CN103326353A - Environmental economic power generation dispatching calculation method based on improved multi-objective particle swarm optimization algorithm - Google Patents

Abstract

The invention relates to an environmental economic power generation dispatching calculation method based on an improved multi-objective particle swarm optimization algorithm. The environmental economic power generation dispatching calculation method based on the improved multi-objective particle swarm optimization algorithm comprises the following steps that an electric system environmental economic dispatching module is firstly built, wherein the electric system environmental economic dispatching module takes the lowest fuel cost and the minimum pollution gas emissions as a dispatching target and takes electric generator force outlet limit, system power balance and spinning reserve as constraint; the multi-objective particle swarm optimization algorithm is improved, the improved multi-objective particle swarm optimization algorithm is applied to electric system environmental economic dispatching calculation, an individual optimal solution is selected according to Pareto dominant conditions, a globally optimal solution is selected by the adoption of a method based on noninferior solution sparseness rank, and a slope method is put forward to delete a solution away from the Pareto optimal frontier according to the slope characteristic of the Pareto optimal frontier; finally, an eclectic optimal solution of the Pareto optimal frontier is selected by the adoption of a fuzzy mathematics method to assist a decider in selecting a dispatching scheme. The environmental economic power generation dispatching calculation method based on the improved multi-objective particle swarm optimization algorithm is simple in calculation, high in operation speed, good in stability, and easy to realize in engineering.

Description

Based on the environmental economy power generation dispatching method for solving that improves multi-target particle group algorithm

Technical field

The invention belongs to electric power system multiple-objection optimization dispatching technique field, particularly a kind of based on the environmental economy power generation dispatching method for solving that improves multi-target particle group algorithm.

Background technology

The electric power system economic dispatch is under the condition that satisfies power supply and demand balance and unit output bound, finds the solution to make system's cost of electricity-generating or the minimum scheduling scheme of fuel cost.Yet, fired power generating unit in power generation process inevitably to dusty gass such as airborne release oxysulfide, nitrogen oxide and carbon dioxide.Along with the enhancing of people's environmental consciousness, the discharge capacity of restriction dusty gas also becomes an important regulation goal of electric power system, and electric power system changes the target-rich environment economic dispatch into by original single goal economic dispatch.

Compare other reduction of discharging measures, the environmental economy scheduling enjoys researcher's favor because of its small investment instant effect.Contain the multi-objective optimization question of environmental economy scheduling factor, its early stage method for solving adopts leash law and weight coefficient and method more.Leash law is with the new constraint of dusty gas discharge index as economic dispatch, and it is found the solution and still belongs to single goal optimization, but this method is not considered the trade-off relation between environment and economy.Weight coefficient and method be a plurality of optimization aim linear combinations, thereby multiple-objection optimization is converted into single goal optimization, and this method obtains one group of Pareto optimal solution by the weight coefficient of adjusting each target, but need repeatedly move algorithm.In addition, this method lacks the basic research of selecting optimum weight coefficient.

Environmental economy scheduling is a high dimensional nonlinear optimization problem, is difficult to find its globally optimal solution based on the traditional optimization of gradient etc.Therefore in recent years, particle cluster algorithm is characteristics such as simple, easy to operate, fast convergence rate, is widely used in the economic dispatch of electric power system, and obtained certain effect.Particle cluster algorithm is proposed in nineteen ninety-five by Kenndy and the Eberhart of the U.S. the earliest, is used for the process of looking for food of simulation flock of birds, and algorithm carries out the intelligent guidance optimizing by interparticle cooperation, competition.At present, existing scholar uses particle cluster algorithm and finds the solution multi-objective optimization question.When multi-target particle group algorithm was expanded to environmental economy scheduling field, algorithm was optimized simultaneously to a plurality of targets, but the contradiction between each target makes the globally optimal solution of multi-target particle group algorithm not unique, can only obtain one group of Pareto optimal solution.How reasonably to select globally optimal solution and the individual optimal solution of population to become one of key of finding the solution multi-objective optimization question.

Summary of the invention

The objective of the invention is to overcome existing method system restriction when finding the solution environmental economy power generation dispatching scheme and fail strict Pareto optimality forward position (the Pareto optimal front that satisfies or obtain, POF) drawback uniformly that distributes inadequately extensively, a kind of new environmental economy power generation dispatching method for solving based on improvement multi-target particle group algorithm has been proposed, the environmental economy power generation dispatching has been set up Mathematical Modeling, provided and made the strict processing method that satisfies of constraint, improved the choosing method of the individual optimal solution of multi-target particle group and globally optimal solution, proposed to screen the solution that is dominant according to the slope characteristics in Pareto optimality forward position, realized popularity and uniformity that the Pareto optimality forward position distributes; This method not only is fit to disregard the environmental economy scheduling of network loss, especially is fit to adopt B coefficient matrix method to find the solution the environmental economy scheduling problem of network loss.

For realizing purpose of the present invention, technical scheme provided by the invention is:

A kind of environmental economy power generation dispatching method for solving based on improvement multi-target particle group algorithm may further comprise the steps,

Step 1, set up the Mathematical Modeling of environmental economy scheduling;

The Mathematical Modeling of environmental economy scheduling comprises target function and constraints; Target function comprises that fuel cost is minimum and the dusty gas discharge capacity is minimum; Constraints comprises unit output constraint, power-balance constraint, spinning reserve constraint;

Concrete form is:

$\left\{\begin{array}{c}F\left(P_G\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}(a_i+b_i{P}_{\mathrm{Gi}}+c_i{P}_{\mathrm{Gi}}^2)\\ E\left(P_G\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\[{10}^{-2}({\mathrm{\α}}_i+{\mathrm{\β}}_i{P}_{\mathrm{Gi}}+{\mathrm{\γ}}_i{P}_{\mathrm{Gi}}^2)+{\mathrm{\ξ}}_i\exp \left({\mathrm{\λ}}_i{P}_{\mathrm{Gi}}\right)\]\\ s.t.\\ P_{\mathrm{Gi}\min }\≤P_{\mathrm{Gi}}\≤P_{\mathrm{Gi}\max }\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_{\mathrm{Gi}}-P_D-P_l=0\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_{\mathrm{Gi}\max }-P_D-P_l\≥P_{\mathrm{SR}}\end{array}\right.---\left(1\right)$

