CN114880931B - Multi-objective optimization method for power distribution network based on weight dependency - Google Patents
Multi-objective optimization method for power distribution network based on weight dependency Download PDFInfo
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Abstract
The invention discloses a power distribution network multi-objective optimization method based on weight dependence, which comprises the following steps: step S1: inputting model data such as power distribution network system nodes, loads and the like; step S2: determining an optimized object and initializing population codes; step S3: determining an optimization target and constraint conditions; step S4: calculating the total objective function value of the individuals with different weight combinations; step S5: calculating the weight dependency degree, and eliminating individuals with large weight dependency degree in the population; step S6: selecting among the remaining individuals; step S7: self-adaptive crossover and mutation operation; step S8: judging whether convergence conditions are reached after the male parent and the female parent are subjected to two-generation genetic operation; step S9: and (5) ending the iteration to obtain an optimal solution. The invention does not need subjective determination of weight in the optimizing model, and the obtained optimal solution has stronger applicability in actual engineering.
Description
Technical Field
The invention relates to the field of power distribution network planning, in particular to a power distribution network multi-objective optimization method based on weight dependence.
Background
As multiple types of distributed energy are incorporated into the grid, the power system optimization problem is transformed from the original single-objective optimization into a complex multi-objective optimization problem. While pursuing that a plurality of targets reach the maximum value or the minimum value, the conventional optimizing algorithm cannot meet the requirement of the existing model, and a weighting method is often adopted to weight each target function so as to obtain a so-called optimal solution.
Most of the existing methods adopt a method of manually determining weights, and the obtained optimal solution set is greatly influenced by the weights. In the optimization model, the subjectivity is too strong, so that the model solving precision is not high and is inconsistent with the actual situation, and the actual application value of the calculation result is lost.
Disclosure of Invention
The invention aims to provide a power distribution network multi-objective optimization method based on weight dependency, which avoids the subjective weight selecting process in a power distribution network multi-objective optimization model and improves the applicability of an optimization solution in actual engineering.
The technical scheme adopted by the invention is as follows:
a power distribution network multi-objective optimization method based on weight dependency comprises the following steps:
Step S1: inputting system data of a power distribution network, wherein the total number of nodes is n, the load of each node of the system is represented as P li+jQli, wherein P li represents the active load at a node i, and Q li represents the reactive load at the node i;
Step S2: determining the optimized object as the distributed power capacity at each node, performing initial population coding, and initializing the population under the constraint condition:
wherein Pop represents the initial population and p m1 represents the 1 st code of individual m in the population;
step S3: constructing an objective function of a multi-objective optimization model of the power distribution network, and establishing constraint conditions;
step S4: calculating objective functions of different individuals, and calculating total objective function values according to different weights
Step S5: calculating the weight dependence degree Dep m of the population individuals, and eliminating the individuals with large weight dependence degree in the population:
Where Pop (o,:) represents the o-th row of the population sequence, Representing the average value of the weight dependence of the population individuals.
Step S6: selecting an individual with the optimal objective function value under each group of weights in the N groups of weight ratios from the rest individuals as a parent, and entering the next genetic operation;
step S7: performing crossover and mutation operation, reducing crossover and mutation probability for individuals with higher fitness, and improving crossover and mutation probability for individuals with lower fitness;
step S8: when the iteration times reach a set value or the optimal solution converges, judging that a convergence condition is reached; if yes, executing a step S9, otherwise returning to the step S4;
step S9: and (5) stopping iteration to obtain an optimal solution.
Further, the step S3 specifically includes the following:
the objective function of the optimization model is:
(1) The combined cost F 1 is the lowest
min F1＝min{Cinv+Cins+Cprice+Cmain+Cenv} (3)
Wherein, C inv represents the investment cost of the distributed power supply of the power distribution network, C ins represents the installation cost of the distributed power supply of the power distribution network, C price represents the purchase cost of the power distribution network to the main network, C main represents the operation and maintenance cost, and C env represents the emission of CO 2 and the environmental benefit loss cost.
Where k inv、kins、kmain represents an investment cost coefficient, an installation cost coefficient and a maintenance cost coefficient of the distributed power supply, P dgi represents a distributed power supply injection active power at a node i, C charge represents an electricity price cost coefficient, P li represents an active load at the node i, ploss ij represents a branch network loss of the power distribution network, and k co2、kd represents a carbon emission penalty coefficient and an environmental benefit loss cost coefficient, respectively.
