CN1564416A - Reactive optimizing method of power system based on coordinate evolution - Google Patents

Abstract

The method includes following steps: dividing control variables (as plant or animal communities) for system reactive optimization into several groups, and each variable is corresponding to a flock in coevolution method; inputting original data, initializing each flock, calculating adaptation function value of each chromosome in initial flocks; based on previous generation, generating new generation through genetics operations of selection, chiasma, variation; calculating adaptation function value fro new generation; selecting optimum chromosome; evolutionary optimization of ecosystem is completed after optimizing each flock; determining whether condition of convergence of genetic algorithm is met, and outputting optimized result. In the invention, problem to be solved is mapped to ecosystem including multiple flocks. Coevolution of interactive flocks makes optimization of system.

Description

Reactive power optimization of power system method based on coevolution

Technical field

The present invention relates to a kind of method that is used for the power system reactive power power optimization, particularly a kind of reactive power optimization of power system method based on coevolution

Background technology

In electric power system, need carry out the reactive power management with control voltage levvl and reduction active loss.REACTIVE POWER means commonly used have generator voltage, load tap changer position, shunt capacitor and reactor group etc.Reactive management in the electric power system can be divided into again: reactive power planning, reactive power operation planning, reactive power scheduling and control etc.Reactive power planning is installation site and the quantity of determining reactive apparatus in the system, should reduce the investment of reactive apparatus, the idle operation of optimization system again; Reactive power operation planning is to utilize existing reactive apparatus to come the idle operation conditions of improvement system, promptly controls voltage levvl and reduces active loss; The purpose of reactive power scheduling and control is to optimize the real time execution of reactive apparatus, finishes in former seconds to a few hours at scheme implementation.All can set up Optimization Model to these a few class reactive management problems.

The Mathematical Modeling of 1 idle work optimization problem

Reactive power optimization of power system, be meant by reasonable disposition the reactive-load compensation equipment installation site and the capacity of (comprising shunt capacitor and reactor), the on-load transformer tap changer gear, idle the exerting oneself of generator/compensator (or respective nodes voltage magnitude), under the various constraintss that satisfy system's operation, make that the rate of qualified voltage of system's operation is the highest, active loss is minimum.Its Mathematical Modeling is as follows:

1) system load flow constraint equation

Variable in the idle work optimization problem can be divided into control variables and state variable, and control variables is each node building-out capacitor (reactance) value C, on-load tap-changing transformer no-load voltage ratio T, adjustable voltage generator set end voltage V _gState variable is that node voltage V and generator inject idle Q _gTherefore the power flow equation formula can be write as the succinct form that control variables and state variable are represented

H(V，Q _g，C，T，V _g)＝0；?????????????????????????????(1)

2) variable bound condition

The variable bound condition is divided control variables constraints and state variable constraints.As follows respectively:

The control variables constraint

C _min≤C≤C _max；T _min≤T≤T _max；V _gmin≤V _g≤V _gmax????????????????(2)

The state variable constraint

V _min≤V≤V _max；Q _gmin≤Q _g≤Q _gmax???????????????????????????????(3)

3) augmented objective function

The purpose of idle work optimization is to satisfy the investment that reduces reactive apparatus under the situation of various constraintss and reducing active loss.For the state variable constraint, need be write as the form of penalty function.The general objectives function of idle work optimization can be written as:

minF＝f+P _v+P _Q

Wherein f is a target to be optimized, can be write as different forms for different idle work optimization problems: in the reactive power planning problem, f is reactive apparatus investment cost and operating cost and electric energy loss expense sum; For idle operation planning problem, f is network loss; For reactive power scheduling and control problem, be the target that actual idle operation will be optimized.

For example, for the reactive power operation planning problem, target function can be written as:

minF＝ΔP+P _v+P _Q???????????????????????????????????????????????(4)

Δ P is active loss in the formula, P _v, P _QBe respectively the out-of-limit and idle out-of-limit penalty term of voltage.

For other idle work optimization problems, can write out corresponding target function according to the optimization aim of reality.

The existing method of 2 idle work optimization problems

From mathematics, above-mentioned all kinds of idle work optimization problems all are high dimension, non-protruding, discrete, nonlinear complicated optimum problem, and it is very big to find the solution difficulty, and existing derivation algorithm has genetic algorithm, simulated annealing, Tabu search method, interior point method etc.Wherein genetic algorithm is to use more class methods in idle work optimization, and genetic algorithm is a kind of computation model that solves optimization problem by the simulating nature evolutionary process.

Utilize the genetic algorithm for solving optimization problem, at first tackle point in this problem feasible zone encode (the most frequently used is binary coding), then in feasible zone some codings of random choose form as the evolution starting point the 1st generation code set, and calculate the target function value that each is separated.Use for reference the term in the biology, be called chromosome corresponding to the coding of feasible solution, each of evolutionary process is called population for chromosome, and the target function value of feasible solution (through after certain conversion) is as chromosomal fitness.Use for reference living nature natural selection and natural genetic mechanism, utilize to select operator from each for press the chromosome sample of the big or small random choose chromosome of fitness before the population as reproductive process, choice mechanism should guarantee that fitness high dyeing body can keep more sample, and the chromosome that fitness is lower then keeps less sample or is eliminated.In reproductive process subsequently, genetic algorithm is used intersection and the two kinds of operators that make a variation carry out genetic manipulation to the sample after selecting, two chromosomal some positions that crossover operator is selected at random, mutation operator then directly reverses to a certain position of the random choose in the chromosome.Just produce population of future generation by the genetic manipulation of selecting and intersect, make a variation like this, repeated above-mentioned selection and genetic process, till termination condition is met.The optimal solution of evolutionary process in last generation separated the resulting final result of optimization problem with genetic algorithm exactly.

