CN105207233A - Reactive power optimization method based on combination of Metropolis-Hastings and PSO (Particle Swarm Optimization) - Google Patents

Abstract

The invention discloses a reactive power optimization method based on combination of Metropolis-Hastings and PSO (Particle Swarm Optimization). The method comprises the following steps: generating an initial swarm, calculating the fitness value of each particle, updating the individual extremum and the global extremum of each particle, updating the speed and the position of the particle swarm, performing sampling on the particle swarm by adopting Metropolis-Hastings, calculating the probability of acceptance, comparing the probability of acceptance with a random number to determine the next generation swarm; when the next generation iteration meets the end condition, outputting the result, and otherwise performing iterative computation to obtain the fitness value of each particle of the next generation particle swarm. According to the reactive power optimization method based on combination of Metropolis-Hastings and PSO, provided by the invention, the characteristics of the two kinds of algorithms are combined, on the advantage foundation that the PSO algorithm is simple, easy to realize, high in rate of convergence and fewer in adjustment parameters, the diversity of the swarm is enhanced, the defect of local convergence is effectively overcome, the calculation speed is high, and the calculating accuracy is higher.

Description

Based on the idle work optimization method that Metropolis-Hastings and PSO combines

Technical field

The present invention relates to a kind of idle work optimization method combined based on Metropolis-Hastings and PSO.

Background technology

Reactive power optimization of power system plays key effect to power system voltage stabilization, it relates to randomness that distributed power source exerts oneself, reactive power compensator drops into the determination of capacity, the adjustment of the adjustment of load tap changer and generator terminal voltage, has non-linear, discreteness, uncertainty, dynamic and multiple target feature.Along with modern power systems scale expanding day and distributed power source the improving constantly of permeability in power distribution network, the difficulty of idle work optimization is also increasing, also more and more higher to the requirement of derivation algorithm, if quickly converge on optimal solution, can restrain reliably.

Particle swarm optimization algorithm (ParticleSwarmOptimization, PSO) is a kind of new stochastic evolution computational methods that Kennedy and Eberhart proposed in nineteen ninety-five.This algorithm comes from the research to flock of birds predation, is a kind of general heuristic search technique.PSO algorithm is as a kind of multipoint random searching algorithm based on iteration, each particle represents a solution, the fitness value of each particle is determined according to certain rule, individual optimal solution is obtained by the history fitness value of more each particle, globally optimal solution is obtained by the individual optimal solution of more all particles, according to certain rule, iteration renewal is carried out to population, guide particle in solution space, follow these two optimal particle and search for, thus the optimal solution of the problem that is optimized.PSO algorithm is simple, computational speed is fast, be easy to convergence, easily realize, robustness is good, and needs the parameter of adjustment less, shown boundless application prospect, but PSO algorithm also also exists self shortcoming simultaneously in electric power system and other field.

PSO algorithm also exists precocious and restrains the phenomenon slowed down, the diversity of population increases along with iteration and declines, cause converging to globally optimal solution, for the pluses and minuses of particle cluster algorithm, numerous scholar proposes multiple Modified particle swarm optimization algorithm to improve the convergence property of particle swarm optimization algorithm.Shi and Eberhart proposed the innovatory algorithm of inertial factor linear decrease in 1998, made algorithm have larger exploring ability at the search initial stage, and can obtain more accurate result in the later stage.Kennedy and the Mendes again topological structure of a nearly step to population has done research, from the interparticle information flow of sociological " smallworlds " concept research, propose a series of topological structure, and analyzed by the performance of a large amount of experimental studies to all kinds of topological structure.The combination of PSO algorithm and other optimized algorithm is the focus of current PSO linguistic term, such as, in PSO, introduce the selection of genetic algorithm, intersection, mutation operator; The concept guides mutation operation etc. of " speed " in PSO is used in differential evolution algorithm.

Markov chain Monte-Carlo method originates from the work of the forties in 20th century a collection of physicist Metropolis, VonNeumarm etc. the earliest, through the development of decades, Markov chain Monte-Carlo method has become the important method solving complicated calculations problem in natural science and technical field.Metropolis algorithm is Markov chain Monte-Carlo method first iteration sampling technique, and Hastings was promoted in 1970 obtains Metropolis-Hastings algorithm.

