CN103500997A - Electric power system dispatching method based on hybrid multi-objective lambda iteration method and Newton method - Google Patents

Abstract

The invention discloses an electric power system dispatching method based on the hybrid multi-objective lambda iteration method and the Newton method. The electric power system dispatching method comprises the following steps that 1) relevant data of each generator set of an electric power system are obtained; 2) a mathematical optimization model for the electric power system environmental economy scheduling problem is built; 3) an EED problem without regard to electric transmission line loss is solved by means of the multi-objective lambda iteration method, and Pareto optimal solutions are obtained; 4) each Pareto optimal solution is taken as an initial solution, an EDE problem with consideration to electric transmission line loss is solved by means of the Newton method, and an optimal solution set is obtained; 5) a final solution is determined in the optimal solution set by means of a multi-objective decision method; 6) the final solution is used as an instruction to be sent to a relevant power station or unit through an automatic generation control device, and unit electricity generation power is controlled through the automatic generation control device. The electric power system dispatching method based on the hybrid multi-objective lambda iteration method and the Newton method is small in calculated amount, short in calculating time, and high in convergence precision, and greatly improves the economy and efficiency of electricity generation of the electric power system.

Description

Power system dispatching method based on mixing multiple target λ iterative method and Newton method

Technical field

The present invention relates to a kind of power system dispatching method, especially a kind of power system dispatching method based on mixing multiple target λ iterative method and Newton method, belong to operation, analysis and the scheduling field of electric power system.

Background technology

Economic dispatch is an important basic problem of electric power system ^{[1] [2] [3]}, along with environment in recent years is polluted and to be become a global problem, as the electric power enterprise of pollutant emission main source, be required to reduce pollutant emission.Take China as example, and in total discharge of national SO2 and NOx, fired power generating unit has accounted for respectively 42.5% and 38.0%.For reducing discharge, a kind of mode is that desulfurization and nitrogen rejection facility are installed, and another kind of mode is the less scheme of discharge of selecting in the generating Optimized Operation.Traditional economic dispatch has become a multi-objective optimization question for this reason, i.e. environmental economy scheduling problem [4] in the present invention, and this problem requires to reduce cost of electricity-generating and pollutant emission value simultaneously.

In order to solve this problem, scholars have adopted weighting method ^{[5] [6] [7] [8]}the advantage of weighting method is that its method is simple, but the setting of its weights but and be not easy, and need to rule of thumb be arranged, and for different problems, different weights need be set, even same problem but parameter (as system loading) are different, also need to arrange different weights.This deficiency has reduced its practicality in solving practical problems.The method that another kind addresses this problem is multi-objective Evolutionary Algorithm ^{[4] [9] [10] [11] [12] [13] [14] [15] [16] [17]}.The advantage of multi-objective Evolutionary Algorithm is that it can be used for solving the various protruding discontinuous complicated optimum problem of leading, but these algorithms are in the situation that lack the problem specifying information, that solution space is carried out to its efficiency of random search is low, and amount of calculation is large.Along with described problem unit quantity increases, its solution space more sophisticated, the amount of calculation that these algorithms expend sharply increases and solving precision can not be guaranteed.Multi-objective Evolutionary Algorithm adopts penalty function method mostly for the processing of constraints, and the penalty function value is not quite similar for different system, need to rule of thumb adjust setting, has reduced its practicality in solving practical problems.

The above-mentioned list of references of mentioning is as follows:

[1]Q.H.Wu，and Y.J.Cao.Dispatching.Encyclopedia of Electrical and Electronics Engineering，John Wiley&Sons Inc.，edited by John G.Webster，1999.

[2]Q.H.Wu，and J.T.Ma.Power system optimal reactive power dispatch using evolutionary programming[J].IEEE Transactions on Power Systems，1995，10(3)：1243-1249.

[3] Hou Yunhe, Xiong Xingen, Wu Yaowu, etc. the Power System Economic Load Dispatch based on the broad sense ant group algorithm [J]. Proceedings of the CSEE, 2003,23 (3): 59-64.

[4]C.X.Guo，J.P.Zhan，and Q.H.Wu.Dynamic economic emission dispatch based on group search optimizer with multiple producers[J].Electric Power Systems Research，2012，86：8-16.

[5]A.K.Basu，A.Bhattacharya，S.Chowdhury，and S.P.Chowdhury.Planned Scheduling for Economic Power Sharing in a CHP-Based Micro-Grid[J].IEEE Transactions on Power Systems，2012，27(1)：30-38.

[6]L.Bayon，J.Grau，M.Ruiz，and P.Suarez.The exact solution of the environmental／economic dispatch problem[J].IEEE Transactions on Power Systems，2012，27(2)：723-731.

[7]P.Venkatesh，R.Gnanadass，and N.Padhy.Comparison and application of evolutionary programming techniques to combined economic emission dispatch with line flow constraints[J].IEEE Transactions on Power Systems，2003，18(2)：688-697.

[8]C.Palanichamy and N.S.Babu.Analytical solution for combined economic and emissions dispatch[J].Electric Power Systems Research，2008，78(7)：1129-1137.

[9]M.Abido.Environmental／economic power dispatch using multiobjective evolutionary algorithms[J].IEEE Transactions on Power Systems，2003，18(4)：1529-1537.

[10]L.H.Wu，Y.N.Wang，X.F.Yuan，and S.W.Zhou.Environmental／economic power dispatch problem using multi-objective differential evolution algorithm[J].Electric Power Systems Research，2010，80(9)：1171-1181.

[11]Q.H.Wu，Z.Lu，M.S.Li，and T.Y.Ji.Optimal placement of facts devices by a group search optimizer with multiple producer.in Evolutionary Computation.CEC2008.IEEE Congress on，Jun.2008，pp.1033-1039..

[12]S.He，Q.H.Wu，and J.R.Saunders.Group search optimizer：An optimization algorithm inspired by animal searching behavior[J].IEEE Transactions on Evolutionary Computation，2009，13(5)：973-990.

[13]X.Xia and A.M.Elaiw.Optimal dynamic economic dispatch of generation：A review[J].Electric Power Systems Research，2010，80(8)：975-986.

