CN107958424A - A kind of Economic Dispatch strategy based on improvement gravitation search algorithm - Google Patents

A kind of Economic Dispatch strategy based on improvement gravitation search algorithm Download PDF

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CN107958424A
CN107958424A CN201610894009.0A CN201610894009A CN107958424A CN 107958424 A CN107958424 A CN 107958424A CN 201610894009 A CN201610894009 A CN 201610894009A CN 107958424 A CN107958424 A CN 107958424A
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search algorithm
gravitation search
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economic
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任建文
易琛
戚建文
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North China Electric Power University
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The present invention provides a kind of power system environment Economic Scheduling Policy based on improvement multiple target gravitation search algorithm, and this method comprises the following steps：I, structure considers, with the total operating cost minimum of system and the minimum object function of pollutant discharge amount, to establish power system environment economic optimization scheduling model at the same time；II, establish the power system environment economic load dispatching model for considering system operation cost and pollutant emission cost, and proposes a kind of multiple target gravitation search algorithm of improving and the model is solved；III, for basic gravitation search algorithm convergence rate it is slow the problem of, the inspiration by particle swarm optimization algorithm during more new individual position improves the location update formula of gravitation search algorithm；IV, in order to guide colony close to Pareto optimal solution sets region and ensure that algorithm disaggregation is uniformly distributed, using elite retention strategy；V, best compromise solution is produced using fuzzy set theory, scheduling scheme is provided for decision-maker.

Description

A kind of Economic Dispatch strategy based on improvement gravitation search algorithm
Technical field
It is a kind of based on improving gravitation search algorithm specifically the present invention relates to grid company economic load dispatching field Power system environment Economic Scheduling Policy.
Background technology
The main energy sources raw material of current social still based on the non-renewable energy resources such as coal, oil, natural gas, on the one hand with The fast development of social economy, energy consumption sharply increases, and global energy crisis is further serious；On the other hand, fossil fuel Substantial amounts of pollutant can be produced in combustion, not only causes environmental pollution, can also trigger greenhouse effects.Conventional electric power system Economic load dispatching is must to be with the minimum simple target of fired power generating unit fuel cost, the Economic Development Mode of country's proposition in recent years Resource-conserving and formulated the various laws and regulations of limitation thermal power plant contaminant gases discharge for this.Therefore, scheduling weight The multiple target that single goal steering of the heart by only considering economic factor takes into account economic benefit and environmental protection etc. shifts.
Power system environment economic load dispatching (environmental economic dispatch, EED) is one non-thread Property, the multi-objective optimization question with non-convex optimal forward position.Handle the problem key be to consider financial cost and environment into This two conflicting target, more preferable scheduling scheme is provided for dispatcher.The processing method of early stage is concentrated on more Targeted transformation is single goal, and method has Exchanger Efficiency with Weight Coefficient Method, Subordinate Function and constraint Condition Method etc..But, on the one hand, each weight Definite no clear and definite guideline of coefficient, and sound out needs and take considerable time, and to the target with non-convex forward position It is helpless；Membership function has construction reasonability defect.As the appearance and development of heuritic approach, its optimizing ability are continuous Enhancing, more and more scholars directly solve multi-objective problem using heuritic approach.Mainly include modified at present Multi-objective particle swarm algorithm, chaos sequence and adaptive re-configuration police are to basic differential evolution algorithm, dual stage process scheduling algorithm.
But any of the above method generally has the following problems：1) it is easy to be absorbed in local optimum, causes the optimizing energy of algorithm Power reduces；2) the optimal forward position distribution of the Pareto disaggregation obtained is less uniform；3) algorithm renewal process is complicated, difficulty in computation compared with Greatly.For this reason, present invention introduces a kind of novel gravitation search algorithm and making improvements and solving EED problems, the algorithm is comprehensive Close and consider local and global Optimal Searching, and the feasible of simulating, verifying institute extracting method is carried out with IEEE30 node systems Property and validity.
The content of the invention
The purpose of the present invention is the deficiency for existing method, proposes a kind of based on the power train for improving gravitation search algorithm System environmental economy scheduling strategy, on the basis of ensureing supply of electric power, reduces the energy consumption and polluted gas of fired power generating unit to the greatest extent Discharge.