The way of Metropolis-Hastings method is as follows: to make π (X) be Stationary Distribution, first by suggestion distribution q (X _t, X ^*) produce a potential transfer X _t→ X ^*; Then according to probability α (X _t, X ^*) (0≤α≤1) determine whether accept, that is obtaining potential branchpoint X ^*after, according to α (X _t, X ^*) size decide X ^*whether be the state value of chain at subsequent time; Be uniformly distributed extraction random number u from [0,1], then the state of Markov Chain subsequent time is:

$X_{t+1}=\left\{\begin{array}{cc}{X}^{*},& u\≤\mathrm{\α}(X_t,X^{*})\\ X_t,& u>\mathrm{\α}(X_t,X^{*})\end{array}\right.$

Conventional method makes acceptance probability be

$\mathrm{\α}(X_t,X^{*})=\min \left\{1,\frac{\mathrm{\π}\left(X^{*}\right)q(X^{*},X_t)}{\mathrm{\π}\left(X_t\right)q(X_t,X^{*})}\right\}$

Concerning Metropolis-Hastings sampling, the selection of suggestion distribution is very important, although suggestion distribution can adopt arbitrary form, choosing of suggestion distribution is directly connected to whole markovian convergence rate and covering space scope.Conventional probability-distribution function is uniformly distributed, normal distribution etc.

Equally distributed probability-distribution function is

$F\left(X\right)=\left\{\begin{array}{cc}0,& x<a\\ \frac{x-a}{b-a},& a\&le;x\&le;b\\ 1,& x\&GreaterEqual;b\end{array}\right.$

The probability-distribution function of normal distribution is

$F\left(X\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&delta;}}\underset{-\mathrm{\&infin;}}{\overset{x}{\&Integral;}}{e}^{-\frac{{(t-\mathrm{\&mu;})}^2}{2{\mathrm{\&sigma;}}^2}}dt.$

Summary of the invention

The present invention is in order to solve the problem, propose a kind of idle work optimization method combined based on Metropolis-Hastings and PSO, Metropolis-Hasting algorithm combines with PSO algorithm by this method, Metropolis-Hasting sampling is carried out to the population in iterative process, make particle according to the form of probability random search nearby of normal distribution, be equivalent to be applied with disruption and recovery to particle, contribute to strengthening population diversity, solve in existing reactive power optimization of power system process, PSO algorithm is precocious and restrain the shortcoming slowed down.

To achieve these goals, the present invention adopts following technical scheme:

A kind of idle work optimization method combined based on Metropolis-Hastings and PSO, comprise: set up primary group according to electric network composition, population initial parameter is set, particle swarm optimization algorithm (PSO) is utilized to be optimized particle each in primary group, find the optimal solution of population, upgrade population, Metropolis-Hasting algorithm is utilized to sample to the particle in the population after renewal, determine particle of future generation, repeated optimization, upgrade the operation of population, continuous iteration is until population meets idle work optimization termination condition, export idle work optimization result, carry out reactive power optimization of power system.

Further, primary group is set up according to the idle parameter of substation equipment, the concrete grammar arranging population initial parameter is: (a) arranges population scale, dimension, according to electric network composition determination particle composition, and the position of initialization population and speed;

B () arranges the individual history optimal solution that current location is each particle, more individual history optimal solution, determines globally optimal solution; Search volume, search speed scope are set, meet termination condition and inertia weight.

In described step (a), particle composition comprises generator terminal voltage amplitude, load tap changer position, reactive power compensator compensation capacity and distributed power source and exerts oneself.

In described step (b), termination condition is algorithm maximum iteration time or convergence precision.

Further, utilize particle swarm optimization algorithm (PSO) to be optimized particle each in primary group, find the optimal solution of population, upgrade the method for population, specifically comprise:

(1) evaluate each particle, calculate the fitness value of each particle according to the target function of Reactive Power Optimazation Problem;

(2) by comparing each particle fitness value and individual optimal solution, individual optimal solution is upgraded; By comparing the fitness value of current particle individual optimal solution and the fitness value of globally optimal solution, upgrade globally optimal solution;

(3) according to the particle rapidity after renewal and position, determine speed and the position of population, if particle rapidity exceedes search speed scope, with the upper lower limit value of search speed scope for particle rapidity, if particle rapidity exceedes search volume, with the border of search volume for particle position.

In described step (1), the target function of Reactive Power Optimazation Problem comprises the active loss of reduction system, reduces voltage deviation, reduces investment cost or reduce environmental pollution.

In described step (2), to each particle, the fitness value of current particle is compared with the fitness value of individual optimal solution, if the fitness value of current particle is better, determine particle current location, upgrade individual optimal solution, the fitness value of current particle individual optimal solution after upgrading is compared with the fitness value of globally optimal solution, if the fitness value of particle individual optimal solution is more excellent, then upgrade globally optimal solution, determine particle current location.

In described step (3), speed update method is: the speed after renewal equal former speed be multiplied by the value of inertia weight and Studying factors be multiplied by the random value being uniformly distributed middle extraction be multiplied by the difference of particle position and the original position determined when upgrading individual optimal solution and globally optimal solution and.

In described step (3), location updating method is, the position after renewal equals upgrade front position and upgrade rear speed sum.