[14]M.Basu.Dynamic economic emission dispatch using nondominted sorting genetic algprthim-II[J].Electric Power Energy System，2008，30(2)：140-149.

[15]L.H.Wu，Y.N.Wang，X.F.Yuan，and S.W.Zhou.Environmental／economic power dispatch problem using multi-objective differential evolution algorithm[J].Electric Power Systems Research，2010，80(9)：1171-1181.

[16]J.-B.Park，Y.-W.Jeong，J.-R.Shin，and K.Lee.An improved particle swarm optimization for nonconvex economic dispatch problems[J].IEEE Transactions on Power Systems，2010，25(1)：156-166.

[17]L.Wang and C.Singh.Balancing risk and cost in fuzzy economic dispatch including wind power penetration based on particle swarm optimization[J].Electric Power Systems Research，2008，78(8)：1361-1368.

Summary of the invention

The objective of the invention is, in order to solve above-mentioned prior art, the weighted value between the different target function to be set, penalty function value corresponding to constraints is not quite similar for different system, need to rule of thumb adjust setting, and solving precision can not be guaranteed, spent computing time is longer defect also, a kind of large-scale electrical power system problem that is applicable to solving is provided, can improves the power system dispatching method based on mixing multiple target λ iterative method and Newton method of business efficiency.

Purpose of the present invention can reach by taking following technical scheme:

Power system dispatching method based on mixing multiple target λ iterative method and Newton method is characterized in that comprising the following steps:

1) obtain the exert oneself upper limit and the lower limit data of every unit in the electric power system with many generating sets, the coefficient data of exert oneself-fuel cost function, the coefficient data of the function of exerting oneself-discharge, B coefficient data and the system total load data of transmission line loss;

2) according to step 1) data that obtain, set up the mathematical optimization model of power system environment Economic Dispatch Problem;

3) according to step 2) model set up, based on multiple target Kuhn column gram optimal conditions, adopt multiple target λ iterative method (M λ I) to solve the power system environment Economic Dispatch Problem of not considering transmission line loss, obtain one group of Pareto optimum solution;

4) using step 3) each Pareto optimum solution of obtaining is as initial solution, adopts Newton Algorithm to consider the power system environment Economic Dispatch Problem of transmission line loss, obtains optimal solution set;

5) adopt Multiobjective Decision Making Method in step 4) determine final the solution in the optimal solution set that obtains;

6) using step 5) the final solution determined sends to relevant power plant or unit as instruction by automatic power-generating controller for use, by the automatic control and adjustment device of power plant or unit, realizes the control to unit generation power.

Concrete, step 1) in described electric power system, unit quantity is n _gplatform, step 2) process of establishing of mathematical optimization model of described power system environment Economic Dispatch Problem, specific as follows:

2.1) exert oneself-fuel cost function of unit i is shown below:

$f_{\mathrm{fuel}}\left(x_i\right)=a_i+b_i{x}_i+c_i{x}_i^2---\left(1\right)$

Wherein, 1≤i≤n _g, f _fuel(x _i) be the exert oneself-fuel cost function of unit i, x _ifor the meritorious of unit exerted oneself, a _i, b _iand c _iexert oneself-fuel cost coefficient for unit i;

2.2) function of exerting oneself-discharge of unit i is shown below:

$f_{\mathrm{emi}}\left(x_i\right)={\mathrm{\α}}_i+{\mathrm{\β}}_i{x}_i+{\mathrm{\γ}}_i{x}_i^2+{\∈}_i{e}^{{\mathrm{\ξ}}_i{x}_i}---\left(2\right)$

Wherein, f _emi(x _i) be the function of exerting oneself-discharge of unit i, α _i, β _i, γ _i, ∈ _iand ξ _ithe function coefficients of exerting oneself-discharge for unit i;

2.3) upper limit and the lower limit constraint of exerting oneself of unit i is shown below:

$x_i^{\min }\≤x_i\≤x_i^{\max }---\left(3\right)$

Wherein, with be respectively the exert oneself upper limit and the lower limit of unit i;

2.4) consider that the load balancing constraint of transmission line loss is shown below:

$\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{x}_i-x_D-x_L=0---\left(4\right)$

Wherein, x _dfor system total load, x _lfor transmission line loss, x _lthe B Y-factor method Y that employing is shown below calculates:

$x_L=\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}\underset{j=1}{\overset{n_g}{\mathrm{\Σ}}}{x}_i{B}_{\mathrm{ij}}{x}_j+\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{B}_{i0}{x}_i+B_{00}---\left(5\right)$

Wherein, B _ij, B _i0and B ₀₀b coefficient for transmission line loss;

2.5) consider that the mathematical optimization model of power system environment Economic Dispatch Problem of transmission line loss is as follows:

$\begin{array}{c}\mathrm{Minimize}:f\left(x\right)=\left[\begin{array}{c}{f}_1\left(x\right)\\ f_2\left(x\right)\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{f}_{\mathrm{fuel}}\left(x_i\right)\\ \underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{f}_{\mathrm{emi}}\left(x_i\right)\end{array}\right]\\ s.t.\left(3\right)\left(4\right)\left(5\right)\end{array}---\left(6\right)$

Wherein, f _fuel(x _i) and f _emi(x _i) by formula (1) and formula (2), meaned respectively.

Concrete, step 3) described employing multiple target λ solution by iterative method is not considered the power system environment Economic Dispatch Problem of transmission line loss, obtains Pareto optimum solution, specific as follows:

3.1) value of exerting oneself of given firm output unit;

3.2) for a very large λ value, try to achieve every meritorious exerting oneself that unit is corresponding, calculate the generation load amount of unbalance;

3.3) for a very little λ value, try to achieve every meritorious exerting oneself that unit is corresponding, calculate the generation load amount of unbalance;

3.4) if step 3.2) and step 3.3) the generation load amount of unbalance jack per line that calculates, there do not is potential Pareto optimum solution, return to step 3.1); If step 3.2) and step 3.3) the generation load amount of unbalance that calculates jack per line not, adopt dichotomy to revise λ value, until find a λ value, meritorious the exerting oneself of every unit of its correspondence meets load balancing, preserve the meritorious of this λ value and every unit and exert oneself, meritorious the exerting oneself of each unit is Pareto optimum solution.

