CN114282427A - Solving method for environmental economic power generation dispatching based on differential evolution - Google Patents

Solving method for environmental economic power generation dispatching based on differential evolution Download PDF

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CN114282427A
CN114282427A CN202111357034.2A CN202111357034A CN114282427A CN 114282427 A CN114282427 A CN 114282427A CN 202111357034 A CN202111357034 A CN 202111357034A CN 114282427 A CN114282427 A CN 114282427A
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王业琴
张艺怀
杨艳
胡冰垚
耿涛
李文涛
洪程
薛鹏程
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Huaiyin Institute of Technology
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a differential evolution-based solution method for environmental economic power generation dispatching, which comprises the steps of firstly establishing environmental economic dispatching mathematics; in the initial stage, the accuracy of a dynamic mutation operator enhancement algorithm is introduced, then a multi-target particle swarm algorithm is improved, the improved multi-target particle swarm algorithm is applied to the environmental economic dispatching of the power system, meanwhile, the individual optimal solution is solved according to the pareto dominance condition, the non-inferior solution set of the individual optimal solution is solved, and the solutions are pruned by using the cycle crowding distance; the resulting archive set of these solutions can find the minimum of fuel cost and the minimum of gas emissions. Compared with the prior art, the method increases the diversity of the pareto optimal solution by using differential evolution, controls the size of an external filing set by adopting the cycle congestion distance, improves the uniformity of the pareto equilibrium surface, has high running speed and good stability, is easy to realize in engineering, and accounts for network loss in power balance.

Description

Solving method for environmental economic power generation dispatching based on differential evolution
Technical Field
The invention belongs to the technical field of multi-target optimization scheduling of an electric power system, and particularly relates to a solving method for realizing environment economy power generation scheduling by an improved multi-target particle swarm optimization algorithm based on differential evolution.
Background
The electric power industry is a basic industry of national economy, is a major industry supported by the country, and plays an important role in the economic development process of China. The economic dispatching of the power system is an important subject of power system analysis, and the task is to solve a dispatching scheme which enables the power generation cost or fuel of the system to be the lowest on the premise of meeting the inequality constraint conditions such as the equality constraint condition of load balance, the output of a generator and the like.
In recent years, with the demand for environmental protection, many countries have enacted regulations on the emission of harmful gases. For the problem of economic dispatch, a plurality of targets such as environmental requirements, power generation cost and the like need to be considered. Recently, the problem of environmental and economic dispatching of power systems has become a topic of hot research. The main research content is that on the premise of guaranteeing the power load, the running condition of each generator set or power plant is dispatched in an optimized mode, the load of each generator set is distributed reasonably, the cost is saved, and meanwhile, the energy consumption and the environmental pollution are reduced. The total cost of the system required to generate electricity or the total amount of fuel consumed is minimized.
The environmental economic scheduling is a high-dimensional nonlinear optimization problem, and a global optimal solution of the environmental economic scheduling is difficult to find by a traditional optimization method. The particle swarm algorithm is widely applied to economic dispatching of the power system due to the characteristics of simplicity, easiness in operation, high convergence speed and the like, and achieves certain effect. When the multi-target particle swarm optimization is expanded to the field of environmental economic dispatching, the multi-target particle swarm optimization is optimized simultaneously, and the contradiction among all targets ensures that the global optimal solution of the multi-target particle swarm optimization is not unique and only one group of pareto optimal solutions can be obtained. The reasonable selection of the global optimal solution of the population and the optimal solution of the individual becomes one of the keys for solving the target optimization problem. The method has practical social significance for realizing safe and economic operation of the power system.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to overcome the defects that the system constraint is not strictly met or the diversity of the pareto frontier is insufficient and the distribution is not uniform when the economic power generation scheduling scheme is solved by the conventional method, and provides a differential evolution-based solution method for the environmental economic power generation scheduling.