Wherein, P _GThe force vector of gaining merit for generating set; P _GiFor the meritorious of fired power generating unit i exerted oneself; N is the fired power generating unit sum; F (P _G) be total fuel cost of system; E (P _G) be the gross contamination gas emissions of system; a _i, b _i, c _iFuel cost coefficient for fired power generating unit i; α _i, β _i, γ _i, ζ _i, λ _iBe respectively the dusty gas discharge capacity coefficient of fired power generating unit i; P _Gimin, P _GimaxBe respectively meritorious the exerting oneself and maximum meritorious exerting oneself of minimum of fired power generating unit i; P _DBe system's total load demand; P _lFor network loss is always transmitted in system; P _SRFor to the system reserve capacity under the constant load;

Step 2, multi-target particle group algorithm is improved;

Improvement to multi-target particle group algorithm is mainly reflected in constraint processing, individual optimal solution and choosing of globally optimal solution and finding the solution of Pareto optimality forward position;

The method that constraint handle to adopt penalty and constraint modifying factor to combine, and embody by fitness function, the concrete form of fitness function be as the formula (2):

$\min Y=\left\{\begin{array}{c}\min \[F\left(X\right),E\left(X\right)\];\mathrm{if\; A}\\ \min \[F\left(X\right)+M_{F}P\left(X\right),E\left(X\right)+M_{E}P\left(X\right);\mathrm{if\; B}\]\end{array}---\left(2\right)\right.$

In the formula, F (X), E (X) are respectively the former target function of economic dispatch and environment scheduling; M _F, M _EBe penalty factor; M _FP (X), M _EP (X) is penalty term; After A represented to use constraint modifying factor method to the particle correction, particle can satisfy equality constraint and inequality constraints; B represents to revise the back particle and still runs counter to a constraint at least;

Multi-target particle group's individual optimal solution and globally optimal solution are selected as follows:

The initial solution that population is produced at random is as the initial individual optimal solution of each particle, define to judge particle and the interparticle relation of being dominant of the previous generation of this iteration generation afterwards according to the Pareto noninferior solution, the particle of previous generation if the particle that this iteration produces is dominant, then the individual optimal solution with particle is updated to the particle that this iteration produces; Otherwise, the individual optimal solution of particle is not upgraded;

Population produces overall Pareto optimality disaggregation according to the condition of being dominant in each iterative process, historical Pareto optimality disaggregation initial value equals overall Pareto optimality disaggregation initial value, the overall Pareto optimality disaggregation that each iteration is produced is incorporated historical Pareto optimality disaggregation into afterwards, and upgrades historical Pareto optimality disaggregation according to the interparticle relation of being dominant; According to the degree of rarefication ordering, select historical Pareto optimal solution to concentrate the particle of degree of rarefication maximum as globally optimal solution;

Improve the distribution that separate in the Pareto optimality forward position:

Adopt the solution on the slope method screening Pareto optimality forward position; To the solution i on the Pareto optimality forward position, establish the particle that is adjacent and be respectively solution i-1 reconciliation i+1, calculate the slope between the particle by formula (3), formula (4):

$k_{i,i+1}=\frac{(f_{2,i}-f_{2,i+1})/(f_{2,\max }-f_{2,\min })}{(f_{1,i}-f_{1,i+1})/(f_{1,\max }-f_{1\min })}---\left(3\right)$

$k_{i-1,i+1}=\frac{(f_{2,i-1}-f_{2,i+1})/(f_{2,\max }-f_{2,\min })}{(f_{1,i-1}-f_{1,i+1})/(f_{1,\max }-f_{1\min })}---\left(4\right)$

In the formula, k _{I, i+1}For Pareto optimal solution i is adjacent the standard slope of separating between the i+1, k _{I-1, i+1}Be two standard slopes separated i-1 and i+1 between adjacent with Pareto optimal solution i; If k _{I, i+1}＞k _{I-1, i+1}, illustrate that then Pareto optimal solution i is nearer from desirable Pareto optimality forward position, keep such solution; If k _{I, i+1}≤ k _{I-1, i+1},

It is far away to illustrate that then Pareto optimal solution i departs from desirable Pareto optimality forward position, deletes such solution;

Step 3, find the solution environmental economy scheduling according to improved multi-target particle group algorithm in the step 2, obtain the Pareto optimality forward position of environmental economy scheduling;

Step 4, on the basis, Pareto optimality forward position that step 3 obtains, adopt mathematics method to calculate the satisfaction of each Pareto optimal solution;

The satisfaction of each Pareto optimal solution in certain one dimension target function is:

${\mathrm{\&mu;}}_i^m=\left\{\begin{array}{cc}1,& f_i^m\&le;f^{m,\min }\\ \frac{f^{m,\max }-f_i^m}{f^{m,\max }-f^{m,\min }},& f^{m,\min }<f_i^m<f^{m,\mathrm{<figure-callout\; id="0"\; label="max"\; filenames="130521102835.png,130521102838.png"\; state="\{\{state\}\}">max</figure-callout>}}\\ 0,& f_i^m\&GreaterEqual;f^{m,\max }\end{array}\right.---\left(5\right)$

In the formula,

Be the m dimension target function value of i optimal solution, m ∈ 1,2 ..., N _Obj, f ^{M, min}, f ^{M, max}Be respectively minimum value and the maximum of m dimension target function value;

The satisfaction of each Pareto optimal solution is:

${\mathrm{\&mu;}}_i=\frac{\underset{m=1}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i^m}{\underset{i=1}{\overset{N_c}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i^m}---\left(6\right)$

In the formula, N _CFor POF goes up the number of separating, select the Pareto optimal solution of satisfaction maximum as compromise optimal solution, select to take into account the optimal scheduling scheme of economy and environment with aid decision person.

Described step 3 may further comprise the steps,

Step 3.1, initialization;

The speed of initialization population and position arrange maximum iteration time K, given study factor c ₁, c ₂, inertia weight initial value, penalty factor value M _E, M _F, estimate initial population, the individual optimal solution of each particle of initialization, the globally optimal solution of population, overall Pareto optimality disaggregation and historical Pareto optimality disaggregation according to the fitness function in the formula (2);

Step 3.2, calculate the inertia weight w of this iteration according to formula (7);

In the formula, K is maximum iteration time, and k is the current iteration number of times, w _Max=0.9, w _Min=0.4;

$w=w_{\max }-\frac{w_{\max }-w_{\min }}{K}k---\left(7\right)$

Step 3.3, upgrade each particle's velocity and position according to formula (8);

$\left\{\begin{array}{c}{v}_{i,j}^{k+1}=w*v_{i,j}^k+c_1{r}_1*(p_{i,j}^k-x_{i,j}^k)+c_2{r}_2*(g_j^k-x_{i,j}^k)\\ x_{i,j}^{k+1}=x_{i,j}^k+v_{i,j}^{k+1}\end{array}\right.j=\mathrm{1,2},...,n---\left(8\right)$