The concrete scheme that the employing genetic algorithm is carried out idle work optimization is as follows:

1) adapts to function:,, adapt to function and be chosen for for the target function of (4) formula for meeting the characteristics of genetic algorithm maximizing

$\mathrm{fitness}=\frac{C}{F}.$

2) chromosome coding: with compensation condenser (reactor) group number, on-load transformer tap changer gear and adjustable voltage generator terminal voltage, it is encoded into symbol string (chromosome) by certain compound mode, each chromosome i.e. body one by one, separate for one of the expression optimization problem, i.e. X=[SC|TP|VG].Or be written as:

X＝[SC ₁，SC ₂，K，SC _n，TP ₁，TP ₂，K，TP _m，VG ₁，VG ₂，K，VG _l]

c _i＝SC _i·Δc _i

t _i＝1.0+TP _i·Δt _i

v _i＝v _i0+VG _i·Δv _i

SC wherein _iX is the encoded radio of i building-out capacitor (reactance), TP _iBe the encoded radio of i load tap changer gear, VG _iBe the encoded radio of i platform generator voltage adjustment amount, be discrete variable.N is the number of building-out capacitor (reactance) device mounting points; M is the number of on-load tap-changing transformer; 1 is the adjustable voltage generator number.Δ c _i, Δ t _iWith Δ v _iBe respectively the step-length of building-out capacitor (reactance) step-length, every grade of tap no-load voltage ratio of transformer and generator voltage.c _iBe the capacity of i building-out capacitor (reactance), t _iBe the no-load voltage ratio of i load tap changer, v _I0Be i the former terminal voltage of generator, v _iBe i generator voltage.

3) genetic manipulation:

Select---choose from population by certain probability and some chromosome is used to raise up seed as parents, producing new chromosome joins in the population of future generation, allow the good chromosome that is suitable for living environment that the chance that more raises up seed is arranged, thereby make good characteristic be able to heredity.

Intersect---for choose be used to breed each to chromosome, select same position randomly, parents' chromosome at this location swap, is formed two new chromosomes.

Variation---for by the new chromosome of selecting and interlace operation generates, for chromosomal each gene, all be changed to new value with certain probability, mutation operation can be introduced new information in chromosome.

Genetic algorithm has following characteristics:

1) genetic algorithm is that coding (being chromosome) to the problem parameter is evolved, rather than directly parameter itself is optimized;

2) search procedure of genetic algorithm is to begin search from the code set (being initial population) that problem is separated, rather than separates from single, can realize multipath search, provides the optimum on the global sense, inferior excellent multiple prioritization scheme.

3) genetic algorithm uses this information of target function value (fitness) of feasible solution to search for, and does not need other information such as derivative;

4) selection, intersection, these three operators that make a variation of genetic algorithm use all are random operations, rather than determine rule.

Genetic algorithm is with its distinctive adaptability, both solved the reactive power optimization of power system problem because of non-protruding, discrete, the non-linear problem that is difficult to optimize, can avoid the dimension calamity again, find globally optimal solution, be a kind of comparatively effective method of finding the solution the reactive power optimization of power system problem.But owing to need search for fully in solution space, amount of calculation is very big, and for larger practical power systems, computing time is long, and the problem of convergence too early can occur, is absorbed in locally optimal solution, therefore often is difficult to drop into practical.In modern power systems, often need the idle subregion of carrying out is optimized, realize idle in-situ balancing, avoid idle long-distance transmissions; Or carry out the optimal control of component voltage level to idle, so that realize the classification adjustment of voltage; Maybe to consider multi-period idle coordination optimization strategy.These problems have all increased the difficulty of finding the solution of idle work optimization problem.

Summary of the invention

The object of the present invention is to provide a kind of ecosystem that problem to be optimized is mapped as a plurality of populations compositions, each groupy phase mutual effect in the ecosystem, the common evolution, thereby make the continuous evolution of whole system, reach the reactive power optimization of power system method based on coevolution of problem final optimization pass purpose with evolvement of Ecosystem.

For achieving the above object, the method that the present invention adopts is:

1) at first system's idle work optimization control variables is divided into some groups by the population division methods, every group of population corresponding to Cooperative Evolutionary;

2) input initial data;

3) each population to coevolution carries out initialization;

1. each population is carried out loop control;

2. each population is encoded and generate initial population respectively at random;

3. calculate each chromosomal adaptation functional value in each initial population;

4) cooperate optimization adopts the genetic algorithm evolutionary optimization for each population, and the evolution of each population operation is independently carried out;

1. each population is carried out loop control;

2. operate in selection, intersection, mutation genetic and produce population of new generation on the basis of former generation population;

3. calculate it and adapt to functional value carrying out each chromosome decoding back of population behind the genetic manipulation;

4. choose the current optimum chromosome of population and represent as chromosome, each population is carried out evolutionary optimization after, evolutionary optimization of whole ecological system is finished;

5. judge that whether the cooperate optimization condition of convergence satisfies, and satisfies as if the condition of convergence, then end loop; Otherwise, return cooperate optimization;

5) optimizing process finishes, and the result is optimized in output.