The technical scheme is as follows: the invention provides an environmental economy power generation scheduling solving method based on differential evolution, which comprises the following steps:
step 1: establishing an environmental economic dispatching mathematical model, wherein the environmental economic dispatching mathematical model comprises a target function and a constraint condition; the fuel cost and the emission of the pollution gas are at least two objective functions, the power balance constraint is used as an equality constraint condition, and the unit generating capacity constraint is an inequality constraint condition;
step 2: in the initial stage of algorithm iteration, the variation probability of particles is increased to expand the search area of the algorithm, and the dynamic variation probability formula is as follows:
Figure BDA0003357836810000021
wherein currentgen represents a current algebra, totalgen represents a total algebra;
and step 3: the method comprises the following steps of improving a multi-target particle swarm algorithm, selecting an individual optimal solution and a global optimal solution of a multi-target particle swarm, and solving a pareto optimal front edge, wherein the specific operations are as follows:
individual optimal solution: in the non-dominance solution set generated in each generation, pop solutions are generated by adopting a variation strategy of a differential evolution algorithm to form a new population Q, the new population Q is subjected to differential evolution and then compared to generate a non-inferior solution set, the non-inferior solution set and the current-generation dominance solution set are combined to generate an updated Pareto optimal solution set, and the updated Pareto optimal solution set is added into an external archive set;
global optimal solution: the particle swarm generates a global pareto optimal solution set according to dominance conditions in each iteration process, the initial value of the historical pareto optimal solution set is equal to the initial value of the global pareto solution set, then the global pareto optimal solution sets generated in each iteration are sorted according to the sparsity degree, and the particles with the largest sparsity in the pareto optimal solution are selected as the global optimal solution;
improving the distribution of the pareto optimal leading edge solution:
screening a solution on the pareto optimal leading edge by adopting a crowding distance algorithm; two sub-targets f1 and f2 are set, and if P [ i ] distance is the aggregation distance of the individual i, the function value of the individual i is as follows:
P[i]distance＝(P[i+1]·f1-P[i-1]·f2)+(P[i+1]·f2-P[i-1]·f2)
in order to avoid the defects of the single congestion sorting algorithm, a dynamic operator can be added, and a cycle congestion sorting method is adopted to improve the uniformity of the Pareto optimal leading edge.
And 4, step 4: obtaining a pareto optimal front edge of the environmental economic dispatch according to the environmental economic power generation dispatching solving method of the improved multi-target particle swarm optimization algorithm based on differential evolution in the step 3;
and 5: on the basis of the pareto optimal leading edge obtained in the step 4, a fuzzy membership function is adopted to express the degree of satisfaction corresponding to each objective function in each pareto optimal solution, and the fuzzy membership function is defined as follows:
Figure BDA0003357836810000031
in the formula, when muiWhen 0, it means that the value is completely different from the value of a certain objective function, and when μiWhen the value is 1, the method indicates that the certain objective function value is completely agreed;
for each solution in the pareto solution set, its normalized satisfaction value is solved using the following equation:
Figure BDA0003357836810000032
in the formula, M is the number of pareto optimal solution sets; n is a radical ofobjFor the number of objective functions, the optimal compromise solution is to have the maximum standard satisfaction value mukThe decision maker is assisted to select the optimal scheduling scheme which gives consideration to economy and environment.
Further, the specific form of the objective function and the constraint condition in step 1 is as follows:
Figure BDA0003357836810000033
Figure BDA0003357836810000034
wherein, ai，bi，ciThe system coefficient of the generator set; pGiThe active power of the ith generator; fi(PGi) The consumption characteristic of the ith generator is obtained; pLOSSThe system loss is considered; alpha is alphai，βi，λi，ξiAnd gammaiThe system coefficient of the generator set; ei(PGi) Is the ithA discharge function of the station generator; pGi min，PGi maxRespectively outputting the minimum active power and the maximum active power of the ith generator; pMIs the total load demand of the system; pLOSSFor system network loss, BooIs a scalar quantity, B is a matrix with dimensions of N x N.