(2) Network loss F 2 is lowest
min F2＝min∑Plossij (5)
In the formula, ploss ij represents the branch loss of the power distribution network.
(3) Minimum system voltage fluctuation F 3
Where U i represents the voltage magnitude at the i-th node of the power distribution network and ΔU i represents the voltage ripple at the i-th node of the power distribution network.
Constraint conditions of the optimization model are as follows:
(1) Power distribution network tide equation constraint
Wherein P dgi、Qdgi represents active power and reactive power injected by the distributed power supply respectively, P li、Qli represents active power and reactive power load respectively, U i、Uj represents voltage at nodes i and j respectively, theta ij represents node power phase angle difference, and G ij、Bij represents conductance and reactance of a branch respectively.
(2) Distributed power capacity constraint
Where P dgmax represents the maximum capacity that the distributed power supply is allowed to install at a node and P dgtotal represents the total capacity of the distributed power supply that the entire power distribution network is allowed to install.
Further, the step S4 specifically includes the following:
and calculating objective functions of different individuals in the initial population, and calculating the total objective function value according to different weights.
Where ψ represents different weight combinations and α k、βk represents the kth set of weights.
In the method, in the process of the invention,Representing the calculation of the overall objective function value of the individual m by the weight ratio of the kth group, F 10、F20、F30 representing the reference values of the three objective functions, respectively,/>Respectively representing the objective functions of the individual m.
Further, the step S5 specifically includes the following:
the individual weight dependence Dep m is calculated.
Where Ω m represents the set of total objective function values for individual m under different weights.
Depm＝D(Ωm)+R(Ωm) (13)
Where D (Ω m)、R(Ωm) represents the variance and range, respectively, of the set Ω m:
R(Ωm)＝maxfm-minfm (15)
Where N represents the number of groups of weights, Mean values representing the total objective function maxf m、minfm represent the maximum and minimum values, respectively, in the set Ω m.
Further, the step S6 specifically includes the following:
selecting an individual with the optimal objective function value under each group of weights in the N groups of weight ratios as a parent, and entering the next genetic operation:
Where Pop par represents the parent population, { y 1;y2;...;yN } represents the individual with the best performance under the N weights, f y x represents the overall objective function value of the individual y under the x weight, Representing the optimal objective function values for all individuals under the x-th set of weights.
Further, the step S7 specifically includes the following:
The probability of crossover and mutation is reduced for individuals with higher fitness, the probability of crossover and mutation is improved for individuals with lower fitness, and the efficiency of genetic evolution and population preference are improved.
Fitness of individualsCan be expressed as:
crossover probability:
where p cross (m) represents the crossover probability of individual m, Respectively represent the maximum value and the minimum value of the crossover probability,/>Representing the fitness average of individual m under the k-group weight calculation, fit avg represents the fitness average of all individuals, fit max represents the maximum of fitness of all individuals.
Probability of variation:
Wherein p mut (m) represents the mutation probability of the individual m, The maximum value and the minimum value of the mutation probability are respectively represented.
Compared with the prior art, the invention has the following beneficial effects: the invention describes the relevance of the individual and the target weight by defining the weight dependence, eliminates the individual greatly influenced by the subjective weight, does not need to subjectively determine the weight in the process of solving the multiple targets, has good applicability under the selection of different groups of weights, and has greater significance in actual engineering reference.
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The invention is described in further detail below with reference to the drawings and detailed description;
Fig. 1 is a flow chart of a power distribution network multi-objective optimization method based on weight dependency.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application.
As shown in fig. 1, the invention discloses a power distribution network multi-objective optimization algorithm based on weight dependency, which comprises the following steps:
Step S1: inputting system data of a power distribution network, wherein the total number of nodes is n, the load of each node of the system is represented as P li+jQli, wherein P li represents the active load at a node i, and Q li represents the reactive load at the node i;
Step S2: determining the optimized object as the distributed power capacity at each node, performing initial population coding, and initializing the population under the constraint condition:
wherein Pop represents the initial population and p m1 represents the 1 st code of individual m in the population;
step S3: constructing an objective function of a multi-objective optimization model of the power distribution network, and establishing constraint conditions;
step S4: calculating objective functions of different individuals, and calculating total objective function values according to different weights
Step S5: calculating the weight dependence degree Dep m of the population individuals, and eliminating the individuals with large weight dependence degree in the population:
Where Pop (o,:) represents the o-th row of the population sequence, Representing the average value of the weight dependence of the population individuals.
