CN104036331A

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

Info

Publication number: CN104036331A
Application number: CN201410240515.9A
Authority: CN
Inventors: 李相俊; 宁阳天; 麻秀范; 杨水丽; 惠东; 陈金详
Original assignee: State Grid Corp of China SGCC; China Electric Power Research Institute Co Ltd CEPRI; North China Electric Power University; Electric Power Research Institute of State Grid Fujian Electric Power Co Ltd; State Grid Fujian Electric Power Co Ltd
Current assignee: State Grid Corp of China SGCC; China Electric Power Research Institute Co Ltd CEPRI; North China Electric Power University; Electric Power Research Institute of State Grid Fujian Electric Power Co Ltd; State Grid Fujian Electric Power Co Ltd
Priority date: 2014-05-30
Filing date: 2014-05-30
Publication date: 2014-09-10
Anticipated expiration: 2034-05-30
Also published as: CN104036331B

Abstract

The invention relates to a dynamic economic dispatching method of electric power system based on improved particle swarm algorithm, including: setting each parameter of particle swarm algorithm; generating initial particle swarm; setting upper and lower limit constraints of particle speed; calculating the adaptability of each particle according to the objective function value; compare the fitness value of each particle, find out the historical optimal value and position of each particle, and the particle and its position that reach the global optimal value; update the position and speed of each particle; judge the position and speed of the particle Whether it exceeds the limit, if it exceeds the limit, adjust the position and speed of the particle to the constraint range; speed up the particle speed; if it reaches the number of iterations, stop the iteration and get the final result; the present invention uses the particle swarm algorithm to solve the power system For the dynamic economic scheduling problem, it has been improved, and the adaptive algorithm is used to adjust the particle speed. When the search falls into a local search, the search is more targeted, and good results are obtained.

Description

A Dynamic Economic Dispatch Method of Power System Based on Improved Particle Swarm Algorithm

技术领域technical field

本发明涉及一种电力系统优化运行的经济调度方法，具体讲涉及一种基于改进粒子群算法的电力系统动态经济调度方法。The invention relates to an economic scheduling method for optimal operation of a power system, in particular to a dynamic economic scheduling method for a power system based on an improved particle swarm algorithm.

背景技术Background technique

机组运行需要成本，电力系统运行过程需要考虑运行的经济性，不同的机组成本函数不同，不同的出力方案的经济成本也有所不同。经济调度的目的在于一定周期内，优化各机组的出力，以获得最优的出力水平，从而使成本最小。机组前后时段的出力还涉及到机组的爬坡能力约束，机组前后时段的出力密切相关，这就需要进行电力系统的动态经济调度。电力系统动态经济调度是电力系统安全经济运行的一部分，其目的是在满足各种安全性约束以及电能质量要求的条件下安排机组的运行方式，使系统总的运行费用最小。The operation of the unit requires cost, and the operation of the power system needs to consider the economics of operation. Different units have different cost functions, and the economic costs of different output schemes are also different. The purpose of economic dispatch is to optimize the output of each unit within a certain period to obtain the optimal output level and minimize the cost. The output of the unit in the front and rear periods also involves the constraints of the unit’s climbing ability, and the output of the unit in the front and rear periods is closely related, which requires dynamic economic dispatch of the power system. Dynamic economic dispatch of power system is a part of safe and economic operation of power system. Its purpose is to arrange the operation mode of units under the condition of meeting various safety constraints and power quality requirements, so as to minimize the total operating cost of the system.

动态经济调度所涉及的变量较多，需要同时考虑等式和不等式的约束条件，现有优化算法难以满足计算要求。问题维数较高、约束条件严格，造成各个可行解对应目标函数值较为接近，使用标准的粒子群算法时，容易造成搜索陷入局部最优，从而过早收敛，对全局最优解搜索的停滞。There are many variables involved in dynamic economic scheduling, and the constraints of equality and inequality need to be considered at the same time. The existing optimization algorithms are difficult to meet the calculation requirements. The problem dimension is high and the constraints are strict, so that the corresponding objective function values of each feasible solution are relatively close. When using the standard particle swarm optimization algorithm, it is easy to cause the search to fall into a local optimum, thereby prematurely converging, and the search for the global optimal solution is stagnant. .