Further, the specific operation of solving the individual optimal solution in step 3 is as follows: for arbitrary particles piRandomly selecting two particles pi,r1And pi,r2New subject ZiIs defined as:
Zi＝pi+F·(pi,r1+pi,r2)
wherein p isiFor the global optimum position of the ith particle, pi,r1And pi,r2Is two different individuals in the current non-inferior solution set, i ═ 1, 2.. pop, pop is the number of new individuals; f is in [0,1 ]]The coefficient of proportionality between, the variation particle is 50% of the population size.
Further, the step 4 comprises the following steps:
step 4.1: initialization:
initializing the speed and the position of a population, setting the maximum iteration number K, giving learning factors c1 and c2 and initial values of inertial weight, and initializing the individual optimal solution, the global optimal solution of the population, a global pareto optimal solution set and a historical pareto optimal solution set of each particle;
step 4.2: calculating the inertia weight omega of the iteration:
Figure BDA0003357836810000041
in the formula, TmaxIs the maximum number of iterations, t is the current number of iterations, ωmax＝0.9,ωmin＝0.4；
Step 4.3: calculating the network loss of each particle according to the objective function and the constraint condition;
step 4.4: calculating an adaptive value of each particle according to the objective function and the constraint condition;
step 4.5: update each particle velocity and position:
Figure BDA0003357836810000042
in the formula, r1，r2Is [0,1 ]]Subject to a uniform distribution of random numbers over the interval,
Figure BDA0003357836810000043
respectively the flight velocity and position of the particle i in the j-dimensional space in the k-th iteration,
Figure BDA0003357836810000044
for the position component of the individual optimum of particle i in the j-th dimension in the k-th iteration,
Figure BDA0003357836810000045
the position component of the global optimal value of the population in the j-dimensional space in the k-th iteration is used;
step 4.6: searching a global pareto optimal solution set of the iteration;
step 4.7: carrying out differential evolution on the current non-dominated solution set, and adding a newly obtained new non-inferior solution set into an external filing set;
step 4.8: updating an external archive set, selecting non-dominated solutions in the particles into the external archive set, deleting dominated individuals in the external archive set, calculating the aggregation distance of each individual when the non-dominated solutions in the external archive set are larger than the archive capacity, and pruning the aggregation distance by adopting an improved cycle congestion distance;
step 4.9: updating the global optimal positions of the particles, and selecting the optimal position for each particle from an external filing set by adopting a multi-target adaptive roulette method;
step 4.10: updating the local optimal position of the particle, comparing a new solution obtained in the particle flight process with the existing local optimal position of the particle, if the new solution dominates the local optimal position, the new solution is the new local optimal position, and if the new solutions are not dominated by each other, one of the new solutions is randomly selected from the new solution and the new local optimal position as the new self best position;
step 4.11: judging whether the maximum iteration times is reached, if so, ending, and outputting a pareto optimal solution set; otherwise go to step 4.3.
Has the advantages that:
1. the invention has the advantages of simple operation, high operation speed, good stability, easy engineering realization and network loss calculation in power balance.
2. The method introduces a global pareto optimal solution set and a historical pareto optimal solution set in a multi-target particle swarm algorithm, and increases the diversity of the pareto optimal solutions by using differential evolution for part of individuals; the size of an external filing set is controlled by adopting the circulation congestion distance, so that the uniformity of a pareto equilibrium surface is improved; the method for selecting the global optimal position of the particles by adopting the multi-target adaptive roulette method is a non-inferior solution which is obtained by an algorithm and is uniformly distributed in a target space, and meanwhile, the loss of an effective pareto optimal solution is avoided.
3. The invention can rapidly calculate the pareto optimal front edge of economic environment scheduling, and the front edge is widely and uniformly distributed.