Concrete, described generation load amount of unbalance is the difference between the total generated output of each unit and system total load.

Concrete, meritorious the exerting oneself that described every unit is corresponding makes to meet equal difference than micro-gaining rate rule between every two units.

Concrete, step 5) described Multiobjective Decision Making Method adopts the sort method that approaches ideal value, specific as follows:

5.1) at first, calculate the weighting decision matrix v of standardization _ij:

$v_{\mathrm{ij}}={\mathrm{\ω}}_i(f_i^{+}-f_{\mathrm{ij}})/(f_i^{+}-f_i^{-}),i=\mathrm{1,2,3},\·\·\·,N_{\mathrm{obj}},j=\mathrm{1,2,3},\·\·\·,J$

Wherein, $f_i^{-}=\underset{j}{\min }{f}_{\mathrm{ij}},f_i^{+}=\underset{j}{\max }{f}_{\mathrm{ij}},{\mathrm{\ω}}_i=\frac{1}{N_{\mathrm{obj}}}\underset{j=i}{\overset{N_{\mathrm{obj}}}{\mathrm{\Σ}}}\frac{1}{j},i=\mathrm{1,2,3},\·\·\·,N_{\mathrm{obj}},$ F _ijfor j in optimal solution set i the target function value of separating, N _objfor the number of target in multiple-objection optimization, J is the number of separating in optimal solution set;

5.2) calculate respectively ideal point A ⁺ideal point A least ^-:

$A^{-}=\{v_1^{-},v_2^{-},\·\·\·,v_N^{-}\}$

$A^{-}=\{v_1^{-},v_2^{-},\·\·\·,v_N^{-}\}$

Wherein, $v_i^{+}=\underset{j}{\max }{v}_{\mathrm{ij}},v_i^{-}=\underset{j}{\min }{v}_{\mathrm{ij}};$

5.3) calculate respectively the distance B of each optimal solution to ideal point ⁺with to the distance B of ideal point least ^-:

$D_j^{+}=\sqrt{{\mathrm{\Σ}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{+})}^2}$

$D_j^{-}=\sqrt{{\mathrm{\Σ}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{-})}^2}$

Wherein, j=1,2,3 ... J;

5.4) calculate the distance of each optimal solution than R _j:

$R_j=D_j^{-}/(D_j^{-}+D_j^{+})$

Wherein, j=1,2,3 ... J;

5.5) by R _jmaximum optimal solution is chosen as final unit maintenance and the scheme of exerting oneself.

The present invention has following beneficial effect with respect to prior art:

1, the inventive method is according to the multiple target kuhn tucker condition, and the solution of trying to achieve is globally optimal solution but not approximate optimal solution; Its amount of calculation and unit quantity are linear, are applicable to solving the large-scale electrical power system problem.

2, the inventive method is in being applicable to the large-scale electrical power system problem of a large amount of units, amount of calculation is little, computing time is short, convergence precision is high, its with the obvious advantage aspect precision and amount of calculation in containing the large-scale electrical power system of a large amount of units, can greatly improve economy and the efficiency of electric power system generating.

The accompanying drawing explanation

The power system dispatching method flow schematic diagram that Fig. 1 is the inventive method.

Fig. 2 is the Pareto forward position curve chart that the inventive method and MOPSO algorithm obtain on 6 unit EED problems.

Fig. 3 is the Pareto forward position curve chart that the inventive method and MOPSO algorithm obtain on 14 unit EED problems.

Fig. 4 is the Pareto forward position curve chart that the inventive method and MOPSO algorithm obtain on 140 unit EED problems.

Embodiment

Embodiment 1:

As shown in Figure 1, the power system dispatching method based on mixing multiple target λ iterative method and Newton method of the present embodiment comprises the following steps:

1) obtain and there is n _gthe exert oneself upper limit and the lower limit data of every unit in the electric power system of platform generating set

with

the coefficient data a of exert oneself-fuel cost function _i, b _i, c _i, the function of exerting oneself-discharge coefficient data α _i, β _i, γ _i, ∈ _i, ξ _i, transmission line loss B coefficient data B _ij, B _i0, B ₀₀with system total load data x _d;

2) according to step 1) data that obtain, the mathematical optimization model of setting up the power system environment Economic Dispatch Problem is EED model (following statement is write respectively EED problem and EED model by environmental economy scheduling problem and environmental economy scheduling model), specific as follows:

2.1) exert oneself-fuel cost function of unit i as shown in the formula quadratic polynomial shown in:

$f_{\mathrm{fuel}}\left(x_i\right)=a_i+b_i{x}_i+c_i{x}_i^2---\left(1\right)$

Wherein, 1≤i≤n _g, f _fuel(x _i) be the exert oneself-fuel cost function of unit i, x _ifor the meritorious of unit exerted oneself, a _i, b _iand c _iexert oneself-fuel cost coefficient for unit i;

2.2) unit i exert oneself-discharge function as shown in the formula quadratic polynomial and the exponential depth sum shown in:

$f_{\mathrm{emi}}\left(x_i\right){=\mathrm{\α}}_i+{\mathrm{\β}}_i{x}_i+{\mathrm{\γ}}_i{x}_i^2+{\∈}_i{e}^{{\mathrm{\ξ}}_i{x}_i}---\left(2\right)$

Wherein, f _emi(x _i) be the function of exerting oneself-discharge of unit i, α _i, β _i, γ _i, ∈ _iand ξ _ithe function coefficients of exerting oneself-discharge for unit i;

2.3) upper limit and the lower limit constraint of exerting oneself of unit i is shown below:

$x_i^{\min }\≤x_i\≤x_i^{\max }---\left(3\right)$

Wherein,

with be respectively the exert oneself upper limit and the lower limit of unit i;

2.4) consider that the load balancing constraint of transmission line loss is shown below:

$\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{x}_i-x_D-x_L=0---\left(4\right)$

Wherein, x _dfor system total load, x _lfor transmission line loss, x _lthe B Y-factor method Y that employing is shown below calculates:

$x_L=\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}\underset{j=1}{\overset{n_g}{\mathrm{\Σ}}}{x}_i{B}_{\mathrm{ij}}{x}_j+\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{B}_{i0}{x}_i+B_{00}---\left(5\right)$

Wherein, B _ij, B _i0and B ₀₀b coefficient for transmission line loss;

2.5) consider that the EED model of transmission line loss is as follows:

$\begin{array}{c}\mathrm{Minimize}:f\left(x\right)=\left[\begin{array}{c}{f}_1\left(x\right)\\ f_2\left(x\right)\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{f}_{\mathrm{fuel}}\left(x_i\right)\\ \underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{f}_{\mathrm{emi}}\left(x_i\right)\end{array}\right]\\ s.t.\left(3\right)\left(4\right)\left(5\right)\end{array}---\left(6\right)$

Wherein, f _fuel(x _i) and f _emi(x _i) by formula (1) and formula (2), meaned respectively;

3) according to step 2) the EED model set up, based on multiple target Kuhn column gram optimal conditions, adopt multiple target λ iterative method (M λ I) to solve the EED problem of not considering transmission line loss, obtain Pareto optimum solution, specific as follows:

3.1) value of exerting oneself of given firm output unit;

3.2) for a very large λ value (establishing this value for-0.00001), try to achieve every meritorious exerting oneself that unit is corresponding, calculate the generation load amount of unbalance;

3.3) for a very little λ value (establishing this value for-6000), try to achieve every meritorious exerting oneself that unit is corresponding, calculate the generation load amount of unbalance;

3.4) if step 3.2) and step 3.3) the generation load amount of unbalance jack per line that calculates, there do not is potential Pareto optimum solution, return to step 3.1); If step 3.2) and step 3.3) the generation load amount of unbalance that calculates jack per line not, adopt dichotomy to revise λ value, until find a λ value, meritorious the exerting oneself of every unit of its correspondence meets load balancing, preserve the meritorious of this λ value and every unit and exert oneself, meritorious the exerting oneself of each unit is Pareto optimum solution.

Can be expressed as formula (7) for a Model for Multi-Objective Optimization that contains equation and inequality constraints:

Minimize：f(x)

s.t.g(x)≤0 (7)

h(x)＝0

If for a Pareto optimum solution of formula (7), exist one group (λ, u, v) to meet formula (8):

$\begin{array}{c}\▿f\left(\stackrel{\‾}{x}\right)\mathrm{\λ}+\▿g\left(\stackrel{\‾}{x}\right)u+\▿h\left(\stackrel{\‾}{x}\right)v=0\\ \left[u\right]g\left(\stackrel{\‾}{x}\right)=0\\ \mathrm{\λ}\≥0,\mathrm{\λ}\≠0,u\≥0\end{array}---\left(8\right)$

If wherein

, u _i=0, wherein set

and λ>=0, λ ≠ 0 means that each element of λ the inside is more than or equal to 0, but can not equal 0 by each element simultaneously;

The f that the EED model is corresponding, g and h can mean an accepted way of doing sth (9):

$f_1\left(x\right)=\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}(a_i+b_i{x}_i+c_i{x}_i^2)$

$f_2\left(x\right)=\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}({\mathrm{\α}}_i+{\mathrm{\β}}_i{x}_i+{\mathrm{\γ}}_i{x}_i^2+{\∈}_i{e}^{{\mathrm{\ξ}}_i{x}_i})$

$g_i\left(x\right)={-x}_i+x_i^{\min }\≤0,i\∈I_0---\left(9\right)$

$g_{(i+n_g)}\left(x\right)=x_i-x_i^{\max }\≤0,i\∈I_0$

$h\left(x\right)=\underset{i=1}{\overset{n_g}{\mathrm{\Σ}}}{x}_i-x_D-x_L=0$

Wherein, I ₀=1,2 ..., n _g;

According to the multiple target kuhn tucker condition, if

a Pareto optimum solution:

$\begin{array}{c}\▿f\left(\stackrel{\‾}{x}\right)\mathrm{\λ}+\▿g\left(\stackrel{\‾}{x}\right)u+\▿h\left(\stackrel{\‾}{x}\right)v=\left[\begin{array}{c}{\mathrm{\λ}}_1\frac{\∂f_1}{\∂x_1}+{\mathrm{\λ}}_2\frac{\∂f_2}{\∂x_1}+\underset{i=1}{\overset{{2n}_g}{\mathrm{\Σ}}}{u}_i\frac{\∂g_i}{\∂x_i}+v\frac{\∂h}{\∂x_1}\\ {\mathrm{\λ}}_1\frac{\∂f_1}{\∂x_2}+{\mathrm{\λ}}_2\frac{\∂f_2}{\∂x_2}+\underset{i=1}{\overset{{2n}_g}{\mathrm{\Σ}}}{u}_i\frac{\∂g_i}{\∂x_2}+v\frac{\∂h}{\∂x_2}\\ .\\ .\\ .\\ {\mathrm{\λ}}_1\frac{\∂f_1}{\∂x_{n_g}}+{\mathrm{\λ}}_2\frac{\∂f_2}{\∂x_{n_g}}+\underset{i=1}{\overset{{2n}_g}{\mathrm{\Σ}}}{u}_i\frac{\∂g_i}{\∂x_{n_g}}+v\frac{\∂h}{\∂x_{n_g}}\end{array}\right]\\ =\left[\begin{array}{c}{\mathrm{\λ}}_1\frac{\∂f_1}{\∂x_1}+{\mathrm{\λ}}_2\frac{\∂f_2}{\∂x_1}+u_1\frac{\∂g_1}{\∂x_1}+u_{(1+n_g)}\frac{\∂g_{(1+n_g)}}{\∂x_1}+v\frac{\∂h}{\∂x_1}\\ {\mathrm{\λ}}_1\frac{\∂f_1}{\∂x_2}+{\mathrm{\λ}}_2\frac{\∂f_2}{\∂x_2}+u_2\frac{\∂g_2}{\∂x_2}+u_{(2+n_g)}\frac{\∂g_{(2+n_g)}}{\∂x_2}+v\frac{\∂h}{\∂x_2}\\ .\\ .\\ .\\ {\mathrm{\λ}}_1\frac{\∂f_1}{\∂x_{n_g}}+{\mathrm{\λ}}_2\frac{\∂f_2}{\∂x_{n_g}}+u_{n_g}\frac{\∂g_{n_g}}{\∂x_{n_g}}+u_{\left({2n}_g\right)}\frac{\∂g_{\left(2n_g\right)}}{\∂x_{n_g}}+v\frac{\∂h}{\∂x_{n_g}}\end{array}\right]=0\end{array}---\left(10\right)$