In order to achieve the above object, the technical solution adopted by the present invention is：
It is a kind of that synthesis is established based on the power system environment Economic Scheduling Policy for improving gravitation search algorithm, the method Consider the power system environment economic load dispatching model of system operation cost and pollutant emission cost, and it is more to propose a kind of improvement Target gravitation search algorithm (IGSA) solves the model, reduces total energy consumption and the pollution of fired power generating unit to greatest extent The discharge of gas.
A kind of power system environment Economic Scheduling Policy based on improvement gravitation search algorithm, the described method includes following step Suddenly：
Step 1：Build and consider at the same time with the total operating cost minimum of system and the minimum object function of pollutant discharge amount, And meet the multi-objective Model of the constraintss such as system power Constraints of Equilibrium, the constraint of generating set output bound, establish electricity Force system environmental economy Optimal Operation Model, power system environment Economic Dispatch Problem is expressed as to be based on nonlinear multiple target Optimization problem；
Step 2：Establish the power system environment economy tune for considering system operation cost and pollutant emission cost Model is spent, and proposes a kind of multiple target gravitation search algorithm (IGSA) of improving and the model is solved.The algorithm is by NSGA- The thought of noninferior solution sequence and crowding distance in II introduces basic gravitation search algorithm and is used to handle individual partial ordering relation；
Step 3：For basic gravitation search algorithm convergence rate it is slow the problem of, by particle during more new individual position The inspiration of colony optimization algorithm improves the location update formula of gravitation search algorithm；
Step 4：In order to guide colony close to Pareto optimal solution sets region and ensure that algorithm disaggregation is uniformly distributed, use Elite retention strategy；
Step 5：Best compromise solution is produced using fuzzy set theory, scheduling scheme is provided for decision-maker.Sample calculation analysis is tested The feasibility and validity for carrying algorithm are demonstrate,proved, to realize that the balance optimizing of power system economy and the feature of environmental protection provides one New method.
As further describing, the total operating cost minimum of system and pollutant emission are considered while being mentioned in step 1 The multiple objective function of minimum target is measured, the two object functions are shown below respectively：
In formula：F is total system operation cost；PGiFor the output of i-th generator；N is generating set in system；Fi (PGi) for the operating cost of i-th generator.Wherein the operating cost of generator can usually use the quadratic function of active power To represent, ai, biAnd ciFor the operating cost coefficient of i-th generator；E is total pollutant emission cost；Ei(PGi) it is i-th The pollutant emission cost of platform generator；α i, βi, γi, ζiAnd λiFor the pollutant emission characteristic coefficient of i-th generator.
As further describing, step 2, which is mentioned, is improved basic gravitation search algorithm, to strengthen its global search Ability, avoids being absorbed in locally optimal solution；And increase enhancing population diversity measure reply premature convergence problem.
As further describing, the problem of basic gravitation search algorithm convergence rate is slow is directed in step 3, the present invention is changed Into the inspiration of type particle cluster algorithm, weight factor is introduced in location formula.Population location update formula introduce weight because When son or contraction factor, algorithm optimization performance can have been arrived and greatly improved.Location update formula is represented by this time：
xi d(t+1)=w × xi d(t)+vi d(t+1)
ω is introduced weight in formula.Dynamic self-adapting weight is used herein.
W=wmax-(wmax-wmin)×t/T
As further describing, the elite retention strategy in NSGA-II is utilized to pass through non-dominated ranking and meter in step 4 More excellent solution is chosen after calculating crowding distance, so that colony is close to Pareto optimal solution sets area, while also ensure that disaggregation point The uniformity of cloth.
Further, in step 5 IEEE30 node systems example show carried algorithm have good convergence property and The optimal forward positions of Pareto being evenly distributed, demonstrate the validity and reasonability of algorithm.
Compared with the conventional method, the beneficial effects of the invention are as follows：The present invention, which establishes, considers economy and the feature of environmental protection Electric system Multiobjective Scheduling model.It is introduced into a kind of novel gravitation search algorithm and applies it in the solution of model, Premature convergence problem for algorithm and the defects of be easy to be absorbed in local optimum, sorted respectively using noninferior solution, introduce crowding distance, Elite is retained and is improved using strategies such as particle historical informations to strengthen its population diversity and ability of searching optimum. IEEE30 node system examples show that carried algorithm has good convergence property and the optimal forward positions of Pareto being evenly distributed, Demonstrate the validity and reasonability of algorithm.