Utilize Metropolis-Hasting algorithm to sample to the particle in the population after renewal, determine the method for particle of future generation, specifically comprise:

(I) Metropolis-Hasting sampling is carried out to particle, recommend distribution to adopt normal distribution, calculate acceptance probability, by the random number of extraction and comparing of acceptance probability, determine particle of future generation;

(II) whether inspection meets termination condition, if met, then terminates to calculate, exports optimum results, otherwise, proceed to the step utilizing particle swarm optimization algorithm to be optimized particle each in population of future generation.

In described step (II), whether inspection meets termination condition, if iterations reaches maximum iteration time, or final result is less than given convergence precision, then calculate end, and Output rusults.

Optimum results comprises particle optimal solution, i.e. each variable parameter of constituent particle, and according to this solution to additional result such as the system losses after reactive power optimization, voltage levvl, investment, environmentals.

Beneficial effect of the present invention is:

(1) present invention incorporates the characteristic of two kinds of algorithms, simple at PSO algorithm, be easy to, on the few advantage basis of realization, fast convergence rate, adjustment parameter, can population diversity be strengthened, effectively overcome the shortcoming of local convergence, computational speed is fast, and computational accuracy is higher;

(2) the present invention is based on the Reactive Power Optimization Algorithm for Tower that Metropolis-Hastings and PSO combines and can solve reactive power optimization of power system problem, make reactive power optimization result more reasonable, effective raising system voltage level, reduce grid loss, ensure power system security economical operation.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

As shown in Figure 1, perform step 01, start;

Then, perform step 02, initialization, generate initial population.Population scale N and dimension d is set; Determine that particle forms, comprise generator terminal voltage amplitude, load tap changer position, reactive power compensator compensation capacity, distributed power source exert oneself; Each particle is made up of these variablees, and the quantity of these variablees determines dimensionality of particle d, the position X of random initializtion population _i=(X _i1, X _i2..., X _id) and speed V _i=(V _i1, V _i2..., V _id); Current location is made to be the individual history optimal solution pbest of each particle _i, more individual history optimal solution pbest _i, find out globally optimal solution gbest; Search volume [X is set _min, X _max], search speed scope [-V _max, V _max], Studying factors C ₁and C ₂, algorithm maximum iteration time T _maxor convergence precision ε; For normal distribution; Determine inertia weight ω computing formula, such as, adopt following computing formula:

${\mathrm{\&omega;}}_t={\mathrm{\&omega;}}_{max}-{\left(\frac{{\mathrm{\&omega;}}_{max}-{\mathrm{\&omega;}}_{\min }}{T_{max}}\right)}^{2}t$

T in formula _maxit is maximum iteration time; T is current iteration number of times; ω _t, ω _max, ω _minmaximum, the minimum value of the inertia weight of the t time iteration, inertia weight permission value respectively.

Then, perform step 03, evaluate each particle, the target function of Reactive Power Optimazation Problem is generally the active loss of reduction system, and reduce voltage deviation, investment cost is few, and environmental pollution is little, calculates the fitness value of each particle according to target function;

After execution of step 03, perform step 04, to each particle, by the fitness value of current particle and individual optimal solution pbest _ifitness value compare, if the fitness value of current particle is better, then current particle position is set to P _i, and upgrade individual optimal solution pbest _i; By current particle individual optimal solution pbest _ifitness value compare with the fitness value of globally optimal solution gbest, if particle individual optimal solution pbest _ifitness value more excellent, then upgrade globally optimal solution gbest, corresponding particle position is set to P _g;

Then, perform step 05, upgrade speed and the position of each particle with following formula.

V _i(t+1)＝ω _t×V _i(t)+C ₁×r ₁×(P _i(t)-X _i(t))+C ₂×r ₂×(P _g(t)-X _i(t))

R ₁and r ₂from being uniformly distributed the random number extracted in [0,1].

X _i(t+1)＝X _i(t)+V _i(t+1)

If particle rapidity is greater than V _max, then speed is set to V _maxif be less than-V _max, then speed is set to-V _max.If particle position exceeds X _max, then particle position is set to X _maxif exceed X _min, then particle position is set to X _min;

$V=\left\{\begin{array}{cc}{V}_{max},& V>V_{max}\\ V,& V_{\min }\&le;V\&le;V_{max}\\ -V_{\min },& V<-V_{\min }\end{array}\right.$

$X=\left\{\begin{array}{cc}{X}_{max},& X>X_{max}\\ X,& X_{\min }\&le;X\&le;X_{max}\\ X_{\min },& X<X_{\min }\end{array}\right.$

Then, perform step 06, Metropolis-Hasting sampling is carried out to particle.Determine initial distribution π (X), recommend to be distributed as normal distribution, make particle with the form of normal distribution random search nearby, obtain particle of future generation.

Then, perform step 07, be calculated as follows acceptance probability.

