CN103050983A - Mixed algorithm-based economic operation optimization method for regional power grid - Google Patents

Abstract

The invention discloses a mixed algorithm-based economic operation optimization method for a regional power grid. The economic operation optimization method for the regional power grid is based on the particle swarm optimization and the prime-dual interior point method. According to the economic operation optimization method for the regional power grid provided by the invention, the intelligent algorithm and the classical algorithm are effectively combined with each other, the discrete variable is optimized by the particle swarm optimization, and the continuous variable optimization and the individual adaptation degree estimation are carried out in each generation of the particle swarm optimization by the prime-dual interior point method, so that the algorithm has the advantages of the convenient variable process of the intelligent algorithm and the high optimization ability of the classical algorithm.

Description

A kind of area power grid economical operation optimization method based on hybrid algorithm

Technical field

The invention belongs to electric power system optimization operation field, be specifically related to a kind of area power grid economical operation optimization method based on hybrid algorithm.

Background technology

Reactive Power Optimazation Problem is under the prerequisite that satisfies system's operation constraint, by distributing rationally of reactive power compensator, reaches the problem of active power loss minimum.The reactive power flow that can optimize electrical network by the idle work optimization scheduling distributes, and reduces active loss and the voltage loss of electrical network, thereby improves quality of voltage, and the electricity consumption device security is moved reliably.Aspect the fail safe and economy that guarantee modern power systems, the importance of idle work optimization scheduling has obtained global concern.

Experts and scholars have launched a large amount of research work to this both at home and abroad in decades, the classic algorithm such as quadratic programming, Newton method and interior point method have been proposed, such algorithm computational speed is fast, the optimizing ability is strong, but process the discrete variable difficulty, therefore Recent study person introduces the various intelligent algorithms such as genetic algorithm, particle cluster algorithm, ant group algorithm in the calculating of idle work optimization, has obtained certain achievement, has promoted further developing of Reactive Power Optimazation Problem research.

It is convenient that intelligent algorithm is processed discrete variable, have global optimizing ability, but computational speed is slow, may be absorbed in locally optimal solution.Ordinary particle group's algorithm is all transferred to particle cluster algorithm with variable to be optimized and is optimized, and what estimate that link adopts at individual fitness is that trend is calculated, if the discrete variable in the variable to be optimized is separated with continuous variable, optimize discrete variable by particle cluster algorithm, adopt former dual interior point to calculate and estimate link at individual fitness, optimize simultaneously continuous variable.

Therefore, need a kind of new area power grid economical operation optimization method.

Summary of the invention

Goal of the invention: the present invention is directed to the defective of prior art aspect reactive power optimization of power system, a kind of new area power grid economical operation optimization method based on hybrid algorithm that adopts is provided.

Technical scheme: for solving the problems of the technologies described above, the area power grid economical operation optimization method based on hybrid algorithm of the present invention adopts following technical scheme:

A kind of area power grid economical operation optimization method based on hybrid algorithm, described area power grid economical operation optimization method may further comprise the steps based on particle cluster algorithm and former dual interior point:

(1) network parameter of acquisition electric power system;

(2) set Population Size, maximum iteration time, crossover probability and the variation probability of particle cluster algorithm, set slack variable, Lagrange multiplier and the penalty factor initial value of former dual interior point;

(3) take the discrete variable of network parameter described in the step (1) as variable to be optimized, generate at random the initial population of particle cluster algorithm;

(4) keep each individual discrete variable of population constant, adopt former dual interior point that each individual continuous variable of population is optimized and obtain target function value, and the target function value that optimization is obtained is as the individual fitness of population, and obtains the individual and global optimum's individuality of local optimum of population according to described individual fitness;

(5) according to following formula more translational speed and the position of new particle:

x _i,j(t+1)＝x _i,j(t)+v _i,j(t+1)

Wherein,

Be inertia weight, c ₁And c ₂Be the study factor, r ₁And r ₂Be uniform random number between 0 to 1, p _{I, j}, p _{G, j}Be respectively the control variables value of particle when pbest and gbest position;

(6) keep each individual discrete variable of population constant, adopt former dual interior point that each individual continuous variable of population is optimized, and the target function value that optimization is obtained is as the individual fitness of population, and according to the local optimum of described individual fitness Population Regeneration individual and global optimum's individuality;

(7) repeating step 5-6 is until reach the described maximum iteration time of step (2).

Further, network parameter in the step (1) comprises that bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio, transformer impedance and generator reactive bound.

Further, discrete variable is transformer voltage ratio and reactive compensation capacity described in the step (2).

