CN110175413B - Power distribution network reconstruction method and device based on R2 index multi-target particle swarm algorithm - Google Patents
Power distribution network reconstruction method and device based on R2 index multi-target particle swarm algorithm Download PDFInfo
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Abstract
The invention relates to a power distribution network reconstruction method and device based on an R2 index multi-target particle swarm algorithm, wherein the method comprises the following steps: s1, acquiring original data of a power distribution network, and performing particle swarm coding according to a network structure; s2, adopting a particle swarm algorithm to carry out iterative solution to obtain an optimal reconstruction network topology; in the iterative process, the particle swarm is updated based on the R2 index, specifically, elite particle swarm and updated particle swarm are integrated into a candidate solution set RR, and a uniformly distributed weight vector Λ and ideal point z are adopted * And trimming the candidate solution set RR, sorting the R2 contribution values of the candidate solutions to the weight vector lambda from large to small, and setting the number of the candidate solutions to form a particle swarm of the next iteration. Compared with the prior art, the invention has the advantages of high convergence, good diversity and the like.
Description
Technical Field
The invention relates to the technical field of reconstruction optimization of power distribution networks, in particular to a method and a device for reconstructing a power distribution network based on an R2 index multi-target particle swarm algorithm.
Background
The distribution system is an important part responsible for providing energy for final consumers, a large amount of power loss and extra cost are generated at the stage, the distribution network reconstruction means that the running structure of the distribution network is optimized by changing the opening and closing states of switches on the distribution network on the premise of meeting the basic requirements of system voltage, current, line capacity and the like, so that one or more targets of optimizing load balancing, improving node voltage offset, eliminating overload, reducing network active power loss and the like are achieved, and the distribution network reconstruction is a multi-constraint, multi-target and nonlinear combination optimization relationship.
The reconstruction of a power distribution network is a complex large-scale non-specified polynomial combination optimization problem, and the current research methods for the reconstruction of the power distribution network can be roughly divided into two types: one is a traditional mathematical optimization algorithm, namely, the reconstruction problem of the power distribution network is described by a mathematical model to obtain an optimization result independent of the initial structure of the network, but the reconstruction problem of the power distribution network is the combined optimization belonging to a large-scale network, so that the occupied memory of a computer is large, and the operation difficulty is high; the other is an artificial intelligent algorithm, wherein the particle swarm optimization algorithm is a swarm intelligent algorithm following the genetic algorithm and the ant colony algorithm, migration and clustering behaviors in the birdcage feeding process are simulated, particles fly continuously in the optimal direction in the iteration process, if the particles meet local optimization, the particle speed can be quickly reduced to zero, the particles are stopped before the particles appear premature convergence, and the local extremum points are difficult to jump out. There are many algorithms proposed to solve the problem of high-dimensional multi-objective optimization, and an algorithm based on an evaluation index adopts the evaluation index as a selection standard to measure the quality of the solution, and a selection mechanism selects a better solution by comparing the quality of the solution, and the algorithm represents such as IBEA and HypE, and although the algorithm can well process some high-dimensional multi-objective optimization problems, the algorithm is very sensitive to the shape of the pareto front, so that convergence and diversity cannot be balanced well.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a power distribution network reconstruction optimization method based on an R2 index multi-target particle swarm algorithm.
The aim of the invention can be achieved by the following technical scheme:
a power distribution network reconstruction method based on an R2 index multi-target particle swarm algorithm comprises the following steps:
s1, acquiring original data of a power distribution network, and performing particle swarm coding according to a network structure;
s2, adopting a particle swarm algorithm to carry out iterative solution to obtain an optimal reconstruction network topology;
in the iterative process, the population of particles is updated based on the R2 index, and in particular,
the elite particle swarm and the updated particle swarm are integrated into a candidate solution set RR, and a weight vector Λ and an ideal point z which are uniformly distributed are adopted * And trimming the candidate solution set RR, sorting the R2 contribution values of the candidate solutions to the weight vector lambda from large to small, and setting the number of the candidate solutions to form a particle swarm of the next iteration.
The calculation process of the R2 contribution value of the candidate solution to the weight vector Λ is as follows:
initializing R2 contribution value C of candidate solution a ＝0；
Calculating TCH utility value of candidate solution pair weight vector
Wherein lambda is j Not less than 0, andx represents a candidate solution;
calculating the R2 contribution value of the candidate solution to the set of weight vectors Λ:
in the iterative process, if the algebraic individual optimal pBest is continuously set unchanged, resetting the speed and position information of the particles by adopting a Gaussian learning strategy, wherein the formula is as follows:
wherein, the average value of mu Gaussian random number, sigma 2 Is the variance of the gaussian random number,represents the position of the particle i in the j-th dimension at the t+1st iteration, x gb (j) Represents the global optimal position of the j-th dimension at the ith iteration, x pb，i (j) The individual optimal position of the particle i in the j-th dimension at the t-th iteration is represented.
