CN114880931A - Power distribution network multi-objective optimization method based on weight dependency - Google Patents
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Abstract
The invention discloses a multi-objective optimization method for a power distribution network based on weight dependency, which comprises the following steps: step S1: inputting model data such as nodes, loads and the like of a power distribution network system; step S2: determining an optimized object, and carrying out initialization population coding; step S3: determining an optimization target and a constraint condition; step S4: calculating the total objective function values of individuals with different weight combinations; step S5: calculating the weight dependence degree, and eliminating individuals with large weight dependence degree in the population; step S6: selecting among the remaining individuals; step S7: self-adaptive crossover and mutation operations; step S8: after the father and son genetic operations, judging whether a convergence condition is reached; step S9: and finishing iteration to obtain an optimal solution. The invention does not need to subjectively determine the weight in the optimizing model, and the obtained optimal solution has stronger applicability in the 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
With the integration of various types of distributed energy into a power grid, the power system optimization problem is changed from the original single-target optimization into a complex multi-target optimization problem. While pursuing a plurality of targets to reach the maximum value or the minimum value, the traditional optimization algorithm cannot meet the requirements of the existing model, and a weighting method is often adopted to perform weighting processing on each target function to obtain a so-called optimal solution.
Most of the existing methods adopt a method of artificially determining weights, and the obtained optimized solution set is greatly influenced by the weights. In the optimization model, the solution accuracy of the model is not high and is inconsistent with the actual situation easily caused by the excessively strong subjectivity, so that the calculation result loses the real application value.
Disclosure of Invention
The invention aims to provide a power distribution network multi-objective optimization method based on weight dependency, which avoids the process of subjectively selecting weights in a power distribution network multi-objective optimization model and improves the applicability of an optimization solution in practical engineering.
The technical scheme adopted by the invention is as follows:
a multi-objective optimization method for a power distribution network based on weight dependency comprises the following steps:
step S1: inputting data of the power distribution network system, wherein the total number of nodes is n, and the load of each node of the system is represented as P li +jQ li In which P is li Representing the active load at node i, Q li Represents the reactive load at node i;
step S2: determining an optimized object as the capacity of the distributed power supply at each node, performing initial population coding, and initializing a population under the constraint condition:
in the formula, Pop represents the initial population, p m1 1 st code representing an individual m in the population;
step S3: constructing a target function of a multi-target optimization model of the power distribution network, and establishing constraint conditions;
step S4: calculating objective functions of different individuals, and calculating total objective function value according to different weights
Step S5: calculating weight dependence Dep of population individuals m And (3) eliminating individuals with large weight dependence in the population:
in the formula, Pop (o,: indicates the o-th line of the population sequence,
mean values representing the weight dependence of individual populations.
Step S6: selecting the individuals with the optimal target function value under each group weight in the N groups of weight ratios as parents from the rest individuals, and entering the next step of genetic operation;
step S7: performing crossover and mutation operations, reducing crossover and mutation probabilities for individuals with higher fitness, and improving crossover and mutation probabilities for individuals with lower fitness;
step S8: when the iteration times reach a set value or the optimal solution is converged, judging that a convergence condition is reached; if yes, executing step S9, otherwise returning to step S4;
step S9: and stopping iteration to obtain an optimal solution.
Further, the step S3 specifically includes the following steps:
the objective function of the optimization model is:
(1) combined cost F 1 Lowest level of
min F 1 ＝min{C inv +C ins +C price +C main +C env } (3)
In the formula, C inv Represents the investment cost of the distributed power supply of the distribution network, C ins Represents the installation cost of the distributed power supply of the distribution network, C price Representing the cost of electricity from the distribution network to the main network, C main Represents the cost of operation and maintenance, C env Represents CO 2 Costs are lost in emissions and environmental benefits.
In the formula, k inv 、k ins 、k main Respectively represents the investment cost coefficient, the installation cost coefficient and the maintenance cost coefficient of the distributed power supply, P dgi Indicating distributed power injection active power at node i, C charge Representing the cost coefficient of electricity price, P li Representing the active load at node i, Ploss ij Representing branch loss, k, of the distribution network co2 、k d Respectively representing a carbon emission penalty coefficient and an environmental benefit loss cost coefficient.