Wherein, λ >=0, λ ≠ 0, u >=0;

Formula (10) can three kinds of situations of a minute accepted way of doing sth (11)～(13) be discussed:

If λ ₁=0 and λ ₂>0:

$\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}=\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i}+\frac{B_1{u}_1-B_2{u}_i}{{\mathrm{\&lambda;}}_2}=-\frac{v}{{\mathrm{\&lambda;}}_2}---\left(11\right)$

If λ ₂=0 and λ ₁>0:

$\frac{{\&PartialD;f}_1}{\&PartialD;x_1}=\frac{{\&PartialD;f}_1}{\&PartialD;x_i}+\frac{B_1{u}_1-B_2{u}_i}{{\mathrm{\&lambda;}}_1}=-\frac{v}{{\mathrm{\&lambda;}}_1}---\left(12\right)$

If λ ₂=0 and λ ₁>0:

$\begin{array}{c}\frac{\frac{{\&PartialD;f}_1}{\&PartialD;x_1}-\frac{\&PartialD;f_1}{\&PartialD;x_i}}{\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i}}=\frac{B_1{u}_1-B_2{u}_i}{{\mathrm{\&lambda;}}_1(\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i})}-\frac{{\mathrm{\&lambda;}}_2}{{\mathrm{\&lambda;}}_1},\&ForAll;i\&NotElement;I_1\\ \frac{\&PartialD;f_1}{\&PartialD;x_1}=\frac{\&PartialD;f_1}{\&PartialD;x_i}+\frac{B_1{u}_1-B_2{u}_i}{{\mathrm{\&lambda;}}_1},\&ForAll;i\&Element;I_1\end{array}---\left(13\right)$

Wherein, $I_1=\{i:\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i}=0,i\&NotEqual;1\};$

According to x ₁and x _iwhether be positioned at its exert oneself upper limit and lower limit border, formula (11)～(13) can be divided into 4 kinds of situations:

If a $x_i\&NotEqual;x_i^{\min }$ And $x_i\&NotEqual;x_i^{\max },$ $\&ForAll;i\&Element;I_0,$ B ₁=0, B ₂=0;

If b ( $x_1\&NotEqual;x_1^{\min }$ Order $x_1\&NotEqual;x_1^{\max }$ ) and ( $x_i=x_i^{\min }$ Or $x_i=x_i^{\max },i\&NotEqual;1$ ), B ₁=0, B ₂=1;

If c $x_1=x_1^{\min }$ And $x_i=x_i^{\min },$ B ₁=1, B ₂=1;

If d $x_1=x_1^{\min }$ And $x_i\&NotEqual;x_i^{\min },$ B ₁=1, B ₂=0;

Formula (10) is that solving of formula (11)～(13) can be divided into two steps:

Solve formula (11) and (12) in the first step:

Solving of formula (11): can adopt simply the λ iterative method, a given initial lambda values and determine exerting oneself of every unit meeting formula (11).If

increase λ ₀value, if

reduce λ ₀value, until formula (11) and be met, the solution of now trying to achieve is for making target function f simultaneously ₂(x) minimized solution, according to formula (11) and

the monotonic increase characteristic, if for a given λ ₀, have ${\mathrm{\&lambda;}}_0<\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i^{\min }},$ Order $x_i=x_i^{\min },$ If for a given λ ₀, have ${\mathrm{\&lambda;}}_0>\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i^{\max }},$ Order $x_i=x_i^{\max }.$

Solving of formula (12): can adopt simply the λ iterative method, a given initial lambda values

and determine exerting oneself of every unit meeting formula (12).If

increase λ ₀value, if

reduce λ ₀value, until formula (12) and

be met, the solution of now trying to achieve is for making target function f simultaneously ₁(x) minimized solution, according to formula (12) and the monotonic increase characteristic, if for a given λ ₀, have ${\mathrm{\&lambda;}}_0<\frac{\&PartialD;f_1}{\&PartialD;x_i^{\min }},$ Order $x_i=x_i^{\min },$ If for a given λ ₀, have ${\mathrm{\&lambda;}}_0>\frac{\&PartialD;f_1}{\&PartialD;x_i^{\max }},$ Order $x_i=x_i^{\max }.$

Solving formula (13) in second step: the program pseudo-code (λ in table 1 as shown in following table 1 and table 2 that solves the EED problem of not considering transmission line loss _lbe made as-0.00001, λ _sbe made as-6000), table 2 is a subprogram pseudo-code table in table 1.

The pseudo-code table of table 1 multiple target λ iterative method program

Table 2 obtains the pseudo-code table of unit output program according to λ

In table 2, have 2 need to describe: the one, how to judge

with whether meet formula (13), first judgement

the above-mentioned b class of take describes as example, i.e. B ₁=0, B ₂=1, if

and in formula (13), the second row meets; If $(\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_i^{\min }}<0),$ And $(\frac{\&PartialD;f_1}{\&PartialD;x_1}-\frac{\&PartialD;f_1}{\&PartialD;x_i})/(\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i})<\mathrm{\&lambda;},$ The first row in formula (13) meets; If $(\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_i^{\min }}<0),$ And $(\frac{\&PartialD;f_1}{\&PartialD;x_1}-\frac{\&PartialD;f_1}{\&PartialD;x_i})/(\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}-\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000382924340000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_i})>\mathrm{\&lambda;},$ The first row in formula (13) meets; In like manner, can judge similarly

whether meet formula (13).

