CN104036331A - Dynamic and economical dispatching method of power system based on improved particle swarm optimization - Google Patents

Abstract

The invention relates to a dynamic and economical dispatching method of a power system based on the improved Particle Swarm Optimization (PSO). The method includes: setting various parameters of the PSO; generating an initial particle swarm; setting upper and lower limits for the particle velocity; calculating the fitness value of each particle according to an object function; comparing the fitness value of each particle to find out the historicaloptimum value and the position of each particle, and to find out the particle that has the most optimum value and the position thereof; updating the position and the velocity of each particle; determining whether the position and the velocity of the particles are beyond the limit or not, if the position and the velocity of the particles are beyond the limit, adjusting the position and the velocity of the particles into the constraint range, speeding up the velocity of the particles; and if the iterations frequencies are reached, stopping iteration and obtaining a final result. The method of the invention is improved in solving the dynamic and economical dispatching problem of a power system by using the PSO and adjusts the velocity of the particles by an adaptive algorithm. When searching is limited to local searching, a more targeted way is employed to obtain a good result.

Description

A kind of Electrical Power System Dynamic economic load dispatching method based on improving particle cluster algorithm

Technical field

The present invention relates to a kind of economic load dispatching method of electric power system optimization operation, specifically relate to a kind of Electrical Power System Dynamic economic load dispatching method based on improving particle cluster algorithm.

Background technology

Unit operation needs cost, and Operation of Electric Systems process need is considered the economy of operation, and different unit cost functions is different, and the financial cost of the different schemes of exerting oneself is also different.The object of economic load dispatching is in some cycles, optimizes exerting oneself of each unit, to obtain the optimum force level that goes out, thereby makes cost minimization.Before and after unit, exerting oneself of period also relates to the climbing capacity constraint of unit, and exerting oneself of unit front and back period is closely related, and this just need to carry out the dynamic economic dispatch of electric system.Electrical Power System Dynamic economic load dispatching is a part for power system security economical operation, its objective is the method for operation that arranges unit under the condition that meets various security constraints and quality of power supply requirement, makes the total operating cost of system minimum.

The related variable of dynamic economic dispatch is more, need to consider the constraint condition of equation and inequality simultaneously, and existing optimized algorithm is difficult to meet calculation requirement.Problem dimension is higher, constraint condition is strict, causes the corresponding target function value of each feasible solution comparatively approaching, while using the particle cluster algorithm of standard, easily causes search to be absorbed in local optimum, thus Premature Convergence, the stagnation to globally optimal solution search.

The existing method that solves Premature Convergence is mainly the diversity that guarantees particle, avoids the iteration later stage, and population individuality is similar, is absorbed in Local Search.As in conjunction with genetic algorithm to the position of particle intersect, the operation such as variation, to guarantee the diversity of particle.But because the constraint condition of dynamic economic dispatch is comparatively strict, solution space is limited in very little scope, and this processing ease to particle position is out-of-limit, specific aim is also strong not simultaneously, and dynamic economic dispatch problem has some limitations.

In carrying out Electrical Power System Dynamic economic load dispatching, for fear of being absorbed in Local Search, the existing particle cluster algorithm that has generally adopts the method that particle position is adjusted, as in conjunction with genetic algorithm, to particle intersect, the operation such as variation.But easy ten million particle of these methods is out-of-limit, and not strong to the specific aim of region of search in the iteration later stage, the waste of easy ten million iterative process.

Summary of the invention

For the deficiencies in the prior art, the object of this invention is to provide a kind of Electrical Power System Dynamic economic load dispatching method based on improving particle cluster algorithm, the present invention improves the iterative formula of particle cluster algorithm, add adaptive approach, so that particle rapidity is adjusted, and according to constraint condition, particle is adjusted, not out-of-limit to guarantee particle.Particle cluster algorithm after adopt improving solves the dynamic economic dispatch of electric system, with in the situation that meeting related constraint condition, obtains the force level that of each unit day part after optimizing.

The object of the invention is to adopt following technical proposals to realize:

The invention provides a kind of Electrical Power System Dynamic economic load dispatching method based on improving particle cluster algorithm, its improvements are, described method comprises the steps:

A, the parameter of particle cluster algorithm is set;

B, generation primary group;

C, the constraint of the speed bound of particle in Electrical Power System Dynamic economic load dispatching is set;

D, determine the adaptive value of particle;

The adaptive value of E, comparison particle, finds out historical optimal value and the position thereof of each particle, and the particle and the position thereof that reach global optimum;

F, according to local optimum and all optimal value upgrade position and the speed of each particle;

G, according to constraint condition, and the bound of particle rapidity constraint judge the position of particle and speed whether out-of-limit, if out-of-limit, the position of particle and speed are adjusted in restriction range;

H, employing adaptive approach, adjust particle position;

If I reaches iterations, stop iteration, obtain final result.

Further, in described steps A, the required parameters of particle cluster algorithm is set, described parameter comprises weight factor, the study factor, population scale number and iterations, and weight factor is got ω _max=0.9, ω _min=0.4, the study factor is got c ₁=c ₂=3.05, population scale and iterations, according to actual conditions setting, comprise that being set to population scale counts N=40, iterations C=500.