Beneficial effect: area power grid economical operation optimization method of the present invention intelligent algorithm and classic algorithm are carried out effective combination, adopt particle cluster algorithm to optimize discrete variable, in every generation of particle cluster algorithm, adopt former dual interior point to carry out continuous variable optimization and the assessment of ideal adaptation degree, thereby so that algorithm have the convenient and strong advantage of classic algorithm optimizing ability of intelligent algorithm treatment variable concurrently.

Description of drawings

Fig. 1 is the flow chart of the area power grid economical operation optimization method based on hybrid algorithm of the present invention;

Fig. 2 is the structural representation of IEEE-14 node system;

Fig. 3 is the structural representation of IEEE-30 node system;

Fig. 4 is the structural representation of IEEE-57 node system;

The structural representation of Fig. 5 foot IEEE-118 node system;

Fig. 6 is PSO convergence of algorithm curve;

Fig. 7 is the convergence curve of the area power grid economical operation optimization method based on hybrid algorithm of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, further illustrate the present invention, should understand these embodiment only is used for explanation the present invention and is not used in and limits the scope of the invention, after having read the present invention, those skilled in the art all fall within the application's claims limited range to the modification of the various equivalent form of values of the present invention.

Population (particle swarm optimization, PSO) optimized algorithm is proposed by doctor Eberhart and doctor Kennedy, comes from the research to the flock of birds predation.In the PSO algorithm, each solution of optimization problem is conceptualized as particle.All particles have an adaptive value f who is determined by target function, also have a speed v to determine direction and the distance of their flight.Each particle is known so far the desired positions gbest that desired positions pbest that oneself is found and whole colony find, particle decides next step action by pbest and gbest.

At first initialization a group of PSO algorithm random particles, then particles are just followed current optimal particle and are searched in solution space.Position and the speed of supposing i particle in the d dimension search volume are respectively X ⁱ=(x _{I, 1}x _{I, 2}X _{I, d}) and V ⁱ=(v _{I, 1}v _{I, 2}V _{I, d}).Particle upgrades speed and the position of oneself by following the tracks of individual optimal value pbest and global optimum gbest, concrete formula is as follows:

v _i,j(t+1)=wv _i,j(t)+c ₁r ₁[p _i，j-x _i,j(t)]+c ₂r ₂[p _g，j-x _i，j(t)]

x _i，j(t+1)=x _i，j(t)+v _i，j(t+1)

Wherein, w is inertia weight, c ₁And c ₂Be the study factor, r ₁And r ₂Be uniform random number between 0 to 1, p _{I, j}, p _{G, j}Be respectively the control variables value of particle when pbest and gbest position.

From Karmarkar proposes to have the interior point method of linear programming of polynomial computation complexity in 1984 noons since, interior point method with its convergence rapidly, the advantages such as strong robustness have won the green grass or young crops of optimizing the field scholar and have narrowed, and are widely used in fields such as Optimal Power Flow Problems, state estimation.

The Optimal Power Flow Problems problem is the complex nonlinear planning problem that a class comprises equation, inequality constraints, and its Mathematical Modeling can be described with following formula:

$\left\{\begin{array}{cc}\min & f\left(x\right)\\ s.t.& h\left(x\right)=0\\ & \underset{\_}{g}\≤g\left(x\right)\≤\stackrel{\_}{g}\end{array}\right.$

Wherein x is variable to be optimized, and f (x) is target function, and h (x), g (x) are respectively equality constraint and inequality constraints,

Be respectively the bound of g (x) with g.

Former dual interior point (primM-dual interior point method, PDIPM) basic thought is at first by introducing slack variable, inequality constraints is converted into equality constraint, then adopt barrier function that slack variable is retrained, find the solution by method of Lagrange multipliers again:

$L=f\left(x\right)-y^{T}h\left(x\right)-z^T[g\left(x\right)-l-\underset{\_}{g}]-w^T[g\left(x\right)+u-\stackrel{\_}{g}]-\mathrm{\μ}\underset{j=1}{\overset{r}{\mathrm{\Σ}}}\ln \left(l_j\right)-\mathrm{\μ}\underset{j=1}{\overset{r}{\mathrm{\Σ}}}\ln \left(u_j\right)$

Wherein y, z, w are Lagrange multiplier, and l, u are slack variable.