Brief description of the drawings
Fig. 1 is：The layering schematic diagram of one embodiment of the invention.
Fig. 2 is：The calculating schematic diagram of crowding distance between the same level individual of one embodiment of the invention.
Fig. 3 is：The Pareto forward positions of the EED problems of the basic gravitation search algorithm of one embodiment of the invention.
Fig. 4 is：The Pareto forward positions of the EED problems of the inventive algorithm of one embodiment of the invention.
Fig. 5 is：The operating cost convergence curve of the basic gravitation search algorithm of one embodiment of the invention.
Fig. 6 is：The pollutant discharge amount convergence curve of the basic gravitation search algorithm of one embodiment of the invention.
Fig. 7 is：The operating cost convergence curve of the innovatory algorithm of one embodiment of the invention.
Fig. 8 is：The pollutant discharge amount convergence curve of one embodiment of the invention.
Embodiment
Technical scheme is described in further detail below by drawings and examples.
It is of the present invention a kind of based on the power system environment Economic Scheduling Policy for improving gravitation search algorithm, including such as Lower step：
Step 1：Build and consider at the same time with the total operating cost minimum of system and the minimum object function of pollutant discharge amount, And meet the multi-objective Model of the constraintss such as system power Constraints of Equilibrium, the constraint of generating set output bound, establish electricity Force system environmental economy Optimal Operation Model, power system environment Economic Dispatch Problem is expressed as to be based on nonlinear multiple target Optimization problem；
Object function is：
Constraints is：
System power Constraints of Equilibrium
In formula：PloadFor the total workload demand of system.
Generating set output bound constrains
PG, min≤PGi≤PGi, max
In formula：PGi, minAnd PGi, maxThe output bound of respectively i-th unit.
Step 2：Establish the power system environment economy tune for considering system operation cost and pollutant emission cost Model is spent, and proposes a kind of multiple target gravitation search algorithm (IGSA) of improving and the model is solved.The algorithm is by NSGA- The thought of noninferior solution sequence and crowding distance in II introduces basic gravitation search algorithm and is used to handle individual partial ordering relation；
For a given multi-objective problem minf (x), if x*∈ X, and other are not presentMeetAnd at least one strict inequality is set up, then x*It is known as Pareto optimal solutions, all Pareto The set of optimal solution forms Pareto optimal solution sets.
Assuming that x1And x2For two decision variables in X, if x1Dominate x2(x1＜ x2), it is necessary to while meet following two Part：
After drawing Pareto optimal solution sets, best compromise is provided for policymaker using the fuzzy membership in fuzzy mathematics Solution.Each the satisfaction of the corresponding each object function of Pareto optimal solutions is：
F in formulaiFor target function value；fI, maxAnd fI, minThe respectively maximin of respective objects function.μi=0 represents It is completely dissatisfied；μi=1 represents to be entirely satisfactory.The standardization satisfaction of each optimal solution is solved using following formula：
In formulaFor the standardization satisfaction of i-th of optimal solution；NpFor optimal solution number.Maximum standardization satisfaction is taken to make For best compromise solution.
The scholars such as Rashed were inspired by the law of universal gravitation in 2009 and propose a kind of new swarm intelligence optimization calculation Method --- gravitation search algorithm.The outstanding feature of the New Algorithm is that whole colony is sought by the graviational interaction between individual Excellent, gravitation plays the role of transmitting information.Designed according to algorithm, individual quality is bigger, and its gravitation is also bigger.Finally drawing Under the action of power, whole colony is mobile towards the individual direction of quality maximum and is centered around around it, so as to find problem most Excellent solution.Each Search of Individual has position, acceleration, four state variables of speed and quality.Wherein, position represents problem Solution, speed are used for more new position, and acceleration is used for renewal speed, and quality is used for the quality for evaluating individual.Gravitation search algorithm has There is the characteristics of flow is simple, and parameter setting is few, can be combined well with optimization problem, it is easy to accomplish.
With basic gravitation search algorithm is other heuristic algorithms as, it may have is easy to be absorbed in local optimum and precocious Defect.The present invention is improved basic gravitation search algorithm for this, to strengthen its ability of searching optimum, avoids being absorbed in part Optimal solution；And increase enhancing population diversity measure reply premature convergence problem.
