CN105207233B - Based on the idle work optimization method that Metropolis Hastings are combined with PSO - Google Patents
Based on the idle work optimization method that Metropolis Hastings are combined with PSO Download PDFInfo
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- CN105207233B CN105207233B CN201510718158.7A CN201510718158A CN105207233B CN 105207233 B CN105207233 B CN 105207233B CN 201510718158 A CN201510718158 A CN 201510718158A CN 105207233 B CN105207233 B CN 105207233B
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Abstract
The invention discloses a kind of idle work optimization method being combined with PSO based on Metropolis Hastings, this method is by generating initial population, calculate each particle fitness value, more new particle individuality extreme value and global extremum, then after updating particle populations speed and position, Metropolis Hasting sampling is carried out to population, calculate acceptance probability, it is compared by acceptance probability and random number, it is determined that population of future generation, after iteration of future generation meets termination condition, output result, otherwise, iterative calculation each particle fitness value of population of future generation；Present invention incorporates two kinds of characteristics of algorithm, PSO algorithms it is simple, be easily achieved, on the basis of the advantage that fast convergence rate, adjusting parameter are few, population diversity can be strengthened, effectively overcome the shortcoming of local convergence, calculating speed is fast, and computational accuracy is higher.
Description
Technical field
The present invention relates to a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings.
Background technology
Reactive power optimization of power system plays key effect to power system voltage stabilization, and it is related to what distributed power source was exerted oneself
Randomness, reactive power compensator put into determination, the adjustment of load tap changer and the adjustment of generator terminal voltage of capacity, tool
The characteristics of having non-linear, discreteness, uncertainty, dynamic and multiple target.As modern power systems scale expands day by day
With the continuous improvement of distributed power source permeability in power distribution network, the difficulty of idle work optimization is also increasing, to derivation algorithm
It is required that also more and more higher, if quickly converging on optimal solution, can reliably restrain.
Particle swarm optimization algorithm (Particle Swarm Optimization, PSO) is that Kennedy and Eberhart exist
A kind of new stochastic evolution computational methods that nineteen ninety-five proposes.The algorithm comes from the research to flock of birds predation, is a kind of logical
Heuristic search technique.PSO algorithms represent one as a kind of multipoint random searching algorithm based on iteration, each particle
Solution, the fitness value of each particle is determined according to certain rule, and individuality is obtained by the history fitness value for comparing each particle
Optimal solution, globally optimal solution is obtained by the individual optimal solution of relatively more all particles, and population is changed according to certain rule
In generation, updates, and guiding particle follows the two optimal particles to scan in solution space, so as to obtain the optimal solution of optimization problem.
PSO algorithms are simple, calculating speed is fast, be easy to convergence, easily realize, robustness is good, and need the parameter of adjustment less, in electricity
Force system and other field have shown boundless application prospect, but PSO algorithms there is also self shortcoming simultaneously.
PSO algorithms have the phenomenon that precocious and convergence slows down, and the diversity of population declines as iteration increases, causes
Globally optimal solution cannot be converged to, for the advantage and disadvantage of particle cluster algorithm, numerous scholars propose various Modified particle swarm optimizations
Algorithm is improving the convergence property of particle swarm optimization algorithm.Shi and Eberhart proposed inertial factor linear decrease in 1998
Innovatory algorithm so that algorithm has larger exploring ability at the search initial stage, and can obtain more accurate result in the later stage.
Topological structures of the Kennedy and Mendes again further to population is studied, general from sociological " small worlds "
Thought is set out and studies interparticle information flow, it is proposed that a series of topological structure, and is opened up to all kinds of by substantial amounts of experimental study
The performance for flutterring structure is analyzed.The combination of PSO algorithms and other optimized algorithms is the focus of current PSO linguistic terms, example
Selection, intersection, the mutation operator of genetic algorithm are introduced such as in PSO；" speed " is general in borrowing PSO in differential evolution algorithm
Thought instructs mutation operation etc..
Markov chain Monte-Carlo method earliest originate from a collection of physicist Metropolis forties in 20th century,
The work of Von Neumarm etc., by the development of decades, Markov chain Monte-Carlo method have become natural science and
The important method of complicated calculations is solved the problems, such as in technical field.Metropolis algorithms are Markov chain Monte-Carlo methods
One iteration sampling technique, Hastings was promoted in 1970 obtains Metropolis-Hastings algorithms.