The population of system of the present invention idle work optimization control variables is divided can be according to the actual requirement of idle work optimization, and the idle work optimization control variables of whole system is divided into the M group according to the population division methods, supposes i (the group control variables availability vector Ω of 1≤i≤M) _iExpression,

${\mathrm{\Ω}}_i=[c_i^{\left(i\right)},c_2^{\left(i\right)},K,c_{n_i}^{\left(i\right)},t_1^{\left(i\right)},t_2^{\left(i\right)},K,t_{m_i}^{\left(i\right)},v_1^{\left(i\right)},v_2^{\left(i\right)},K,v_{l_i}^{\left(i\right)}](i=\mathrm{1,2},...,M)$

Wherein, c is building-out capacitor, the reactance value of compensation point, n _iIt is the number of building-out capacitor in i the population, reactor mounting points; T is the on-load tap-changing transformer no-load voltage ratio, m _iIt is on-load tap-changing transformer number in i the population; V is the adjustable voltage generator terminal voltage, l _iBe adjustable voltage generator number in i the population,

The idle control variables of whole system is Ω=[Ω ₁, Ω ₂..., Ω _i..., Ω _M];

The input initial data comprises:

A. trend calculated data: comprise a circuit-switched data, various operational mode load and generator output data;

B. various constraintss comprise control variables constraints, state variable constraints;

C. the position of reactive-load compensation equipment, capacity and cost;

D. idle control variables is described, the meaning of the idle control variables of this data description and required basic parameter when evolutionary optimization is encoded;

E. idle control variables population dividing data is promptly carried out the method that population is divided to idle control variables.

Each population of coevolution is carried out initialization to be comprised:

(1) coding also generates initial population at random

One group of idle work optimization control variables of the swarm optimization of each coevolution is for the i (group of 1≤i≤M) control variables vector Ω _i, it is encoded to the chromosome x of i population _i, be formulated as:

$X_i=[{\mathrm{SC}}_1^{\left(i\right)},{\mathrm{SC}}_2^{\left(i\right)},K,{\mathrm{SC}}_{n_i}^{\left(i\right)},{\mathrm{TP}}_1^{\left(i\right)},{\mathrm{TP}}_2^{\left(i\right)},K,{\mathrm{TP}}_{m_i}^{\left(i\right)},{\mathrm{VG}}_1^{\left(i\right)},{\mathrm{VG}}_2^{\left(i\right)},K,{\mathrm{VG}}_{l_i}^{\left(i\right)}],(i=\mathrm{1,2},K,M)$

Wherein, SC is the encoded radio of building-out capacitor, reactance, n _iIt is the number of building-out capacitor in i the population, reactor mounting points; TP is the encoded radio of on-load tap-changing transformer gear, m _iIt is on-load tap-changing transformer number in i the population; VG is the encoded radio of adjustable voltage generator terminal voltage adjustment amount, l _iBe adjustable voltage generator number in i the population, coding can adopt binary system or decimal coded,

Control variables value and its encoded radio satisfy following relation:

$c_k^{\left(i\right)}={\mathrm{SC}}_k^{\left(i\right)}\·\mathrm{\Δ}{c}_k^{\left(i\right)}$

$t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·\mathrm{\Δ}{t}_k^{\left(i\right)}$

$v_k^{\left(i\right)}=v_{k0}^{\left(i\right)}+{\mathrm{VG}}_k^{\left(i\right)}\·\mathrm{\Δ}{v}_k^{\left(i\right)}$

Wherein, Δ c _k ⁽ⁱ⁾, t _K0 ⁽ⁱ⁾, Δ t _k ⁽ⁱ⁾, v _K0 ⁽ⁱ⁾, Δ v _k ⁽ⁱ⁾Value be taken from corresponding idle control variables respectively and describe; Each evolutionary optimization population is by N _PopIndividual such chromosome is formed;

(2) chromosome fitness assessment in the initial population

Because for each population, its chromosome coding is only represented a part of control variables of idle work optimization, need to combine the idle work optimization control variables that just can obtain whole system with the idle work optimization control variables of other population chromosome representatives, therefore to i population, suppose to generate at random new chromosome x ' _i, when assessing, fitness carries out according to the following steps:

A. to X ' _iPress $t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·\mathrm{\Δ}{t}_k^{\left(i\right)}$ Decode, generate its control variables vector Ω ' _i

B. from a remaining M-1 population, respectively select a chromosome and represent X _j(1≤j≤M, j ≠ i), the representative of initial population is chosen as wherein any one chromosome, presses $t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·\mathrm{\Δ}{t}_k^{\left(i\right)}$ The decoding back generates control variables vector Ω separately _j(1≤j≤M, j ≠ i), then with Ω ' _iThe common idle control variables vector Ω ' that constitutes whole system, Ω '=[Ω ₁, Ω ₂..., Ω ' _i..., Ω _M]