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FIG. 1 is a flowchart of a method for solving the environmental economic power generation scheduling based on differential evolution.
Detailed Description
The invention will be further explained with reference to the drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The invention discloses a differential evolution-based solution method for environmental economic power generation scheduling, which mainly comprises the following steps:
s1, establishing an environmental economic dispatching mathematical model;
the environmental economic dispatching model comprises an objective function and a constraint condition, the fuel cost and the emission of the pollution gas are at least two objective functions, the power balance constraint is used as an equality constraint condition, and the unit generating capacity constraint is an inequality constraint condition;
objective function 1: minimizing fuel consumption function
Figure BDA0003357836810000061
Wherein, ai，bi，ciThe system coefficient of the generator set; pGiThe active power of the ith generator; fi(PGi) Is the consumption characteristic of the ith generator.
The objective function 2: minimizing the pollution emission function. The minimum pollutant gas emission amount belongs to the environmental dispatch, and for the convenience of calculation, a comprehensive pollutant gas emission model is adopted, so that the total pollutant gas emission amount of the system can be expressed as follows:
Ei(PGi)＝αi+βiPGi+γiPGi 2+ξiexp(λiPGi) (2)
wherein alpha isi，βi，λi，ξiAnd gammaiIs the system coefficient of the generator set, Ei(PGi) As a function of the emissions of the ith generator.
The operation constraint conditions of the generator are as follows:
PGi min≤PGi≤PGi max (3)
wherein, PGi min，PGi maxThe minimum and maximum active power output of the ith generator respectively.
Active power balance constraint conditions:
Figure BDA0003357836810000062
in the formula: pMIs the total load demand of the system; pLOSSIs the system network loss.
The network loss solution uses the B coefficient method, BooIs a scalar, B is an N x N dimensional matrix, and the calculation formula is as follows:
Figure BDA0003357836810000063
integrating the objective function and the constraint condition to obtain a mathematical model of the EED problem:
Figure BDA0003357836810000071
in the formula: x is a solution vector of the optimization problem; h. g is equality constraint and inequality constraint of the model respectively; l, K are the total number of equality and inequality constraints, respectively;
s2, mutation operators;
in the initial stage of algorithm iteration, the search area of the algorithm is expanded by increasing the variation probability of particles, and the convergence speed is slowed down; with the increase of iterative algebra, the variation probability of particles is dynamically reduced, and the convergence speed of the algorithm is accelerated. The dynamic variation probability formula is as follows:
Figure BDA0003357836810000072
wherein currentgen represents the current generation number, totalgen represents the total generation number.
S3, improving the multi-target particle swarm algorithm
When the particle swarm algorithm is selected to solve the power system environment economic dispatching scheme, firstly, the standard particle swarm algorithm is expanded into a multi-target particle swarm algorithm, then the particle swarm algorithm is improved by using a method based on differential evolution, and the method is mainly embodied in the selection of an individual optimal solution and a global optimal solution and the solution of the pareto optimal front edge:
in order to increase the diversity of the non-inferior solution sets, in the non-dominant solution set generated in each generation, pop solutions are generated by adopting a variation strategy of a differential evolution algorithm to form a new population Q, the new population Q is subjected to differential evolution and then compared to generate the non-inferior solution set, the non-inferior solution set and the current-generation dominant solution set are combined to generate an updated Pareto optimal solution set, and the updated Pareto optimal solution set is added into an external archive set.The specific operation is as follows: for arbitrary particles piRandomly selecting two particles pi,r1And pi,r2New subject ZiIs defined as:
Zi＝pi+F·(pi,r1+pi,r2) (8)
wherein p isiFor the global optimum position of the ith particle, pi,r1And pi,r2Is two different individuals in the current non-inferior solution set, i ═ 1, 2.. pop, pop is the number of new individuals; f is in [0,1 ]]The coefficient of proportionality between, the variation particle is 50% of the population size.