The way of Metropolis-Hastings methods is as follows：To make π (X) for Stationary Distribution, it is distributed by suggestion first
q(Xt,X*) produce a potential transfer Xt→X*；Then according to probability α (Xt,X*) (0≤α≤1) come decide whether receive,
That is obtaining potential branchpoint X*Afterwards, according to α (Xt,X*) size determine X*Whether it is state of the chain in subsequent time
Value；Extraction random number u is uniformly distributed from [0,1], then the state of Markov Chain subsequent time is：
Conventional method is to make the acceptance probability be
For Metropolis-Hastings sampling, it is proposed that the selection of distribution is critically important, although suggestion distribution can be used
Arbitrary form, but the selection of suggestion distribution is directly connected to whole markovian convergence rate and covering spatial dimension.Often
Be uniformly distributed with probability-distribution function, normal distribution etc..
Equally distributed probability-distribution function is
The probability-distribution function of normal distribution is
The content of the invention
The present invention is in order to solve the above problems, it is proposed that a kind of to be combined with PSO based on Metropolis-Hastings
With PSO algorithms be combined Metropolis-Hasting algorithms by idle work optimization method, this method, to the particle in iterative process
Group carries out Metropolis-Hasting sampling, makes particle according to the form of probability nearby random search of normal distribution,
Disruption and recovery is applied with equivalent to particle, helps to strengthen population diversity, solve existing reactive power optimization of power system mistake
Cheng Zhong, PSO algorithm are precocious and restrain the shortcoming for slowing down.
To achieve these goals, the present invention is adopted the following technical scheme that：
A kind of idle work optimization method being combined with PSO based on Metropolis-Hastings, including：According to power network knot
Build vertical primary group, population initial parameter be set, using particle swarm optimization algorithm (PSO) in primary group each
Particle is optimized, find population optimal solution, update population, using Metropolis-Hasting algorithms to renewal after
Population in particle be sampled, it is determined that particle of future generation, repeated optimization, update the operation of population, continuous iteration is straight
Meet idle work optimization termination condition to population, 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 tool of population initial parameter is set
Body method is：A () sets population scale, dimension, determine that particle is constituted according to electric network composition, initializes position and the speed of population
Degree；
B () sets the individual history optimal solution that current location is each particle, relatively more individual history optimal solution, it is determined that global
Optimal solution；Search space, search speed scope are set, termination condition and inertia weight is met.
In the step (a), particle composition includes generator terminal voltage amplitude, load tap changer position, idle benefit
Repay device compensation capacity and distributed power source is exerted oneself.
In the step (b), termination condition is algorithm maximum iteration or convergence precision.
Further, each particle in primary group is optimized using particle swarm optimization algorithm (PSO), finds grain
The optimal solution of subgroup, the method for updating population, specifically includes：
(1) each particle is evaluated, the object function according to Reactive Power Optimazation Problem calculates the fitness value of each particle；
(2) by the comparing to each particle fitness value and individual optimal solution, individual optimal solution is updated；By to current
The fitness value of particle individual optimal solution and the fitness value of globally optimal solution compare, and update globally optimal solution；
(3) according to the particle rapidity after renewal and position, speed and the position of population are determined, if particle rapidity exceedes searching
Rope velocity interval, the upper lower limit value with search speed scope is as particle rapidity, if particle rapidity exceedes search space, to search for sky
Between border be particle position.
In the step (1), the object function of Reactive Power Optimazation Problem includes that the active loss of reduction system, reduction voltage are inclined
Difference, reduction investment cost reduce environmental pollution.
In the step (2), to each particle, by the fitness value of current particle and the fitness value ratio of individual optimal solution
Compared with, if the fitness value of current particle is more preferably, determine particle current location, update individual optimal solution, by renewal after current grain
The fitness value of sub- individual optimal solution compares with the fitness value of globally optimal solution, if the fitness value of particle individual optimal solution
It is more excellent, then globally optimal solution is updated, determine particle current location.
In the step (3), speed update method is：Speed after renewal be equal to former speed be multiplied by the value of inertia weight with
Studying factors are multiplied by and are uniformly distributed the random value of middle extraction and are multiplied by the particle for updating and determining when individual optimal solution and globally optimal solution
Position and original position difference and.
In the step (3), location updating method is, the position after renewal be equal to after updating front position and updating speed it
With.
The particle in the population after renewal is sampled using Metropolis-Hasting algorithms, it is determined that of future generation
The method of particle, specifically includes：
(I) Metropolis-Hasting sampling is carried out to particle, recommends distribution to use normal distribution, calculated and receive general
Rate, the comparing of random number and acceptance probability by extracting, it is determined that particle of future generation；
(II) check whether to meet termination condition, if it is satisfied, then terminating to calculate, export optimum results, otherwise, be transferred to profit
The step of being optimized to each particle in population of future generation with particle swarm optimization algorithm.