In the formula, r ₁, r ₂Be the equally distributed random number of obedience on [0,1] interval,

,

Be respectively particle i flying speed and position in the j dimension space in the k time iteration,

Be the individual optimal value of the particle i location components in the j dimension space in the k time iteration, Be the global optimum of the population location components in the j dimension space in the k time iteration;

Step 3.4, the meritorious of independent unit of revising each particle are exerted oneself;

Step 3.5, calculate the fitness value of each particle according to formula (2);

Step 3.6, seek the overall Pareto optimality disaggregation of this iteration;

Step 3.7, employing slope method deleting history Pareto optimal solution are concentrated and are departed from desirable Pareto optimality forward position solution far away;

Step 3.8, concentrate at historical Pareto optimal solution, the dusty gas discharging is measured minimum value and fuel cost and is got except two solutions of minimum value, all the other is separated press the degree of rarefication ordering, and the particle of selection degree of rarefication maximum is as globally optimal solution;

Step 3.9, judge whether the number that historical Pareto optimal solution concentrate to be separated surpasses predefined capacity N _C, if do not surpass, changeed for the tenth step; If surpass, keep the dusty gas discharging and measure minimum value and fuel cost and get that two of minimum value separate and the degree of rarefication ordering is positioned at preceding N _C-2 solution is deleted all the other solutions, changes for the tenth step;

Step 3.10, judge whether to reach maximum iteration time K, if do not have, iterations adds 1, empties overall Pareto optimality disaggregation, changes for second step; Otherwise directly export the Pareto optimality forward position.

The implementation procedure of described step 3.4 is as follows,

Meritorious the exerting oneself of independent unit calculated with following formula:

$P_{\mathrm{Gd}}=P_D+P_l-\underset{\underset{j\&NotEqual;d}{j=1}}{\overset{N}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Gj}}---\left(9\right)$

P in the formula (9) _GjBe other unit output values except independent unit in the system, if do not consider the network loss P in the formula (9) _l, the meritorious P that exerts oneself of independent unit then _GdCan directly be found the solution by the value of exerting oneself of known load value and other units and obtain; If consider network loss, then,

$P_l=\left[\begin{array}{cc}{P}_{\mathrm{Gd}}& P_{\mathrm{Ga}}\end{array}\right]\left[\begin{array}{cc}{B}_{\mathrm{dd}}& B_{\mathrm{da}}\\ B_{\mathrm{ad}}& B_{\mathrm{aa}}\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{Gd}}\\ P_{\mathrm{Ga}}^T\end{array}\right]+\left[\begin{array}{cc}{B}_{0d}& B_{0a}\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{Gd}}\\ P_{\mathrm{Ga}}^T\end{array}\right]+B_{00}---\left(10\right)$

In the formula, P _GaFor removing the force vector of gaining merit of other (N-1) platform generating sets behind the independent unit, P _Ga=[P _G1, P _G2..., P _Gd-1, P _Gd+1..., P _GN], B _AaBe (N-1) * (N-1) matrix, B _Da, B _0aBe (N-1) dimension row vector, B _AdBe (N-1) dimensional vector, B _Dd, B _0d, B ₀₀Be scalar;

With formula (10) substitution formula (9), obtain one behind the abbreviation about P _GdQuadratic equation:

$a{P}_{\mathrm{Gd}}^2+b{P}_{\mathrm{Gd}}+c=0---\left(11\right)$

In the formula,

a＝B _dd (12)

$b=P_{\mathrm{Ga}}{B}_{\mathrm{ad}}+B_{\mathrm{da}}{P}_{\mathrm{Ga}}^T+B_{0d}-1---\left(13\right)$

$c=P_{\mathrm{Ga}}{B}_{\mathrm{aa}}{P}_{\mathrm{Ga}}^T+B_{0a}{P}_{\mathrm{Ga}}^T+B_{00}+P_D-\mathrm{sum}\left(P_{\mathrm{Ga}}\right)---\left(14\right)$

In the formula (14), sum (P _Ga) be vectorial P _GaIn each element sum, solve an equation (11) can obtain about P _GdTwo solutions

Then independent unit meritorious exert oneself into:

$P_{\mathrm{Gd}}=\min \{P_{\mathrm{Gd}}^1,P_{\mathrm{Gd}}^2\}---\left(15\right)$

Compared with prior art, the present invention has following beneficial effect:

1, computing of the present invention is simple, and the speed of service is fast, and has stability preferably, is easy to Project Realization; Its method that combines with constraint modifying factor and penalty function is come the treatment system constraint, and has taken into account network loss in power-balance, adopts the B Y-factor method Y to find the solution network loss.

2, the present invention has introduced overall Pareto optimality disaggregation and historical Pareto optimality disaggregation in multi-target particle group algorithm, has redefined the individual optimal solution of particle and the globally optimal solution of population.

3, the present invention can go out the Pareto optimality forward position of environmental economy scheduling by rapid solving, and the forward position is widely distributed evenly, and can provide compromise optimal solution for the policymaker according to mathematics method.

Description of drawings:

Fig. 1 is for improving the key diagram of the distribution situation of separating in the Pareto optimality forward position with the slope method.

Fig. 2 is algorithm flow chart of the present invention.

Fig. 3 is the economic dispatch convergence curve.

Fig. 4 is environment scheduling convergence curve.

Fig. 5 is the economic dispatch optimal value (example 1) under the different initial solutions.

Fig. 6 is 50 environment scheduling optimal values (example 1) under the different initial solutions.

The POF that Fig. 7 obtains for the slope method (example 1).

The POF that Fig. 8 obtains for the slope method (example 2).

The POF that Fig. 9 obtains for the degree of rarefication ranking method (example 1).

The POF that Figure 10 obtains for the degree of rarefication ranking method (example 2).

Concrete execution mode

The invention will be further described below in conjunction with accompanying drawing.

The present invention includes following steps:

Step 1, set up the Mathematical Modeling of environmental economy scheduling

The Mathematical Modeling of power system environment economic dispatch comprises target function and constraints two parts.Target function comprises that fuel cost is minimum and the dusty gas discharge capacity is minimum; Constraints comprises unit output constraint, power-balance constraint, spinning reserve constraint.