Further, in described step B, according to the load level of day part in the computing interval, share at random the force level that of each unit, according to population scale number, repeat this step, obtain primary group; Comprise:

Random generate the random array that line number is unit number, columns hop count while being, the element of this array is positive number, and each column element sum is one; To load the period and be multiplied by corresponding row and can obtain primary, repeat this operation, obtain whole primary group, for m particle, generate as follows:

$P_m=\left[\begin{array}{ccccc}{P}_{\mathrm{1,1}}& ...& P_{1,t}& ...& P_{1,T}\\ P_{i,1}& ...& P_{i,t}& ...& P_{i,T}\\ ...& ...& ...& ...& ...\\ P_{M,1}& ...& P_{M,t}& ...& P_{M,T}\end{array}\right]---\left(1\right);$

P _i,t＝a _i,t·P _D,t (2)；

a _1,t+a _2,t+…+a _i,t+…a _M,t＝1 (3)；

Wherein: T represents the time hop count of economic load dispatching, be one day 24 hours, take per hour is a section, totally 24 periods, M represents unit number; a _i,trepresenting the i platform proportional element of unit t period, is random generation, meets (3) formula, therefore (3) formula represents that the proportional element sum for all M platforms of t period is 1, P _d,tbe the size of the load of t period, adopt same procedure to generate other particles.

Further, in described step C, according to the bound constraint of each unit, determine the speed bound of each particle, the difference that the bound of particle rapidity is exerted oneself according to unit bound is reduced, reduction scope is 1%, be in particle rapidity, be limited to the unit output upper limit deduct the lower limit of exerting oneself difference 1%, under particle rapidity, be limited to unit output lower limit deduct the upper limit of exerting oneself difference 1%.

Further, in described step D, according to the primary group who obtains in step B, determine the adaptive value of particle according to Electrical Power System Dynamic economic load dispatching objective function, Electrical Power System Dynamic economic load dispatching objective function is:

$f={\mathrm{\Σ}}_t^T{\mathrm{\Σ}}_i^M(a_i\·{P_{i,t}}^2+b_i\·P_{i,t}+c_i)---\left(4\right);$

Wherein: P _i,tbe exerting oneself of i platform unit t period, the time hop count that T is dynamic economic dispatch, M is for participating in the unit number of dynamic economic dispatch; a _i, b _i, c _irepresent respectively corresponding COST system, specifically according to unit situation, determine;

Corresponding adaptive value is:

f _a＝f (5)；

Using Electrical Power System Dynamic economic load dispatching objective function result of calculation as particle adaptive value, target function value is less, and adaptive value is less, and the fitness of particle is higher.

Further, the constraint of the bound of Electrical Power System Dynamic economic load dispatching comprises power-balance constraint, the constraint of unit output bound and unit ramp loss;

Wherein power-balance constraint represents by following expression formula:

${\mathrm{\Σ}}_{i=1}^M{P}_{i,t}=P_{D,t}+P_{\mathrm{loss},t}---\left(6\right);$

Wherein: P _d,tbe the payload of t period, P _{loss, t}the network loss size of t period;

Network loss is calculated and is adopted B Y-factor method Y to calculate, and expression formula is as follows:

P _loss,t＝P _t ^T*B*P _t (7)；

Wherein: P _tbe the column vector of t each unit output of period, P _t ^trepresent P _ttransposition, the matrix that B is M * M, for calculating network loss;

The constraint of unit output bound represents by following expression formula:

P _i ^min≤P _i,t≤P _i ^max (8)；

Wherein: P _i ^minand P _i ^maxrepresent respectively i the platform lower limit of exerting oneself and the upper limit of unit t period;

Unit ramp loss represents by following expression formula:

$R_i^d\mathrm{\Δt}\≤P_{i,t}-P_{i,t-1}\≤R_i^u\mathrm{\Δt}---\left(9\right);$

Wherein: for downward Ramp Rate, it is negative value; for Ramp Rate upwards, on the occasion of; Δ t represents two time intervals between scheduling slot.

Further, in described step e, relatively the adaptive value of each particle, determines the highest particle of particle fitness, finds the historical optimal value of each particle, i.e. local optimum, and particle position, and global optimum and particle position; If iteration, finds global optimum and corresponding particle position for the first time;

In particle cluster algorithm, the population number of population is comprised number of particles, and each individuality of population the inside is all called a particle; Each feasible solution is all particles in population, and each particle has two attributes, and displacement and speed are all expressed as a matrix-vector, are shown below:

$P_m=\left[\begin{array}{ccccc}{P}_{\mathrm{1,1}}& ...& P_{1,t}& ...& P_{1,T}\\ P_{i,1}& ...& P_{i,t}& ...& P_{i,T}\\ ...& ...& ...& ...& ...\\ P_{M,1}& ...& P_{M,t}& ...& P_{M,T}\end{array}\right]---\left(10\right);$

$V_m=\left[\begin{array}{ccccc}{V}_{\mathrm{1,1}}& ...& V_{1,t}& ...& V_{1,T}\\ V_{i,1}& ...& V_{i,t}& ...& V_{i,T}\\ ...& ...& ...& ...& ...\\ V_{M,1}& ...& V_{M,t}& ...& V_{M,T}\end{array}\right]---\left(11\right);$

Wherein: P _mbe the displacement of m particle, P _i,tbe exerting oneself of i platform unit t period, i.e. the position of particle; V _mv _mthe speed of individual particle, V _i,tit is the correction of exerting oneself of the i platform unit t period of correspondence; T is the time hop count of dynamic economic dispatch; M is for participating in the unit number of dynamic economic dispatch; In Electrical Power System Dynamic economic load dispatching, the position of particle represents exerting oneself of each unit day part, and line number represents unit number, hop count when columns represents.

