CN104348173B - It is a kind of based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth - Google Patents

It is a kind of based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth Download PDF

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CN104348173B
CN104348173B CN201410469609.3A CN201410469609A CN104348173B CN 104348173 B CN104348173 B CN 104348173B CN 201410469609 A CN201410469609 A CN 201410469609A CN 104348173 B CN104348173 B CN 104348173B
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卢道远
陈冬沣
欧周
孟安波
李专
陈智慧
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Jieyang Power Supply Bureau of Guangdong Power Grid Co Ltd
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Jieyang Power Supply Bureau Guangdong State Grid Co ltd
Guangdong University of Technology
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Abstract

The invention discloses a kind of Method for Reactive Power Optimization in Power based on improved CSO algorithms, the algorithm is a kind of based on the swarm intelligence searching algorithm for improving crossover algorithm (ICSO) in length and breadth, mainly including lateral cross, crossed longitudinally and three operators of differential variation.Lateral cross is neither repeatedly matched by all particles in population are carried out with two, between pairing particle and its outer rim is carried out search and updated;Crossed longitudinally is that all dimensions are matched, and then carries out arithmetic crossover;Differential variation finally carries out optimum selecting by entering row variation disturbance to each particle, intersecting, and three operators not only accelerate convergence rate, maintain the multiformity of population by selection operation Population Regeneration.The beneficial effects of the present invention is:The improvement of the present invention between crossover algorithm (ICSO) fast convergence rate, population Inner are individual in length and breadth communication for information completely, global convergence ability by force, particle multiformity it is good, for reactive power optimization of power system, this high-dimensional, multiple constraint, nonlinear complicated practical problem have the good suitability.

Description

It is a kind of based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth
Technical field
The present invention relates to a kind of Method for Reactive Power Optimization in Power, is calculated based on improvement CSO (ICSO) more particularly, to a kind of The Method for Reactive Power Optimization in Power of method.
Background technology
Reactive power optimization of power system has extremely important meaning to the efficient, stable of power system, economical operation.As The typical optimization problem of of power system, idle work optimization are referred on the basis of various constraintss are met, are sent out by control The extreme voltage output of motor, reactive compensation capacity, on-load transformer tap changer carry out the reactive power flow of reasonable disposition electrical network Distribution so that network outages are minimum, improves system voltage quality, and then improves safety and the economy of system.This is One non-linear, the optimization problem that various dimensions, multiple constraint, continuous and discontinuous variable combine.
In recent years, with the development of intelligent algorithm, more and more it is used based on the optimized algorithm of biocenose intelligence Come above reactive power optimization of power system problem, such as:Particle cluster algorithm (PSO), evolution algorithm (EA), genetic algorithm (GA), group search Rope algorithm (GSO), artificial bee colony algorithm (ACO), ant group algorithm (ACO), difference algorithm (DE) etc..
Though these algorithms respectively have feature, and face has made some progress to varying degrees, for power system without Work(optimizes this multiple constraint, the complicated optimum problem of non-linear, high latitude still has many drawbacks.Such as:Genetic algorithm (GA) Long operational time;Particle cluster algorithm (PSO) is easily trapped into local optimum;Evolution algorithm (EA), artificial bee colony algorithm (ACO), group The particle multiformity such as searching algorithm (GSO) are poor, and control parameter is more etc..In addition, many algorithm global convergence abilities, for idle The global convergence ability for optimizing this complex model is not strong enough, is easily trapped into local optimum.
Therefore, how to enable a kind of algorithm efficiently, quickly and accurately to converge to optimal solution and be always a technology difficulty Topic.
The content of the invention
The technical problem to be solved, is just to provide and a kind of is ensureing particle multiformity and algorithm the convergence speed Under the premise of, while and the Method for Reactive Power Optimization in Power based on improvement CSO algorithms with powerful global convergence ability.