C. calculate at the idle work optimization target function value F=f+P of the idle control variables of total system during by Ω ' value _v+ P _Q, for the reactive power operation planning problem, this target function is minF=Δ P+P _v+ P _Q, and try to achieve and adapt to function f itness=C/F, C is chosen as arbitrarily positive constant, as chromosome x ' _iFitness;

(3) the evolution operation of selecting, intersect, make a variation generates new population

For each population, adopt the evolution operation of selecting, intersect, make a variation to generate new population, the evolution operation of Cooperative Evolutionary can adopt any common evolution algorithm to carry out;

(4) chromosome fitness assessment in the new population

After adopting the evolution operation of selecting, intersect, make a variation to generate new population, each chromosome in the new population is carried out the fitness assessment by the step of fitness assessment, new population chromosome fitness appraisal procedure is identical with initial population chromosome fitness appraisal procedure, and (5) choose the chromosome representative of new population

Choose the current optimum chromosome of population, promptly the chromosome that fitness is the highest is represented as chromosome;

(6) judgement of optimization end condition

Whether the end condition of judging idle work optimization satisfies, and satisfies if optimize end condition, and then the idle work optimization process finishes, and the result is optimized in output; Otherwise, return each population is optimized again, optimize end condition and can be taken as evolutionary process and reach certain algebraically, or continuous some generation evolution idle work optimization target function values do not improve.

Output idle work optimization result, this result comprises:

A. the idle programme of system, the i.e. position of reactive-load compensation equipment, capacity and investment cost;

B. the idle operating scheme of system, the building-out capacitor that line modes such as promptly various fortune generator voltage scopes drop into down, capacity, load tap changer gear and the generator voltage of reactance;

C. the system load flow result of calculation after the reactive power compensation;

D. various operation constraints after the reactive power compensation.

The present invention uses for reference the coevolution mechanism of occurring in nature, on the basis of the single population evolutionary optimization of tradition method, introduce the notion of the ecosystem, the tradition evolutionary optimization is mapped as problem to be optimized the evolution of single population, and the present invention is mapped as the ecosystem that a plurality of populations are formed with problem to be optimized, each groupy phase mutual effect in the ecosystem, the common evolution, thus make the continuous evolution of whole system, reach the purpose of optimization with evolvement of Ecosystem.

Description of drawings

Fig. 1 is the exemplary plot of single system of the present invention;

Fig. 2 is an optimization method schematic diagram of the present invention;

Fig. 3 is an overview flow chart of the present invention;

Fig. 4 is coding of the present invention and generates the initial population flow chart at random;

Fig. 5 is chromosome fitness estimation flow figure in the population of the present invention;

Fig. 6 is that the present invention's select, intersect, make a variation operation of evolving generates the new population flow chart;

Fig. 7 is convergence property figure of the present invention;

Fig. 8 is the distribution map that the present invention finally separates.

Embodiment

Below in conjunction with accompanying drawing the present invention is described in further detail.

Referring to Fig. 1, principle of the present invention for convenience of explanation, having adopted a single system here is example, and this system is made up of three power supply area A, B, C, and each service area is the subproblem of an idle work optimization, in optimization, represents with a population.C wherein ₁, T ₁, G ₁Be respectively building-out capacitor (reactance), on-load tap-changing transformer, the adjustable voltage generator of regional A; C ₂, T ₂, G ₃Be respectively building-out capacitor (reactance), on-load tap-changing transformer, the adjustable voltage generator of area B; C ₃, C ₄Be respectively two building-out capacitors (reactance) of zone C, T ₃, T ₄Be respectively two on-load tap-changing transformers of zone C.The practical power systems of idle work optimization may be than single system complexity shown in Figure 1 many.

Fig. 2 has illustrated the thinking of three parts of this single system based on the idle work optimization of Cooperative Evolutionary, and promptly each idle subproblem can adopt evolution algorithm to evolve independently, and by representing the method for common construction system model to cooperate with each other with other populations.With the population A is example: population A is independently selecting the cross and variation genetic manipulation to generate new chromosome x ₁=[SC ₁, TP ₁, VG ₁, VG ₂]; When the quality that this idle work optimization subproblem of assessment is separated, need to calculate its contribution for the whole system idle work optimization, therefore choose the representative X of an idle control variables separately from population B and population C ₂=[SC ₂, TP ₂, VG ₃] and X ₃=[SC ₃, SC ₄, TP ₃, TP ₄], with the chromosome x of population A ₁The common chromosome x=[X that constitutes whole system control variables correspondence ₁, X ₂, X ₃], and then can obtain the adaptive value of total system target function, and weigh the newly-generated chromosomal adaptive value of population A with the quality of this value.The evolutionary process of population B and population C is identical therewith.Evolution and the cooperation by separately of 3 populations makes generator voltage, and load tap changer run location and reactive power compensator installation site and switching mode etc. are more and more reasonable, and the operation conditions of whole system constantly improves.This process carrying out is repeatedly optimized till the end condition until satisfy.