In the step (II), check whether to meet termination condition, if iterations reaches maximum iteration, or
Final result is then calculated and terminated less than given convergence precision, and output result.
Each variable parameter of optimum results including particle optimal solution, i.e. constituent particle, and according to this solution to power network without
The additional results such as system losses, voltage level, investment, environmental after work(optimization.
Beneficial effects of the present invention are：
(1) present invention incorporates two kinds of characteristics of algorithm, PSO algorithms it is simple, be easily achieved, fast convergence rate, adjustment
On the basis of the few advantage of parameter, population diversity can be strengthened, effectively overcome the shortcoming of local convergence, calculating speed is fast, calculates
Precision is higher；
(2) present invention can solve electric power based on Metropolis-Hastings with the Reactive Power Optimization Algorithm for Tower that PSO is combined
System Reactive Power optimization problem, makes reactive power optimization result more reasonable, effectively improves system voltage level, reduces grid and damages
Consumption, ensures power system security economical operation.
Brief description of the drawings
Fig. 1 is schematic flow sheet of the invention.
Specific embodiment：
The invention will be further described with embodiment below in conjunction with the accompanying drawings.
As shown in figure 1, performing step 01, start；
Then, step 02 is performed, initialization generates initial population.Population scale N and dimension d is set；Determine particle group
Into, including generator terminal voltage amplitude, load tap changer position, reactive power compensator compensation capacity, distributed power source go out
Power etc.；Each particle is made up of these variables, and the quantity of these variables determines dimensionality of particle d, random initializtion particle
The position X of groupi=(Xi1,Xi2,...,Xid) and speed Vi=(Vi1,Vi2,...,Vid)；It is the individual of each particle to make current location
Body history optimal solution pbesti, relatively more individual history optimal solution pbesti, find out globally optimal solution gbest；Search space is set
[Xmin,Xmax], search speed scope [- Vmax,Vmax], Studying factors C1And C2, algorithm maximum iteration TmaxOr convergence precision
ε；It is normal distribution；Inertia weight ω computing formula are determined, for example with formula is calculated as below：
T in formulamaxIt is maximum iteration；T is current iteration number of times；ωt、ωmax、ωminIt is respectively the t times iteration
Inertia weight, inertia weight allow maximum, the minimum value of value.
Then, step 03 is performed, each particle is evaluated, the object function of Reactive Power Optimazation Problem is usually that reduction system has
Work(is lost, and reduces voltage deviation, and investment cost is few, and environmental pollution is small etc., and the fitness of each particle is calculated according to object function
Value；
After execution of step 03, step 04 is performed, to each particle, by the fitness value and individual optimal solution of current particle
pbestiFitness value compare, if current particle fitness value more preferably, current particle position is set to Pi, and update
Individual optimal solution pbesti；By current particle individual optimal solution pbestiFitness value and globally optimal solution gbest fitness
Value compares, if particle individual optimal solution pbestiFitness value it is more excellent, then update globally optimal solution gbest, correspondence particle
Position is set to Pg；
Then, step 05 is performed, speed and the position of each particle is updated with equation below.
Vi(t+1)=ωt×Vi(t)+C1×r1×(Pi(t)-Xi(t))+C2×r2×(Pg(t)-Xi(t))
r1And r2It is the random number extracted from [0,1] is uniformly distributed.
Xi(t+1)=Xi(t)+Vi(t+1)
If particle rapidity is more than Vmax, then speed is set to Vmax, if less than-Vmax, then be set to speed-
Vmax.If particle position exceeds Xmax, then particle position is set to XmaxIf exceeding Xmin, then particle position is set to
Xmin；
Then, step 06 is performed, Metropolis-Hasting sampling is carried out to particle.Determine initial distribution π (X), push away
Recommend and be distributed as normal distribution, make particle nearby random search in the form of normal distribution, obtain particle of future generation.
Then, step 07 is performed, acceptance probability is calculated as follows.
Then, step 08 is performed, extraction random number u is uniformly distributed from [0,1], be compared with acceptance probability, pressed
Equation below determines particle of future generation.
Then step 09 is performed, checks whether to meet iteration termination condition, if iterations reaches maximum iteration
Tmax, or final result less than given convergence precision ε, then calculating terminates, and output result, otherwise goes to step 03.
Finally, step 10 is performed, is terminated.
Above-mentioned all steps are completed in MATLAB emulation platforms.