Target function 1: fuel cost is minimum.The minimum economic dispatch that belongs to of fuel cost, the fuel cost curve of every generating set is represented with a quadratic function usually, the total fuel cost F (P of system _G) can be expressed as:

$F\left(P_G\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(a_i+b_i{P}_{\mathrm{Gi}}+c_i{P}_{\mathrm{Gi}}^2)---\left(1\right)$

In the formula: N is the fired power generating unit sum; a _i, b _i, c _iFuel cost coefficient for fired power generating unit i; P _GiFor the meritorious of fired power generating unit i exerted oneself.P _GBe system's fired power generating unit force vector of gaining merit, can be expressed as:

$P_G=[P_{G1},P_{G2},...,P_{\mathrm{GN}}]---\left(2\right)$

Target function 2: the dusty gas discharge capacity is minimum.The minimum environment that belongs to of dusty gas discharge capacity is dispatched, fired power generating unit is discharged multiple dusty gas in power generation process, each dusty gas discharge capacity all can be set up functional relation separately with meritorious the exerting oneself of fired power generating unit, but calculate for convenient, adopt dusty gas comprehensive discharge model, then system's gross contamination gas emissions can be expressed as:

$E\left(P_G\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[{10}^{-2}({\mathrm{\&alpha;}}_i+{\mathrm{\&beta;}}_i{P}_{\mathrm{Gi}}+{\mathrm{\&gamma;}}_i{P}_{\mathrm{Gi}}^2)+{\mathrm{\&zeta;}}_i\exp \left({\mathrm{\&lambda;}}_i{P}_{\mathrm{Gi}}\right)]---\left(3\right)$

In the formula: α _i, β _i, γ _i, ζ _i, λ _iBe respectively the dusty gas discharge capacity coefficient of fired power generating unit i.

The fired power generating unit constraint of exerting oneself:

P _Gimin≤P _Gi≤P _Gimax (4)

In the formula: P _Gimin, P _GimaxBe respectively meritorious the exerting oneself and maximum meritorious exerting oneself of minimum of fired power generating unit i.

The power-balance constraint:

$\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Gi}}-P_D-P_l=0---\left(5\right)$

In the formula: P _DBe system's total load demand, P _lFor network loss is always transmitted in system.Network loss is found the solution and is adopted the B Y-factor method Y, and its computing formula is as follows:

$P_l=P_{G}B{P}_G^T+B_0{P}_G^T+B_{00}---\left(6\right)$

In the formula:

Be P _GTransposition, B is that N * N ties up matrix, B ₀Be N dimension row vector, B ₀₀It is a scalar.

The spinning reserve constraint:

There are problems such as unit outage and load prediction error in electric power system, for tackling the influence that these problems are brought to power system dispatching, will consider the spinning reserve constraint in scheduling.System's spinning reserve capacity satisfies following constraint:

$\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Gi}\max }-P_D-P_l\&GreaterEqual;P_{\mathrm{SR}}---\left(7\right)$

In the formula: P _SRFor to the system reserve capacity under the constant load, generally get 5% of system's total load.

Above-mentioned target function and each constraints are combined, can obtain EED(environmental/economic dispatch) Mathematical Modeling of problem:

$\left[\begin{array}{c}\min Y\left(X\right)=\min [F\left(X\right),E\left(X\right)]\\ s.t.\\ h_i\left(X\right)=0,i=\mathrm{1,2},...,L\\ g_j\left(X\right)\&GreaterEqual;0,j=\mathrm{1,2},...,K\end{array}\right.---\left(8\right)$

In the formula: X=P _GSolution vector for optimization problem; H, g are respectively equality constraint and the inequality constraints of model; L, K are respectively the sum of equality constraint and inequality constraints.

Step 2, multi-target particle group algorithm is improved

When selecting for use particle cluster algorithm to find the solution the power system environment economic dispatch program, at first the particle cluster algorithm of standard to be extended to multi-target particle group algorithm, then multi-target particle group algorithm be improved.Improvement to multi-target particle group algorithm is mainly reflected in constraint processing, individual optimal solution and choosing of globally optimal solution and finding the solution of Pareto optimality forward position.

Improve the constraint processing method:

Particle cluster algorithm is when finding the solution the constrained optimization problem, and its method of handling constraint mainly is divided into two classes: 1) Means of Penalty Function Methods; 2) design constraint modifying factor.Based on this, the present invention combines above-mentioned two kinds of methods, has proposed a kind of new constraint processing method.

At first design constraint modifying factor, this constraint processing method is only at equality constraint.

If p _Gi=[P _G1, P _G2..., P _GN] a meritorious scheduling scheme of representative system, p _GiIn each element represent meritorious the exerting oneself of N platform generating set respectively.For satisfying the meritorious balance in the formula (5), select one of capacity maximum in the N platform unit as independent unit, meritorious the exerting oneself of independent unit calculated with following formula:

$P_{\mathrm{Gd}}=P_D+P_l-\underset{\underset{j\&NotEqual;d}{j=1}}{\overset{N}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Gj}}---\left(9\right)$

P in the formula (9) _GjBe other unit output values except independent unit in the system, if do not consider the network loss P in the formula (9) _l, the meritorious P that exerts oneself of independent unit then _GdCan directly be found the solution by the value of exerting oneself of known load value and other units and obtain; If consider network loss, then to P in the formula (6) _G, B, B ₀Cut apart, and formula (6) be rewritten into following form:

$P_l=\left[\begin{array}{cc}{P}_{\mathrm{Gd}}& P_{\mathrm{Ga}}\end{array}\right]\left[\begin{array}{cc}{B}_{\mathrm{dd}}& B_{\mathrm{da}}\\ B_{\mathrm{ad}}& B_{\mathrm{aa}}\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{Gd}}\\ P_{\mathrm{Ga}}^T\end{array}\right]+\left[\begin{array}{cc}{B}_{0d}& B_{0a}\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{Gd}}\\ P_{\mathrm{Ga}}^T\end{array}\right]+B_{00}---\left(10\right)$

In the formula: P _GaFor removing the force vector of gaining merit of other (N-1) platform generating sets behind the independent unit, P _Ga=[P _G1, P _G2..., P _Gd-1, P _Gd+1..., P _GN], B _AaBe (N-1) * (N-1) matrix, B _Da, B _0aBe (N-1) dimension row vector, B _AdBe (N-1) dimensional vector, B _Dd, B _0d, B ₀₀Be scalar.