$\mathrm{\&alpha;}(X_t,X^{*})=\min \left\{1,\frac{\mathrm{\&pi;}\left(X^{*}\right)q(X^{*},X_t)}{\mathrm{\&pi;}\left(X_t\right)q(X_t,X^{*})}\right\}$

Then, perform step 08, be uniformly distributed extraction random number u from [0,1], compare with acceptance probability, decide particle of future generation by following formula.

$X_{t+1}=\left\{\begin{array}{cc}{X}^{*},& u\&le;\mathrm{\&alpha;}(X_t,X^{*})\\ X_t,& u>\mathrm{\&alpha;}(X_t,X^{*})\end{array}\right.$

Then perform step 09, whether inspection meets iteration termination condition, if iterations reaches maximum iteration time T _max, or final result is less than given convergence precision ε, then calculate end, and Output rusults, otherwise forward step 03 to.

Finally, perform step 10, terminate.

Above-mentioned to complete at MATLAB emulation platform in steps.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1. the idle work optimization method combined based on Metropolis-Hastings and PSO, it is characterized in that: comprising: set up primary group according to electric network composition, population initial parameter is set, particle swarm optimization algorithm is utilized to be optimized particle each in primary group, find the optimal solution of population, upgrade population, Metropolis-Hasting algorithm is utilized to sample to the particle in the population after renewal, determine particle of future generation, repeated optimization, upgrade the operation of population, continuous iteration is until population meets idle work optimization termination condition, export idle work optimization result, carry out reactive power optimization of power system.

2. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 1, it is characterized in that: set up primary group according to electric network composition, the concrete grammar arranging population initial parameter comprises:

A () arranges population scale, dimension, according to electric network composition determination particle composition, and the position of initialization population and speed;

B () arranges the individual history optimal solution that current location is each particle, more individual history optimal solution, determines globally optimal solution; Search volume, search speed scope are set, meet termination condition and inertia weight.

3. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 2, it is characterized in that: in described step (a), particle composition comprises generator terminal voltage amplitude, load tap changer position, reactive power compensator compensation capacity and distributed power source and exerts oneself.

4. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 2, it is characterized in that: in described step (b), termination condition is algorithm maximum iteration time or convergence precision.

5. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 1, it is characterized in that: utilize particle swarm optimization algorithm (PSO) to be optimized particle each in primary group, find the optimal solution of population, upgrade the method for population, specifically comprise:

(1) evaluate each particle, calculate the fitness value of each particle according to the target function of Reactive Power Optimazation Problem;

(2) by comparing each particle fitness value and individual optimal solution, individual optimal solution is upgraded; By comparing the fitness value of current particle individual optimal solution and the fitness value of globally optimal solution, upgrade globally optimal solution;

(3) according to the particle rapidity after renewal and position, determine speed and the position of population, if particle rapidity exceedes search speed scope, with the upper lower limit value of search speed scope for particle rapidity, if particle rapidity exceedes search volume, with the border of search volume for particle position.

6. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 5, it is characterized in that: in described step (1), the target function of Reactive Power Optimazation Problem comprises the active loss of reduction system, reduces voltage deviation, reduces investment cost or reduce environmental pollution.

7. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 5, it is characterized in that: in described step (2), to each particle, the fitness value of current particle is compared with the fitness value of individual optimal solution, if the fitness value of current particle is better, determine particle current location, upgrade individual optimal solution, the fitness value of current particle individual optimal solution after upgrading is compared with the fitness value of globally optimal solution, if the fitness value of particle individual optimal solution is more excellent, then upgrade globally optimal solution, determine particle current location.

8. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 5, it is characterized in that: in described step (3), speed update method is: the speed after renewal equal former speed be multiplied by the value of inertia weight and Studying factors be multiplied by the random value being uniformly distributed middle extraction be multiplied by the difference of particle position and the original position determined when upgrading individual optimal solution and globally optimal solution and;

In described step (3), location updating method is, the position after renewal equals upgrade front position and upgrade rear speed sum.

9. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 1, it is characterized in that: utilize Metropolis-Hasting algorithm to sample to the particle in the population after renewal, determine the method for particle of future generation, specifically comprise:

(I) Metropolis-Hasting sampling is carried out to particle, calculate acceptance probability, by the random number of extraction and comparing of acceptance probability, determine particle of future generation;

(II) whether inspection meets termination condition, if met, then terminates to calculate, exports optimum results, otherwise, proceed to the step utilizing particle swarm optimization algorithm to be optimized particle each in population of future generation.

(III) in Metropolis-Hasting algorithm, distribution is recommended to adopt normal distribution.

10. a kind of idle work optimization method combined based on Metropolis-Hastings and PSO as claimed in claim 9, it is characterized in that: in described step (II), whether inspection meets termination condition, if iterations reaches maximum iteration time, or final result is less than given convergence precision, then calculate end, and Output rusults.