When the particle swarm algorithm is adopted for iterative solution, topology inspection is carried out on a network corresponding to each particle when the particle swarm is obtained each time, whether the topology is qualified is judged, if yes, solution is continued, and if not, the particle swarm is reconstructed.
And performing topology inspection on the network corresponding to each particle by adopting a depth-first search method.
The topology inspection specifically comprises the following steps:
101 Acquiring a distribution network structure corresponding to the particles, and generating a node association matrix;
102 Obtaining branch number N and effective node number N based on the node association matrix, judging whether n=n-1 exists, if yes, executing step 103), and if not, judging that the topology is unqualified;
103 Judging whether island exists in the power distribution network structure, if so, judging that the topology is unqualified, and if not, judging that the power distribution network is radial, and judging that the topology is qualified.
The judging whether the power distribution network structure has islands specifically comprises:
obtaining nodes at two ends of a branch according to the node incidence matrix;
disconnecting a certain branch, taking a node at one end of the branch as a starting point and a node at the other end as an end point, judging whether the other end node can be searched from the node at one end by using a deep search method, and if so, determining that the two nodes are communicated;
traversing all nodes, judging whether all nodes are communicated, if so, not forming an island, and if not, forming an island.
The power distribution network reconstruction device based on the R2 index multi-target particle swarm algorithm comprises a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the method.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, the power distribution network reconstruction is carried out by adopting the multi-target particle swarm algorithm based on the R2 index, the R2 index is used for quantifying the merits of the candidate solutions in the dispute through constructing a proper utility function, the candidate solution with larger utility is selected, the convergence and the diversity of the integrated candidate solution can be comprehensively balanced by the R2 index, the accuracy and the uncertainty of the algorithm can be balanced, the calculated amount is small, and the running speed is high.
(2) The method can improve the selection capability of the reconstruction process on the candidate solution, obtain the candidate solution with good convergence and diversity, and solve the technical problem of a large number of infeasible solutions in the reconstruction of the power distribution network by adopting a Gaussian learning strategy to assist the particle swarm to jump out of the local Pareto front.
(3) The invention adopts a Gaussian learning strategy to assist the particle swarm to jump out of the local optimal front, the particles are easy to sink into the local optimal and early-maturing convergence in the process of flying to the individual optimal and group optimal directions, and the particle swarm which is trapped into the local optimal front is subjected to speed and position information reset by adopting the Gaussian learning strategy.
(4) The invention adopts the particle swarm algorithm comprehensively using the R2 index and the Gaussian learning strategy, comprehensively considers the convergence and diversity of population individuals, ensures the convergence and diversity of the whole candidate solution, has less calculation amount of the algorithm, and effectively improves the optimizing speed and precision.
(5) According to the invention, the network loss of the power distribution system can be reduced through the power distribution network reconstruction optimization method, the benefit of the power grid is effectively improved, the quality of power supply is improved, and the operation safety and economic benefit of the power distribution network are comprehensively improved.
Drawings
FIG. 1 is a flowchart of an algorithm of the present invention.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
Example 1
The embodiment provides a power distribution network reconstruction method based on an R2 index multi-target particle swarm algorithm, which comprises the steps of firstly obtaining original data of a power distribution network, and carrying out particle swarm coding according to a network structure; and then adopting a particle swarm algorithm to carry out iterative solution to obtain the optimal reconstruction network topology, and updating the particle swarm based on the R2 index in the iterative process, specifically,
the elite particle swarm and the updated particle swarm are integrated into a candidate solution set RR, and a weight vector Λ and an ideal point z which are uniformly distributed are adopted * And trimming the candidate solution set RR, sorting the R2 contribution values of the candidate solutions to the weight vector lambda from large to small, and setting the number of the candidate solutions to form a particle swarm of the next iteration.
As shown in fig. 1, the above power distribution network reconstruction method specifically includes the following steps:
s1: initializing a population, and encoding the particle population according to a network structure.
S2: and (3) performing topology inspection on the network corresponding to each particle, judging whether the topology is qualified, if so, continuing to solve, executing the step (S3), and if not, returning to the step (S1) to reconstruct the particle swarm.