For multi-objective optimization question, the non-bad relation individual in population analyze critically important.The present invention uses for reference The method of non-dominated ranking in NSGA-II, is classified whole colony.Concrete operations are as follows：
(1) if individual xi dDo not dominated in current all individuals by other individuals, then the individual is referred to as Pareto Non-dominant；Each individual in colony is investigated, finds out the non-dominant individuals of all Pareto, and it is rank=1 to assign its level；
(2) individual of rank=1 is rejected from current group, then repeats (1) process, produces the second level individual collections And it is rank=2 to assign level；
(3) and so on, layer sorting is carried out to all individuals in colony.
It is as shown in Figure 1 to be layered schematic diagram.Assumed group scale is 5, and object function number is 2.
Distribution distribution to Pareto optimal forward position of the colony in space is extremely important.The dense degree of individual reflects group The distribution situation of body, portrays distribution situation using the crowding distance between individual is calculated herein for this.In general, dense degree Big individual crowding distance is small.On the basis of hierarchical, individual crowding distance can be by same level The sum of distance of adjacent thereto two individual on each sub-goal characterizing.As Fig. 2 illustrates, it is assumed that a Bi-objective is asked Topic, the crowding distance of i-th of individual are individual in target f for the i-th -1 individual and i+11And f2On the sum of distance, that is, The length and width of rectangle shown in figure and.But financial cost may have very big difference with Environmental costs in value range, for this reason, A object function is normalized herein.If d (i) represents the crowding distance of i-th of individual, fk(i) i-th is represented Functional value of the body on k-th of sub-goal.When target problem has m sub-goal, d (i) can be expressed as：
In formulaWithThe minimum and maximum functional value of respectively k-th of sub-goal.
After non-dominated ranking and calculating crowding distance, each individual has two attributes：Level number and it is crowded away from From value.The partial ordering relation between individual can be then defined according to the two attributes.When meeting following formula, individual i is better than individual j
Rank (i) ＜ rank (j)
Or rank (i)=rank (j), d (i) ＞ d (j)
Use for reference particle cluster algorithm in speed more new formula, using individual historical information and social information share come Improve the diversity of search space.It can be expressed as using the speed more new formula after mass society Information Sharing strategy：
Rand in formula1, rand2And rand3It is that equally distributed stochastic variable is obeyed on [0,1]；c1And c2For study because Sub- constant；xd Ip, bestFor the current optimal locations of individual i；xd G, bestRepresent current group optimal location.Individual i best position calculations Step, calculates other particles and its crowding distance, takes the position of the minimum individual of crowding distance；Colony's optimal location takes crowding distance Maximum individual position.
Step 3：For basic gravitation search algorithm convergence rate it is slow the problem of, by particle during more new individual position The inspiration of colony optimization algorithm improves the location update formula of gravitation search algorithm；
For basic gravitation search algorithm convergence rate it is slow the problem of, the present invention inspired by improved Particle Swarm Algorithm, Weight factor is introduced in location formula.Population location update formula is when introducing weight factor or contraction factor, algorithm Optimization performance, which can arrive, to be greatly improved.Location update formula is represented by this time：
xi d(t+1)=w × xi d(t)+vi d(t+1)
ω is introduced weight in formula.Dynamic self-adapting weight is used herein.
W=wmax-(wmax-wmin)×t/T
Step 4：In order to guide colony close to Pareto optimal solution sets region and ensure that algorithm disaggregation is uniformly distributed, use Elite retention strategy；
The present invention utilizes the elite retention strategy in NSGA-II to be chosen by non-dominated ranking and after calculating crowding distance More excellent solution, so that colony is close to Pareto optimal solution sets area, while also ensure that the uniformity of disaggregation distribution.Main step Suddenly it is：
(1) progeny population target function value is evaluated；
(2) parent (previous generation's optimal solution) colony P is mergedtWith progeny population Qt, form the colony R that scale is 2Nt；
(3) to RtIn it is all individual carry out non-dominated rankings and calculate crowding distances operation, and according to it is defined above partially Order relation chooses excellent individual one by one until population size quantity reaches N, other are then eliminated.