Further, in described step F, according to the resulting local optimum of step e and particle position, and all optimal value and particle position, according to following expression formula more speed and the position of new particle:

$V_m^{k+1}=\mathrm{\ω}\·V_m^k+c_1\·r_1\·({\mathrm{pbest}}_m^k-P_m^k)+c_2\·r_2\·({\mathrm{gbest}}^k-P_m^k)+\mathrm{\Δ}{V}_m^k---\left(12\right);$

$P_m^{k+1}=P_m^k+V_m^{k+1}+\mathrm{\Δ}{P}_m^k---\left(13\right);$

Wherein: the adjustment amount that represents respectively speed and position; be the speed in k generation of m particle, the speed in k+1 generation of m particle; be the k generation of m particle, for the k+1 generation of m particle; be the historical optimal value of m particle, gbest ^kit is the global optimum of the k time iteration; ω is inertial factor, for weighing global search and the local search ability of particle cluster algorithm; ω value is more greatly more easy to algorithm and increases search space, and the more little local optimal searching of more easily carrying out of value adopts self-adaptation to adjust the mode of inertial factor, that is:

$\mathrm{\ω}={\mathrm{\ω}}_{\max }-\frac{{\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min }}{C}k---\left(14\right);$

Wherein: ω _maxget 0.9, ω _minget the maximum times that 0.4, C is iteration, k is current iterations; c ₁, c ₂for the study factor, be respectively and control particle to the maximum step-length of individual optimum and global optimum's locality flight; Get c ₁=c ₂=3.05;

for adjusting out-of-limit particle, when particle is out-of-limit, according to (6), (7), (8), (9) formula, according to following rule, particle is adjusted:

1) according to speed bound, constraint is adjusted unit output, on unit, in limited time, is exerted oneself and is limited to the upper limit, and unit is more lower in limited time, is exerted oneself and is limited to lower limit;

2) according to climbing constraint, unit output is adjusted, when unit is upwards climbed, if out-of-limit, unit output is limited to the upwards upper limit of climbing; When unit is climbed, if out-of-limit, unit output is limited to the lower limit of downward climbing downwards;

3) according to the unit output after adjusting, recalculate network loss;

4) calculate the amount of unbalance that day part is exerted oneself, i.e. difference between day part unit output sum and load, distributes amount of unbalance according to the big or small of the micro-gaining rates of consumption such as unit and in conjunction with the bound units limits of each unit.

Further, for particle rapidity, be limited within the scope of constraint of velocity, constraint of velocity formula is as follows:

$V_m^k\left[i\right]\left[j\right]=\left\{\begin{array}{cc}{V}_m^k\left[i\right]{\left[j\right]}_{\max },& \mathrm{if}{V}_m^k\left[i\right]\left[j\right]>V_m^k\left[i\right]{\left[j\right]}_{\max }\\ V_m^k\left[i\right]{\left[j\right]}_{\min },& \mathrm{if}{V}_m^k\left[i\right]\left[j\right]<V_m^k\left[i\right]{\left[j\right]}_{\min }\end{array}\right.---\left(15\right);$

Wherein: for the i of particle rapidity is capable, the element of j row, for the i of particle rapidity is capable, the maximal value defined in the element of j row, for the i of particle rapidity is capable, the minimum value defined in the element of j row; The maximum of particle rapidity, minimum value are according to following formula setting:

$V_m^k{\left[i\right]}_{\max }=({P_i}^{\max }-{P_i}^{\min })/100---\left(16\right);$

$V_m^k{\left[i\right]}_{\min }=({P_i}^{\min }-{P_i}^{\max })/100---\left(17\right);$

Wherein: be respectively the upper and lower bound of corresponding i platform unit speed in particle, will be extended to the transversal vector with period corresponding length, obtain speed limit and lower limit that particle i is capable.

Further, in described step H, according to obtaining global optimum in step e, the global optimum of twice relatively, adopts adaptive approach, according to the order of magnitude of the difference of twice global optimum, particle rapidity is adjusted, and absolute value is larger, and adjustment degree is larger; Carry out as follows:

In particle cluster algorithm, along with the increase of iterations, may be absorbed in local optimum, now the speed of particle can reduce thereupon, thus particle rapidity is adjusted, that is:

v ₁＝v ₀+Δv (18)；

Wherein: v ₀, v ₁be respectively the particle rapidity before and after adjusting, the speed amount of Δ v for adjusting, adopts adaptive algorithm during adjustment, and adaptive algorithm formula is as follows:

$\mathrm{\&Delta;v}=\left\{\begin{array}{c}0,\mathrm{\&lambda;}>0.01\\ v_{\mathrm{ini}}\&CenterDot;r_3,0.001<\mathrm{\&lambda;}\&le;0.01\\ v_{\mathrm{ini}}\&CenterDot;r_4,0<\mathrm{\&lambda;}\&le;0.001\end{array}\right.---\left(19\right);$

Wherein: v _inifor initial velocity set in particle cluster algorithm, r ₃random number for-0.1 to 0.1, r ₄random number for-0.01 to 0.01, for random number r ₃, r ₄need be with setting according to reality, λ calculates according to following formula:

$\mathrm{\&lambda;}=\frac{|{f_{\mathrm{best}}}^k-{f_{\mathrm{best}}}^{k-1}|}{{f_{\mathrm{best}}}^k}---\left(20\right);$

Wherein: f _best ^kbe that k is for the global optimum position of particle, f _best ^k-1k-1 is the twice global optimum difference relative scale in front and back for the position λ of global optimum of particle, the adjustment of accordingly speed being raised speed, and before and after avoiding, twice global optimum is too close, sinks into local optimum.

Further, in described step I, the iterative algorithm of having set according to steps A, judge whether iterations reaches: if reach iterations C=500, stop calculating, obtain particle global optimum and be final particle position, this particle position is each unit exerting oneself at day part, thereby calculate net result, net result comprises going out force level and calculating the unit operation total expenses in economic cycle of each unit day part; If do not reach iterations, turn back to step D, continue to calculate.