Step S6: selecting an individual with the optimal objective function value under each group of weights in the N groups of weight ratios from the rest individuals as a parent, and entering the next genetic operation;
step S7: performing crossover and mutation operation, reducing crossover and mutation probability for individuals with higher fitness, and improving crossover and mutation probability for individuals with lower fitness;
step S8: when the iteration times reach a set value or the optimal solution converges, judging that a convergence condition is reached; if yes, executing a step S9, otherwise returning to the step S4;
step S9: and (5) stopping iteration to obtain an optimal solution.
In this embodiment, the step S3 specifically includes the following:
the objective function of the optimization model is:
(1) The combined cost F 1 is the lowest
min F1＝min{Cinv+Cins+Cprice+Cmain+Cenv} (3)
Wherein, C inv represents the investment cost of the distributed power supply of the power distribution network, C ins represents the installation cost of the distributed power supply of the power distribution network, C price represents the purchase cost of the power distribution network to the main network, C main represents the operation and maintenance cost, and C env represents the emission of CO 2 and the environmental benefit loss cost.
Where k inv、kins、kmain represents an investment cost coefficient, an installation cost coefficient and a maintenance cost coefficient of the distributed power supply, P dgi represents a distributed power supply injection active power at a node i, C charge represents an electricity price cost coefficient, P li represents an active load at the node i, ploss ij represents a branch network loss of the power distribution network, and k co2、kd represents a carbon emission penalty coefficient and an environmental benefit loss cost coefficient, respectively.
(2) Network loss F 2 is lowest
min F2＝min∑Plossij (5)
In the formula, ploss ij represents the branch loss of the power distribution network.
(3) Minimum system voltage fluctuation F 3
Where U i represents the voltage magnitude at the i-th node of the power distribution network and ΔU i represents the voltage ripple at the i-th node of the power distribution network.
Constraint conditions of the optimization model are as follows:
(1) Power distribution network tide equation constraint
Wherein P dgi、Qdgi represents active power and reactive power injected by the distributed power supply respectively, P li、Qli represents active power and reactive power load respectively, U i、Uj represents voltage at nodes i and j respectively, theta ij represents node power phase angle difference, and G ij、Bij represents conductance and reactance of a branch respectively.
(2) Distributed power capacity constraint
Where P dgmax represents the maximum capacity that the distributed power supply is allowed to install at a node and P dgtotal represents the total capacity of the distributed power supply that the entire power distribution network is allowed to install.
In this embodiment, the step S4 specifically includes the following steps:
and calculating objective functions of different individuals in the initial population, and calculating the total objective function value according to different weights.
Where ψ represents different weight combinations and α k、βk represents the kth set of weights.
In the method, in the process of the invention,Representing the calculation of the overall objective function value of the individual m by the weight ratio of the kth group, F 10、F20、F30 representing the reference values of the three objective functions, respectively,/>Respectively representing the objective functions of the individual m.
In this embodiment, the step S5 specifically includes the following:
the individual weight dependence Dep m is calculated.
Where Ω m represents the set of total objective function values for individual m under different weights.
Depm＝D(Ωm)+R(Ωm) (13)
Where D (Ω m)、R(Ωm) represents the variance and range, respectively, of the set Ω m:
R(Ωm)＝maxfm-minfm (15)
Where N represents the number of groups of weights, Mean values representing the total objective function maxf m、minfm represent the maximum and minimum values, respectively, in the set Ω m.
In this embodiment, the step S6 specifically includes the following:
selecting an individual with the optimal objective function value under each group of weights in the N groups of weight ratios as a parent, and entering the next genetic operation:
Where Pop par represents the parent population, { y 1;y2;...;yN } represents the individual with the best performance under the N weights, f y x represents the overall objective function value of the individual y under the x weight, Representing the optimal objective function values for all individuals under the x-th set of weights.
In this embodiment, the step S7 specifically includes the following:
The probability of crossover and mutation is reduced for individuals with higher fitness, the probability of crossover and mutation is improved for individuals with lower fitness, and the efficiency of genetic evolution and population preference are improved.