解决过早收敛的现有方法主要是保证粒子的多样性，避免迭代后期，粒子群个体相似，陷入局部搜索。如结合遗传算法对粒子的位置进行交叉、变异等操作，以保证粒子的多样性。但由于动态经济调度的约束条件较为严格，解空间被限制在很小的范围，这种对粒子位置的操作容易越限，同时针对性也不够强，动态经济调度问题存在一定的局限性。The existing methods to solve premature convergence are mainly to ensure the diversity of particles, avoiding the late iteration, the particle swarm individuals are similar, and fall into local search. For example, the genetic algorithm is used to perform operations such as crossover and mutation on the position of the particles to ensure the diversity of the particles. However, due to the strict constraints of dynamic economic scheduling, the solution space is limited to a small range, and the operation on the particle position is easy to exceed the limit, and at the same time, the pertinence is not strong enough, so the dynamic economic scheduling problem has certain limitations.

在进行电力系统动态经济调度中，为了避免陷入局部搜索，现的有粒子群算法普遍采用对粒子位置进行调整的方法，如结合遗传算法，对粒子进行交叉、变异等操作。但这些方法容易千万粒子越限，并在迭代后期对搜索区域的针对性不强，容易千万迭代过程的浪费。In the dynamic economic dispatching of power system, in order to avoid falling into local search, the existing particle swarm optimization algorithm generally adopts the method of adjusting the position of the particle, such as combining the genetic algorithm to perform operations such as crossover and mutation on the particle. However, these methods are easy to exceed the limit by tens of millions of particles, and the pertinence of the search area is not strong in the late iteration, and it is easy to waste tens of millions of iterations.

发明内容Contents of the invention

针对现有技术的不足，本发明的目的是提供一种基于改进粒子群算法的电力系统动态经济调度方法，本发明对粒子群算法的迭代公式进行了改进，加入自适应方法，以对粒子速度进行调整，并根据约束条件对粒子进行调整，以保证粒子不越限。采用改进后的粒子群算法对电力系统的动态经济调度进行求解，以在满足相关约束条件的情况下，获得优化后的各机组各时段的出力水平。In view of the deficiencies in the prior art, the purpose of the present invention is to provide a dynamic economic dispatch method for power systems based on the improved particle swarm algorithm. The present invention improves the iterative formula of the particle swarm algorithm and adds an adaptive method to adjust the particle speed Make adjustments, and adjust the particles according to the constraints to ensure that the particles do not exceed the limit. The improved particle swarm optimization algorithm is used to solve the dynamic economic dispatching of the power system, so as to obtain the optimized output level of each unit at each time period under the condition of satisfying the relevant constraints.

本发明的目的是采用下述技术方案实现的：The object of the present invention is to adopt following technical scheme to realize:

本发明提供一种基于改进粒子群算法的电力系统动态经济调度方法，其改进之处在于，所述方法包括下述步骤：The present invention provides a method for dynamic economic dispatching of power systems based on improved particle swarm optimization algorithm. The improvement is that the method includes the following steps:

A、设置粒子群算法的参数；A. Set the parameters of the particle swarm optimization algorithm;

B、生成初始粒子群；B. Generate initial particle swarm;

C、设置粒子在电力系统动态经济调度中的速度上下限约束；C. Set the upper and lower limits of the speed of the particles in the dynamic economic dispatch of the power system;

D、确定粒子的适应值；D. Determine the fitness value of the particle;

E、比较粒子的适应值，找出每个粒子的历史最优值及其位置，以及达到全局最优值的粒子及其位置；E. Compare the fitness value of the particles, find out the historical optimal value and its position of each particle, and the particle and its position that reach the global optimal value;

F、根据局部最优值以及全部最优值更新每个粒子的位置和速度；F. Update the position and velocity of each particle according to the local optimum and all optimum values;

G、根据约束条件，以及粒子速度的上下限约束判断粒子的位置和速度是否越限，若越限，将粒子的位置和速度调整至约束范围内；G. According to the constraint conditions and the upper and lower limits of the particle velocity, judge whether the position and velocity of the particle exceed the limit. If it exceeds the limit, adjust the position and velocity of the particle to the constraint range;

H、采用自适应方法，对粒子位置进行调整；H, using an adaptive method to adjust the particle position;

I、若达到迭代次数，停止迭代，得到最终的结果。I. If the number of iterations is reached, stop the iteration and get the final result.

进一步地，所述步骤A中，设置粒子群算法所需的各个参数，所述参数包括权重因子、学习因子、粒子群规模数和迭代次数，权重因子取ω_max＝0.9，ω_min＝0.4，学习因子取c₁＝c₂＝3.05，粒子群规模和迭代次数根据实际情况设置，包括设置为粒子群规模数N＝40，迭代次数C＝500。Further, in the step A, each parameter required by the particle swarm optimization algorithm is set, and the parameters include a weight factor, a learning factor, a particle swarm size number and the number of iterations, and the weight factor is ω _max =0.9, ω _min =0.4, The learning factor is c ₁ =c ₂ =3.05, the size of the particle swarm and the number of iterations are set according to the actual situation, including setting the size of the particle swarm N=40 and the number of iterations C=500.