Above-mentioned technical problem is solved, the technical solution used in the present invention is:
A kind of Method for Reactive Power Optimization in Power based on improvement CSO algorithms, it is characterised in that comprise the following steps:
S1, with the minimum object function of system active power loss, it is considered to equality constraint and inequality constraints, sets up power system Idle work optimization model;
S2, with reference to reactive power optimization of power system model initialization population;
S3, enters selection operation after execution is crossed longitudinally;
S4, enters selection operation after performing lateral cross;
S5, enters selection operation after performing differential variation;
S6, it is no that judgement reaches end condition:If reaching maximum iteration time, end loop, output result;Otherwise, turn Step 3.
In described step S1, the minimum target function type of system active power loss is:
Wherein, Ploss is system active power loss;Ui, UjIt is node i respectively, the voltage magnitude of j;Gij, θijRespectively node Conductance and phase difference of voltage between i, j;N refers to Population Size;
Equality constraint formula (2) is:
Wherein, PgiAnd PdiThe respectively active output and burden with power of node i;QgiAnd QdiThe idle output of node i respectively And load or burden without work;BijFor node i, the susceptance between j;
Inequality constraints is:
Wherein, Ugi.minAnd Ugi.maxThe respectively voltage upper and lower limit of electromotor i;Qci.minAnd Qci.maxRespectively electric capacity is mended Repay the switching group number upper and lower limit of device i;KTi.minAnd KTi.maxThe respectively tap position upper and lower limit of ULTC i; ULi.minAnd ULi.maxThe respectively voltage upper and lower limit of load bus i;QGi.minAnd QGi.maxRespectively electromotor i is idle to exert oneself Upper and lower limit;
Formula (1), (2) and (3) constitutes reactive power optimization of power system model.
Described step S2 initialization population is specially:
Setting Population Size N, control variable number D, D is dimension, including:Generator terminal voltage, UgReactive compensation capacity Qc, ULTC no-load voltage ratio KT;Maximum iteration time Maxgen, crossed longitudinally rate pvc, lateral cross rate phc, difference intersection Rate CR, random initializtion population X in the search space of problem is tieed up in D, wherein, it is X that i-th is individuali=[Xi1,Xi2,…XiD]。
In step S3, execution is crossed longitudinally to specifically include following sub-step:
S3-1 obtains parent population, namely the solution obtained after differential variation, and first on behalf of initial population;
S3-2 is normalized to the every one-dimensional of parent individuality, and formula is as follows:
Wherein, i ∈ (1, N), j ∈ (1, D);PjminAnd PjmaxRespectively jth ties up the upper and lower limit of control variable;K is current Algebraically;
S3-3 carries out two to all dimensions in population and neither repeatedly matches, and has N/2 pair, and two adjacent numbers are the sequence of pairing Number;
S3-4 is taken out per a pair in order successively, if d1, d2Bidimensional is selected;
S3-5 is in crossed longitudinally rate pvcUnder, the d of particle X (i)1And d2Dimension execution is crossed longitudinally, and formula is as follows:
MSvc(i,d1)=rX (i, d1)+(1-r)·X(i,d2)i∈N(1,M),d1,d2∈N(1,D);
Wherein, r is the uniform random number on [0,1];MSvc(i,d1) for the d of particle X (i)1Dimension filial generation;
S3-6 repeats sub-step S3-4 and step S3-5d/2 time;
S3-7 is to MDvcRenormalization is carried out, golden mean of the Confucian school solution is obtained, formula is as follows:
MSvc(i, j)=MSvc(i,j)·(Pjmax-Pjmin)+Pjmin
S3-8 performs selection operation, the solution DS that is dominant after acquisition is crossed longitudinallyvc
In step S4, perform lateral cross and specifically include following sub-step:
S4-1 obtains parent population, namely the crossed longitudinally solution DS that is dominantvc
S4-2 to population in all individualities carry out two and neither repeatedly match, have N/2 pair, two adjacent numbers are pairing Sequence number;
S4-3 is taken out per a pair in order successively, if particle X (i) and X (j) are removed;
S4-4 is in lateral cross probability PhcUnder horizontal line performed to the d dimensions of particle X (i) and X (j) intersect, formula is as follows:
MShc(i, d)=r1·X(i,d)+(1-r1)·X(j,d)+c1·(X(i,d)-X(j,d))
MShc(j, d)=r1·X(j,d)+(1-r2)·X(i,d)+c1·(X(j,d)-X(i,d))
Wherein, d ∈ (1, D);r1,r2For the uniform random number on [0,1];c1,c2For uniform between [- 1,1] Distribution random numbers;X (i, d) and X (j, d) is respectively the d dimensions of particle i and j;MShc(i, d) and MShc(j, d) is respectively horizontal Golden mean of the Confucian school solution after intersection;
S4-5 repeat steps S4-3 and step S4-4N/2 time;
S4-6 performs selection operation, obtains the solution DS that is dominant after lateral crosshc
In step S5, perform differential variation and specifically include following sub-step:
S5-1 obtains the solution DS that is dominant of parent population, i.e. lateral crosshc
S5-2 is individual to each in kth generationI ∈ (1, N), carry out mutation operation as the following formula:
Wherein, r1∈(1,N),r2∈(1,N),r3∈ (1, N), and i ≠ r1≠r2≠r3;MF ∈ [0.05,2], are scaling The factor;For individualityVariant.