With formula (10) substitution formula (9), obtain one behind the abbreviation about P _GdQuadratic equation:

${\mathrm{aP}}_{\mathrm{Gd}}^2+{\mathrm{bP}}_{\mathrm{Gd}}+c=0---\left(11\right)$

In the formula:

a＝B _dd

(12)

$b=P_{\mathrm{Ga}}{B}_{\mathrm{ad}}+B_{\mathrm{da}}{P}_{\mathrm{Ga}}^T+B_{0d}-1---\left(13\right)$

$c=P_{\mathrm{Ga}}{B}_{\mathrm{aa}}{P}_{\mathrm{Ga}}^T+B_{0a}{P}_{\mathrm{Ga}}^T+B_{00}+P_D-\mathrm{sum}\left(P_{\mathrm{Ga}}\right)---\left(14\right)$

In the formula (14), sum (P _Ga) be vectorial P _GaIn each element sum, solve an equation (11) can obtain about P _GdTwo solutions

Then independent unit meritorious exert oneself into:

$P_{\mathrm{Gd}}=\min \{P_{\mathrm{Gd}}^1,P_{\mathrm{Gd}}^2\}---\left(15\right)$

Revise the particle that does not satisfy equality constraint by the design constraint factor, two kinds of results are arranged, first kind after the correction: equality constraint satisfies, and independent unit output P _GdSatisfy its exert oneself constraint, i.e. P _Gd∈ [P _Gdmin, P _Gdmax]; Second kind: equality constraint satisfies, but independent unit output P _GdExceed its scope of exerting oneself.

When revised result belongs to second kind of situation, if P _Gd＜P _Gdmin, then make P _Gd=P _GdminIf P _Gd＞P _Gdmax, then make P _Gd=P _Gdmax

When using constraint modifying factor method still can not make particle satisfy equality constraint or particle not satisfy inequality constraints, then handle constraint by penalty function method.

Constrained optimization problem in the formula (8) is made auxiliary function:

Z(X,M _F,M _E)＝[P _F(X,M _F),P _E(X,M _E)] (16)

Wherein:

P _F(X,M _F)＝F(X)+M _FP(X) (17)

P _E(X,M _E)＝E(X)+M _EP(X) (18)

$P\left(X\right)=\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{\left|h_i\left(X\right)\right|}^2+\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left[\min \right\{g_j\left(X\right),0\left\}\right]}^2---\left(19\right)$

P _F, P _EBe respectively the penalty about fuel cost and dusty gas discharge capacity, M _F, M _EBe penalty factor, M _FP (X), M _EP (X) is penalty term.

Get M _F, M _EBe suitably big or small positive number, then the constrained optimization problem in the formula (8) is converted into and asks unconstrained problem Z (X, M _F, M _E)=[P _F(X, M _F), P _E(X, M _E)] get the problem of the solution of minimum value.M _F, M _EValue identical or close with the order of magnitude of target function value, its concrete value size is adjusted voluntarily and is chosen according to the emulation testing result by the experimenter.

If unconstrained problem minZ (X, M _F, M _E) optimal solution X ^*Satisfy equality constraint h _i(X)=0, i=1,2 ..., L and inequality constraints g _j(X) 〉=0, j=1,2 ..., K, then X ^*It is exactly the optimal solution of former problem.

Carry constraint processing method is applied in the multi-target particle group algorithm, namely is calculated as follows the fitness value of each particle:

$\min Y=\left\{\begin{array}{cc}\min [F\left(X\right),E\left(X\right)];\mathrm{if}& A\\ \min [F\left(X\right)+M_{F}P\left(X\right),E\left(X\right)+M_{E}P\left(X\right);\mathrm{if}& B]\end{array}\right.---\left(20\right)$

In the formula: after A represented to use constraint modifying factor method to the particle correction, particle can satisfy equality constraint and inequality constraints; B represents, revises the back particle and still runs counter to a constraint at least.

Improve the choosing method of the individual minimax solution of multi-target particle group and global extremum solution:

One of basic characteristics of multi-objective optimization question are the contradiction between each target, and when namely improving certain desired value with certain scheme, this scheme may make another desired value become bad.Contradiction between each target makes the solution of multi-objective optimization question not unique, and the set of all noninferior solutions that replace is also referred to as the Pareto optimality disaggregation, and it is defined as follows.

Definition 1: for the multi-objective optimization question of minimizing, if x ₁, x ₂All be the solution vector in the feasible zone, when following two conditions that and if only if satisfy simultaneously, claim x ₁Be dominant, or claim x ₁Domination x ₂:

$\&ForAll;i\&Element;\{\mathrm{1,2},...,N_{\mathrm{obj}}\}:f_i\left(x_1\right)\&le;f_i\left(x_2\right)---\left(21\right)$

$\&Exists;j\&Element;\{\mathrm{1,2},...,N_{\mathrm{obj}}\}:f_j\left(x_1\right)<f_j\left(x_2\right)---\left(22\right)$

In the formula, N _ObjNumber for target function.In the whole feasible zone of target function, if there is not other feasible solution dominations x ₁, then claim x ₁Be noninferior solution or Pareto optimal solution.The set of being made up of all Pareto optimal solutions is called Pareto optimality disaggregation or Pareto optimality forward position.

Because there is not unique globally optimal solution in multi-target particle group algorithm, therefore need redefine multi-target particle group's individual optimal solution and globally optimal solution.The present invention proposes to select as follows multi-target particle group's individual minimax solution and global extremum solution:

Overall Pareto optimality disaggregation and historical Pareto optimality disaggregation are set in multi-target particle group algorithm.Overall situation Pareto optimality disaggregation is used for depositing all Pareto optimal solutions that the current iteration process produces, and can obtain by following flow process rapid solving:

Suppose to contain m particle in the population, each particle has N _ObjIndividual target function value, the then overall Pareto optimality disaggregation that produces by the each iteration of following program looks:

1) makes i=1;

2) to all j=1,2 ..., m and j ≠ i come comparison particle x with formula (21) and formula (22) _iWith particle x _j

3) if there is j, make particle x _jDomination x _i, then with particle x _iBe labeled as inferior solution;

4) if i＞m turns to 5); Otherwise make i=i+1, turn to 2);

5) remove the solution that all are labeled, all remaining systems of solutions become the overall Pareto optimality disaggregation of this iteration.

Historical Pareto optimality disaggregation is used for depositing the Pareto optimal solution in the whole iterative process.In each iterative process, incorporate the overall Pareto optimality disaggregation that this iteration produces into historical Pareto optimality disaggregation, and according to the condition searching noninferior solution wherein that is dominant of the Pareto in formula (21) and the formula (22), delete all inferior solutions.

Individual optimal solution: the initial solution that population is produced at random is as the initial individual optimal solution of each particle, judge particle and the interparticle relation of being dominant of the previous generation that this iteration produces according to formula (21) and formula (22) afterwards, the individual optimal solution of last iteration if the particle that this iteration produces is dominant, then the individual optimal solution with particle is updated to the particle that this iteration produces; Otherwise, the individual optimal solution of particle is not upgraded.