The 2nd, how through type (13) is determined x _ivalue.Two kinds of methods are arranged usually, and a kind of is direct solution; Another kind is to obtain by tabling look-up, for a fixing x ₁value, by each x _icorresponding value be stored in advance in a table, in the solution procedure of M λ I, table look-at obtains x _ivalue.Due to the look-up table Simple fast, in the computational process of the present embodiment, adopt look-up table.

4) in step (3), because transmission line loss is considered, so in this step using step 3) each Pareto optimum solution of obtaining is as initial solution, adopts Newton Algorithm to consider the EED problem of transmission line loss, obtain optimal solution set, specific as follows:

Adopt Taylor expansion, formula (8) can be expressed as to formula (14):

$\begin{array}{c}\&dtri;f\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&lambda;}+{\&dtri;}^{2}f\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&lambda;\&Delta;x}+\&dtri;f\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&Delta;\&lambda;}\\ +\&dtri;g\left(\stackrel{\&OverBar;}{x}\right)u+{\&dtri;}^{2}g\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&mu;\&Delta;x}+\&dtri;g\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&Delta;\&mu;}\\ +\&dtri;h\left(\stackrel{\&OverBar;}{x}\right)v+{\&dtri;}^{2}h\left(\stackrel{\&OverBar;}{x}\right)\mathrm{v\&Delta;x}+\&dtri;h\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&Delta;v}=0\\ -\left[\mathrm{\&mu;}\right]g\left(\stackrel{\&OverBar;}{x}\right)-\left[\mathrm{\&mu;}\right]\&dtri;g{\left(\stackrel{\&OverBar;}{x}\right)}^T\mathrm{\&Delta;x}-\left[g\left(\stackrel{\&OverBar;}{x}\right)\right]\mathrm{\&Delta;\&mu;}=0\\ h\left(\stackrel{\&OverBar;}{x}\right)+\&dtri;h{\left(\stackrel{\&OverBar;}{x}\right)}^T\mathrm{\&Delta;x}=0\end{array}---\left(14\right)$

Formula (14) can be write the compact form of an accepted way of doing sth (15):

A×Δy＝b (15)

Wherein

Δy＝[Δx Δλ Δμ Δv] ^T (16)

$A=\left[\begin{array}{cccc}M& \&dtri;f\left(\stackrel{\&OverBar;}{x}\right)& \&dtri;g\left(\stackrel{\&OverBar;}{x}\right)& \&dtri;h\left(\stackrel{\&OverBar;}{x}\right)\\ -\left[\mathrm{\&mu;}\right]\&dtri;g{\left(\stackrel{\&OverBar;}{x}\right)}^T& 0& -\left[g\left(\stackrel{\&OverBar;}{x}\right)\right]& 0\\ \&dtri;h{\left(\stackrel{\&OverBar;}{x}\right)}^T& 0& 0& 0\end{array}\right]---\left(17\right)$

$b=\left[\begin{array}{c}-r_{\mathrm{dual}}\\ -r_{\mathrm{cent}}\\ -h\left(\stackrel{\&OverBar;}{x}\right)\end{array}\right]=\left[\begin{array}{c}-\&dtri;f\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&lambda;}-\&dtri;g\left(\stackrel{\&OverBar;}{x}\right)u-\&dtri;h\left(\stackrel{\&OverBar;}{x}\right)v\\ \left[\mathrm{\&mu;}\right]g\left(\stackrel{\&OverBar;}{x}\right)\\ -h\left(\stackrel{\&OverBar;}{x}\right)\end{array}\right]---\left(18\right)$

In formula (17):

$M={\&dtri;}^{2}f\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&lambda;}+{\&dtri;}^{2}g\left(\stackrel{\&OverBar;}{x}\right)\mathrm{\&mu;}+{\&dtri;}^{2}h\left(\stackrel{\&OverBar;}{x}\right)v---\left(19\right)$

Adopt Newton Algorithm to consider that the program pseudo-code of the EED problem of transmission line loss is listed in the table below in 3.

Table 3 adopts the pseudo-code table of the program of Newton Algorithm EED problem

5) adopt Multiobjective Decision Making Method in step 4) determine final the solution in the optimal solution set that obtains; Described multiobjective decision-making adopts the sort method (Technique for Order Preference by Similarity to Ideal Solution, TOPSIS) that approaches ideal value.TOPSIS comprises the following steps:

5.1) at first, calculate the weighting decision matrix v of standardization _ij:

$v_{\mathrm{ij}}={\mathrm{\&omega;}}_i(f_i^{+}-f_{\mathrm{ij}})/(f_i^{+}-f_i^{-}),i=\mathrm{1,2,3},...,N_{\mathrm{obj}},j=\mathrm{1,2,3},...,J---\left(20\right)$

Wherein, $f_i^{-}=\underset{j}{\min }{f}_{\mathrm{ij}},f_i^{+}=\underset{j}{\max }{f}_{\mathrm{ij}},{\mathrm{\&omega;}}_i=\frac{1}{N_{\mathrm{obj}}}\underset{j=i}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}\frac{1}{j},i=\mathrm{1,2,3},...,N_{\mathrm{obj}},$ F _ijfor j in optimal solution set i the target function value of separating, N _objfor the number of target in multiple-objection optimization, J is the number of separating in optimal solution set;

5.2) calculate respectively ideal point A ⁺ideal point A least ^-:

$A^{-}=\{v_1^{-},v_2^{-},...,v_N^{-}\}$

$A^{-}=\{v_1^{-},v_2^{-},...,v_N^{-}\}$

Wherein, $v_i^{+}=\underset{j}{\max }{v}_{\mathrm{ij}},v_i^{-}=\underset{j}{\min }{v}_{\mathrm{ij}};$

5.3) calculate respectively the distance B of each optimal solution to ideal point ⁺with to the distance B of ideal point least ^-:

$D_j^{+}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{+})}^2}$

$D_j^{-}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{-})}^2}$

Wherein, j=1,2,3 ... J;

5.4) calculate the distance of each optimal solution than R _j:

$R_j=D_j^{-}/(D_j^{-}+D_j^{+})$

Wherein, j=1,2,3 ... J;

5.5) by R _jmaximum optimal solution is chosen as final unit maintenance and the scheme of exerting oneself;

6) using step 5) the final solution determined sends to relevant power plant or unit as instruction by automatic power-generating controller for use, by the automatic control and adjustment device of power plant or unit, realizes the control to unit generation power.