(2) Network loss F 2 Lowest level of
min F 2 ＝min∑Ploss ij (5)
In the formula, Ploss ij Representing the branch loss of the distribution network.
(3) System voltage fluctuation F 3 Lowest level of
In the formula of U i Representing the magnitude of the voltage, DeltaU, at the ith node of the distribution network i Representing the value of the voltage fluctuation at the ith node of the distribution network.
The constraint conditions of the optimization model are as follows:
(1) power flow equality constraint of power distribution network
In the formula, P dgi 、Q dgi Respectively representing the injected active and reactive power, P, of the distributed power supply li 、Q li Respectively representing active and reactive loads, U i 、U j Representing the voltages at nodes i, j, respectively, theta ij Represents the node power phase angle difference, G ij 、B ij Representing the conductance and reactance of the branch, respectively.
(2) Distributed power capacity constraints
In the formula, P dgmax Representing the maximum capacity, P, of the distributed power supply that is allowed to be installed at a node dgtotal Representing the total capacity of the distributed power supply that the entire distribution network allows installation.
Further, the step S4 specifically includes the following steps:
and calculating objective functions of different individuals in the initial population, and calculating a total objective function value according to different weights.
In the formula,. psi. k 、β k Representing the kth set of weights.
In the formula (I), the compound is shown in the specification,
representing the calculation of the total objective function value, F, of the individual m by the kth set of weight ratios 10 、F 20 、F 30 Respectively representing the reference values of the three objective functions,
respectively representing the objective function of the individual m.
Further, the step S5 specifically includes the following steps:
calculating weight dependence Dep of individuals m 。
In the formula, omega m Representing the total set of objective function values for individual m at different weights.
Dep m ＝D(Ω m )+R(Ω m ) (13)
In the formula, D (omega) m )、R(Ω m ) Respectively represent the set omega m Variance and range of (c):
R(Ω m )＝maxf m -minf m (15)
wherein N represents the number of sets of weights,
mean value, maxf, representing the overall objective function m 、minf m Respectively represent the set omega m Maximum and minimum values of (a).
Further, the step S6 specifically includes the following steps:
and selecting an individual with the optimal value of the target function under each group of weights in the N groups of weight ratios as a parent, and entering the next genetic operation:
in the formula, Pop par Represents a parent population, { y 1 ；y 2 ；...；y N Denotes the individual with the best performance under N groups of weights, f y x Representing the overall objective function value of the individual y under the x-th set of weights,
representing the optimal objective function value for all individuals under the x-th set of weights.
Further, the step S7 specifically includes the following steps:
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 and population excellence of genetic evolution are improved.
Individual fitness
Can be expressed as:
cross probability:
in the formula, p cross (m) represents the cross probability of an individual m,
respectively representing the maximum and minimum of the cross probability,
denotes the fitness average value, fit, of the individual m under the calculation of k groups of weights avg Denotes the fitness mean, fit, of all individuals max Represents the maximum value of fitness of all individuals.
The mutation probability:
in the formula, p mut (m) represents the mutation probability of the individual m,
respectively representing the maximum and minimum of the mutation probability.
By adopting the technical scheme, compared with the prior art, the invention has the following beneficial effects: the invention describes the relevance between 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 multiple targets, has good applicability under different groups of weight selection, and has larger significance for practical engineering reference.
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The invention is described in further detail below with reference to the accompanying drawings and the detailed description;
FIG. 1 is a flow diagram of a multi-objective optimization method of a power distribution network based on weight dependency of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the 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 data of the power distribution network system, wherein the total number of nodes is n, and the load of each node of the system is represented as P li +jQ li In which P is li Representing the active load at node i, Q li Represents the reactive load at node i;
step S2: determining an optimized object as the capacity of the distributed power supply at each node, performing initial population coding, and initializing a population under the constraint condition:
in the formula, Pop represents the initial population, p m1 1 st code representing an individual m in the population;
step S3: constructing a target function of a multi-target optimization model of the power distribution network, and establishing constraint conditions;
step S4: calculating objective functions of different individuals, and calculating total objective function value according to different weights
Step S5: calculating weight dependence Dep of population individuals m And (3) eliminating individuals with large weight dependence in the population:
in the formula, Pop (o,: indicates the o-th line of the population sequence,
represents the average value of the weight dependence of individual population.