Referring to Fig. 3, below the content of each block diagram is carried out simple declaration:

1. frame is divided into some groups with system's idle work optimization control variables by the population division methods, every group of population corresponding to Cooperative Evolutionary;

2. frame is imported initial data;

3.～5. frame is the initialization to each population of coevolution.3. frame is the loop control to each population; 4. frame is encoded to each population and is generated initial population respectively at random; 5. frame calculates each chromosomal adaptation functional value in each initial population.

6.～10. the content of frame is the Co-evolution Optimization process, wherein 6.～9. frame is the optimizing process for each population, can adopt genetic algorithm or other evolutionary optimization algorithms, its operation of evolving is identical with common evolution algorithm, and the evolution operation of each population is independently carried out.6. frame is the loop control to each population; 7. frame operates in selection, intersection, mutation genetic and produces population of new generation on the basis of former generation population; 8. frame calculates it and adapts to functional value carrying out each chromosome decoding back of population behind the genetic manipulation; 9. frame is chosen the chromosome representative of each population; After each population carried out evolutionary optimization, evolutionary optimization of whole ecological system was finished.10. frame judges that whether the genetic algorithm converges condition satisfies, and satisfies as if the condition of convergence, then end loop; Otherwise, return 6. frame.

The frame finishes based on the reactive power optimization of power system process of coevolution, output result of calculation.

Each module detail flowchart of idle work optimization method based on coevolution below is described respectively.

1) population of idle work optimization control variables is divided

Cooperative Evolutionary at first will be carried out the population division with numerous control variables, and each population is corresponding to an idle work optimization subproblem.In the idle work optimization problem, Cooperative Evolutionary is carried out the population division according to the actual requirement of idle work optimization to control variables.As need the idle subregion of carrying out is optimized, realized idle in-situ balancing, avoid idle long-distance transmissions, just the idle control variables in the same zone can be divided into a population; Carry out the optimal control of component voltage level as need to idle, so that the classification adjustment of realization voltage can divide the idle control variables in the same electric pressure into same population; As considering multi-period idle coordination optimization, then can the idle control variables in the discontinuity surface divide same population into when same.Also multiple population division methods can be combined, select only division methods according to actual conditions.

4. frame is according to the actual requirement of idle work optimization, and the idle work optimization control variables of whole system is divided into the M group according to the population division methods, supposes i (the group control variables availability vector Ω of 1≤i≤M) _iRepresent,

${\mathrm{\Ω}}_i=[c_1^{\left(i\right)},c_2^{\left(i\right)},K,c_{n_i}^{\left(i\right)},t_1^{\left(i\right)},t_2^{\left(i\right)},K,t_{m_i}^{\left(i\right)},v_1^{\left(i\right)},v_2^{\left(i\right)},K,v_{l_i}^{\left(i\right)}],(i=\mathrm{1,2},...,M)----\left(5\right)$

Wherein, c is building-out capacitor (reactance) value of compensation point, n _iIt is the number of building-out capacitor (reactance) device mounting points in i the population; T is the on-load tap-changing transformer no-load voltage ratio, m _iIt is on-load tap-changing transformer number in i the population; V is the adjustable voltage generator terminal voltage, l _iIt is adjustable voltage generator number in i the population.

The idle control variables of whole system can be written as

Ω＝[Ω ₁，Ω ₂，...，Ω _i，...，Ω _M]????????????????????????????(6)

2) initial data input and processing

2. frame is imported initial data, and initial data comprises:

A. the trend calculated data comprises a circuit-switched data, various operational mode load and generator output data etc.

B. various constraintss comprise control variables constraints, as the capacity limit of building-out capacitor (reactance), the restriction of load tap changer gear, generator voltage scope etc.; State variable constraints is as node voltage restriction, the generator reactive power limit, the constraint of circuit trend etc.

C. the position of reactive-load compensation equipment, capacity and cost.

D. idle control variables is described, the meaning of the idle control variables of this data description and required basic parameter when evolutionary optimization is encoded:

For building-out capacitor (reactance), the form that idle control variables is described is:

Compensation point name node number building-out capacitor (reactance) step-length

name????????i????????????Δc

For the on-load tap-changing transformer no-load voltage ratio, the form that idle control variables is described is:

Every grade of tap no-load voltage ratio of the non-standard no-load voltage ratio side gusset of transformer name standard no-load voltage ratio side gusset number former no-load voltage ratio

name???????i????????j????????????t ₀????????Δt

For generator voltage, the form that idle control variables is described is:

Generator name node number primary voltage voltage step size

name????????i???????v ₀?????Δv

E. idle control variables population dividing data is promptly carried out the method that population is divided to idle control variables, can describe the additional sign in back in idle control variables and illustrate.

3) coding also generates initial population at random

4. the frame coding also generates initial population at random.One group of idle work optimization control variables of the swarm optimization of each coevolution is for the i (group of 1≤i≤M) control variables vector Ω _i, it is encoded to the chromosome x of i population _i, be formulated as:

$X_i=[{\mathrm{SC}}_1^{\left(i\right)},{\mathrm{SC}}_2^{\left(i\right)},K,{\mathrm{SC}}_{n_i}^{\left(i\right)},{\mathrm{TP}}_1^{\left(i\right)},{\mathrm{TP}}_2^{\left(i\right)},K,{\mathrm{TP}}_{m_i}^{\left(i\right)},{\mathrm{VG}}_1^{\left(i\right)},{\mathrm{VG}}_2^{\left(i\right)},K,{\mathrm{VG}}_{l_i}^{\left(i\right)}],(i=\mathrm{1,2},K,M)----\left(7\right)$

Wherein, SC is the encoded radio of building-out capacitor (reactance) c, n _iIt is the number of building-out capacitor (reactance) device mounting points in i the population; TP is the encoded radio of on-load tap-changing transformer gear, m _iIt is on-load tap-changing transformer number in i the population; VG is the encoded radio of adjustable voltage generator terminal voltage adjustment amount, l _iIt is adjustable voltage generator number in i the population.Coding can adopt binary system or decimal coded.