Embodiment 2:

Validity for the power system dispatching method based on mixing multiple target λ iterative method and Newton method of checking the above embodiment of the present invention 1, the present embodiment is respectively with 6 units, the system of 14 units and 140 units is example, the data of described three systems are the document from the above-mentioned background technology [15] and [16] middle acquisition respectively, wherein the total load of 6 machine set systems is 283.4MW, the total load of 14 machine set systems is 950MW, and the total load of 140 units is 49342MW.

In order to compare, adopt the described EED problem of MOPSO Algorithm for Solving simultaneously.In MOPSO, population number and maximum iteration time arrange as shown in table 4.While with MOPSO, solving described EED problem, adopt penalty function method to process constraints, the absolute value that is about to the amount of unbalance of the equality constraint shown in formula (4) is multiplied by penalty factor and is added in corresponding target function, and the penalty factor adopted also is listed in the table below in 4.

System	The population number	Maximum iteration time	f 1Corresponding penalty factor	f 2Corresponding penalty factor
					6 units	50	100	5000	3
14 units	400	400	2000	4
					140 units	800	600	20000	40

Parameter and the penalty factor settings of table 4MOPSO algorithm in 3 systems

Fig. 2 has meaned that the method for the embodiment of the present invention 1 solves the solution that described 6 units obtain, also meaned the result that adopts the described problem of MOPSO Algorithm for Solving to obtain simultaneously, Fig. 3 has meaned that the method for the embodiment of the present invention 1 solves the solution that described 14 machine set systems obtain, and has also meaned the result that adopts the described problem of MOPSO Algorithm for Solving to obtain simultaneously.

Can see, with the result that adopts the MOPSO algorithm to obtain, adopt expansion λ iterative method can access the solution that simultaneously there is less generating cost value and less transmission line loss value, show that convergence precision is high.

For method validity in solving large-scale electrical power system of verifying the embodiment of the present invention 1, also for solving the EED problem of an electric power system that contains 140 units, also listed the result that adopts the described problem of MOPSO Algorithm for Solving to obtain, as shown in Figure 4 simultaneously.

The method of the embodiment of the present invention 1 at a processor is core ^tMon the personal computer of i7-2600CPU3.40GHz, realize, it solves 6 machine set systems, the result of 14 machine set systems and 140 machine set systems, the Δ index obtained and the time spent are listed in the table below in 5, list C λ IN and MOPSO and solve the Δ index obtained and the time spent (notes: considered transmission line loss when solving 6 units and 14 machine set system simultaneously in table 5, but do not consider transmission line loss owing to lacking data when solving 140 machine set system, table 5, Fig. 2, Fig. 3, the difference of M λ I and C λ IN in Fig. 4: what M λ I meaned is multiple target λ iterative method, only containing step 3 and not containing step 4, what C λ IN meaned is to mix multiple target λ iterative method and Newton method, has comprised step 3 and step 4 simultaneously).

In sum, the invention provides a kind of simple electric power system Multiobjective Scheduling method efficiently, its amount of calculation is little, computing time is short, convergence precision is high, its with the obvious advantage aspect precision and amount of calculation in containing the large-scale electrical power system of a large amount of units, greatly improved economy and the efficiency of electric power system generating.

Three kinds of distinct methods of table 5 solve the Δ index of the result that the EED problem obtains and the time spent in 3 systems

The above; it is only patent preferred embodiment of the present invention; but the protection range of patent of the present invention is not limited to this; anyly be familiar with those skilled in the art in the disclosed scope of patent of the present invention; according to the present invention, the technical scheme of patent and inventive concept thereof are equal to replacement or are changed, and all belong to the protection range of patent of the present invention.

Claims (6)

1. the power system dispatching method based on mixing multiple target λ iterative method and Newton method is characterized in that comprising the following steps:

1) obtain the exert oneself upper limit and the lower limit data of every unit in the electric power system with many generating sets, the coefficient data of exert oneself-fuel cost function, the coefficient data of the function of exerting oneself-discharge, B coefficient data and the system total load data of transmission line loss;

2) according to step 1) data that obtain, set up the mathematical optimization model of power system environment Economic Dispatch Problem;

3) according to step 2) model set up, based on multiple target Kuhn column gram optimal conditions, adopt multiple target λ solution by iterative method not consider the power system environment Economic Dispatch Problem of transmission line loss, obtain one group of Pareto optimum solution;

4) using step 3) each Pareto optimum solution of obtaining is as initial solution, adopts Newton Algorithm to consider the power system environment Economic Dispatch Problem of transmission line loss, obtains optimal solution set;

5) adopt Multiobjective Decision Making Method in step 4) determine final the solution in the optimal solution set that obtains;

6) using step 5) the final solution determined sends to relevant power plant or unit as instruction by automatic power-generating controller for use, by the automatic control and adjustment device of power plant or unit, realizes the control to unit generation power.

