;
(3.2.8) set the set of all partitioned nodes to Ω 1 To a
If i ∈ Γ l Then the partition matrix E 'is to be adjusted' k Line ith element E' k，i，l =1, otherwise E' k，i，l ＝0；
(3.2.9) set the set of all non-partitioned overlapping nodes to Ω 2 To for
If the overlapped subareas have boundaries, dividing the node l into the subarea with the minimum node number, if the subarea with the minimum node number has a plurality of subareas, dividing the node l into the subarea with the minimum serial number, and adjusting the subarea matrix E 'to be adjusted' k Updating the sub-region set corresponding to the node l;
(3.2.10) assuming that i =1, j =2, i and j are both sub-region numbers;
(3.2.11) if j > M, i = i +1, j = i +1, and entering the (3.2.12) th step, and otherwise entering the (3.2.13) th step;
(3.2.12) if i = M, entering the (3.2.15) step, otherwise, entering the (3.2.13) step;
(3.2.13) obtaining a set Λ of overlapping nodes of the sub-region i and the sub-region j i，j If the node sets are overlapped, Λ i，j If the current is an empty set, j = j +1, and the step (3.2.11) is entered, otherwise, the step (3.2.14) is entered;
(3.2.14) if overlapping node set Λ i，j The node is not partitioned, and the sub-area i and the sub-area j are overlapped for the first time, then the node is used as a boundary node shared by the sub-area i and the sub-area j, and a partition matrix E 'to be adjusted is adjusted' k Updating a subregion set corresponding to the boundary node, wherein j = j +1, and entering the step (3.2.11);
(3.2.15) setting the adjusted partition matrix E k ＝E′ k If E is k ＝E k-1 Then step (3.2.16) is entered, otherwise E is entered k Node marking contained inFor the partitioned node, the expansion times k = k +1, and the step (3.2.3) is entered;
(3.2.16) according to partition matrix E k Outputting a partition result;
(3.3) acting a selection operator on the population, and reserving the individuals with the highest fitness;
(3.4) acting the crossover operator and the mutation operator on the selected population to generate a next generation, wherein the evolution algebra d = d +1;
(3.5) if the evolution algebra D is less than D, entering the step (3.2), otherwise, entering the step (3.6);
and (3.6) outputting the individual with the highest fitness as an optimal solution.
Specific examples are given below:
employing IEEE 33 node algorithm and PG&The method provided by the invention is verified by an example of the E69 node, and the example topological connection relation is shown in FIGS. 2 and 3. Let the cross probability p C =0.3, genetic probability p M =0.1, the number of initial population individuals is 5000, and the maximum evolution algebra D =100, after the partitioning process according to the present invention is performed, the partitioning result of the IEEE 33 node example is shown in fig. 4, the specific partitioning scheme is shown in table 1, and PG is&The partitioning result of the E69 node algorithm is shown in fig. 5, and the specific partitioning scheme is shown in table 2. Therefore, the partitioning result obtained by solving by using the method provided by the invention can ensure that the number of nodes between the sub-regions has smaller difference, and the validity of the method is verified.
TABLE 1 IEEE 33 node example partition scheme obtained by solving by the method of the invention
| Region numbering | Center node numbering | Node numbering within a region | Region(s)Number of |
| 1 | 1 | 1，2，3，4，5，19，20，21，22，23，24，25 | 12 |
| 2 | 29 | 5，6，7，26，27，28，29，30，31，32，33 | 11 |
| 3 | 12 | 7，8，9，10，11，12，13，14，15，16，17，18 | 12 |
Table 2 PG and E69 node sample partitioning scheme
Claims (3)
1. A distribution network distributed state estimation oriented synchronous phasor measurement configuration partitioning method is characterized by comprising the following steps:
1) For a selected power distribution system, acquiring a topological connection relation of a power distribution network, constructing an adjacent matrix A, and setting the number M of sub-regions;
2) Establishing a synchronous phasor measurement configuration partition model facing to the distributed state estimation of the power distribution network;
3) Solving the synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation in the step 2) through a genetic algorithm; the method comprises the following steps:
(3.1) setting genetic AlgorithmThe length of a chromosome of a middle individual is equal to the number M of subregions, the value set of genes on the chromosome is a set omega formed by all nodes of a power distribution system, omega = {1, 2.., N }, N represents the total number of the nodes of the power distribution system to be partitioned, an initial population is generated randomly, an evolution algebra d =1, and a cross probability p is set C Genetic probability p M And a maximum evolution algebra D;
(3.2) obtaining an initial center node through chromosomes of individuals in a group, partitioning the power distribution network by using a center expansion partitioning method, and further calculating the fitness of the individuals; the central extension partition method comprises the following steps:
(3.2.1) setting all the nodes not to be partitioned, randomly acquiring M nodes as initial central nodes, and marking the initial central nodes as partitioned nodes;