S5-3 is to each individuality in populationCrossover operation is carried out, formula is as follows:
Wherein, CRFor crossover probability, 0.2 is set to;Rnb (i) is a random integers between [1, N];After intersection The experiment vector for obtaining;
S5-4 performs selection operation.Calculate trial vectorAdaptive value, if compared withIt is more excellent, thenIt is no Then,
Described selection operation is as follows:
If the adaptive value of golden mean of the Confucian school solution MS (i) is better than its parent X (i), DS (i) ← MS (i);Otherwise, DS (i) ← X (i).
Compared with prior art, the present invention has following significant effect:
(1) ICSO algorithms proposed by the present invention are simple and clear, and control parameter is few, it is easy to operate, when reducing algorithm operation Between;
(2) the crossed longitudinally and lateral cross operator used by ICSO algorithms proposed by the present invention causes population changing every time All particles or all dimensions is all made to be matched two-by-two in generation, compromise updates, competition takes excellent, takes full advantage of each in colony Individual information.And crossed longitudinally and lateral cross is alternateed and is carried out, and the optimal way of this interlock type causes particle Individual information rapidly can be spread in population, reached good alternating current function, drastically increase the complete of algorithm Office's convergence capabilities;
(3) the differential variation operator used by ICSO algorithms proposed by the present invention causes particle in quick renewal process Population diversity can be kept well, improve the ability that algorithm jumps out local optimum.
Description of the drawings
Fig. 1 is the power system embodiment IEEE-57 node system figure using the present invention;
Fig. 2 is the flow chart based on the Method for Reactive Power Optimization in Power for improving CSO algorithms of the present invention;
Fig. 3 is ICSO algorithms and original CSO algorithms and PSO convergence of algorithm curve charts.
Specific embodiment
It is illustrated in figure 1 the power system embodiment IEEE-57 node system figure using the present invention.
The system includes 7 electromotors, 3 reactive-load compensation points and 15 ULTCs.Voltage adjusting range is [0.95,1.1], reactive-load compensation are located at 18,25,53 nodes, and point 10 grades of regulations, the upper limit are respectively 0.2,0.1,0.1, have load to adjust Pressure transformer has 17 grades of regulation stalls, and no-load voltage ratio range of accommodation is [0.9,1.1].Reference power is 100MW, initial active of system Network loss is 0.3030pu.
As carried out by Fig. 2, the Method for Reactive Power Optimization in Power based on improvement CSO algorithms of the present invention is in IEEE57 nodes system Flow chart in system example, comprises the following steps:
Step 1, with the minimum object function of system active power loss, it is considered to equality constraint and inequality constraints, sets up electric power System Reactive Power Optimized model;
Step 2, with reference to reactive power optimization of power system model initialization population;
Step 3, enters selection operation after execution is crossed longitudinally;
Step 4, enters selection operation after performing lateral cross;
Step 5, enters selection operation after performing differential variation;
Step 6, end condition:If reaching maximum iteration time, end loop, output result;Otherwise, 3 are gone to step;
In the step 1, reactive power optimization of power system model includes object function and constraints, and object function is to be System active power loss, constraints include equality constraint and inequality constraints.