Globally optimal solution: globally optimal solution is concentrated from historical Pareto optimal solution and is chosen.According to separating the degree of rarefication ordering of concentrating each particle, select the particle of degree of rarefication maximum as the globally optimal solution of current iteration.

Improve the distribution that separate in the Pareto optimality forward position:

The present invention proposes to improve the distribution situation that separate in the Pareto optimality forward position with the slope method.As shown in Figure 1, be example with a binocular mark optimization problem, f ₁, f ₂Be respectively each target function value, suppose that A, B are arranged on the gained Pareto optimality forward position, C, D, E, F6 separate.As can be seen, A, B, D, E, a F5 point all are arranged on the curve of desirable Pareto optimality forward position (shown in the figure dotted line) from accompanying drawing 1, though the C point also belongs to Pareto optimal solution, it departs from optimum forward position, and when the C point departs from far, k are arranged _CD＜k _BD, k _CDBe the slope between C, the D, k at 2 _BDBe the slope between B, the D at 2.Because f ₁, f ₂The dimension difference, therefore be calculated as follows the slope between the Pareto optimal solution:

$k_{i,i+1}=\frac{(f_{2,i}-f_{2,i+1})/(f_{2,\max }-f_{2,\min })}{(f_{1,i}-f_{1,i+1})/(f_{1,\mathrm{amx}}-f_{1\min })}---\left(23\right)$

$k_{i-1,i+1}=\frac{(f_{2,i-1}-f_{2,i+1})/(f_{2,\max }-f_{2,\min })}{(f_{1,i-1}-f_{1,i+1})/(f_{1,\max }-f_{1\min })}---\left(24\right)$

In the formula: k _{I, i+1}For Pareto optimal solution i is adjacent the standard slope of separating between the i+1, k _{I-1, i+1}Be two standard slopes separated i-1 and i+1 between adjacent with Pareto optimal solution i.If k _{I, i+1}＞k _{I-1, i+1}, illustrate that then Pareto optimal solution i is nearer from desirable Pareto optimality forward position, keep such solution; If k _{I, i+1}≤ k _{I-1, i+1}, it is far away to illustrate that then Pareto optimal solution i departs from desirable Pareto optimality forward position, deletes such solution.

Step 3, find the solution the Pareto optimality forward position of environmental economy scheduling with improved multi-target particle group algorithm in the step 2, algorithm flow as shown in Figure 2, concrete steps are as follows:

Step 3.1: initialization.The speed of initialization population and position arrange maximum iteration time K, given study factor c ₁, c ₂, inertia weight initial value, penalty factor value M _E, M _F, estimate initial population, the individual optimal solution of each particle of initialization, the globally optimal solution of population, overall Pareto optimality disaggregation and historical Pareto optimality disaggregation according to the fitness function in the formula (20).

Step 3.2: calculate the inertia weight w of this iteration according to formula (25), in the formula, K is maximum iteration time, and k is the current iteration number of times, w _Max=0.9, w _Min=0.4.

$w=w_{\max }-\frac{w_{\max }-w_{\min }}{K}k---\left(25\right)$

Step 3.3: upgrade each particle's velocity and position according to formula (26).In the formula, r ₁, r ₂Be the equally distributed random number of obedience on [0,1] interval,

Be respectively particle i flying speed and position in the j dimension space in the k time iteration, Be the individual optimal value of the particle i location components in the j dimension space in the k time iteration,

Be the global optimum of the population location components in the j dimension space in the k time iteration.

$\left\{\begin{array}{c}{v}_{i,j}^{k+1}=w*v_{i,j}^k+c_1{r}_1*(p_{i,j}^k-x_{i,j}^k)+c_2{r}_2*(g_j^k-x_{i,j}^k)\\ x_{i,j}^{k+1}=x_{i,j}^k+v_{i,j}^{k+1}\end{array}\right.j=\mathrm{1,2},..,n---\left(26\right)$

Step 3.4: the independent unit output of revising each particle according to formula (9) to formula (15).

Step 3.5: the fitness value that calculates each particle according to formula (20).

Step 3.6: the overall Pareto optimality disaggregation of seeking this iteration.

Step 3.7: with the concentrated desirable Pareto optimality forward position solution far away that departs from of slope method deleting history Pareto optimal solution.

Step 3.8: concentrate at historical Pareto optimal solution, the dusty gas discharging is measured minimum value and fuel cost and is got except two solutions of minimum value, all the other is separated press the degree of rarefication ordering, and the particle of selection degree of rarefication maximum is as globally optimal solution.

Step 3.9: judge historical Pareto optimal solution concentrates the number of separating whether to surpass predefined capacity N _C, if do not surpass, changeed for the tenth step; If surpass, keep the dusty gas discharging and measure minimum value and fuel cost and get that two of minimum value separate and the degree of rarefication ordering is positioned at preceding N _C-2 solution is deleted all the other solutions, changes for the tenth step.

Step 3.10: judge whether to reach maximum iteration time K, if do not have, iterations adds 1, empties overall Pareto optimality disaggregation, changes for second step; Otherwise directly export the Pareto optimality forward position.

Step 4, on the basis, Pareto optimality forward position that step 3 obtains, adopt mathematics method to calculate the satisfaction of each Pareto optimal solution.

Behind the Pareto optimality forward position of the problem of being optimized, adopt mathematics method to calculate the satisfaction of each Pareto optimal solution, select compromise optimal solution with aid decision person.The satisfaction of each Pareto optimal solution in certain one dimension target function is:

${\mathrm{\&mu;}}_i^m=\left\{\begin{array}{cc}1,& f_i^m\&le;f^{m,\min }\\ \frac{f^{m,\max }-f_i^m}{f^{m,\max }-f^{m,\min }},& f^{m,\min }<f_i^m<f^{m,\mathrm{<figure-callout\; id="0"\; label="max"\; filenames="130521102835.png,130521102838.png"\; state="\{\{state\}\}">max</figure-callout>}}\\ 0,& f_i^m\&GreaterEqual;f^{m,\max }\end{array}\right.---\left(27\right)$

In the formula:

Be the m dimension target function value of i optimal solution, m ∈ 1,2 ..., N _Obj, f ^{M, min}, f ^{M, max}Be respectively minimum value and the maximum of m dimension target function value.

The satisfaction of each Pareto optimal solution is:

${\mathrm{\&mu;}}_i=\frac{\underset{m=1}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i^m}{\underset{i=1}{\overset{N_c}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i^m}---\left(28\right)$

In the formula: N _CFor POF goes up the number of separating, select the Pareto optimal solution of satisfaction maximum as compromise optimal solution.