进一步地，所述步骤B中，根据计算期间内各时段的负荷水平随机分摊到各个机组的出力水平，按照粒子群规模数重复该步骤，获得初始粒子群；包括：Further, in the step B, according to the load level of each time period in the calculation period, the output level of each unit is randomly allocated to the output level of each unit, and this step is repeated according to the size of the particle swarm to obtain the initial particle swarm; including:

随机生成行数为机组数、列数为时段数的随机数组，该数组的元素均为正数，且每一列元素相加之和均为一；将时段负荷乘以相应的列即可得到初始粒子，重复该操作，即得到整个初始粒子群，即对于第m个粒子生成如下：Randomly generate a random array with the number of rows as the number of units and the number of columns as the number of time periods. The elements of the array are all positive numbers, and the sum of the elements in each column is one; multiply the time period load by the corresponding column to get the initial Particles, repeat this operation to obtain the entire initial particle group, that is, for the mth particle to be generated as follows:

${P P}_{m m} = = [\begin{matrix} {P P}_{1,1 1,1} & . . . . . . & {P P}_{11,, t t} & . . . . . . & {P P}_{11,, T T} \\ {P P}_{i i,, 11} & . . . . . . & {P P}_{i i,, t t} & . . . . . . & {P P}_{i i,, T T} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {P P}_{M m,, 11} & . . . . . . & {P P}_{M m,, t t} & . . . . . . & {P P}_{M m,, T T} \end{matrix}] - - - - - - ((11));;$

P_i,t＝a_i,t·P_D,t (2)；P _i,t = a _i,t P _D,t (2);

a_1,t+a_2,t+…+a_i,t+…a_M,t＝1 (3)；a _1,t +a _2,t +...+a _i,t +...a _M,t = 1 (3);

其中：T表示经济调度的时段数，为一天24小时，以每小时为一个段，共24个时段，M表示机组数；a_i,t表示第i台机组第t时段的比例元素，为随机生成，满足(3)式，故(3)式表示对于第t时段所有M台的比例元素之和为1，P_D,t为第t时段的负荷的大小，采用相同方法生成其他粒子。Among them: T represents the number of time slots for economic scheduling, which is 24 hours a day, with each hour as a segment, a total of 24 time slots, _M represents the number of units; Generation, satisfying the formula (3), so the formula (3) means that the sum of the proportional elements of all M units for the t-th period is 1, P _D,t is the size of the load in the t-th period, and other particles are generated by the same method.

进一步地，所述步骤C中，根据各机组的上下限约束确定各个粒子的速度上下限，粒子速度的上下限根据机组上下限出力之差进行缩减，缩减范围为1％，即粒子速度上限为机组出力上限减去出力下限之差的1％，粒子速度下限为机组出力下限减去出力上限之差的1％。Further, in the step C, the upper and lower limits of the speed of each particle are determined according to the upper and lower limit constraints of each unit, and the upper and lower limits of the particle speed are reduced according to the difference between the upper and lower limit output of the unit, and the reduction range is 1%, that is, the upper limit of the particle speed is 1% of the difference between the upper limit of unit output minus the lower limit of output, and the lower limit of particle velocity is 1% of the difference between the lower limit of unit output and the upper limit of output.

进一步地，所述步骤D中，根据步骤B中所获得的初始粒子群，根据电力系统动态经济调度目标函数确定粒子的适应值，电力系统动态经济调度目标函数为：Further, in the step D, according to the initial particle group obtained in the step B, the fitness value of the particles is determined according to the objective function of the dynamic economic dispatch of the power system, and the objective function of the dynamic economic dispatch of the power system is:

$f f = = {Σ Σ}_{t t}^{T T} {Σ Σ}_{i i}^{M m} (({a a}_{i i} \cdot &Center Dot; {P P}_{i i,, t t}^{22} + + {b b}_{i i} \cdot &Center Dot; {P P}_{i i,, t t} + + {c c}_{i i})) - - - - - - ((44));;$