Concrete form with the minimum object function of system active power loss is:
Wherein, Ploss is system active power loss;Ui, UjIt is node i respectively, the voltage magnitude of j;Gij, θijRespectively node Conductance and phase difference of voltage between i, j.
Equality constraint is:
Wherein, PgiAnd PdiThe respectively active output and burden with power of node i;QgiAnd QdiThe idle output of node i respectively And load or burden without work;BijFor node i, the susceptance between j.
Inequality constraints is:
Wherein, Ugi.minAnd Ugi.maxThe respectively voltage upper and lower limit of electromotor i;Qci.minAnd Qci.maxRespectively electric capacity is mended Repay the switching group number upper and lower limit of device i;KTi.minAnd KTi.maxThe respectively tap position upper and lower limit of ULTC i; ULi.minAnd ULi.maxThe respectively voltage upper and lower limit of load bus i;QGi.minAnd QGi.maxRespectively electromotor i is idle to exert oneself Upper and lower limit;
In the step 2, initialization is specially:
Setting Population Size N=40, control variable number D=25 (i.e. dimension, including:Electromotor UgSet end voltage, idle benefit Repay capacity Qc, ULTC no-load voltage ratio KT), maximum iteration time Maxgen=200, crossed longitudinally rate pvc=1, laterally hand over Fork rate phc=0.6, difference crossing-over rate CR=0.2, random initializtion population X in the receipts rope space of problem is tieed up in D, wherein, i-th Individual is Xi=[Xi1,Xi2,...XiD]。
In the step 3, crossed longitudinally concretely comprising the following steps is performed:
(1) obtain parent population (solution for obtaining after differential variation, first on behalf of initial population);
(2) the every one-dimensional of parent individuality is normalized, formula is as follows:
Wherein, i ∈ (1, N), j ∈ (1, D);PjminAnd PjmaxRespectively jth ties up the upper and lower limit of control variable;K is current Algebraically.
(3) two neither repeatedly pairings (total N/2 to) are carried out to all dimensions in population, two adjacent numbers are the sequence of pairing Number;
(4) take out per a pair successively in order, if d1, d2Bidimensional is selected;
(5) in crossed longitudinally rate pvcUnder, the d of particle X (i)1And d2Dimension execution is crossed longitudinally, and formula is as follows:
MSvc(i,d1)=rX (i, d1)+(1-r)·X(i,d2)i∈N(1,M),d1,d2∈N(1,D)
Wherein, r is the uniform random number on [0,1];MSvc(i,d1) for the d of particle X (i)1Dimension filial generation;
(6) repeat step (4) and step (5) d/2 time;
(7) to MDvcRenormalization is carried out, golden mean of the Confucian school solution is obtained, formula is as follows:
MSvc(i, j)=MSvc(i,j)·(Pjmax-Pjmin)+Pjmin
(8) selection is performed, the solution DS that is dominant after acquisition is crossed longitudinallyvc
In the step 4, concretely comprising the following steps for lateral cross is performed:
(1) obtain parent population (the i.e. crossed longitudinally solution DS that is dominantvc);
(2) to population in all individualities carry out two neither repeatedly pairings (total N/2 to), two adjacent numbers are pairing Sequence number;
(3) take out per a pair successively in order, if particle X (i) and X (j) are removed;
(4) in lateral cross probability PhcUnder horizontal line performed to the d dimensions of particle X (i) and X (j) intersect, formula is as follows:
MShc(i, d)=r1·X(i,d)+(1-r1)·X(j,d)+c1·(X(i,d)-X(j,d))
MShc(j, d)=r1·X(j,d)+(1-r2)·X(i,d)+c1·(X(j,d)-X(i,d))
Wherein, d ∈ (1, D);r1,r2For the uniform random number on [0,1];c1,c2For uniform between [- 1,1] Distribution random numbers;X (i, d) and X (j, d) is respectively the d dimensions of particle i and j;MShc(i, d) and MShc(j, d) is respectively horizontal Golden mean of the Confucian school solution after intersection;
(5) repeat step (3) and step (4) N/2 time;
(6) selection operation is performed, obtains the solution DS that is dominant after lateral crosshc
In the step 5, comprising the following steps that for differential variation is performed:
(1) obtain parent population (the i.e. solution DS that is dominant of lateral crosshc);
(2) it is individual to each in kth generationI ∈ (1, N), carry out mutation operation as the following formula:
Wherein, r1∈(1,N),r2∈(1,N),r3∈ (1, N), and i ≠ r1≠r2≠r3;MF ∈ [0.05,2], are scaling The factor;For individualityVariant.