2. the power system dispatching method based on mixing multiple target λ iterative method and Newton method according to claim 1, is characterized in that: step 1) unit quantity is n in described electric power system _gplatform, step 2) process of establishing of mathematical optimization model of described power system environment Economic Dispatch Problem, specific as follows:

2.1) exert oneself-fuel cost function of unit i is shown below:

$f_{\mathrm{fuel}}\left(x_i\right)=a_i+b_i{x}_i+c_i{x}_i^2---\left(1\right)$

Wherein, 1≤i≤n _g, f _fuel(x _i) be the exert oneself-fuel cost function of unit i, x _ifor the meritorious of unit exerted oneself, a _i, b _iand c _iexert oneself-fuel cost coefficient for unit i;

2.2) function of exerting oneself-discharge of unit i is shown below:

$f_{\mathrm{emi}}\left(x_i\right)={\mathrm{\&alpha;}}_i+{\mathrm{\&beta;}}_i{x}_i+{\mathrm{\&gamma;}}_i{x}_i^2+{\&Element;}_i{e}^{{\mathrm{\&xi;}}_i{x}_i}---\left(2\right)$

Wherein, f _emi(x _i) be the function of exerting oneself-discharge of unit i, α _i, β _i, γ _i, ε _iand ξ _ithe function coefficients of exerting oneself-discharge for unit i;

2.3) upper limit and the lower limit constraint of exerting oneself of unit i is shown below:

$x_i^{\min }\&le;x_i\&le;x_i^{\max }---\left(3\right)$

Wherein,

with

be respectively the exert oneself upper limit and the lower limit of unit i;

2.4) consider that the load balancing constraint of transmission line loss is shown below:

$\underset{i=1}{\overset{n_g}{\mathrm{\&Sigma;}}}{x}_i-x_D-x_L=0---\left(4\right)$

Wherein, x _dfor system total load, x _lfor transmission line loss, x _lthe B Y-factor method Y that employing is shown below calculates:

$x_L=\underset{i=1}{\overset{n_g}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n_g}{\mathrm{\&Sigma;}}}{x}_i{B}_{\mathrm{ij}}{x}_j+\underset{i=1}{\overset{n_g}{\mathrm{\&Sigma;}}}{B}_{i0}{x}_i+B_{00}---\left(5\right)$

Wherein, B _ij, B _i0and B ₀₀b coefficient for transmission line loss;

2.5) consider that the mathematical optimization model of power system environment Economic Dispatch Problem of transmission line loss is as follows:

$\begin{array}{c}\mathrm{Minimize}:f\left(x\right)=\left[\begin{array}{c}{f}_1\left(x\right)\\ f_2\left(x\right)\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{n_g}{\mathrm{\&Sigma;}}}{f}_{\mathrm{fue\; l}}\left(x_i\right)\\ \underset{i=1}{\overset{n_g}{\mathrm{\&Sigma;}}}{f}_{\mathrm{e\; mi}}\left(x_i\right)\end{array}\right]\\ s.t.\left(3\right)\left(4\right)\left(5\right)\end{array}---\left(6\right)$

Wherein, f _fuel(x _i) and f _emi(x _i) by formula (1) and formula (2), meaned respectively.

3. the power system dispatching method based on mixing multiple target λ iterative method and Newton method according to claim 1 and 2, it is characterized in that: step 3) described employing multiple target λ solution by iterative method do not consider the power system environment Economic Dispatch Problem of transmission line loss, obtain Pareto optimum solution, specific as follows:

3.1) value of exerting oneself of given firm output unit;

3.2) for a very large λ value, try to achieve every meritorious exerting oneself that unit is corresponding, calculate the generation load amount of unbalance;

3.3) for a very little λ value, try to achieve every meritorious exerting oneself that unit is corresponding, calculate the generation load amount of unbalance;

3.4) if step 3.2) and step 3.3) the generation load amount of unbalance jack per line that calculates, there do not is potential Pareto optimum solution, return to step 3.1); If step 3.2) and step 3.3) the generation load amount of unbalance that calculates jack per line not, adopt dichotomy to revise λ value, until find a λ value, meritorious the exerting oneself of every unit of its correspondence meets load balancing, preserve the meritorious of this λ value and every unit and exert oneself, meritorious the exerting oneself of each unit is Pareto optimum solution.

4. the power system dispatching method based on mixing multiple target λ iterative method and Newton method according to claim 3, it is characterized in that: described generation load amount of unbalance is the difference between the total generated output of each unit and system total load.

5. the power system dispatching method based on mixing multiple target λ iterative method and Newton method according to claim 3, it is characterized in that: meritorious the exerting oneself that described every unit is corresponding makes to meet equal difference than micro-gaining rate rule between every two units.

6. the power system dispatching method based on mixing multiple target λ iterative method and Newton method according to claim 1, is characterized in that: step 5) described Multiobjective Decision Making Method adopts the sort method that approaches ideal value, specific as follows:

5.1) at first, calculate the weighting decision matrix v of standardization _ij:

v _ij=ω _i(f _i ⁺-f _ij)／(f _i ⁺-f _j ^-)，i=1，2，3，…，N _obj，j＝1，2，3，…，J

Wherein, ${f_i}^{-}=\underset{j}{\min }{f}_{\mathrm{ij}},{f_i}^{+}=\underset{j}{\max }{f}_{\mathrm{ij}},{\mathrm{\&omega;}}_i=\frac{1}{N_{\mathrm{obj}}}\underset{j=i}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}\frac{1}{j},i=\mathrm{1,2,3},...,N_{\mathrm{obj}},$ F _ijfor j in optimal solution set i the target function value of separating, N _objfor the number of target in multiple-objection optimization, J is the number of separating in optimal solution set;

5.2) calculate respectively ideal point A ⁺ideal point A least ^-:

$A^{-}=\{v_1^{-},v_2^{-},...,v_N^{-}\}$

$A^{-}=\{v_1^{-},v_2^{-},...,v_N^{-}\}$

Wherein, $v_i^{+}=\underset{j}{\max }{v}_{\mathrm{ij}},v_i^{-}=\underset{j}{\min }{v}_{\mathrm{ij}};$

5.3) calculate respectively the distance B of each optimal solution to ideal point ⁺with to the distance B of ideal point least ^-:

$D_j^{+}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{+})}^2}$

$D_j^{-}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{-})}^2}$

Wherein, j=1,2,3 ... J;

5.4) calculate the distance of each optimal solution than R _j:

$R_j=D_j^{-}/(D_j^{-}+D_j^{+})$

Wherein, j=1,2,3 ... J;

5.5) by R _jmaximum optimal solution is chosen as final unit maintenance and the scheme of exerting oneself.

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