Control variables value and its encoded radio satisfy following relation:

$c_k^{\left(i\right)}={\mathrm{SC}}_k^{\left(i\right)}\·\mathrm{\Δ}{c}_k^{\left(i\right)}$

$t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·\mathrm{\Δ}{t}_k^{\left(i\right)}----\left(8\right)$

$v_k^{\left(i\right)}=v_{k0}^{\left(i\right)}+{\mathrm{VG}}_k^{\left(i\right)}\·\mathrm{\Δ}{v}_k^{\left(i\right)}$

Wherein, Δ c _k ⁽ⁱ⁾, t _K0 ⁽ⁱ⁾, Δ t _k ⁽ⁱ⁾, v _K0 ⁽ⁱ⁾, Δ v _k ⁽ⁱ⁾Value be taken from corresponding idle control variables respectively and describe.

Each evolutionary optimization population is by N _PopIndividual such chromosome is formed.4. the detailed process of frame such as Fig. 5.

4) chromosome fitness assessment in the initial population

5. frame is assessed each chromosomal fitness in the population.Because for each population, its chromosome coding is only represented a part of control variables of idle work optimization, need to combine the idle work optimization control variables that just can obtain whole system with the idle work optimization control variables of other population chromosome representatives, therefore to i population, suppose to generate at random new chromosome x ' _i, when assessing, fitness need carry out the calculating of following steps:

A. to X ' _iBy formula decode (8), generates its control variables vector Ω ' _i

B. from a remaining M-1 population, respectively select a chromosome and represent X _j(1≤j≤M, j ≠ i), the representative of initial population is chosen as wherein any one chromosome, and by formula (8) decoding back generates control variables vector Ω separately _j(1≤j≤M, j ≠ i), then with Ω ' _iThe common idle control variables vector Ω ' that constitutes whole system.

Ω′＝[Ω ₁，Ω′ ₂，...，Ω′ _i...，Ω _M]

C. by formula (4) calculate the idle work optimization target function value F when the idle control variables of total system press Ω ' value, and try to achieve and adapt to function f itness=C/F (C is chosen as arbitrarily just constant), as chromosome x ' _iFitness.

5. the detailed process of frame such as Fig. 6.

5) selection, intersection, variation etc. are evolved to operate and are generated new population

7. frame is the main process of evolutionary optimization, for each population, adopts selection, intersection, variation etc. to evolve and operates the generation new population.The evolution operation of Cooperative Evolutionary can adopt any common evolution algorithm such as genetic algorithm, evolutional programming or evolution strategy etc. to carry out, and is example with the genetic algorithm, its detailed process such as Fig. 7.

6) chromosome fitness assessment in the new population

After adopting evolution operations such as selection, intersection, variation to generate new population, carry out the fitness assessment to each chromosome in the new population.8. frame is assessed each chromosomal fitness in the population.Because for each population, its chromosome coding is only represented a part of control variables of idle work optimization, need to combine the idle work optimization control variables that just can obtain whole system with the idle work optimization control variables of other population chromosome representatives, therefore to i population, suppose to operate by evolving the new chromosome x of generation ' _i, when fitness is assessed, need carry out the calculating identical with (5).

7) chromosome of choosing new population is represented

Described in (5), in population of assessment during chromosomal fitness, the idle work optimization control variables of acquisition whole system of could decoding combine with the chromosome representative of other population.For each population, it is very big to the optimization influential effect of idle work optimization how to choose the chromosome representative.9. frame is chosen the current optimum chromosome of population, and promptly the chromosome that fitness is the highest is represented as chromosome.

8) judgement of optimization end condition

10. frame judges whether the end condition of idle work optimization satisfies.Satisfy if optimize end condition, then the idle work optimization process finishes, and the result is optimized in output; Otherwise, return each population be optimized again.The optimization end condition can be taken as evolutionary process and reaches certain algebraically, or continuous some generation evolution idle work optimization target function values do not improve.

9) idle work optimization result's output

frame output idle work optimization result of calculation, this result comprises:

A. the idle programme of system, the i.e. position of reactive-load compensation equipment, capacity and investment cost etc.

B. the idle operating scheme of system, capacity, load tap changer gear and the generator voltage etc. of the building-out capacitor (reactance) that line modes such as promptly various fortune generator voltage scopes drop into down.

C. the system load flow result of calculation after the reactive power compensation.

D. after the reactive power compensation various operations constraint as the situation that satisfies of node voltage restriction, the generator reactive power limit, the constraint of circuit trend etc.

Compare with genetic algorithm, the present invention is having very strong advantage aspect the searching idle work optimization problem globally optimal solution, and convergence is good, the quality height of separating.The directly parallelization of this method improves optimal speed greatly.