Compared with the prior art, the beneficial effect that the present invention reaches is:

Electrical Power System Dynamic economic load dispatching method based on improving particle cluster algorithm provided by the invention, is characterized in that the particle position forming based on particle rapidity constraint and economic load dispatching constraint condition retrains particle rapidity and particle position that each iteration is obtained and adjusts.Existing particle cluster algorithm, according to the variation of adaptive value, particle rapidity is not adjusted, when the speed to particle is adjusted, when iteration is absorbed in Local Search, the basic vanishing of particle rapidity, be unfavorable for jumping out Local Search, therefore in the present invention, adaptive value based on obtaining for twice before and after iteration is carried out particle position adjustment, particle rapidity is raised speed, to jump out Local Search, in speed-raising process, adopt adaptive approach, assurance particle can be jumped out Local Search, also can guarantee the function of search among a small circle of particle, and adopt the method for regulating the speed can go more targetedly to carry out search, thereby in Electrical Power System Dynamic economic load dispatching, carry out better optimizing, to meet related physical constraint, and consider in the situation of network loss, realize the minimum load of generating, thereby realizing generating total expenses minimizes, reach the object of dynamic economic dispatch.

Accompanying drawing explanation

Fig. 1 is the process flow diagram based on improving the Electrical Power System Dynamic economic load dispatching method of particle cluster algorithm provided by the invention;

Fig. 2 is the decomposition sub-step of basis provided by the invention (6), (7), (8), (9) formula adjustment particle position.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

The process flow diagram of the Electrical Power System Dynamic economic load dispatching method based on improvement particle cluster algorithm provided by the invention as shown in Figure 1, comprises the steps:

A, the required parameters of particle cluster algorithm is set, described parameter comprises weight factor, the study factor, population scale number and iterations, and weight factor is got ω _max=0.9, ω _min=0.4, the study factor is got c ₁=c ₂=3.05, population scale and iterations, according to actual conditions setting, comprise that being set to population scale counts N=40, iterations C=500.

B, according to the load level of day part in the computing interval, share at random the force level that of each unit, according to population scale number, repeat this step, obtain primary group; Comprise:

Random generate the random array that line number is unit number, columns hop count while being, the element of this array is positive number, and each column element sum is one; To load the period and be multiplied by corresponding row and can obtain primary, repeat this operation, obtain whole primary group, for m particle, generate as follows:

$P_m=\left[\begin{array}{ccccc}{P}_{\mathrm{1,1}}& ...& P_{1,t}& ...& P_{1,T}\\ P_{i,1}& ...& P_{i,t}& ...& P_{i,T}\\ ...& ...& ...& ...& ...\\ P_{M,1}& ...& P_{M,t}& ...& P_{M,T}\end{array}\right]---\left(1\right);$

P _i,t＝a _i,t·P _D,t (2)；

a _1,t+a _2,t+…+a _i,t+…a _M,t＝1 (3)；

Wherein: T represents the time hop count of economic load dispatching, be one day 24 hours, take per hour is a section, totally 24 periods, M represents unit number; a _i,trepresenting the i platform proportional element of unit t period, is random generation, but must meet (3) formula, therefore (3) formula represents that the proportional element sum for all M platforms of t period is 1, P _d,tbe the size of the load of t period, adopt same procedure to generate other particles.

C, the speed bound constraint of particle is set: the speed bound of determining each particle according to the bound constraint of each unit, the difference that the bound of particle rapidity is exerted oneself according to unit bound is reduced, reduction scope is 1%, be in particle rapidity, be limited to the unit output upper limit deduct the lower limit of exerting oneself difference 1%, under particle rapidity, be limited to unit output lower limit deduct the upper limit of exerting oneself difference 1%.

D, according to objective function, calculate the adaptive value of each particle:

According to the primary group who obtains in step B, according to Electrical Power System Dynamic economic load dispatching objective function, determine the adaptive value of particle, Electrical Power System Dynamic economic load dispatching objective function is:

$f={\mathrm{\&Sigma;}}_t^T{\mathrm{\&Sigma;}}_i^M(a_i\&CenterDot;{P_{it}}^2+b_i\&CenterDot;P_{it}+c_i)---\left(4\right);$

Wherein: P _itbe exerting oneself of i platform unit t period, the time hop count that T is dynamic economic dispatch, M is for participating in the unit number of dynamic economic dispatch; a _i, b _i, c _irepresent respectively corresponding COST system, specifically according to unit situation, determine;

Corresponding adaptive value is:

f _a＝f (5)；

Using Electrical Power System Dynamic economic load dispatching objective function result of calculation as particle adaptive value, target function value is less, and adaptive value is less, and the fitness of particle is higher.

Further, the constraint of the bound of Electrical Power System Dynamic economic load dispatching comprises power-balance constraint, the constraint of unit output bound and unit ramp loss;

Wherein power-balance constraint represents by following expression formula:

${\mathrm{\&Sigma;}}_{i=1}^M{P}_{it}=P_{D,t}+P_{\mathrm{loss},t}---\left(6\right);$

Wherein: P _d,tbe the payload of t period, P _{loss, t}the network loss size of t period;

Network loss is calculated and is adopted B Y-factor method Y to calculate, and expression formula is as follows:

P _loss,t＝P _t ^T*B*P _t (7)；

Wherein: P _tbe the column vector of t each unit output of period, P _t ^trepresent P _ttransposition, the matrix that B is M * M, for calculating network loss;

The constraint of unit output bound represents by following expression formula:

P _i ^min≤P _it≤P _i ^max (8)；

Wherein: P _i ^minand P _i ^maxrepresent respectively i the platform lower limit of exerting oneself and the upper limit of unit t period;

Unit ramp loss represents by following expression formula:

$R_i^d\mathrm{\&Delta;t}\&le;P_{i,t}-P_{i,t-1}\&le;R_i^u\mathrm{\&Delta;t}---\left(9\right);$

Wherein: for downward Ramp Rate, it is negative value; for Ramp Rate upwards, on the occasion of; Δ t represents two time intervals between scheduling slot.