The topology inspection is carried out on the network corresponding to each particle by adopting a depth-first search method, specifically:
101 Acquiring a distribution network structure corresponding to particles, generating a node association matrix, wherein the number of rows of the node association matrix represents the number of nodes, the number of columns of the matrix represents the number of branches, the association matrix is a sparse matrix, and only 0 and 1,0 represent nodes which are not connected with branches, and 1 represents nodes which are connected with branches;
102 Obtaining branch number N and effective node number N based on the node association matrix, judging whether n=n-1 exists, if yes, executing step 103), and if not, judging that the topology is unqualified;
103 Judging whether island exists in the power distribution network structure, if so, judging that the topology is unqualified, and if not, judging that the power distribution network is radial, and judging that the topology is qualified.
The judging whether the power distribution network structure has islands specifically comprises:
obtaining nodes at two ends of a branch according to the node incidence matrix;
disconnecting a certain branch, taking a node at one end of the branch as a starting point and a node at the other end as an end point, judging whether the other end node can be searched from the node at one end by using a deep search method, and if so, determining that the two nodes are communicated;
traversing all nodes, judging whether all nodes are communicated, if so, not forming island, and enabling the power distribution network to be radial, and if one node cannot find a corresponding termination node, forming the isolated node of the power distribution network, and not meeting the radial judging requirement.
S3: particle swarm updating operation.
Updating the position and velocity of the particles according to formulas (1) and (2):
correcting the particle boundary crossing problem according to formulas (3) and (4);
wherein:and->Represents the position and velocity of particle i in the j-th dimension at the t+1th iteration, x ub (j) And x lb (j) The upper limit value and the lower limit value of the particles in the j-th dimension are respectively, and the coefficient gamma is 1.
S4: and (3) performing topology inspection on the network corresponding to each particle, judging whether the topology is qualified, if so, continuing to solve, executing the step S5, and if not, returning to the step S3, and reconstructing the particle swarm.
S5: calculating an objective function f (x) for each particle; setting the current position of each particle as a body optimal pBest, and randomly selecting one gBest as global optimal; wherein the objective function f (x) of each particle can be expressed as:
minf(x)＝(f 1 (x)，f 2 (x)，…，f k (x)) (5)
the constraint conditions are as follows:
s.t.g i (x)＝0 i＝1，2，…，p
h i (x)≤0 i＝1，2，…，p
x∈X∈R n
wherein: f (f) i (x) Is the kth objective function; g i (x)、h i (x) The equality constraint and the inequality constraint, respectively.
In the above formula, minf (x) is Pareto optimal solution, assuming that there are two decision variables x 1 And x 2 Solution x is said to be if the following two conditions are satisfied 1 Dominant solution x 2 ：
1) For the followingAll satisfy f i (x 1 )≤f i (x 2 )；
2) At least 1 i.epsilon. {1,2, …, k } causesGet f i (x 1 )＜f i (x 2 )。
X satisfying the above condition 1 Is a Paraton optimal solution for multi-objective optimization.
In this embodiment, three targets are set, and then the objective function is expressed as:
minf(x)＝(f 1 (x)，f 2 (x)，f 3 (x)) (6)
f 3 (x)＝minf 3 ＝min|U i | (9)
objective function f 1 (x) Wherein L is the total number of system branches; r is R i 、U i 、P i 、Q i The resistance, the terminal voltage, the active power and the reactive power of the branch of the ith branch, K i The state of the switch on the branch is that 0 represents opening and 1 represents closing; objective function f 2 (x) In (1), Y i And Z j The states of the sectionalizing switch and the interconnecting switch after reconstruction are respectively represented, the closing is 1, the opening is 0, and m and n are respectively the numbers of the sectionalizing switch and the interconnecting switch in the power distribution network; objective function f 3 (x) The constraints of (2) include: node voltage constraint of U i，min ≤U i ≤U i，max ，U i，min 、U i，max The upper limit voltage and the lower limit voltage of the node i are respectively; the capacity constraint of the branch is S i ≤S i，max ，S i 、S i，max The power through which each branch flows and the line capacity of the branch.
S6: evaluating particles and updating reference point z * ；
S7: the individual optimum pBest is updated.
S8: the population of particles is trimmed based on the R2 index.