The method for improving the selection of the multi-target particle swarm individual extreme value solution and the global value solution comprises the following steps:
one of the basic features of the multiobjective optimization problem is the contradiction between the objectives, i.e. a scheme that improves one objective while at the same time it may degrade another objective. The contradiction between the targets makes the solution of the multi-target optimization problem not unique, and the set of all non-inferior solutions is replaced, which is also called a pareto optimal solution set, and comprises the following steps:
1) initializing all particle serial numbers to 1;
2) any two particles are compared with each other pairwise;
if the individual i dominates the individual j, the number of the individual j is rank (j) ═ 1+ rank (j);
if the individual j dominates the individual i, the number of the individual j is rank (i) ═ 1+ rank (i);
if the individual j and the individual i are not mutually independent, the serial numbers of the individual i and the individual j are not changed;
3) the particles with the sequence number 1 are put into a non-dominant solution set to form a current-generation non-inferior solution set.
At this point, a pareto solution set is formed. Under the condition of multi-objective optimization, the global optimal solution is a set of non-inferior solutions. And selecting an optimal individual for each particle from an external filing set by adopting a multi-target adaptive roulette method, and guiding the particles to gather towards the pareto optimal front edge. The specific process is as follows:
global optimal solution: the multi-objective optimization problem is designed to contain K (K is more than or equal to 2) targets, random numbers l between [0 and K ] are randomly generated for any particle, l is rounded, l is interper [ l ] +1, and then the most example determined by the roulette strategy for the adaptive value of the first objective function is the globally optimal particle of the particle.
Individual optimal particles: comparing a new solution obtained in the flight process with the existing local optimal position of the new solution, if the new solution dominates the local optimal position, the new solution is the new local optimal position, and if the new solutions are not dominated by each other, one of the new solution and the new solution is randomly selected to be used as the new self optimal position; if the local optimal position dominates the new solution, the local optimal position is unchanged;
improving the distribution of the pareto optimal leading edge solution:
the invention provides a method for controlling the size of an external archive set by using a cycle congestion distance algorithm, and improving the distribution condition of the pareto optimal frontier.
Screening a solution on the pareto optimal leading edge by adopting a crowding distance algorithm; two sub-targets f1 and f2 are set, and if P [ i ] distance is the aggregation distance of the individual i, the function value of the individual i is as follows:
P[i]distance＝(P[i+1]·f1-P[i-1]·f2)+(P[i+1]·f2-P[i-1]·f2) (9)
s4, solving the pareto optimal leading edge of environment economic dispatching by using the improved multi-target particle swarm optimization algorithm based on differential evolution in the step S3, wherein the specific steps are as follows:
step 4.1: initialization:
initializing the speed and the position of a population, setting the maximum iteration number K, giving learning factors c1 and c2 and initial values of inertial weight, and initializing the individual optimal solution, the global optimal solution of the population, a global pareto optimal solution set and a historical pareto optimal solution set of each particle;
step 4.2: calculating the inertia weight omega of the iteration according to the formula (10);
in the formula, TmaxIs the maximum number of iterations, t is the current number of iterations, ωmax＝0.9,ωmin＝0.4。
Figure BDA0003357836810000091
Step 4.3: calculating the network loss of each particle according to an environmental economic scheduling mathematical model;
step 4.4: calculating an adaptive value of each particle according to the environmental economic scheduling mathematical model;
step 4.5: update each particle velocity and position:
Figure BDA0003357836810000092
in the formula, r1，r2Is [0,1 ]]Subject to a uniform distribution of random numbers over the interval,
Figure BDA0003357836810000093
respectively the flight velocity and position of the particle i in the j-dimensional space in the k-th iteration,
Figure BDA0003357836810000094
for the position component of the individual optimum of particle i in the j-th dimension in the k-th iteration,
Figure BDA0003357836810000095
the position component of the global optimal value of the population in the j-dimensional space in the k-th iteration is used;
step 4.6: searching a global pareto optimal solution set of the iteration;
step 4.7: and (4) carrying out differential evolution on the current non-dominant solution set by using an equation (8), and adding a newly obtained new non-inferior solution set into an external archive set.