The necessary condition that this problem minimum exists is Lagrangian to the partial derivative of all variablees and multiplier is 0:

$\left\{\begin{array}{c}{L}_x={\▿}_{x}f\left(x\right)-{\▿}_{x}h\left(x\right)y-{\▿}_{x}g\left(x\right)(z+w)=0\\ L_y=h\left(x\right)=0\\ L_z=g\left(x\right)-l-\underset{\_}{g}=0\\ L_w=g\left(x\right)+u-\stackrel{\_}{g}=0\\ L_l=z-\mathrm{\μ}{U}^{-1}e=0\\ L_u=-w-\mathrm{\μ}{L}^{-1}e=0\end{array}\right.$

In the formula

Be respectively f (x), h (x), g (x) to the single order local derviation of x; L ^-1=diag (1/l ₁..., 1/l _r); U ¹=diag (1/u ₁..., 1/u _r); E=[1 ..., 1] ^T

By latter two equation in the formula KKT condition can in the hope of

μ=(l ^TZ-u ^TW)/and 2r, definition C _Gap=l ^TZ-u ^TW.

But facts have proved, when the parameter in the target function during according to the following formula value convergence poor, the general employing

μ＝σC _Gap/2r，

Wherein σ is called Center Parameter, generally gets 0.1, can obtain reasonable convergence in most occasions.Nonlinear System of Equations in the KKT condition can be found the solution with the Newton-Raphson method, with its linearisation, can obtain:

$\left[\begin{array}{cc}{H}^{\′}& {\▿}_{x}h\left(x\right)\\ {\▿}_x^{T}h\left(x\right)& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δx}\\ \mathrm{\Δy}\end{array}\right]=\left[\begin{array}{c}{L}_x^{\′}\\ -L_y\end{array}\right]$

$\left[\begin{array}{cc}I& L^{-1}Z\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\Δz}\\ \mathrm{\Δl}\end{array}\right]=\left[\begin{array}{c}-L^{-1}{L}_l^{\mathrm{\μ}}\\ L_z+{\▿}_x^{T}g\left(x\right)\mathrm{\Δx}\end{array}\right]$

$\left[\begin{array}{cc}I& U^{-1}W\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\Δw}\\ \mathrm{\Δu}\end{array}\right]=\left[\begin{array}{c}-U^{-1}{L}_u^{\mathrm{\μ}}\\ {-L}_w+{\▿}_x^{T}g\left(x\right)\mathrm{\Δx}\end{array}\right]$

Wherein: Δ x, Δ y, Δ z, Δ l, Δ u, Δ w are the correction of x, y, z, l, u, w.

$L_x^{\′}=L_x+{\▿}_{x}g\left(x\right)[L^{-1}(L_l^{\mathrm{\μ}}+Z{L}_z)+U^{-1}(L_u^{\mathrm{\μ}}+W{L}_w)]$

$H^{\′}=H-{\▿}_{x}g\left(x\right)[L^{-1}Z-U^{-1}W]{\▿}_x^{T}g\left(x\right)$

$H=-[{\▿}_x^{2}f\left(x\right)-{\▿}_x^{2}h\left(x\right)y-{\▿}_x^{2}g\left(x\right)\left(\text{z+w}\right)]$

The above-mentioned three prescription journeys of solving equation can obtain the correction of the k time iteration.

Classic algorithm is generally found the solution by means such as differentiates, thereby processes relatively difficulty of discrete variable; Intelligent algorithm is absorbed in locally optimal solution easily, and computing time is long.The pluses and minuses of comprehensive this two classes algorithm, the hybrid algorithm that this paper proposes a kind of PSO and PDIPM combines, discrete variable and continuous variable are optimized synchronously, numerical results shows that this algorithm the convergence speed is fast, the optimizing ability is strong.

The core concept of hybrid algorithm is: take the PSO algorithm as framework, optimize discrete variable, in the each time iterative process of PSO, adopt interior point method population to be carried out the optimization of fitness assessment and continuous variable.

See also shown in Figure 1, in the reactive power optimization of power system problem, the control variables x=[V of system _G, K _T, Q _C], represent respectively generator terminal voltage, on-load tap-changing transformer no-load voltage ratio and reactive compensation capacity, wherein K _T, Q _CBe discrete variable, adopt the PSO algorithm to be optimized continuous variable V _GBe optimized by PDIPM, concrete steps are as follows:

(1) network parameter of acquisition electric power system.Comprise: bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance, the generator reactive bound;

(2) program initialization.Comprise: set Population Size, maximum iteration time, crossover probability and the variation probability of particle cluster algorithm, the slack variable of former dual interior point, Lagrange multiplier and penalty factor initial value;

(3) generate at random population, take discrete variables such as transformer voltage ratio and reactive compensation capacities as variable to be optimized, generate at random the initial population of particle cluster algorithm;

(4) initial value of calculating locally optimal solution and globally optimal solution.Keep each individual discrete variable constant, adopt former dual interior point that each individual continuous variable of population is optimized, and the target function value that optimization is obtained is as the individual fitness of population, and obtains according to this individual and global optimum's individuality of local optimum of population;

(5) according to the following formula translational speed of new particle more:

(6) according to the following formula position of new particle more:

x _i,j(t+1)＝x _i,j(t)+v _i，j(t+1)

(7) optimize continuous variable.Keep each individual discrete variable constant, adopt former dual interior point that each individual continuous variable of population is optimized, and the target function value that optimization is obtained is as the individual fitness of population, the individual and global optimum's individuality of the local optimum of Population Regeneration;

(8) judge whether to reach maximum iteration time, if then Output rusults quits a program, if not, then put iterations and add 1, return (5).