其中：P_i,t为第i台机组第t时段的出力，T为动态经济调度的时段数，M为参与动态经济调度的机组数；a_i、b_i、c_i分别表示相应的成本系统，具体根据机组情况而定；Among them: P _i,t is the output of the i unit in the t period, T is the number of time periods for dynamic economic dispatch, M is the number of units participating in dynamic economic dispatch; a _i , bi _, and c _i represent the corresponding cost system , depending on the situation of the unit;

相应的适应值为：The corresponding fitness values are:

f_a＝f (5)；f _a = f (5);

即以电力系统动态经济调度目标函数计算结果作为粒子适应值，目标函数值越小，适应值越小，粒子的适应度越高。That is, the calculation result of the objective function of the dynamic economic dispatch of the power system is used as the fitness value of the particle. The smaller the objective function value is, the smaller the fitness value is, and the higher the fitness of the particle is.

进一步地，电力系统动态经济调度的上下限约束包括功率平衡约束、机组出力上下限约束和机组爬坡约束；Further, the upper and lower limit constraints of dynamic economic dispatch of power system include power balance constraints, unit output upper and lower limit constraints and unit ramp constraints;

其中功率平衡约束用下述表达式表示：The power balance constraint is expressed by the following expression:

${Σ Σ}_{i i = = 11}^{M m} {P P}_{i i,, t t} = = {P P}_{D D.,, t t} + + {P P}_{loss loss,, t t} - - - - - - ((66));;$

其中：P_D,t为第t时段的负荷大小，P_loss,t第t时段的网损大小；Among them: P _D,t is the load size of the tth time period, P _loss,t is the network loss size of the tth time period;

网损计算采用B系数法计算，表达式如下：The network loss is calculated using the B coefficient method, and the expression is as follows:

P_loss,t＝P_t ^T*B*P_t (7)；P _loss,t =P _t ^T *B*P _t (7);

其中：P_t为第t时段各机组出力的列向量，P_t ^T表示P_t的转置，B为M×M的矩阵，用于计算网损；Among them: P _t is the column vector of the output of each unit in the tth period, P _t ^T represents the transposition of P _t , B is the matrix of M×M, which is used to calculate the network loss;

机组出力上下限约束用下述表达式表示：The upper and lower limits of unit output constraints are expressed by the following expressions:

P_i ^min≤P_i,t≤P_i ^max (8)；P _i ^min ≤ _{P i,t} ≤ P _i ^max (8);

其中：P_i ^min和P_i ^max分别表示第i台机组第t时段的出力的下限和上限；Among them: P _i ^min and P _i ^max represent the lower limit and upper limit of the output of the i unit in the t period of time, respectively;

机组爬坡约束用下述表达式表示：The unit ramp constraint is expressed by the following expression:

${R R}_{i i}^{d d} Δt Δt \leq \leq {P P}_{i i,, t t} - - {P P}_{i i,, t t - - 11} \leq \leq {R R}_{i i}^{u u} Δt Δt - - - - - - ((99));;$

其中：为向下爬坡速度，为负值；为向上爬坡速度，为正值；Δt表示两个调度时段之间的时间间隔。in: is the downward climbing speed, which is a negative value; is the upward climbing speed, which is a positive value; Δt represents the time interval between two scheduling periods.

进一步地，所述步骤E中，比较各粒子的适应值，确定粒子适应度最高的粒子，找到各个粒子的历史最优值，即局部最优值，和粒子位置，以及全局最优值及粒子位置；若第一次迭代，则找到全局最优值及对应粒子位置；Further, in the step E, compare the fitness values of each particle, determine the particle with the highest particle fitness, find the historical optimal value of each particle, that is, the local optimal value, and the particle position, as well as the global optimal value and particle position position; if it is the first iteration, find the global optimal value and the corresponding particle position;

在粒子群算法中，粒子群的种群数为所包含的粒子数量，种群里面每个个体均称为一个粒子；每一个可行解均是种群中的一个粒子，每个粒子都有两个属性，位移和速度，均表示为一个矩阵向量，如下式所示：In the PSO algorithm, the population number of the particle swarm is the number of particles contained, and each individual in the population is called a particle; each feasible solution is a particle in the population, and each particle has two attributes, Both displacement and velocity are expressed as a matrix vector, as shown in the following formula:

${P P}_{m m} = = [\begin{matrix} {P P}_{1,1 1,1} & . . . . . . & {P P}_{11,, t t} & . . . . . . & {P P}_{11,, T T} \\ {P P}_{i i,, 11} & . . . . . . & {P P}_{i i,, t t} & . . . . . . & {P P}_{i i,, T T} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {P P}_{M m,, 11} & . . . . . . & {P P}_{M m,, t t} & . . . . . . & {P P}_{M m,, T T} \end{matrix}] - - - - - - ((1010));;$