The design of mass function is the key using Algorithm for Solving multi-objective problem.When handling single-objective problem, arbitrarily Functional value between target can compare size, and fitness function can directly be defined as object function at this time.But due to more In objective optimisation problems, only there is partial ordering relation between all non-dominant individuals, can not be compared.The present invention uses following steps Designing quality function：
(1) for the individual of rank=1, put the maximum ideal adaptation angle value of d (i) and be set to 2 for the second largest individuals of 1, d (i), press All individuals of the level are carried out fitness assignment by the method；
(2) fitness assignment is carried out to all individuals in all levels according to the method for (1)；
(3) Individual Quality function is updated according to lower two formula and calculated：
Step 5：Best compromise solution is produced using fuzzy set theory, scheduling scheme is provided for decision-maker.Sample calculation analysis is tested The feasibility and validity for carrying algorithm are demonstrate,proved, to realize that the balance optimizing of power system economy and the feature of environmental protection provides one New method.
Algorithm for Solving EED problem steps are：
1) basic parameter is set
1. the operating cost coefficient of setting generator, pollutant discharge coefficient, generator output bound and system Workload demand.
2. algorithm design parameter is set：Population size N, maximum iteration T, factor alpha and G0, Studying factors constant c1And c2, weight coefficient ωmaxAnd ωmin。
2) initialize
1. in EED problems, decision variable is the output of a generator, constructs initial population as the following formula：
PG, i=PG, i, min+rand×(PG, i, max-PG, i, min)
Each individual has n dimensions to represent n platform generating sets in formula；Rand represents to obey between [0,1] equally distributed random Variable.
2. initialized target function, constraints are added in object function with penalty term.
3. initialize iterations t=0.
3) algorithm updates
1. non-dominated ranking is carried out to all individuals and calculates crowding distance.
2. carrying out individual adaptation degree assignment, Individual Quality is calculated.
3. calculate gravitation and acceleration suffered by individual.
4. press the renewal operation that two formulas carry out speed and position：
Rank (i) ＜ rank (j)
Or rank (i)=rank (j), d (i) ＞ d (j)
5. elitist selection operation is carried out to colony using non-dominated ranking and crowding distance.
4) iteration ends
If reaching maximum iteration, algorithm terminates, and otherwise, 3) t=t+1, goes to step.
5) result is exported
Export target function value { F (PG, 1), F (PG, 2) ..., F (PG, N) and corresponding optimal solution { PG, 1, PG, 2..., PG, NAnd best compromise solution.
The present invention carries out proof of algorithm using IEEE30 nodes standard test system as example.The system has 6 thermal motors Group (G1-G6), 41 branch (L1-L41), total load 283.4MW.Inventive algorithm parameter setting is as shown in table 1.
Carried algorithm and basic gravitation search algorithm are respectively applied to the Pareto forward positions obtained by Optimized model by the present invention As shown in Figure 3 and Figure 4.
From above-mentioned Pareto forward positions, it is optimal compared to basic gravitation search algorithm, Pareto that the present invention carries algorithm Disaggregation is distributed more complete, uniform and has stronger search capability.
Contrast convergence property curve (Fig. 5 and Fig. 6) and the convergence of improved searching algorithm of basic gravitation search algorithm Characteristic curve (Fig. 7 and Fig. 8) understands that improved gravitation search algorithm can be obtained by optimal objective function after iteration 40 times Solution, and basic gravitation search algorithm then needs the iteration of nearly 100 times to restrain, and it is good to illustrate that improved algorithm has Convergence property.
In order to verify that the present invention puies forward the validity of algorithm, by result of calculation and non-dominated sorted genetic algorithm (NSGA), Niche genetic algorithm (NPGA), fuzzy multi-cluster multi-objective particle swarm algorithm (FCPSO) are made comparisons, as a result respectively such as table 2, table Shown in 3.
From comparing result, the present invention carry algorithm compared to other algorithms can obtain minimum operating cost and Pollutant discharge amount, can provide the information compared with horn of plenty for decision-making, illustrate the validity and reasonability of the algorithm.
In order to provide decision information to dispatcher, best compromise solution is calculated using fuzzy set theory, as a result such as the institute of table 4 Show.
Table 1 is set for the algorithm parameter of one embodiment of the invention.
Table 2 compares for the lowest coursing cost of one embodiment of the invention.