Fitness of individualsCan be expressed as:
crossover probability:
where p cross (m) represents the crossover probability of individual m, Respectively represent the maximum value and the minimum value of the crossover probability,/>Representing the fitness average of individual m under the k-group weight calculation, fit avg represents the fitness average of all individuals, fit max represents the maximum of fitness of all individuals.
Probability of variation:
Wherein p mut (m) represents the mutation probability of the individual m, The maximum value and the minimum value of the mutation probability are respectively represented.
Preferably, the embodiment describes the relevance of the individual and the target weight by defining the weight dependency, eliminates the individual greatly influenced by the subjective weight, and constructs the multi-target optimization model of the power distribution network.
(1) And calculating objective functions of the population individuals under different objective weight ratios, and determining the weight dependence degree of the population individuals according to the range and variance of the results, so that the condition that the population individuals are influenced by subjective factors can be reflected.
(2) And eliminating individuals with large weight dependence, selecting a preferential individual from the rest population as a parent to enter the next iteration, and obtaining a new offspring population through self-adaptive crossing and mutation.
(3) The multiple groups of weights are calculated and participate in the selection operation in the population evolution process, so that the subjective weight determination process is avoided, and technical support is provided for the optimization treatment of multiple targets of the power distribution network.
Preferably, the embodiment describes the relevance of the individual and the target weight by defining the weight dependency, eliminates the individual greatly influenced by the subjective weight, does not need to subjectively determine the weight in the process of solving the multiple targets, has good applicability under the selection of different groups of weights, and has greater significance in actual engineering reference. The technical effects of the present invention are shown in table 1 in combination with examples.
Table 1 comparison of objective function values of two methods optimal solutions at different weighting ratios
Compared with the prior art, the invention has the following beneficial effects: the invention describes the relevance of the individual and the target weight by defining the weight dependence, eliminates the individual greatly influenced by the subjective weight, does not need to subjectively determine the weight in the process of solving the multiple targets, has good applicability under the selection of different groups of weights, and has greater significance in actual engineering reference.
It will be apparent that the described embodiments are some, but not all, embodiments of the application. Embodiments of the application and features of the embodiments may be combined with each other without conflict. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the application is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Claims (6)
1. A power distribution network multi-objective optimization method based on weight dependency is characterized by comprising the following steps of: which comprises the following steps:
Step S1: inputting system data of a power distribution network, wherein the total number of nodes is n, the load of each node of the system is represented as P li+jQli, wherein P li represents the active load at a node i, and Q li represents the reactive load at the node i;
Step S2: determining the optimized object as the distributed power capacity at each node, performing initial population coding, and initializing the population under the constraint condition:
wherein Pop represents the initial population and p m1 represents the 1 st code of individual m in the population;
step S3: constructing an objective function of a multi-objective optimization model of the power distribution network, and establishing constraint conditions;
step S4: calculating objective functions of different individuals, and calculating total objective function values according to different weights Total objective function value/>The calculation formula of (2) is as follows:
In the method, in the process of the invention, Representing the total objective function value of the individual m calculated according to the weight ratio of the kth group, F 10、F20、F30 representing the reference values of the three objective functions, F 1 m,/>, respectivelyRespectively representing the objective functions of the individual m; alpha k、βk represents the kth group weight;
Step S5: calculating the weight dependence degree Dep m of the population individuals, and eliminating the individuals with large weight dependence degree in the population:
Where Pop (o,:) represents the o-th row of the population sequence, Mean value of the weight dependence degree of population individuals, { } represents empty set;
The specific steps for calculating the weight dependency Dep m of the individual are as follows:
Step S5-1, calculating a total objective function value set omega m of the individual m under different weights, wherein the formula is as follows:
Wherein Ω m represents a set of total objective function values for individual m under different weights;
In step S5-2, the variance D (Ω m) and the range R (Ω m) of the set Ω m are calculated as follows:
R(Ωm)＝maxfm-minfm (15)
Where N represents the number of groups of weights, Average values representing the overall objective function maxf m、minfm represent the maximum and minimum values, respectively, in the set Ω m;
step S5-3, calculating the weight dependence Dep m of the individual, wherein the formula is as follows:
Depm＝D(Ωm)+R(Ωm) (13)
Wherein D (Ω m)、R(Ωm) represents the variance and the range of the set Ω m, respectively;
Step S6: selecting an individual with the optimal objective function value under each group of weights in the N groups of weight ratios from the rest individuals as a parent, and entering the next genetic operation;
step S7: performing crossover and mutation operation, reducing crossover and mutation probability for individuals with higher fitness, and improving crossover and mutation probability for individuals with lower fitness;
Step S8: when the iteration times reach a set value or the optimal solution converges, judging whether a convergence condition is reached; if yes, executing step S9; otherwise, returning to the step S4;
step S9: and (5) stopping iteration to obtain an optimal solution.