Step S6: selecting the individuals with the optimal target function value under each group weight in the N groups of weight ratios as parents from the rest individuals, and entering the next step of genetic operation;
step S7: performing crossover and mutation operations, reducing crossover and mutation probabilities for individuals with higher fitness, and improving crossover and mutation probabilities for individuals with lower fitness;
step S8: when the iteration times reach a set value or the optimal solution is converged, judging that a convergence condition is reached; if yes, executing step S9, otherwise returning to step S4;
step S9: and stopping iteration to obtain an optimal solution.
In this embodiment, the step S3 specifically includes the following steps:
the objective function of the optimization model is:
(1) comprehensive costF 1 Lowest level of
min F 1 ＝min{C inv +C ins +C price +C main +C env } (3)
In the formula, C inv Represents the investment cost of the distributed power supply of the distribution network, C ins Represents the installation cost of the distributed power supply of the distribution network, C price Representing the cost of electricity from the distribution network to the main network, C main Represents the cost of operation and maintenance, C env Represents CO 2 Costs are lost in emissions and environmental benefits.
In the formula, k inv 、k ins 、k main Respectively represents the investment cost coefficient, the installation cost coefficient and the maintenance cost coefficient of the distributed power supply, P dgi Indicating distributed power injection active power at node i, C charge Representing the cost coefficient of electricity price, P li Representing the active load at node i, Ploss ij Representing branch loss, k, of the distribution network co2 、k d Respectively representing a carbon emission penalty coefficient and an environmental benefit loss cost coefficient.
(2) Network loss F 2 Lowest level of
min F 2 ＝min∑Ploss ij (5)
In the formula, Ploss ij Representing the branch loss of the distribution network.
(3) System voltage fluctuation F 3 Lowest level of
In the formula of U i Representing the magnitude of the voltage, DeltaU, at the ith node of the distribution network i Representing the value of the voltage fluctuation at the ith node of the distribution network.
The constraint conditions of the optimization model are as follows:
(1) power flow equality constraint of power distribution network
In the formula, P dgi 、Q dgi Respectively representing the injected active and reactive power, P, of the distributed power supply li 、Q li Respectively representing active and reactive loads, U i 、U j Representing the voltages at nodes i, j, respectively, theta ij Represents the node power phase angle difference, G ij 、B ij Representing the conductance and reactance of the branch, respectively.
(2) Distributed power capacity constraints
In the formula, P dgmax Representing the maximum capacity, P, of the distributed power supply that is allowed to be installed at a node dgtotal Representing the total capacity of the distributed power sources the entire distribution network allows to be installed.
In this embodiment, the step S4 specifically includes the following steps:
and calculating objective functions of different individuals in the initial population, and calculating a total objective function value according to different weights.
In the formula,. psi. k 、β k Representing the kth set of weights.
In the formula (I), the compound is shown in the specification,
representing the calculation of the total objective function value, F, of the individual m by the kth set of weight ratios 10 、F 20 、F 30 Respectively representing the reference values of the three objective functions,
respectively representing the objective function of the individual m.
In this embodiment, the step S5 specifically includes the following steps:
calculating weight dependence Dep of individuals m 。
In the formula, omega m Representing the total set of objective function values for individual m at different weights.
Dep m ＝D(Ω m )+R(Ω m ) (13)
In the formula, D (omega) m )、R(Ω m ) Respectively represent the set omega m Variance and range of (c):
R(Ω m )＝maxf m -minf m (15)
wherein N represents the number of sets of weights,
mean value representing the overall objective function, maxf m 、minf m Respectively represent the set omega m Maximum and minimum values of (a).
In this embodiment, the step S6 specifically includes the following steps:
and selecting an individual with the optimal value of the target function under each group of weights in the N groups of weight ratios as a parent, and entering the next genetic operation:
in the formula, Pop par Represents a parent population, { y 1 ；y 2 ；...；y N Denotes the individual with the best performance under N groups of weights, f y x Representing the overall objective function value of the individual y under the x-th set of weights,
representing the optimal objective function value for all individuals under the x-th set of weights.