The present invention adopts the hybrid algorithm based on population and former dual interior point to solve the reactive power optimization of power system problem, by a plurality of Simulation Examples, the algorithm effect of having verified the present invention's proposition is remarkable, and on the ability that solves the reactive power optimization of power system problem, is better than traditional particle cluster algorithm.

The below introduces three embodiment of the present invention:

Example one

See also Fig. 2, Fig. 6 and shown in Figure 7, the present invention adopts the hybrid algorithm based on PSO and PDIPM that IEEE-14 node example shown in Figure 2 is carried out simulation calculation, and the result is as shown in table 1 below.

Each control variables optimum results of table 1 IEEE-14 node system

Fig. 6 and Fig. 7 are two kinds of convergence of algorithm curves, and by table 2, Fig. 6 and Fig. 7 result as can be known, hybrid algorithm proposed by the invention is compared with PSO, and convergence rate significantly improves, and the optimizing ability also strengthens to some extent.

Example two

See also Fig. 3, Fig. 4 and shown in Figure 5, take the IEEE-30,57 of Fig. 3, Fig. 4 and Fig. 5, a plurality of examples such as 118 as example, the adaptability of checking hybrid algorithm that the present invention carries.Set the PSO maximum iteration time and be 500 times, the hybrid algorithm maximum iteration time is 50 times.

Table 2 has provided the network loss optimum results of each example, and unit is MW.

Each example optimum results of table 2 relatively

By IEEE-30 and IEEE-57 node example network loss optimum results as can be known, this paper algorithm optimizing ability is stronger, and iterations still less, and numerical stability is better.For the IEEE-118 node, because variable is more, solution space is too large, and the PSO algorithm iteration does not still find rational solution 500 times, but hybrid algorithm namely finds globally optimal solution 114.6415MW 48 times, obviously is better than the 132.4737MW that trend is calculated.

Comprehensive above-mentioned numerical results as can be known, the present invention carries that hybrid algorithm optimizing ability is stronger, numerical stability is better, convergence rate is faster, and it is very convenient to process discrete variable.

Claims (3)

1. area power grid economical operation optimization method based on hybrid algorithm, it is characterized in that: described area power grid economical operation optimization method may further comprise the steps based on particle cluster algorithm and former dual interior point:

(1) network parameter of acquisition electric power system;

(2) set Population Size, maximum iteration time, crossover probability and the variation probability of particle cluster algorithm, set slack variable, Lagrange multiplier and the penalty factor initial value of former dual interior point;

(3) take the discrete variable of network parameter described in the step (1) as variable to be optimized, generate at random the initial population of particle cluster algorithm;

(4) keep each individual discrete variable of population constant, adopt former dual interior point that each individual continuous variable of population is optimized and obtain target function value, and the target function value that optimization is obtained is as the individual fitness of population, and obtains the individual and global optimum's individuality of local optimum of population according to described individual fitness;

(5) according to following formula more translational speed and the position of new particle:

x _i，j(t+1)＝x _i,j(t)+v _i，j(t+1)

Wherein,

Be inertia weight, c ₁And c ₂Be the study factor, r ₁And r ₂Be uniform random number between 0 to 1, p _{I, j}, p _{G, j}Be respectively the control variables value of particle when pbest and gbest position;

(6) keep each individual discrete variable of population constant, adopt former dual interior point that each individual continuous variable of population is optimized, and the target function value that optimization is obtained is as the individual fitness of population, and according to the local optimum of described individual fitness Population Regeneration individual and global optimum's individuality;

(7) repeating step 5-6 is until reach the described maximum iteration time of step (2).

2. the area power grid economical operation optimized algorithm based on hybrid algorithm as claimed in claim 1, it is characterized in that, network parameter in the step (1) comprises that bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio, transformer impedance and generator reactive bound.

3. the area power grid economical operation optimized algorithm based on hybrid algorithm as claimed in claim 1 is characterized in that discrete variable is transformer voltage ratio and reactive compensation capacity described in the step (2).

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