Table 3 is minimum relatively for the pollutant emission of one embodiment of the invention.
Table 4 is the best compromise solution of one embodiment of the invention.
Table 1
Table 2
Table 3
Table 4
Understand from the above, the electric system multiple target tune for considering economy and the feature of environmental protection is established by the present invention Spend model.It is introduced into a kind of novel gravitation search algorithm and applies it in the solution of model, for the premature convergence problem of algorithm And the defects of being easy to be absorbed in local optimum, sorted respectively using noninferior solution, introduce crowding distance, elite retains and utilizes grain The strategies such as sub- historical information are improved to strengthen its population diversity and ability of searching optimum.IEEE30 node system examples Show that carried algorithm has good convergence property and the optimal forward positions of Pareto being evenly distributed, demonstrate the validity of algorithm And reasonability.

Claims (3)

  1. It is 1. a kind of based on the Economic Dispatch strategy for improving gravitation search algorithm, it is characterised in that：The described method includes Following steps：
    I, structure considers with the total operating cost minimum of system and the minimum object function of pollutant discharge amount at the same time, and meets The multi-objective Model of the constraintss such as system power Constraints of Equilibrium, the constraint of generating set output bound, establishes electric system ring Border economic optimization scheduling model, power system environment Economic Dispatch Problem is expressed as asking based on nonlinear multiple-objection optimization Topic；
    II, establish the power system environment economic load dispatching model for considering system operation cost and pollutant emission cost, And propose a kind of multiple target gravitation search algorithm (IGSA) of improving and the model is solved.The algorithm is by NSGA-II Noninferior solution sorts and the thought of crowding distance introduces basic gravitation search algorithm and is used to handle individual partial ordering relation；
    III, for basic gravitation search algorithm convergence rate it is slow the problem of, by particle group optimizing during more new individual position The inspiration of algorithm improves the location update formula of gravitation search algorithm；
    IV, in order to guide colony close to Pareto optimal solution sets region and ensure that algorithm disaggregation is uniformly distributed, protected using elite Stay strategy；
    V, best compromise solution is produced using fuzzy set theory, scheduling scheme is provided for decision-maker.Sample calculation analysis, which demonstrates, to be carried The feasibility and validity of algorithm, to realize that the balance optimizing of power system economy and the feature of environmental protection provides a new side Method.
  2. 2. based on a kind of based on the Economic Dispatch strategy for improving gravitation search algorithm, its spy described in claim 1 Sign is：The resource-effective economic load dispatching model of consideration described in step I；Consider to arrange with pollutant so that operating cost is minimum at the same time High-volume minimum object function, builds Model for Multi-Objective Optimization.
  3. 3. based on a kind of based on the Economic Dispatch strategy for improving gravitation search algorithm, its spy described in claim 1 Sign is：The problem of basic gravitation search algorithm convergence rate is slow is directed to described in step III, the present invention is by modified particle swarm The inspiration of algorithm, introduces weight factor in location formula.Population location update formula is introducing weight factor or contraction Because of the period of the day from 11 p.m. to 1 a.m, algorithm optimization performance can have been arrived and greatly improved.
CN201610894009.0A 2016-10-14 2016-10-14 A kind of Economic Dispatch strategy based on improvement gravitation search algorithm Pending CN107958424A (en)

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CN110210756A (en) * 2019-05-31 2019-09-06 华南理工大学 It is a kind of meter and pollutant diffusion mileage Economic Dispatch method
CN112070628A (en) * 2020-09-02 2020-12-11 沈阳工程学院 Intelligent power grid multi-target economic dispatching method considering environmental factors
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CN113904379A (en) * 2021-09-30 2022-01-07 沈阳工程学院 Smart power grid economic dispatching method based on improved particle swarm algorithm
CN113904379B (en) * 2021-09-30 2023-09-05 沈阳工程学院 Smart grid economic dispatching method based on improved particle swarm algorithm
CN114578087A (en) * 2022-01-24 2022-06-03 华北电力大学（保定） Wind speed uncertainty measurement method based on non-dominated sorting and random simulation algorithm
CN114578087B (en) * 2022-01-24 2023-10-13 华北电力大学（保定） Wind speed uncertainty measurement method based on non-dominant sorting and stochastic simulation algorithm

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