Embodiment

Here the multi-target particle group algorithm of application enhancements is found the solution the environmental economy scheduling problem, and verifies validity of the present invention with IEEE6 machine 30 node modular systems.System's total load is 283.4MW, and the bound of exerting oneself of each generating set, fuel cost coefficient and pollutant emission coefficient of discharge are as shown in table 1.

Table 1 generating set data

Calculate B, B that network loss is used ₀, B ₀₀Be the perunit value under the reference capacity 100MVA of system, its value is as follows:

$B=\left[\begin{array}{cccccc}0.13382& -0.0299& 0.0044& -0.0022& -0.0010& -0.0008\\ -0.0299& 0.0487& -0.0025& 0.0004& 0.0016& 0.0041\\ 0.0044& -0.0025& 0.0182& -0.0070& -0.0066& -0.0066\\ -0.0022& 0.0004& -0.0070& 0.0137& 0.0050& 0.0033\\ -0.0010& 0.0016& -0.0066& 0.0050& 0.0109& 0.0005\\ -0.0008& 0.0041& -0.0066& 0.0033& 0.0005& 0.0244\end{array}\right]$

B ₀＝[-0.0107 0.0060 -0.0017 0.0009 0.0002 0.0030]

B ₀₀＝9.8573×10 ^-4

Be the validity of the explanation algorithm of putting forward, consider the emulation of following two kinds of differing complexities:

Example 1: for result that carrying algorithm simulating is obtained and the known results in other document compare, example 1 is not considered the network loss that power-balance is intrafascicular approximately;

Example 2: consider the intrafascicular approximately network loss of power-balance.

For separating on two borders that obtain the Pareto optimality forward position, be that fuel cost is got the solution of minimum value and the solution that minimum value is measured in the dusty gas discharging, and whether the solution on the Pareto optimality forward position that obtains of the checking multi-target particle group algorithm of carrying have good distribution character, at first respectively system carried out economic dispatch with the single goal particle cluster algorithm and environment is dispatched.In the single goal particle cluster algorithm, population is made as 60; Study factor c ₁=c ₂=2; Penalty factor M _F=10, M _E=0.0001; Maximum iteration time is made as 100.

The scheduling result of example 1 and example 2 is shown in table 2, table 3, and from table 2 and table 3 as can be seen, the equality constraint of system can strictly satisfy.

Table 2 example 1 environmental economy scheduling result

Table 3 example 2 environmental economy scheduling result

Fig. 3 and Fig. 4 are respectively the convergence curve of economic dispatch and environment scheduling, and from Fig. 3 and Fig. 4 as can be seen, the inventive method has convergence preferably.

For different initial solutions being described to the influence of scheduling result, allow algorithm that the present invention carries produce initial solution at random 50 times, the distribution of gained economic dispatch optimal value and environment scheduling optimal value is respectively as shown in Figure 5 and Figure 6.

From Fig. 5 and Fig. 6 as can be seen: the inventive method has good ability of searching optimum, and 50 suboptimization all can be found global optimum, and is not subjected to the influence of initial solution.It should be noted that when maximum iteration time reduces, can find the corresponding minimizing of number of times meeting of globally optimal solution.

In multiple-objection optimization, per generation population be made as 60, maximum iteration time is 1000, in example 1 and example 2, the number of separating on the Pareto optimality forward position all is made as 30.Respectively example 1 and example 2 are optimized gained Pareto optimality forward position such as Fig. 7, shown in Figure 8 with carrying multi-target particle group algorithm.If only use the degree of rarefication ranking method, gained Pareto optimality forward position is respectively as Fig. 9 and shown in Figure 10.

Comparison diagram 7, Fig. 8, Fig. 9 and Figure 10 as can be seen, the Pareto optimality forward position that the slope method that the present invention proposes obtains is more smooth evenly than the Pareto optimality forward position of only using the degree of rarefication ranking method to obtain.

As can be seen from Figures 7 and 8, two boundary points in Pareto optimality forward position are distinguished the optimal value of corresponding economic dispatch and environment scheduling, and the result of calculation of each boundary point is as shown in table 4, and compromise optimal solution is as shown in table 5.

Separate on the border of table 4POF

Table 5 optimal solution of trading off

The machine group #	Example 1	Example 2
			G 1	25.1935	25.4726
G 2	36.9593	37.6234
			G 3	53.7415	57.0078
G 4	71.0606	68.1824
			G 5	53.5121	54.6521
G 6	42.9330	43.0657
			Fuel cost/($/h)	608.8184	616.0108
Dusty gas/(t/h)	0.2015	0.2006

Result in the table 4 and the optimization of the single goal in table 2 and the table 3 result are compared, the two differs very little as can be seen, the improved multi-target particle group algorithm that this explanation the present invention proposes all can find border solution preferably under different situations, gained Pareto optimality forward position has a very wide distribution.

Claims (3)

1. one kind based on the environmental economy power generation dispatching method for solving that improves multi-target particle group algorithm, it is characterized in that: may further comprise the steps,

Step 1, set up the Mathematical Modeling of environmental economy scheduling;

The Mathematical Modeling of environmental economy scheduling comprises target function and constraints; Target function comprises that fuel cost is minimum and the dusty gas discharge capacity is minimum; Constraints comprises unit output constraint, power-balance constraint, spinning reserve constraint;

Concrete form is:

Wherein, P _GThe force vector of gaining merit for generating set; P _GiFor the meritorious of fired power generating unit i exerted oneself; N is the fired power generating unit sum; F (P _G) be total fuel cost of system; E (P _G) be the gross contamination gas emissions of system; a _i, b _i, c _iFuel cost coefficient for fired power generating unit i; α _i, β _i, γ _i, ζ _i, λ _iBe respectively the dusty gas discharge capacity coefficient of fired power generating unit i; P _Gimin, P _GimaxBe respectively meritorious the exerting oneself and maximum meritorious exerting oneself of minimum of fired power generating unit i; P _DBe system's total load demand; P _lFor network loss is always transmitted in system; P _SRFor to the system reserve capacity under the constant load;

Step 2, multi-target particle group algorithm is improved;

Improvement to multi-target particle group algorithm is mainly reflected in constraint processing, individual optimal solution and choosing of globally optimal solution and finding the solution of Pareto optimality forward position;

The method that constraint handle to adopt penalty and constraint modifying factor to combine, and embody by fitness function, the concrete form of fitness function be as the formula (2):