Step 4.8: updating the external archive set, selecting the non-dominated solution in the particle into the external archive set, deleting the dominated individual in the external archive set, when the non-dominated solution in the external archive set is larger than the archive capacity, calculating the aggregation distance of each individual according to the formula (9), and pruning the aggregation distance by adopting the improved cycle congestion distance.
Step 4.9: and updating the global optimal positions of the particles, and selecting the optimal position for each particle from an external filing set by adopting a multi-target adaptive roulette method.
Step 4.10: and updating the local optimal position of the particle, comparing the new solution obtained in the particle flight process with the existing local optimal position of the particle, if the new solution dominates the local optimal position, the new solution is the new local optimal position, and if the new solutions are not dominated by each other, one of the new solutions is randomly selected as the new self best position.
Step 4.11: judging whether the maximum iteration times is reached, if so, ending, and outputting a pareto optimal solution set; otherwise 4.3.
S5, on the basis of the pareto optimal leading edge obtained in the step S4, representing the degree of satisfaction corresponding to each objective function in each pareto optimal solution by adopting a fuzzy membership function, and defining the fuzzy membership function as follows:
Figure BDA0003357836810000101
in the formula, when muiWhen 0, it means that the value is completely different from the value of a certain objective function, and when μiWhen 1, it means that the objective function value is completely agreed.
For each solution in the pareto solution set, its normalized satisfaction value is solved using the following equation:
Figure BDA0003357836810000102
in the formula, M is the number of pareto optimal solution sets; n is a radical ofobjFor the number of objective functions, the optimal compromise solution is to have the maximum standard satisfaction value mukThe decision maker is assisted to select the optimal scheduling scheme which gives consideration to economy and environment.
In the specific embodiment of the invention, the method is applied to solve the environmental economic scheduling problem, two conditions of IEEE30BUS and 6 units are used for simulation, and the following table 1 is a parameter table of motor consumption, power limitation and pollution coefficient of the test system.
TABLE 1 Motor consumption, power limit, pollution coefficient parameter table for test system
Figure BDA0003357836810000103
Figure BDA0003357836810000111
The B coefficient for the loss is calculated as follows:
Figure BDA0003357836810000112
B0i＝[0.010731 1.7704-4.0645 3.8453 1.3832 5.5503]*e-03
B00＝0.0014
to illustrate the effectiveness of the algorithm, consider the following two cases:
setting parameters: the population size was 50, the external archive set was 100, F was 50%, the number of iterations was 500, and each set of experiments was run independently 10 times. ω max is 0.9, ω min is 0.4;
case 1:
the system ignores the network loss and considers balance constraint and capacity constraint;
case 2:
the system considers the network loss, and considers the balance constraint and the capacity constraint;
TABLE 2 DE-IMOPSO (differential evolution) Algorithm, Normal particle swarm Algorithm, minimum cost and minimum emissions results in cases 1 and 2
Figure BDA0003357836810000113
Figure BDA0003357836810000121
From the operation results of the DE-IMOPSO (differential evolution) algorithm and the ordinary particle swarm algorithm with the minimum cost and the minimum emission in the cases 1 and 2, the method has better convergence.