(3) to each individuality in populationCrossover operation is carried out, formula is as follows:
Wherein, CRFor crossover probability, 0.2 is set to;Rnb (i) is a random integers between [1, N];After intersection The experiment vector for obtaining;
(4) perform selection operation.Calculate trial vectorAdaptive value, if compared withIt is more excellent, thenIt is no Then,
Selection operation described in the step 3 and step 4, operates as follows:
If golden mean of the Confucian school solution MS (i), adaptive value be better than its parent X (i), then DS (i) ← MS (i);Otherwise, DS (i) ← X (i).
As shown in Figure 3 ICSO algorithms and original CSO algorithms and PSO convergence of algorithm curve charts, it can be seen that ICSO algorithms compared with Other two kinds of algorithms all have found more excellent solution.Although preconvergence speed is not so good as PSO algorithms, the later stage is calculated than original CSO Method and PSO algorithms will be fast, and embody more preferable global convergence performance, it is to avoid Premature Convergence.
Most there is value to contrast for IEEE57 node systems idle work optimization as shown in table 1, can be seen that by contrast, it is various meeting On the premise of constraints, after ICSO optimizations, resulting system losses are minimum, and in the reasonable scope, optimum results make us full Meaning.
Table 1

Claims (5)

1. it is a kind of based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth, it is characterised in that to comprise the following steps:
S1, with the minimum object function of system active power loss, it is considered to equality constraint and inequality constraints, sets up power system reactive power Optimized model;
S2, with reference to reactive power optimization of power system model initialization population;
S3, enters selection operation after execution is crossed longitudinally;
S4, enters selection operation after performing lateral cross;
S5, enters selection operation after performing differential variation;
S6, it is no that judgement reaches end condition:If reaching maximum iteration time, end loop, output result;Otherwise, go to step S3;
In described step S1, the minimum target function type of system active power loss is:
Wherein, Ploss is system active power loss;Ui, UjIt is the voltage magnitude of i-th and j-th node respectively;Gij, θijRespectively For conductance and phase difference of voltage between i-th and j-th node;N refers to Population Size;
Equality constraint formula is:
Wherein, PgiAnd PdiThe active output of respectively i-th node and burden with power;QgiAnd QdiThe nothing of respectively i-th node Work(is exported and load or burden without work;BijFor the susceptance between i-th node and j-th node;
Inequality constraints is:
Wherein, Ugi.minAnd Ugi.maxThe voltage upper and lower limit of respectively i-th electromotor;Qci.minAnd Qci.maxRespectively i-th electric Hold the switching group number upper and lower limit of compensator;KTi.minAnd KTi.maxOn the tap position of respectively i-th ULTC, Lower limit;ULi.minAnd ULi.maxThe voltage upper and lower limit of respectively i-th load bus;QGi.minAnd QGi.maxRespectively i-th generating The upper and lower limit that machine is idle to exert oneself;
Formula (1), (2) and (3) constitutes reactive power optimization of power system model.