From whenObtaining elite particle swarm from the front particle swarm, integrating the elite particle swarm and the updated particle swarm into a candidate solution set RR, and adopting a uniformly distributed weight vector Λ and an ideal point z * And trimming the candidate solution set RR, sorting the R2 contribution values of the candidate solutions to the weight vector lambda from large to small, and setting the number of the candidate solutions to form a particle swarm of the next iteration. The calculation process of the R2 contribution value of the candidate solution to the weight vector Λ is as follows:
initializing R2 contribution value C of candidate solution a ＝0；
Calculating TCH utility value of candidate solution pair weight vector
Wherein lambda is j Not less than 0, andx represents a candidate solution;
calculating the R2 contribution value of the candidate solution to the set of weight vectors Λ:
s9: judging whether algebraic individual optimal pBest is continuously set unchanged, if yes, resetting speed and position information of particles by adopting a Gaussian Learning (GLS) strategy to assist the particle swarm to jump out of a local optimal front edge, wherein the formula is as follows:
wherein, the average value of mu Gaussian random number, sigma 2 Is the variance of the gaussian random number,represents the position of the particle i in the j-th dimension at the t+1st iteration, x gb (j) Represents the global optimal position of the jth dimension at the t-th iteration, x pb，i (j) The individual optimal position of the particle i in the j-th dimension at the t-th iteration is represented.
S10: judging whether the maximum iteration times of the group are reached, if so, outputting a reconstruction optimization structure; otherwise, the step S3 is skipped.
Example 2
The embodiment provides a power distribution network reconstruction device based on an R2 index multi-target particle swarm algorithm, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the method in embodiment 1.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (6)
1. The power distribution network reconstruction method based on the R2 index multi-target particle swarm algorithm is characterized by comprising the following steps of:
s1, acquiring original data of a power distribution network, and performing particle swarm coding according to a network structure;
s2, adopting a particle swarm algorithm to carry out iterative solution to obtain an optimal reconstruction network topology;
in the iterative process, the population of particles is updated based on the R2 index, and in particular,
the elite particle swarm and the updated particle swarm are integrated into a candidate solution set RR, and a weight vector Λ and an ideal point z which are uniformly distributed are adopted * Pruning a candidate solution set RR, sorting the R2 contribution values of the candidate solutions to the weight vector lambda from large to small, and setting the number of the candidate solutions to form a particle swarm of the next iteration in the past;
the calculation process of the R2 contribution value of the candidate solution to the weight vector Λ is as follows:
initializing R2 contribution value C of candidate solution a ＝0；
Calculating TCH utility value of candidate solution pair weight vector
Wherein lambda is j Not less than 0, andx represents a candidate solution, and m is the number of sectionalized switches in the power distribution network;
calculating the R2 contribution value of the candidate solution to the set of weight vectors Λ:
in the iterative process, if the algebraic individual optimal pBest is continuously set unchanged, the speed and position information of the particles are reset by adopting a Gaussian learning GLS strategy, and the formula is as follows:
wherein, the average value of mu Gaussian random number, sigma 2 Is the variance of the gaussian random number,represents the position of the particle i in the j-th dimension at the t+1st iteration, x gb (j) Represents the global optimal position of the jth dimension at the t-th iteration, x pb,i (j) The individual optimal position of the particle i in the j-th dimension at the t-th iteration is represented.
2. The method for reconstructing the power distribution network based on the R2 index multi-target particle swarm algorithm according to claim 1, wherein when the particle swarm algorithm is adopted for iterative solution, topology inspection is carried out on a network corresponding to each particle when each particle swarm is obtained, whether the topology is qualified is judged, if yes, the solution is continued, and if not, the particle swarm is reconstructed.
3. The method for reconstructing the power distribution network based on the R2 index multi-target particle swarm algorithm according to claim 2, wherein the topology inspection is performed on the network corresponding to each particle by adopting a depth-first search method.
4. The method for reconstructing a power distribution network based on an R2 index multi-target particle swarm algorithm according to claim 3, wherein said topology inspection specifically comprises the steps of:
101 Acquiring a distribution network structure corresponding to the particles, and generating a node association matrix;
102 Obtaining branch number N and effective node number N based on the node association matrix, judging whether n=n-1 exists, if yes, executing step 103), and if not, judging that the topology is unqualified;
103 Judging whether island exists in the power distribution network structure, if so, judging that the topology is unqualified, and if not, judging that the power distribution network is radial, and judging that the topology is qualified.
5. The method for reconstructing the power distribution network based on the R2 index multi-target particle swarm algorithm according to claim 4, wherein said determining whether the island exists in the power distribution network structure is specifically:
obtaining nodes at two ends of a branch according to the node incidence matrix;
disconnecting a certain branch, taking a node at one end of the branch as a starting point and a node at the other end as an end point, judging whether the other end node can be searched from the node at one end by using a deep search method, and if so, determining that the two nodes are communicated;
traversing all nodes, judging whether all nodes are communicated, if so, not forming an island, and if not, forming an island.
6. A power distribution network reconstruction device based on an R2 index multi-target particle swarm algorithm, comprising a memory and a processor, wherein the memory stores a computer program, and the processor invokes the computer program to execute the steps of the method according to any one of claims 1 to 5.
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