In the formula, F (X), E (X) are respectively the former target function of economic dispatch and environment scheduling; M _F, M _EBe penalty factor; M _FP (X), M _EP (X) is penalty term; After A represented to use constraint modifying factor method to the particle correction, particle can satisfy equality constraint and inequality constraints; B represents to revise the back particle and still runs counter to a constraint at least;

Multi-target particle group's individual optimal solution and globally optimal solution are selected as follows:

The initial solution that population is produced at random is as the initial individual optimal solution of each particle, define to judge particle and the interparticle relation of being dominant of the previous generation of this iteration generation afterwards according to the Pareto noninferior solution, the particle of previous generation if the particle that this iteration produces is dominant, then the individual optimal solution with particle is updated to the particle that this iteration produces; Otherwise, the individual optimal solution of particle is not upgraded;

Population produces overall Pareto optimality disaggregation according to the condition of being dominant in each iterative process, historical Pareto optimality disaggregation initial value equals overall Pareto optimality disaggregation initial value, the overall Pareto optimality disaggregation that each iteration is produced is incorporated historical Pareto optimality disaggregation into afterwards, and upgrades historical Pareto optimality disaggregation according to the interparticle relation of being dominant; According to the degree of rarefication ordering, select historical Pareto optimal solution to concentrate the particle of degree of rarefication maximum as globally optimal solution;

Improve the distribution that separate in the Pareto optimality forward position:

Adopt the solution on the slope method screening Pareto optimality forward position; To the solution i on the Pareto optimality forward position, establish the particle that is adjacent and be respectively solution i-1 reconciliation i+1, calculate the slope between the particle by formula (3), formula (4):

In the formula, k _{I, i+1}For Pareto optimal solution i is adjacent the standard slope of separating between the i+1, k _{I-1, i+1}Be two standard slopes separated i-1 and i+1 between adjacent with Pareto optimal solution i; If k _{I, i+1}＞k _{I-1, i+1}, illustrate that then Pareto optimal solution i is nearer from desirable Pareto optimality forward position, keep such solution; If k _{I, i+1}≤ k _{I-1, i+1}, it is far away to illustrate that then Pareto optimal solution i departs from desirable Pareto optimality forward position, deletes such solution;

Step 3, find the solution environmental economy scheduling according to improved multi-target particle group algorithm in the step 2, obtain the Pareto optimality forward position of environmental economy scheduling;

Step 4, on the basis, Pareto optimality forward position that step 3 obtains, adopt mathematics method to calculate the satisfaction of each Pareto optimal solution;

The satisfaction of each Pareto optimal solution in certain one dimension target function is:

In the formula, Be the m dimension target function value of i optimal solution, m ∈ 1,2 ..., N _Obj, f ^{M, min}, f ^{M, max}Be respectively minimum value and the maximum of m dimension target function value;

The satisfaction of each Pareto optimal solution is:

In the formula, N _CFor POF goes up the number of separating, select the Pareto optimal solution of satisfaction maximum as compromise optimal solution, select to take into account the optimal scheduling scheme of economy and environment with aid decision person.

It is 2. according to claim 1 that it is characterized in that: described step 3 may further comprise the steps based on the environmental economy power generation dispatching method for solving that improves multi-target particle group algorithm,

Step 3.1, initialization;

The speed of initialization population and position arrange maximum iteration time K, given study factor c ₁, c ₂, inertia weight initial value, penalty factor value M _E, M _F, estimate initial population, the individual optimal solution of each particle of initialization, the globally optimal solution of population, overall Pareto optimality disaggregation and historical Pareto optimality disaggregation according to the fitness function in the formula (2);

Step 3.2, calculate the inertia weight w of this iteration according to formula (7);

In the formula, K is maximum iteration time, and k is the current iteration number of times, w _Max=0.9, w _Min=0.4;

Step 3.3, upgrade each particle's velocity and position according to formula (8);

In the formula, r ₁, r ₂Be the equally distributed random number of obedience on [0,1] interval,

Be respectively particle i flying speed and position in the j dimension space in the k time iteration,

Be the individual optimal value of the particle i location components in the j dimension space in the k time iteration,

Be the global optimum of the population location components in the j dimension space in the k time iteration;

Step 3.4, the meritorious of independent unit of revising each particle are exerted oneself;

Step 3.5, calculate the fitness value of each particle according to formula (2);

Step 3.6, seek the overall Pareto optimality disaggregation of this iteration;

Step 3.7, employing slope method deleting history Pareto optimal solution are concentrated and are departed from desirable Pareto optimality forward position solution far away;

Step 3.8, concentrate at historical Pareto optimal solution, the dusty gas discharging is measured minimum value and fuel cost and is got except two solutions of minimum value, all the other is separated press the degree of rarefication ordering, and the particle of selection degree of rarefication maximum is as globally optimal solution;

Step 3.9, judge whether the number that historical Pareto optimal solution concentrate to be separated surpasses predefined capacity N _C, if do not surpass, changeed for the tenth step; If surpass, keep the dusty gas discharging and measure minimum value and fuel cost and get that two of minimum value separate and the degree of rarefication ordering is positioned at preceding N _C-2 solution is deleted all the other solutions, changes for the tenth step;

Step 3.10, judge whether to reach maximum iteration time K, if do not have, iterations adds 1, empties overall Pareto optimality disaggregation, changes for second step; Otherwise directly export the Pareto optimality forward position.

3. according to claim 2 based on the environmental economy power generation dispatching method for solving that improves multi-target particle group algorithm, it is characterized in that: the implementation procedure of described step 3.4 is,

Meritorious the exerting oneself of independent unit calculated with following formula:

P in the formula (9) _GjBe other unit output values except independent unit in the system, if do not consider the network loss P in the formula (9) _l, the meritorious P that exerts oneself of independent unit then _GdCan directly be found the solution by the value of exerting oneself of known load value and other units and obtain; If consider network loss, then,

In the formula, P _GaFor removing the force vector of gaining merit of other (N-1) platform generating sets behind the independent unit, P _Ga=[P _G1, P _G2..., P _Gd-1, P _Gd+1..., P _GN], B _AaBe (N-1) * (N-1) matrix, B _Da, B _0aBe (N-1) dimension row vector, B _AdBe (N-1) dimensional vector, B _Dd, B _0d, B ₀₀Be scalar;

With formula (10) substitution formula (9), obtain one behind the abbreviation about P _GdQuadratic equation:

In the formula,

a＝B _dd

(12)

In the formula (14), sum (P _Ga) be vectorial P _GaIn each element sum, solve an equation (11) can obtain about P _GdTwo solutions

Then independent unit meritorious exert oneself into:

。

Images