2. The power distribution network multi-objective optimization method based on weight dependency according to claim 1, wherein the method comprises the following steps: the objective function of the optimization model in step S3 is:
(1) The comprehensive cost F 1 is the lowest:
min F1＝min{Cinv+Cins+Cprice+Cmain+Cenv} (3)
Wherein, C inv represents the investment cost of the distributed power supply of the power distribution network, C ins represents the installation cost of the distributed power supply of the power distribution network, C price represents the purchase cost of the power distribution network to the main network, C main represents the operation and maintenance cost, and C env represents the CO 2 emission and environmental benefit loss cost;
Wherein k inv、kins、kmain represents an investment cost coefficient, an installation cost coefficient and a maintenance cost coefficient of the distributed power supply respectively, P dgi represents a distributed power supply injection active power at a node i, C charge represents an electricity price cost coefficient, P li represents an active load at the node i, ploss ij represents a branch network loss of the power distribution network, and k co2、kd represents a carbon emission penalty coefficient and an environmental benefit loss cost coefficient respectively;
(2) Network loss F 2 is lowest:
min F2＝min∑Plossij (5)
in the formula, ploss ij represents the branch loss of the power distribution network;
(3) System voltage ripple F 3 is lowest:
Where U i represents the voltage magnitude at the i-th node of the power distribution network and ΔU i represents the voltage ripple at the i-th node of the power distribution network.
3. The power distribution network multi-objective optimization method based on weight dependency according to claim 1 or 2, wherein the method comprises the following steps: the constraint conditions of the optimization model in the step S3 are as follows:
(1) Constraint of power flow equation of power distribution network:
Wherein P dgi、Qdgi represents active power and reactive power injected by the distributed power supply respectively, P li、Qli represents active power and reactive power respectively, U i、Uj represents voltages at nodes i and j respectively, theta ij represents a node power phase angle difference, and G ij、Bij represents conductance and reactance of a branch respectively;
(2) Distributed power capacity constraints:
Where P dgmax represents the maximum capacity that the distributed power supply is allowed to install at a node and P dgtotal represents the total capacity of the distributed power supply that the entire power distribution network is allowed to install.
4. The power distribution network multi-objective optimization method based on weight dependency according to claim 1, wherein the method comprises the following steps: the weight calculation formula of the different individuals in step S4 is as follows
Where ψ represents different weight combinations and α k、βk represents the kth set of weights.
5. The power distribution network multi-objective optimization method based on weight dependency according to claim 1, wherein the method comprises the following steps: the specific formula of the genetic manipulation in step S6 is as follows:
Where Pop par represents the parent population, { y 1;y2;...;yN } represents the individual with the best performance under the N sets of weights, Representing the overall objective function value of individual y under the x-th set of weights,/>Representing the optimal objective function values for all individuals under the x-th set of weights.
6. The power distribution network multi-objective optimization method based on weight dependency according to claim 1, wherein the method comprises the following steps: the specific steps of step S7 are as follows:
step S7-1, calculating fitness of individual m The calculation formula is as follows:
In step S7-2, the cross probability p cross (m) of m is calculated as follows:
where p cross (m) represents the crossover probability of individual m, Respectively represent the maximum value and the minimum value of the crossover probability,/>Representing the fitness average of individual m under k sets of weight calculations, fit avg representing the fitness average of all individuals, fit max representing the maximum of fitness of all individuals;
in step S7-3, the variation probability p mut (m) of m is calculated as follows:
Probability of variation:
Wherein p mut (m) represents the mutation probability of the individual m, The maximum value and the minimum value of the mutation probability are respectively represented.
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