Although above-mentioned be described with reference to accompanying drawing to specific embodiment of the invention, not to present invention protection model
The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not
Need the various modifications made by paying creative work or deformation still within protection scope of the present invention.
Claims (9)
1. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings, it is characterized in that：Including：According to
Electric network composition sets up primary group, sets population initial parameter, using particle swarm optimization algorithm to every in primary group
Individual particle is optimized, and finds the optimal solution of population, updates population, using Metropolis-Hasting algorithms to updating
The particle in population afterwards is sampled, it is determined that particle of future generation, repeated optimization, the operation of renewal population, continuous iteration
Until population meets idle work optimization termination condition, idle work optimization result is exported, carry out reactive power optimization of power system；According to power network
Structure sets up primary group, and the specific method for setting population initial parameter includes：
A () sets population scale, dimension, determine that particle is constituted according to electric network composition, initializes position and the speed of population；
B () sets the individual history optimal solution that current location is each particle, relatively more individual history optimal solution determines global optimum
Solution；Search space, search speed scope are set, termination condition and inertia weight is met；
Inertia weight ω computing formula are determined, using formula is calculated as below：
T in formulamaxIt is maximum iteration；T is current iteration number of times；ωt、ωmax、ωminIt is respectively the t times inertia power of iteration
Weight, inertia weight allow maximum, the minimum value of value.
2. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 1,
It is characterized in that：In the step (a), particle composition includes generator terminal voltage amplitude, load tap changer position, idle benefit
Repay device compensation capacity and distributed power source is exerted oneself.
3. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 2,
It is characterized in that：In the step (b), termination condition is algorithm maximum iteration or convergence precision.
4. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 1,
It is characterized in that：Each particle in primary group is optimized using particle swarm optimization algorithm (PSO), finds population most
Excellent solution, the method for updating population, specifically includes：
(1) each particle is evaluated, the object function according to Reactive Power Optimazation Problem calculates the fitness value of each particle；
(2) by the comparing to each particle fitness value and individual optimal solution, individual optimal solution is updated；By to current particle
The fitness value of individual optimal solution and the fitness value of globally optimal solution compare, and update globally optimal solution；
(3) according to the particle rapidity after renewal and position, speed and the position of population are determined, if particle rapidity exceedes search speed
Degree scope, the upper lower limit value with search speed scope is as particle rapidity, if particle rapidity exceedes search space, with search space
Border is particle position.
5. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 4,
It is characterized in that：In the step (1), the object function of Reactive Power Optimazation Problem includes that the active loss of reduction system, reduction voltage are inclined
Difference, reduction investment cost reduce environmental pollution.
6. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 4,
It is characterized in that：In the step (2), to each particle, by the fitness value of current particle and the fitness value of individual optimal solution
Compare, if the fitness value of current particle is more preferably, determine particle current location, update individual optimal solution, by renewal after it is current
The fitness value of particle individual optimal solution compares with the fitness value of globally optimal solution, if the fitness of particle individual optimal solution
Value is more excellent, then update globally optimal solution, determines particle current location.
7. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 4,
It is characterized in that：In the step (3), speed update method is：Speed after renewal is equal to the value that former speed is multiplied by inertia weight
It is multiplied by with Studying factors and is uniformly distributed the random value of middle extraction and is multiplied by the grain for updating and determining when individual optimal solution and globally optimal solution
Sub- position and original position difference and；
In the step (3), location updating method is that the position after renewal is equal to speed sum after updating front position and updating.
8. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 1,
It is characterized in that：The particle in the population after renewal is sampled using Metropolis-Hasting algorithms, is determined next
For the method for particle, specifically include：
(I) Metropolis-Hasting sampling is carried out to particle, acceptance probability is calculated, it is general by the random number and receiving that extract
The comparing of rate, it is determined that particle of future generation；
(II) check whether to meet termination condition, if it is satisfied, then terminating to calculate, export optimum results, otherwise, be transferred to and utilize grain
The step of subgroup optimized algorithm is optimized to each particle in population of future generation；
(III) in Metropolis-Hasting algorithms, distribution is recommended to use normal distribution.
9. a kind of idle work optimization method being combined with PSO based on Metropolis-Hastings as claimed in claim 8,
It is characterized in that：In the step (II), check whether to meet termination condition, if iterations reaches maximum iteration, or
Person's final result is then calculated and terminated less than given convergence precision, and output result.
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| CN103152014A (en) * | 2013-01-30 | 2013-06-12 | 中国人民解放军理工大学 | Implementation method of Metropolis-Hastings variation particle swarm resampling particle filter |
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