The above embodiments are merely illustrative of the technical concepts and features of the present invention, and the purpose of the embodiments is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims (4)

1. An environmental economy power generation scheduling solving method based on differential evolution is characterized by comprising the following steps:
step 1: establishing an environmental economic dispatching mathematical model, wherein the environmental economic dispatching mathematical model comprises a target function and a constraint condition; the fuel cost and the emission of the pollution gas are at least two objective functions, the power balance constraint is used as an equality constraint condition, and the unit generating capacity constraint is an inequality constraint condition;
step 2: in the initial stage of algorithm iteration, the variation probability of particles is increased to expand the search area of the algorithm, and the dynamic variation probability formula is as follows:
Figure FDA0003357836800000011
wherein currentgen represents a current algebra, totalgen represents a total algebra;
and step 3: the method comprises the following steps of improving a multi-target particle swarm algorithm, selecting an individual optimal solution and a global optimal solution of a multi-target particle swarm, and solving a pareto optimal front edge, wherein the specific operations are as follows:
individual optimal solution: in the non-dominance solution set generated in each generation, pop solutions are generated by adopting a variation strategy of a differential evolution algorithm to form a new population Q, the new population Q is subjected to differential evolution and then compared to generate a non-inferior solution set, the non-inferior solution set and the current-generation dominance solution set are combined to generate an updated Pareto optimal solution set, and the updated Pareto optimal solution set is added into an external archive set;
global optimal solution: the particle swarm generates a global pareto optimal solution set according to dominance conditions in each iteration process, the initial value of the historical pareto optimal solution set is equal to the initial value of the global pareto solution set, then the global pareto optimal solution sets generated in each iteration are sorted according to the sparsity degree, and the particles with the largest sparsity in the pareto optimal solution are selected as the global optimal solution;
improving the distribution of the pareto optimal leading edge solution:
screening a solution on the pareto optimal leading edge by adopting a crowding distance algorithm; two sub-targets f1 and f2 are set, and if P [ i ] distance is the aggregation distance of the individual i, the function value of the individual i is as follows:
P[i]distance＝(P[i+1]·f1-P[i-1]·f2)+(P[i+1]·f2-P[i-1]·f2)
in order to avoid the defects of the single congestion sorting algorithm, a dynamic operator can be added, and a cycle congestion sorting method is adopted to improve the uniformity of the Pareto optimal leading edge.
And 4, step 4: obtaining a pareto optimal front edge of the environmental economic dispatch according to the environmental economic power generation dispatching solving method of the improved multi-target particle swarm optimization algorithm based on differential evolution in the step 3;
and 5: on the basis of the pareto optimal leading edge obtained in the step 4, a fuzzy membership function is adopted to express the degree of satisfaction corresponding to each objective function in each pareto optimal solution, and the fuzzy membership function is defined as follows:
Figure FDA0003357836800000021
in the formula, when muiWhen 0, it means that the value is completely different from the value of a certain objective function, and when μiWhen the value is 1, the method indicates that the certain objective function value is completely agreed;
for each solution in the pareto solution set, its normalized satisfaction value is solved using the following equation:
Figure FDA0003357836800000022
in the formula, M is the number of pareto optimal solution sets; n is a radical ofobjFor the number of objective functions, the optimal compromise solution is to have the maximum standard satisfaction value mukThe decision maker is assisted to select the optimal scheduling scheme which gives consideration to economy and environment.
2. The differential evolution-based environment economic power generation scheduling solving method according to claim 1, wherein the objective function and the constraint condition in the step 1 are in the following specific forms:
Figure FDA0003357836800000023
Figure FDA0003357836800000024
wherein, ai，bi，ciThe system coefficient of the generator set; pGiThe active power of the ith generator; fi(PGi) The consumption characteristic of the ith generator is obtained; pLOSSThe system loss is considered; alpha is alphai，βi，λi，ξiAnd gammaiThe system coefficient of the generator set; ei(PGi) Is a function of the discharge capacity of the ith generator;
Figure FDA0003357836800000031
respectively outputting the minimum active power and the maximum active power of the ith generator; pMIs the total load demand of the system; pLOSSFor system network loss, BooIs a scalar quantity, B is a matrix with dimensions of N x N.