Adopt Cooperative Evolutionary that the reactive power operation planning problem of China's somewhere practical power systems is optimized.There are 120 nodes, 142 branch roads in this system, 2 generators, 41 on-load tap-changing transformers, 35 reactive power compensation points, and the permission span of load bus voltage is 1.0-1.10, the population here is to divide by power supply area.

The optimization effect of Cooperative Evolutionary

Certain real system of table 1 is optimized the result

Before and after optimizing	Active power loss (MW)	Load bus voltage			Out-of-limit some number of voltage
						Maximum	Minimum value	Mean value
		Before the optimization	???6.42	???1.102					???0.943	???1.0334	?????3
After the optimization	???6.11				???1.088	???1.004	???1.0563	?????0

As can be seen from Table 1, optimize back system voltage level and improve, eliminated voltage and crossed the border a little, and network loss reduced by 4.83%, system's operation is reasonable more economically.

Constringency performance is analyzed

Convergence property of the present invention as shown in Figure 7, abscissa is taken as idle work optimization target function calculation times, ordinate is taken as the chromosome fitness, i.e. fitness=500/F (F is the idle work optimization target function value), this value is big more to show that the idle operation of system is reasonable more.Contrast simple generic algorithm and Cooperative Evolutionary can see that Cooperative Evolutionary can effectively jump out local optimum point and seek better global optimization the optimization of fairly large system, and its good convergence is better than simple generic algorithm greatly.

The quality of optimizing

Simple generic algorithm and Cooperative Evolutionary are calculated respectively 100 times, and transverse axis is taken as the network loss optimal value, and the longitudinal axis is taken as the occurrence number of this network loss optimal value, and the distribution situation of separating as shown in Figure 8.

As can be seen from Figure 8, the result of common genetic algorithm for solving relatively disperses and is difficult to find optimization solution preferably, and the quality of finding the solution of Cooperative Evolutionary has significant improvement.The optimization solution that Cooperative Evolutionary can find simple generic algorithm to be difficult to find; The quality height of separating, the probability that optimization solution occurs is higher, is the very effective method of finding the solution the idle work optimization problem.

Claims (5)

1, a kind of reactive power optimization of power system method based on coevolution is characterized in that carrying out according to the following steps:

1) at first system's idle work optimization control variables is divided into some groups by the population division methods, every group of population corresponding to Cooperative Evolutionary;

2) input initial data;

3) each population to coevolution carries out initialization;

1. each population is carried out loop control;

2. each population is encoded and generate initial population respectively at random;

3. calculate each chromosomal adaptation functional value in each initial population;

4) cooperate optimization adopts the genetic algorithm evolutionary optimization for each population, and the evolution of each population operation is independently carried out;

1. each population is carried out loop control;

2. operate in selection, intersection, mutation genetic and produce population of new generation on the basis of former generation population;

3. calculate it and adapt to functional value carrying out each chromosome decoding back of population behind the genetic manipulation;

4. choose the current optimum chromosome of population and represent as chromosome, each population is carried out evolutionary optimization after, evolutionary optimization of whole ecological system is finished;

5. judge that whether the cooperate optimization condition of convergence satisfies, and satisfies as if the condition of convergence, then end loop; Otherwise, return cooperate optimization;

5) optimizing process finishes, and the result is optimized in output.

2, the reactive power optimization of power system method based on coevolution according to claim 1, it is characterized in that: the population of said system idle work optimization control variables is divided can be according to the actual requirement of idle work optimization, the idle work optimization control variables of whole system is divided into the M group according to the population division methods, supposes i (the group control variables availability vector Ω of 1≤i≤M) _iExpression,

${\mathrm{\Ω}}_i=\[c_1^{\left(i\right)},c_2^{\left(i\right)},K,c_{n_i}^{\left(i\right)},t_1^{\left(i\right)},t_2^{\left(i\right)},K,t_{m_i}^{\left(i\right)},v_1^{\left(i\right)},v_2^{\left(i\right)},K,v_{l_1}^{\left(i\right)}\](i=\mathrm{1,2},...,M)$

Wherein, c is building-out capacitor, the reactance value of compensation point, n _iIt is the number of building-out capacitor in i the population, reactor mounting points; T is the on-load tap-changing transformer no-load voltage ratio, m _iIt is on-load tap-changing transformer number in i the population; V is the adjustable voltage generator terminal voltage, l _iBe adjustable voltage generator number in i the population,

The idle control variables of whole system is Ω=[Ω ₁, Ω ₂..., Ω _i..., Ω _M].

3, the reactive power optimization of power system method based on coevolution according to claim 1, it is characterized in that: said input initial data comprises:

A. trend calculated data: comprise a circuit-switched data, various operational mode load and generator output data;

B. various constraintss comprise control variables constraints, state variable constraints;

C. the position of reactive-load compensation equipment, capacity and cost;

D. idle control variables is described, the meaning of the idle control variables of this data description and required basic parameter when evolutionary optimization is encoded;

E. idle control variables population dividing data is promptly carried out the method that population is divided to idle control variables.