In this embodiment, the step S7 specifically includes the following steps:
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 and population excellence of genetic evolution are improved.
Individual fitness
Can be expressed as:
cross probability:
in the formula, p cross (m) represents the cross probability of an individual m,
respectively representing the maximum and minimum of the cross probability,
representing m individuals in k groupsFitness mean under weight calculation, fit avg Denotes the fitness mean, fit, of all individuals max Represents the maximum value of fitness of all individuals.
The mutation probability:
in the formula, p mut (m) represents the mutation probability of the individual m,
respectively representing the maximum and minimum of the mutation probability.
Preferably, the relevance between the individual and the target weight is described by defining the weight dependency, the individual with large influence of the subjective weight is eliminated, and the multi-objective optimization model of the power distribution network is constructed.
(1) And calculating the target functions of the population individuals under different target weighting ratios, determining the weight dependence of the population individuals according to the range and the variance of the result, and reflecting the condition that the population individuals are influenced by subjective factors.
(2) And eliminating the individuals with high weight dependence, selecting the superior individuals from the rest populations as parents to enter the next iteration, and obtaining new offspring populations through self-adaptive intersection and variation.
(3) The multiple groups of weights are calculated and participate in selection operation in the population evolution process, the process of subjectively determining the weights is avoided, and technical support is provided for the optimization processing of the multi-target problem of the power distribution network.
Preferably, the embodiment describes the relevance between 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 different groups of weight selection, and has greater significance for practical engineering reference. The technical effects of the present invention are shown in table 1 in conjunction with the examples.
TABLE 1 comparison of objective function values of optimal solutions of two methods at different weighting ratios
By adopting the technical scheme, compared with the prior art, the invention has the following beneficial effects: the invention describes the relevance between 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 multiple targets, has good applicability under different groups of weight selection, and has larger significance for practical engineering reference.
It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. The embodiments and features of the embodiments in the present application 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, can be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the present application is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Claims (8)
1. A multi-objective optimization method for a power distribution network based on weight dependency is characterized by comprising the following steps: which comprises the following steps:
step S1: inputting data of the power distribution network system, wherein the total number of nodes is n, and the load of each node of the system is represented as P li +jQ li In which P is li Representing the active load at node i, Q li Represents the reactive load at node i;
step S2: determining an optimized object as the capacity of the distributed power supply at each node, performing initial population coding, and initializing a population under the constraint condition:
in the formula, Pop represents the initial population, p m1 1 st code representing an individual m in the population;
step S3: constructing a target function of a multi-target optimization model of the power distribution network, and establishing constraint conditions;
step S4: calculating objective functions of different individuals, and calculating total objective function value according to different weights
Step S5: calculating weight dependence Dep of population individuals m And (3) eliminating individuals with large weight dependence in the population:
in the formula, Pop (o,: indicates the o-th line of the population sequence,
an average value representing the weight dependence of individual species of the population;
step S6: selecting the individuals with the optimal target function value under each group weight in the N groups of weight ratios as parents from the rest individuals, and entering the next step of genetic operation;
step S7: performing crossover and mutation operations, reducing crossover and mutation probabilities for individuals with higher fitness, and improving crossover and mutation probabilities for individuals with lower fitness;
step S8: when the iteration times reach a set value or the optimal solution is converged, judging whether a convergence condition is reached; if yes, go to step S9; otherwise, return to step S4;
step S9: and stopping iteration to obtain an optimal solution.
2. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 1, wherein: the objective function of the optimization model in step S3 is:
(1) combined cost F 1 Minimum:
min F 1 ＝min{C inv +C ins +C price +C main +C env } (3)
in the formula, C inv Represents the investment cost of the distributed power supply of the distribution network, C ins Represents the installation cost of the distributed power supply of the distribution network, C price Indicating the cost of purchasing electricity from the distribution network to the main network, C main Represents the cost of operation and maintenance, C env Represents CO 2 Cost of emissions and environmental benefit loss;
in the formula, k inv 、k ins 、k main Respectively represents the investment cost coefficient, the installation cost coefficient and the maintenance cost coefficient of the distributed power supply, P dgi Indicating distributed power injection active power at node i, C charge Representing the cost coefficient of electricity price, P li Representing the active load at node i, Ploss ij Represents the branch loss, k, of the distribution network co2 、k d Respectively representing a carbon emission penalty coefficient and an environmental benefit loss cost coefficient;
(2) network loss F 2 Minimum:
min F 2 ＝min∑Ploss ij (5)
in the formula, Ploss ij Representing branch network loss of the power distribution network;
(3) system voltage fluctuation F 3 Minimum:
in the formula of U i Representing the magnitude of the voltage, DeltaU, at the ith node of the distribution network i Representing the value of the voltage fluctuation at the ith node of the distribution network.
3. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 1 or 2, wherein: the constraint conditions of the optimization model in step S3 are:
(1) and (3) power flow equality constraint of the power distribution network:
in the formula, P dgi 、Q dgi Respectively representing the injected active and reactive power, P, of the distributed power supply li 、Q li Respectively representing active and reactive loads, U i 、U j Representing the voltages at nodes i, j, respectively, theta ij Represents the node power phase angle difference, G ij 、B ij Respectively representing the conductance and reactance of the branch;
(2) capacity constraint of distributed power supply:
in the formula, P dgmax Representing the maximum capacity, P, of the distributed power supply that is allowed to be installed at a node dgtotal Representing the total capacity of the distributed power supply that the entire distribution network allows installation.
4. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 1, wherein: the weight calculation formula for different individuals in step S4 is as follows
In the formula,. psi. k 、β k Representing the kth set of weights.
5. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 1 or 4, wherein: total objective function value in step S4
The calculation formula of (a) is as follows:
in the formula (I), the compound is shown in the specification,
representing the calculation of the total objective function value, F, of the individual m by the kth set of weight ratios 10 、F 20 、F 30 Reference values, F, representing three objective functions, respectively 1 m 、
Respectively representing the objective function of the individual m.
6. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 5, wherein: in step S5, the weight dependence Dep of the individual is calculated m The method comprises the following specific steps: :
step S5-1, calculating a total objective function value set omega of the individual m under different weights m The formula is as follows:
in the formula, omega m Representing the total target function value set of the individual m under different weights;
step S5-2, calculating a set omega m Variance D (omega) of m ) And a very poor R (omega) m ) The formula is as follows:
R(Ω m )＝maxf m -minf m (15)
wherein N represents the number of sets of weights,
mean value, maxf, representing the overall objective function m 、minf m Respectively represent the set omega m Maximum and minimum values of;
step S5-3, calculating the weight dependence Dep of the individual m The formula is as follows:
Dep m ＝D(Ω m )+R(Ω m ) (13)
in the formula, D (omega) m )、R(Ω m ) Respectively represent the set omega m Variance and range of (c).
7. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 1, wherein: the specific formula of the genetic manipulation in step S6 is as follows:
in the formula, Pop par Represents a parent population, { y 1 ；y 2 ；...；y N Denotes the individuals under the N sets of weights that each perform best,
representing the overall objective function value of the individual y under the x-th set of weights,
representing the optimal objective function value for all individuals under the x-th set of weights.
8. The multi-objective optimization method for the power distribution network based on the weight dependency degree as claimed in claim 5, wherein: the specific steps of step S7 are as follows:
step S7-1, calculating fitness of individual m
The calculation formula is as follows:
step S7-2, calculating the cross probability p of m cross (m), the calculation formula is as follows:
in the formula, p cross (m) represents the cross probability of an individual m,
respectively representing the maximum and minimum of the cross probability,
denotes the fitness average value, fit, of the individual m under the calculation of k groups of weights avg Denotes the fitness mean, fit, of all individuals max Represents the maximum value of fitness of all individuals;
step S7-3, calculating the mutation probability p of m mut (m), the calculation formula is as follows:
the mutation probability:
in the formula, p mut (m) represents the mutation probability of the individual m,
respectively representing the maximum and minimum of the mutation probability.
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