E, the adaptive value of each particle relatively, determine the highest particle of particle fitness, finds the historical optimal value of each particle, i.e. local optimum, and particle position, and global optimum and particle position; If iteration, finds global optimum and corresponding particle position for the first time;

In particle cluster algorithm, the population number of population is comprised number of particles, and each individuality of population the inside is all called a particle; Each feasible solution is all particles in population, and each particle has two attributes, and displacement and speed are all expressed as a matrix-vector, are shown below:

$P_m=\left[\begin{array}{ccccc}{P}_{\mathrm{1,1}}& ...& P_{1,t}& ...& P_{1,T}\\ P_{i,1}& ...& P_{i,t}& ...& P_{i,T}\\ ...& ...& ...& ...& ...\\ P_{M,1}& ...& P_{M,t}& ...& P_{M,T}\end{array}\right]---\left(10\right);$

$V_m=\left[\begin{array}{ccccc}{V}_{\mathrm{1,1}}& ...& V_{1,t}& ...& V_{1,T}\\ V_{i,1}& ...& V_{i,t}& ...& V_{i,T}\\ ...& ...& ...& ...& ...\\ V_{M,1}& ...& V_{M,t}& ...& V_{M,T}\end{array}\right]---\left(11\right);$

Wherein: P _mbe the displacement of m particle, P _i,tbe exerting oneself of i platform unit t period, i.e. the position of particle; V _mv _mthe speed of individual particle, V _i,tit is the correction of exerting oneself of the i platform unit t period of correspondence; T is the time hop count of dynamic economic dispatch; M is for participating in the unit number of dynamic economic dispatch; In Electrical Power System Dynamic economic load dispatching, the position of particle represents exerting oneself of each unit day part, and line number represents unit number, hop count when columns represents.

F, according to the resulting local optimum of step e and particle position, and all optimal value and particle position, according to following expression formula more speed and the position of new particle:

$V_m^{k+1}=\mathrm{\&omega;}\&CenterDot;V_m^k+c_1\&CenterDot;r_1\&CenterDot;({\mathrm{pbest}}_m^k-P_m^k)+c_2\&CenterDot;r_2\&CenterDot;({\mathrm{gbest}}^k-P_m^k)+\mathrm{\&Delta;}{V}_m^k---\left(12\right);$

$P_m^{k+1}=P_m^k+V_m^{k+1}+\mathrm{\&Delta;}{P}_m^k---\left(13\right);$

Wherein: the adjustment amount that represents respectively speed and position; be the speed in k generation of m particle, the speed in k+1 generation of m particle; be the k generation of m particle, for the k+1 generation of m particle; be the historical optimal value of m particle, gbest ^kit is the global optimum of the k time iteration; ω is inertial factor, for weighing global search and the local search ability of particle cluster algorithm; ω value is more greatly more easy to algorithm and increases search space, and the more little local optimal searching of more easily carrying out of value adopts self-adaptation to adjust the mode of inertial factor, that is:

$\mathrm{\&omega;}={\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{C}k---\left(14\right);$

Wherein: ω _maxget 0.9, ω _minget the maximum times that 0.4, C is iteration, k is current iterations; c ₁, c ₂for the study factor, be respectively and control particle to the maximum step-length of individual optimum and global optimum's locality flight; Get c ₁=c ₂=3.05;

for adjusting out-of-limit particle, when particle is out-of-limit, according to (6), (7), (8), (9) formula, according to following rule, particle is adjusted:

1) according to speed bound, constraint is adjusted unit output, on unit, in limited time, is exerted oneself and is limited to the upper limit, and unit is more lower in limited time, is exerted oneself and is limited to lower limit;

2) according to climbing constraint, unit output is adjusted, when unit is upwards climbed, if out-of-limit, unit output is limited to the upwards upper limit of climbing; When unit is climbed, if out-of-limit, unit output is limited to the lower limit of downward climbing downwards;

3) according to the unit output after adjusting, recalculate network loss;

4) calculate the amount of unbalance that day part is exerted oneself, i.e. difference between day part unit output sum and load, distributes amount of unbalance according to the big or small of the micro-gaining rates of consumption such as unit and in conjunction with the bound units limits of each unit.Etc. the micro-gaining rate of consumption namely i platform unit t period cost is to the local derviation of exerting oneself.

G, according to constraint condition, and the bound of particle rapidity constraint judge the position of particle and speed whether out-of-limit, if out-of-limit, the position of particle and speed are adjusted in restriction range.For particle rapidity, be limited within the scope of constraint of velocity, constraint of velocity formula is as follows:

$V_m^k\left[i\right]\left[j\right]=\left\{\begin{array}{cc}{V}_m^k\left[i\right]{\left[j\right]}_{\max },& \mathrm{if}{V}_m^k\left[i\right]\left[j\right]>V_m^k\left[i\right]{\left[j\right]}_{\max }\\ V_m^k\left[i\right]{\left[j\right]}_{\min },& \mathrm{if}{V}_m^k\left[i\right]\left[j\right]<V_m^k\left[i\right]{\left[j\right]}_{\min }\end{array}\right.---\left(15\right);$

Wherein: for the i of particle rapidity is capable, the element of j row, for the i of particle rapidity is capable, the maximal value defined in the element of j row, for the i of particle rapidity is capable, the minimum value defined in the element of j row; The maximum of particle rapidity, minimum value are according to following formula setting:

$V_m^k{\left[i\right]}_{\max }=({P_i}^{\max }-{P_i}^{\min })/100---\left(16\right);$

$V_m^k{\left[i\right]}_{\min }=({P_i}^{\min }-{P_i}^{\max })/100---\left(17\right);$

Wherein: be respectively the upper and lower bound of corresponding i platform unit speed in particle, will be extended to the transversal vector with period corresponding length, obtain speed limit and lower limit that particle i is capable.