(3.2.2) the number of expansion times k =0, updating the sub-region set corresponding to the initial central node according to the initial central node and constructing a partition matrix E k The number of expansion times k = k +1; wherein the partition matrix E k Is a matrix of dimension M × N, for
l and i respectively represent a node number and a sub-region number, and if the node l is in the sub-region i, E k Row i and column l element E of k，i，l =1, otherwise E k，i，l Is 0, the set of sub-regions Γ l The middle element is the number of the subregion to which the node l belongs, if the node l is in the subregion i, i belongs to the gamma l ；
(3.2.3) setting a partition matrix E 'to be adjusted after the k expansion' k ＝E k-1 A and A are adjacent matrixes, and a partition matrix E 'to be adjusted' k All the non-zero elements in the sub-area are set to be 1, i =1, j =2, and i and j are the numbers of the sub-areas;
(3.2.4) if j > M, i = i +1, j = i +1, and entering the (3.2.5) th step, and otherwise, entering the (3.2.6) th step;
(3.2.5) if i = M, entering the (3.2.8) step, otherwise, entering the (3.2.6) step;
(3.2.6) obtaining a set Λ of overlapping nodes of the sub-region i and the sub-region j i，j If the node set is overlapped i，j If the current is an empty set, j = j +1, and the step (3.2.4) is entered, otherwise, the step (3.2.7) is entered;
(3.2.7) if overlapping node set Λ i，j If there are only two nodes in the partition matrix E ' and the two nodes are all partitioned nodes, the two nodes are respectively used as shared boundary nodes of the sub-area i and the sub-area j, the difference between the maximum area node number and the minimum area node number is compared, the boundary node is selected by taking the minimum difference as a target, and if the differences are the same, the node in the sub-area i before expansion is taken as a boundary, and the partition matrix E ' to be adjusted is adjusted ' k Updating a sub-region set corresponding to the boundary node, wherein j = j +1, and entering the (3.2.4) th step;
(3.2.8) let the set of all partitioned nodes be Ω 1, for
If i ∈ Γ l Then the partition matrix E 'is to be adjusted' k Line i of l element E' k，i，l =1, otherwise E' k，i，l ＝0；
(3.2.9) set the set of all non-partitioned overlapping nodes to Ω 2 To a
If the overlapped subareas have boundaries, dividing the node l into the subarea with the minimum node number, if the subarea with the minimum node number has a plurality of subareas, dividing the node l into the subarea with the minimum serial number, and adjusting the subarea matrix E 'to be adjusted' k Updating the sub-region set corresponding to the node l;
(3.2.10) assuming that i =1, j =2, i and j are both sub-region numbers;
(3.2.11) if j > M, i = i +1, j = i +1, and the step (3.2.12) is entered, otherwise, the step (3.2.13) is entered;
(3.2.12) if i = M, entering the (3.2.15) otherwise entering the (3.2.13) step;
(3.2.13) obtaining the sub-regionOverlap node set Λ of domain i and sub-region j i，j If the node set is overlapped i，j If the current is an empty set, j = j +1, and the step (3.2.11) is entered, otherwise, the step (3.2.14) is entered;
(3.2.14) if overlapping node set Λ i，j The node is not partitioned, and the sub-area i and the sub-area j are overlapped for the first time, then the node is used as a boundary node shared by the sub-area i and the sub-area j, and a partition matrix E 'to be adjusted is adjusted' k Updating a subregion set corresponding to the boundary node, wherein j = j +1, and entering the step (3.2.11);
(3.2.15) setting the adjusted partition matrix E k ＝E′ k If E is k ＝E k-1 Then step (3.2.16) is entered, otherwise E is entered k The nodes contained in the data are marked as partitioned nodes, the expansion times k = k +1, and the step (3.2.3) is carried out;
(3.2.16) according to partition matrix E k Outputting a partition result;
(3.3) acting a selection operator on the population, and reserving the individual with the highest fitness;
(3.4) acting the crossover operator and the mutation operator on the selected population to generate a next generation, wherein the evolution algebra d = d +1;
(3.5) if the evolution algebra D is less than D, entering the step (3.2), otherwise, entering the step (3.6);
(3.6) outputting the individual with the highest fitness as an optimal solution;
4) And outputting the obtained synchronous phasor measurement configuration partition scheme oriented to the distribution network distributed state estimation.
2. The distribution network distributed state estimation-oriented synchronous phasor measurement configuration partitioning method according to claim 1, wherein the number M of the sub-regions in the step 1) is as follows:
wherein N represents the total node number of the power distribution system to be partitioned,
means number->
And rounding down.
3. The distribution network distributed state estimation-oriented synchronous phasor measurement configuration partition method according to claim 1, wherein the distribution network distributed state estimation-oriented synchronous phasor measurement configuration partition model in step 2) is a target function with minimum node number difference between sub-areas, and a mathematical expression is as follows:
wherein, N i Indicating the number of nodes contained in sub-region i.
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