3. The differential evolution-based environmental economic power generation scheduling solving method according to claim 1, wherein the individual maximum in the step 3 is selectedThe specific operation of the optimal solution is as follows: for arbitrary particles piRandomly selecting two particles pi,r1And pi,r2New subject ZiIs defined as:
Zi＝pi+F·(pi,r1+pi,r2)
wherein p isiFor the global optimum position of the ith particle, pi,r1And pi,r2Is two different individuals in the current non-inferior solution set, i ═ 1, 2.. pop, pop is the number of new individuals; f is in [0,1 ]]The coefficient of proportionality between, the variation particle is 50% of the population size.
4. The differential evolution-based environmental economic power generation scheduling solving method according to claim 1, wherein the step 4 comprises the steps of:
step 4.1: initialization:
initializing the speed and the position of a population, setting the maximum iteration number K, giving learning factors c1 and c2 and initial values of inertial weight, and initializing the individual optimal solution, the global optimal solution of the population, a global pareto optimal solution set and a historical pareto optimal solution set of each particle;
step 4.2: calculating the inertia weight omega of the iteration:
Figure FDA0003357836800000032
in the formula, TmaxIs the maximum number of iterations, t is the current number of iterations, ωmax＝0.9,ωmin＝0.4；
Step 4.3: calculating the network loss of each particle according to the objective function and the constraint condition;
step 4.4: calculating an adaptive value of each particle according to the objective function and the constraint condition;
step 4.5: update each particle velocity and position:
Figure FDA0003357836800000033
in the formula, r1，r2Is [0,1 ]]Subject to a uniform distribution of random numbers over the interval,
Figure FDA0003357836800000034
respectively the flight velocity and position of the particle i in the j-dimensional space in the k-th iteration,
Figure FDA0003357836800000041
for the position component of the individual optimum of particle i in the j-th dimension in the k-th iteration,
Figure FDA0003357836800000042
the position component of the global optimal value of the population in the j-dimensional space in the k-th iteration is used;
step 4.6: searching a global pareto optimal solution set of the iteration;
step 4.7: carrying out differential evolution on the current non-dominated solution set, and adding a newly obtained new non-inferior solution set into an external filing set;
step 4.8: updating an external archive set, selecting non-dominated solutions in the particles into the external archive set, deleting dominated individuals in the external archive set, calculating the aggregation distance of each individual when the non-dominated solutions in the external archive set are larger than the archive capacity, and pruning the aggregation distance by adopting an improved cycle congestion distance;
step 4.9: updating the global optimal positions of the particles, and selecting the optimal position for each particle from an external filing set by adopting a multi-target adaptive roulette method;
step 4.10: updating the local optimal position of the particle, comparing a new solution obtained in the particle flight process with the existing local optimal position of the particle, if the new solution dominates the local optimal position, the new solution is the new local optimal position, and if the new solutions are not dominated by each other, one of the new solutions is randomly selected from the new solution and the new local optimal position as the new self best position;
step 4.11: judging whether the maximum iteration times is reached, if so, ending, and outputting a pareto optimal solution set; otherwise go to step 4.3.
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Publication number Priority date Publication date Assignee Title
CN115456428A (en) * 2022-09-19 2022-12-09 淮阴工学院 Environment economic power generation dispatching solving method for improving multi-target particle swarm based on cultural algorithm
CN116882158A (en) * 2023-07-06 2023-10-13 昆明理工大学 Engineering design-oriented piston-ring set-cylinder structure collaborative optimization design method

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115456428A (en) * 2022-09-19 2022-12-09 淮阴工学院 Environment economic power generation dispatching solving method for improving multi-target particle swarm based on cultural algorithm
CN116882158A (en) * 2023-07-06 2023-10-13 昆明理工大学 Engineering design-oriented piston-ring set-cylinder structure collaborative optimization design method
CN116882158B (en) * 2023-07-06 2024-03-26 昆明理工大学 Engineering design-oriented piston-ring set-cylinder structure collaborative optimization design method

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