4, the reactive power optimization of power system method based on coevolution according to claim 1 is characterized in that: said each population to coevolution carries out initialization and comprises:

(1) coding also generates initial population at random

One group of idle work optimization control variables of the swarm optimization of each coevolution is for the i (group of 1≤i≤M) control variables vector Ω _i, it is encoded to the chromosome x of i population _i, be formulated as:

$X_i=\[{\mathrm{SC}}_1^{\left(i\right)},{\mathrm{SC}}_2^{\left(i\right)},K,{\mathrm{SC}}_{n_i}^{\left(i\right)},{\mathrm{TP}}_1^{\left(i\right)},{\mathrm{TP}}_2^{\left(i\right)},K,{\mathrm{TP}}_{m_i}^{\left(i\right)},{\mathrm{VG}}_1^{\left(i\right)},{\mathrm{VG}}_2^{\left(i\right)},K,{\mathrm{VG}}_{l_i}^{\left(i\right)}\],(i=\mathrm{1,2},K,M)$

Wherein, SC is the encoded radio of building-out capacitor, reactance, n _iIt is the number of building-out capacitor in i the population, reactor mounting points; TP is the encoded radio of on-load tap-changing transformer gear, m _iIt is on-load tap-changing transformer number in i the population; VG is the encoded radio of adjustable voltage generator terminal voltage adjustment amount, l _iBe adjustable voltage generator number in i the population, coding can adopt binary system or decimal coded, and control variables value and its encoded radio satisfy following relation:

$c_k^{\left(i\right)}={\mathrm{SC}}_k^{\left(i\right)}\·\mathrm{\Δ}{c}_k^{\left(i\right)}$

$t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·{\mathrm{\Δt}}_k^{\left(i\right)}$

$v_k^{\left(i\right)}=v_{k0}^{\left(i\right)}+{\mathrm{VG}}_k^{\left(i\right)}\·{\mathrm{\Δv}}_k^{\left(i\right)}$

Wherein, Δ c _k ⁽ⁱ⁾, t _K0 ⁽ⁱ⁾, Δ t _k ⁽ⁱ⁾, v _K0 ⁽ⁱ⁾, Δ v _k ⁽ⁱ⁾Value be taken from corresponding idle control variables respectively and describe; Each evolutionary optimization population is by N _PopIndividual such chromosome is formed;

(2) chromosome fitness assessment in the initial population

Because for each population, its chromosome coding is only represented a part of control variables of idle work optimization, need to combine the idle work optimization control variables that just can obtain whole system with the idle work optimization control variables of other population chromosome representatives, therefore to i population, suppose to generate at random new chromosome x _i', when assessing, fitness carries out according to the following steps:

A. to X _i' press $t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·{\mathrm{\Δt}}_k^{\left(i\right)}$ Decode, generate its control variables vector Ω _i';

B. from a remaining M-1 population, respectively select a chromosome and represent X _j(1≤j≤M, j ≠ i), the representative of initial population is chosen as wherein any one chromosome, presses $t_k^{\left(i\right)}=t_{k0}^{\left(i\right)}+{\mathrm{TP}}_k^{\left(i\right)}\·{\mathrm{\Δt}}_k^{\left(i\right)}$ The decoding back generates control variables vector Ω separately _j(1≤j≤M, j ≠ i), then with Ω _i' constitute the idle control variables vector Ω ' of whole system, Ω=[Ω jointly ₁, Ω ₂..., Ω _i..., Ω _M]

C. calculate at the idle work optimization target function value F=f+P of the idle control variables of total system during by Ω ' value _V+ P _Q, for the reactive power operation planning problem, this target function is min F=Δ P+P _V+ P _Q, and trying to achieve adaptation function f itness=C/F, C is chosen as arbitrarily positive constant, as chromosome x _i' fitness;

(3) the evolution operation of selecting, intersect, make a variation generates new population

For each population, adopt the evolution operation of selecting, intersect, make a variation to generate new population, the evolution operation of Cooperative Evolutionary can adopt any common evolution algorithm to carry out;

(4) chromosome fitness assessment in the new population

After adopting the evolution operation of selecting, intersect, make a variation to generate new population, each chromosome in the new population is carried out fitness by the step of fitness assessment assess, new population chromosome fitness appraisal procedure is identical with initial population chromosome fitness appraisal procedure,

(5) chromosome of choosing new population is represented

Choose the current optimum chromosome of population, promptly the chromosome that fitness is the highest is represented as chromosome;

(6) judgement of optimization end condition

Whether the end condition of judging idle work optimization satisfies, and satisfies if optimize end condition, and then the idle work optimization process finishes, and the result is optimized in output; Otherwise, return each population is optimized again, optimize end condition and can be taken as evolutionary process and reach certain algebraically, or continuous some generation evolution idle work optimization target function values do not improve.

5, the reactive power optimization of power system method based on coevolution according to claim 1 is characterized in that: said output idle work optimization result, and this result comprises:

A. the idle programme of system, the i.e. position of reactive-load compensation equipment, capacity and investment cost;

B. the idle operating scheme of system, the building-out capacitor that line modes such as promptly various fortune generator voltage scopes drop into down, capacity, load tap changer gear and the generator voltage of reactance;

C. the system load flow result of calculation after the reactive power compensation;

D. various operation constraints after the reactive power compensation.

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