H, according to obtaining global optimum in step e, relatively before and after the global optimum of twice, adopt adaptive approach, according to the order of magnitude of the difference of twice global optimum, particle rapidity is adjusted, absolute value is larger, adjustment degree is larger; Carry out as follows:

In particle cluster algorithm, along with the increase of iterations, may be absorbed in local optimum, now the speed of particle can reduce thereupon, thus particle rapidity is adjusted, that is:

v ₁＝v ₀+Δv (18)；

Wherein: v ₀, v ₁be respectively the particle rapidity before and after adjusting, the speed amount of Δ v for adjusting, adopts adaptive algorithm during adjustment, and adaptive algorithm formula is as follows:

$\mathrm{\&Delta;v}=\left\{\begin{array}{c}0,\mathrm{\&lambda;}>0.01\\ v_{\mathrm{ini}}\&CenterDot;r_3,0.001<\mathrm{\&lambda;}\&le;0.01\\ v_{\mathrm{ini}}\&CenterDot;r_4,0<\mathrm{\&lambda;}\&le;0.001\end{array}\right.---\left(19\right);$

Wherein: v _inifor initial velocity set in particle cluster algorithm, r ₃random number for-0.1 to 0.1, r ₄random number for-0.01 to 0.01, for random number r ₃, r ₄need be with setting according to reality, λ calculates according to following formula:

$\mathrm{\&lambda;}=\frac{|{f_{\mathrm{best}}}^k-{f_{\mathrm{best}}}^{k-1}|}{{f_{\mathrm{best}}}^k}---\left(20\right);$

Wherein: f _best ^kbe that k is for the global optimum position of particle, f _best ^k-1k-1 is the twice global optimum difference relative scale in front and back for the position λ of global optimum of particle, the adjustment of accordingly speed being raised speed, and before and after avoiding, twice global optimum is too close, sinks into local optimum.

I, the iterative algorithm of having set according to steps A, judge whether iterations reaches: if reach iterations C=500, stop calculating, obtain particle global optimum and be final particle position, this particle position is each unit exerting oneself at day part, thereby calculate net result, net result comprises going out force level and calculating the unit operation total expenses in economic cycle of each unit day part; If do not reach iterations, turn back to step D, continue to calculate.

Embodiment

The electric system example data that the present invention adopts are as follows, and concrete load data is as shown in table 1, and power parameter is as shown in table 2, comes to 6 thermal power generation units, adopts B Effective Coefficient Matrix Method when the present invention calculates network loss, therefore row B matrix of coefficients is in table 3.

Table 1 load parameter

Table 2 unit parameter

Table 3B matrix of coefficients parameter unit: * 10 ^-5

Each unit day part of table 4 is exerted oneself

Table 5 scheduling total generating expense in a few days

The optimum results that table 4 is each unit output of adopt improving population and obtaining.Table 5 is respectively in a few days total generated energy and generating expense of this scheduling that conventional particle cluster algorithm and the improvement self-adaptation particle cluster algorithm adopting in the present invention obtain.

The present invention improves the iterative formula of particle cluster algorithm, adds adaptive approach, so that particle rapidity is adjusted, and according to constraint condition, particle is adjusted, not out-of-limit to guarantee particle.Adopt the particle cluster algorithm after improving to solve the dynamic economic dispatch of electric system, obtained the force level that of each unit day part after optimization, by the particle cluster algorithm contrast with conventional, can find out, the improvement self-adaptation particle cluster algorithm proposing in the present invention can obtain better optimum results.

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit, although the present invention is had been described in detail with reference to above-described embodiment, those of ordinary skill in the field are to be understood that: still can modify or be equal to replacement the specific embodiment of the present invention, and do not depart from any modification of spirit and scope of the invention or be equal to replacement, it all should be encompassed in the middle of claim scope of the present invention.

Claims (11)

1. the Electrical Power System Dynamic economic load dispatching method based on improving particle cluster algorithm, is characterized in that, described method comprises the steps:

A, the parameter of particle cluster algorithm is set;

B, generation primary group;

C, the constraint of the speed bound of particle in Electrical Power System Dynamic economic load dispatching is set;

D, determine the adaptive value of particle;

The adaptive value of E, comparison particle, finds out historical optimal value and the position thereof of each particle, and the particle and the position thereof that reach global optimum;

F, according to local optimum and all optimal value upgrade position and the speed of each particle;

G, according to the bound constraint of constraint condition and particle rapidity judge the position of particle and speed whether out-of-limit, if out-of-limit, the position of particle and speed are adjusted in restriction range;

H, employing adaptive approach, adjust particle position;

If I reaches iterations, stop iteration, obtain final result.

2. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, is characterized in that, in described steps A, described parameter comprises ω _max=0.9 or ω _min=0.4 weight factor, c ₁=c ₂=3.05 the study factor, population scale number and iterations; Population scale and iterations, according to actual conditions setting, comprise that being set to population scale counts N=40, iterations C=500.

3. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, it is characterized in that, in described step B, according to the load level of day part in the computing interval, share at random the force level that of each unit, according to population scale number, repeat this step, obtain primary group; Comprise:

Random generate the random array that line number is unit number, columns hop count while being, the element of this array is positive number, and each column element sum is one; Primary is that period load is multiplied by corresponding row, repeats this operation, obtains whole primary group, for m particle, generates as follows:

$P_m=\left[\begin{array}{ccccc}{P}_{\mathrm{1,1}}& ...& P_{1,t}& ...& P_{1,T}\\ P_{i,1}& ...& P_{i,t}& ...& P_{i,T}\\ ...& ...& ...& ...& ...\\ P_{M,1}& ...& P_{M,t}& ...& P_{M,T}\end{array}\right]---\left(1\right);$

P _i,t＝a _i,t·P _D,t (2)；

a _1,t+a _2,t+…+a _i,t+…a _M,t＝1 (3)；

Wherein: T represents the time hop count of economic load dispatching, one day 24 hours, take per hour was a section, and totally 24 periods, M represents unit number; a _i,trepresenting the i platform proportional element of unit t period, is random generation, meets (3) formula, therefore (3) formula represents that the proportional element sum for all M platforms of t period is 1, P _d,tbe the size of the load of t period, adopt same procedure to generate other particles.

4. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, it is characterized in that, in described step C, according to the bound constraint of each unit, determine the speed bound of each particle, the bound of the difference reduction particle rapidity of exerting oneself according to unit bound, reduction scope is 1%; In particle rapidity, be limited to the unit output upper limit deduct the lower limit of exerting oneself difference 1%, under particle rapidity, be limited to unit output lower limit deduct the upper limit of exerting oneself difference 1%.

5. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, it is characterized in that, in described step D, according to the primary group who obtains in step B, the Electrical Power System Dynamic economic load dispatching objective function representing according to following (4) formula is determined the adaptive value of particle:

$f={\mathrm{\&Sigma;}}_t^T{\mathrm{\&Sigma;}}_i^M(a_i\&CenterDot;{P_{i,t}}^2+b_i\&CenterDot;P_{i,t}+c_i)---\left(4\right);$

Wherein: P _i,tbe exerting oneself of i platform unit t period, the time hop count that T is dynamic economic dispatch, M is for participating in the unit number of dynamic economic dispatch; a _i, b _i, c _irepresent respectively corresponding COST system, specifically according to unit situation, determine;

Corresponding adaptive value is:

f _a＝f (5)；

Using Electrical Power System Dynamic economic load dispatching objective function result of calculation as particle adaptive value, and target function value is less, and adaptive value is less, and the fitness of particle is higher.

6. Electrical Power System Dynamic economic load dispatching method as claimed in claim 5, it is characterized in that, the bound constraint of Electrical Power System Dynamic economic load dispatching comprises power-balance constraint, the unit output bound constraint of following formula (8) expression and the unit ramp loss that following formula (9) represents that following formula (6) represents;

${\mathrm{\&Sigma;}}_{i=1}^M{P}_{i,t}=P_{D,t}+P_{\mathrm{loss},t}---\left(6\right);$

(6) in formula: P _d,tbe the payload of t period, P _{loss, t}the network loss size of t period;

Network loss is calculated and is adopted B Y-factor method Y to calculate, and expression formula is as follows:

P _loss,t＝P _t ^T*B*P _t (7)；

(7) in formula: P _tbe the column vector of t each unit output of period, P _t ^trepresent P _ttransposition, the matrix that B is M * M, for calculating network loss;

P _i ^min≤P _i,t≤P _i ^max (8)；

(8) in formula: P _i ^minand P _i ^maxrepresent respectively i the platform lower limit of exerting oneself and the upper limit of unit t period;

$R_i^d\mathrm{\&Delta;t}\&le;P_{i,t}-P_{i,t-1}\&le;R_i^u\mathrm{\&Delta;t}---\left(9\right);$

(9) in formula: for downward Ramp Rate, it is negative value; for Ramp Rate upwards, on the occasion of; Δ t represents two time intervals between scheduling slot.

7. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, it is characterized in that, in described step e, the adaptive value of each particle relatively, determine the highest particle of particle fitness, find the historical optimal value of each particle, i.e. local optimum, and particle position, and global optimum and particle position; If iteration, finds global optimum and corresponding particle position for the first time;

In particle cluster algorithm, the population number of population is comprised number of particles, and each individuality of population the inside is all called a particle; Each feasible solution is all particles in population, and each particle has two attributes, and displacement and speed are all expressed as a matrix-vector, are shown below:

$P_m=\left[\begin{array}{ccccc}{P}_{\mathrm{1,1}}& ...& P_{1,t}& ...& P_{1,T}\\ P_{i,1}& ...& P_{i,t}& ...& P_{i,T}\\ ...& ...& ...& ...& ...\\ P_{M,1}& ...& P_{M,t}& ...& P_{M,T}\end{array}\right]---\left(10\right);$

$V_m=\left[\begin{array}{ccccc}{V}_{\mathrm{1,1}}& ...& V_{1,t}& ...& V_{1,T}\\ V_{i,1}& ...& V_{i,t}& ...& V_{i,T}\\ ...& ...& ...& ...& ...\\ V_{M,1}& ...& V_{M,t}& ...& V_{M,T}\end{array}\right]---\left(11\right);$

Wherein: P _mbe the displacement of m particle, P _i,tbe exerting oneself of i platform unit t period, i.e. the position of particle; V _mv _mthe speed of individual particle, V _i,tit is the correction of exerting oneself of the i platform unit t period of correspondence; T is the time hop count of dynamic economic dispatch; M is for participating in the unit number of dynamic economic dispatch; In Electrical Power System Dynamic economic load dispatching, the position of particle represents exerting oneself of each unit day part, and line number represents unit number, hop count when columns represents.

8. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, it is characterized in that, in described step F, according to the resulting local optimum of step e and particle position, and all optimal values and particle position, according to following expression formula more speed and the position of new particle:

$V_m^{k+1}=\mathrm{\&omega;}\&CenterDot;V_m^k+c_1\&CenterDot;r_1\&CenterDot;({\mathrm{pbest}}_m^k-P_m^k)+c_2\&CenterDot;r_2\&CenterDot;({\mathrm{gbest}}^k-P_m^k)+\mathrm{\&Delta;}{V}_m^k---\left(12\right);$

$P_m^{k+1}=P_m^k+V_m^{k+1}+\mathrm{\&Delta;}{P}_m^k---\left(13\right);$

Wherein: the adjustment amount that represents respectively speed and position; be the speed in k generation of m particle, the speed in k+1 generation of m particle; for the k+1 generation of m particle; be the historical optimal value of m particle, gbest ^kit is the global optimum of the k time iteration; ω is inertial factor, for weighing global search and the local search ability of particle cluster algorithm; ω value is more greatly more easy to algorithm and increases search space, and the more little local optimal searching of more easily carrying out of value adopts self-adaptation to adjust the mode of inertial factor, that is:

$\mathrm{\&omega;}={\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{C}k---\left(14\right);$

Wherein: ω _maxget 0.9, ω _minget the maximum times that 0.4, C is iteration, k is current iterations; c ₁, c ₂for the study factor, be respectively and control particle to the maximum step-length of individual optimum and global optimum's locality flight; Get c ₁=c ₂=3.05;

for adjusting out-of-limit particle, when particle is out-of-limit, according to (6), (7), (8), (9) formula, according to following rule, particle is adjusted:

1) according to speed bound, constraint is adjusted unit output, on unit, in limited time, is exerted oneself and is limited to the upper limit, and unit is more lower in limited time, is exerted oneself and is limited to lower limit;

2) according to climbing constraint, unit output is adjusted, when unit is upwards climbed, if out-of-limit, unit output is limited to the upwards upper limit of climbing; When unit is climbed, if out-of-limit, unit output is limited to the lower limit of downward climbing downwards;

3) according to the unit output after adjusting, recalculate network loss;

4) calculate the amount of unbalance that day part is exerted oneself, i.e. difference between day part unit output sum and load, distributes amount of unbalance according to the big or small of the micro-gaining rates of consumption such as unit and in conjunction with the bound units limits of each unit.

9. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, is characterized in that, for particle rapidity, is limited within the scope of constraint of velocity, and constraint of velocity formula is as follows:

$V_m^k\left[i\right]\left[j\right]=\left\{\begin{array}{cc}{V}_m^k\left[i\right]{\left[j\right]}_{\max },& \mathrm{if}{V}_m^k\left[i\right]\left[j\right]>V_m^k\left[i\right]{\left[j\right]}_{\max }\\ V_m^k\left[i\right]{\left[j\right]}_{\min },& \mathrm{if}{V}_m^k\left[i\right]\left[j\right]<V_m^k\left[i\right]{\left[j\right]}_{\min }\end{array}\right.---\left(15\right);$

(15) in formula: for the i of particle rapidity is capable, the element of j row, for the i of particle rapidity is capable, the maximal value defined in the element of j row, for the i of particle rapidity is capable, the minimum value defined in the element of j row; The maximum of particle rapidity, minimum value are according to following formula setting:

$V_m^k{\left[i\right]}_{\max }=({P_i}^{\max }-{P_i}^{\min })/100---\left(16\right);$

$V_m^k{\left[i\right]}_{\min }=({P_i}^{\min }-{P_i}^{\max })/100---\left(17\right);$

(16) and in (17) formula: be respectively the upper and lower bound of corresponding i platform unit speed in particle, will be extended to the transversal vector with period corresponding length, obtain speed limit and lower limit that particle i is capable.

10. Electrical Power System Dynamic economic load dispatching method as claimed in claim 1, it is characterized in that, in described step H, according to obtaining global optimum in step e, before and after comparing, the global optimum of twice, adopts adaptive approach, according to the order of magnitude of the difference of twice global optimum, particle rapidity is adjusted, and absolute value is larger, and adjustment degree is larger; Carry out as follows:

Particle rapidity is adjusted, that is:

v ₁＝v ₀+Δv (18)；

(18) in formula: v ₀, v ₁be respectively the particle rapidity before and after adjusting, the speed amount of Δ v for adjusting, adopts adaptive algorithm during adjustment, and adaptive algorithm formula is as follows:

$\mathrm{\&Delta;v}=\left\{\begin{array}{c}0,\mathrm{\&lambda;}>0.01\\ v_{\mathrm{ini}}\&CenterDot;r_3,0.001<\mathrm{\&lambda;}\&le;0.01\\ v_{\mathrm{ini}}\&CenterDot;r_4,0<\mathrm{\&lambda;}\&le;0.001\end{array}\right.---\left(19\right);$

(19) in formula: v _inifor initial velocity set in particle cluster algorithm, r ₃random number for-0.1 to 0.1, r ₄random number for-0.01 to 0.01, for random number r ₃, r ₄need be with setting according to reality, λ calculates according to following formula:

$\mathrm{\&lambda;}=\frac{|{f_{\mathrm{best}}}^k-{f_{\mathrm{best}}}^{k-1}|}{{f_{\mathrm{best}}}^k}---\left(20\right);$

In its (20) formula: f _best ^kbe that k is for the global optimum position of particle, f _best ^k-1k-1 is the twice global optimum difference relative scale in front and back for the position λ of global optimum of particle.

11. Electrical Power System Dynamic economic load dispatching methods as claimed in claim 1, it is characterized in that, in described step I, the iterative algorithm of having set according to steps A, judge whether iterations reaches: if reach iterations C=500, stop calculating, obtain particle global optimum and be final particle position, this particle position is each unit exerting oneself at day part, thereby calculate net result, net result comprises going out force level and calculating the unit operation total expenses in economic cycle of each unit day part; If do not reach iterations, turn back to step C, continue to calculate.