2. according to claim 1 based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth, its feature exists In:Described step S2 initialization population is specially:
Setting Population Size N, control variable number D, D is dimension, including:Generator terminal voltage Ug, reactive compensation capacity Qc, have Voltage adjustment of on-load transformer voltage ratio KT;Maximum iteration time Maxgen, crossed longitudinally rate pvc, lateral cross rate phc, difference crossing-over rate CR, Random initializtion population X in the search space of problem is tieed up in D, wherein, it is X that i-th is individuali=[Xi1,Xi2,...XiD], i ∈ (1,N)。
3. according to claim 2 based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth, its feature exists In:In step S3, execution is crossed longitudinally to specifically include following sub-step:
S3-1 obtains parent population, namely the solution obtained after differential variation, and first on behalf of initial population;
S3-2 is normalized to the every one-dimensional of parent individuality, and formula is as follows:
Wherein, i ∈ (1, N), j ∈ (1, D);PjminAnd PjmaxRespectively jth ties up the upper and lower limit of control variable;K is current algebraically;
S3-3 carries out two to all dimensions in population and neither repeatedly matches, and has D/2 pair, and two adjacent numbers are the sequence number of pairing;
S3-4 is taken out per a pair in order successively, if d1, d2Bidimensional is selected;
S3-5 is in crossed longitudinally rate pvcUnder, kth for population in i-th it is individualD1And d2Dimension performs crossed longitudinally, public affairs Formula is as follows:
MSvc(i,d1)=rXk(i,d1)+(1-r)·Xk(i,d2)i∈(1,N),d1,d2∈(1,D)
Wherein, r is the uniform random number on [0,1];MSvc(i,d1) for kth it is individual for i-th in populationD1Dimension Filial generation;
S3-6 repeats sub-step S3-4 and step S3-5D/2 time;
S3-7 is to MSvcRenormalization is carried out, golden mean of the Confucian school solution is obtained, formula is as follows:
MSvc(i, j)=MSvc(i,j)·(Pjmax-Pjmin)+Pjmin
S3-8 performs selection operation, the solution DS that is dominant after acquisition is crossed longitudinallyvc
4. according to claim 3 based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth, its feature exists In:In step S4, perform lateral cross and specifically include following sub-step:
S4-1 obtains parent population, namely the crossed longitudinally solution DS that is dominantvc
S4-2 to population in all individualities carry out two and neither repeatedly match, have N/2 pair, two adjacent numbers are the sequence of pairing Number;
S4-3 is taken out in order successively per a pair, if kth for population in i-th it is individualIt is individual with j-thIt is removed;
S4-4 is in lateral cross probability PhcUnder to individualityWithD dimensions perform lateral cross, formula is as follows:
MShc(i, d)=r1·Xk(i,d)+(1-r1)·(j,d)+c1(Xk(i,d)-Xk(j,d))
MShc(j, d)=r2·Xk(j,d)+(1-r2)·Xk(i,d)+c2(Xk(j,d)-Xk(i,d))
Wherein, d ∈ (1, D);r1,r2For the uniform random number on [0,1];c1,c2For between [- 1,1] be uniformly distributed with Machine number;Xk(i, d) and Xk(j, d) is respectively d dimension of the kth for i-th and j-th individuality in population;MShc(i, d) and MShc (j, d) is respectively i-th and j-th golden mean of the Confucian school solution MS (i) after lateral cross, the d dimensions of MS (j);
S4-5 repeat steps S4-3 and step S4-4N/2 time;
S4-6 performs selection operation, obtains the solution DS that is dominant after lateral crosshc
5. according to claim 4 based on the Method for Reactive Power Optimization in Power for improving crossover algorithm in length and breadth, its feature exists In:In step S5, perform differential variation and specifically include following sub-step:
S5-1 obtains the solution DS that is dominant of parent population, i.e. lateral crosshc
S5-2 is individual for each in population to kthI ∈ (1, N), carry out mutation operation as the following formula:
Wherein, r1∈(1,N),r2∈(1,N),r3∈ (1, N), and i ≠ r1≠r2≠r3;MF ∈ [0.05,2], are zoom factor;For individualityVariant;
S5-3 is to kth for each individuality in populationCrossover operation is carried out, formula is as follows:
Wherein, CRFor difference crossover probability, 0.2 is set to;Rnb (i) is a random integers between [1, N];After intersection The trial vector for obtainingJth dimension;It is individual for i-th variation in kth+1 generation populationJth dimension;For kth It is individual for i-th in populationJth dimension;
S5-4 performs selection operation:Calculate trial vectorAdaptive value, if compared withIt is more excellent, then assignmentGiveIt is no Then, assignmentGive
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