${V V}_{m m} = = [\begin{matrix} {V V}_{1,1 1,1} & . . . . . . & {V V}_{11,, t t} & . . . . . . & {V V}_{11,, T T} \\ {V V}_{i i,, 11} & . . . . . . & {V V}_{i i,, t t} & . . . . . . & {V V}_{i i,, T T} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {V V}_{M m,, 11} & . . . . . . & {V V}_{M m,, t t} & . . . . . . & {V V}_{M m,, T T} \end{matrix}] - - - - - - ((1111));;$

其中：P_m为第m个粒子的位移，P_i,t为第i台机组第t时段的出力，即粒子的位置；V_m是第V_m个粒子的速度，V_i,t是对应的第i台机组t时段的出力的修正量；T为动态经济调度的时段数；M为参与动态经济调度的机组数；在电力系统动态经济调度中，粒子的位置即表示各个机组各时段的出力，行数表示机组数，列数表示时段数。Among them: P _m is the displacement of the m-th particle, P _i,t is the output force of the i-th unit in the t-period, that is, the position of the particle; V _m is the velocity of the V _m -th particle, and V _i,t is the corresponding The correction amount of the output of the i unit in t period; T is the period number of dynamic economic dispatch; M is the number of units participating in dynamic economic dispatch; in the dynamic economic dispatch of power system, the position of the particle represents the output of each unit in each period , the number of rows represents the number of units, and the number of columns represents the number of time periods.

进一步地，所述步骤F中，根据步骤E所得到的局部最优值和粒子位置，以及全部最优值及粒子位置，根据下述表达式更新粒子的速度与位置：Further, in the step F, according to the local optimal value and particle position obtained in step E, as well as all optimal values and particle positions, the speed and position of the particles are updated according to the following expressions:

${V V}_{m m}^{k k + + 11} = = ω ω \cdot &Center Dot; {V V}_{m m}^{k k} + + {c c}_{11} \cdot &Center Dot; {r r}_{11} \cdot &Center Dot; (({pbest pbest}_{m m}^{k k} - - {P P}_{m m}^{k k})) + + {c c}_{22} \cdot \cdot {r r}_{22} \cdot \cdot (({gbest gbest}^{k k} - - {P P}_{m m}^{k k})) + + Δ Δ {V V}_{m m}^{k k} - - - - - - ((1212));;$

${P P}_{m m}^{k k + + 11} = = {P P}_{m m}^{k k} + + {V V}_{m m}^{k k + + 11} + + Δ Δ {P P}_{m m}^{k k} - - - - - - ((1313));;$

其中：分别表示速度和位置的调整量；为第m个粒子的第k代的速度，第m个粒子的第k+1代的速度；为第m个粒子的第k代，为m个粒子的第k+1代；为第m个粒子的历史最优值，gbest^k为第k次迭代的全局最优值；ω为惯性因子，用于权衡粒子群算法的全局搜索和局部搜索能力；ω取值越大越易于算法增大搜寻空间，取值越小越容易进行局部寻优，采用自适应调整惯性因子的方式，即：in: Respectively represent the adjustment amount of speed and position; is the velocity of the kth generation of the mth particle, The velocity of the k+1th generation of the mth particle; is the kth generation of the mth particle, is the k+1th generation of m particles; is the historical optimal value of the m-th particle, gbest ^k is the global optimal value of the k-th iteration; ω is the inertia factor, which is used to weigh the global search and local search capabilities of the particle swarm optimization algorithm; the larger the value of ω, the easier the algorithm Increase the search space, the smaller the value, the easier it is to carry out local optimization, and adopt the method of adaptively adjusting the inertia factor, namely:

$ω ω = = {ω ω}_{max max} - - \frac{{ω ω}_{max max} - - {ω ω}_{min min}}{C C} k k - - - - - - ((1414));;$

其中：ω_max取0.9，ω_min取0.4，C为迭代的最大次数，k为目前迭代次数；c₁、c₂为学习因子，分别为控制粒子向个体最优和全局最优位置方向飞行的最大步长；取c₁＝c₂＝3.05；Among them: ω _max is set to 0.9, ω _min is set to 0.4, C is the maximum number of iterations, k is the current number of iterations; c ₁ and c ₂ are learning factors, which control the particle to fly to the individual optimal position and the global optimal position respectively. Maximum step size; take c ₁ =c ₂ =3.05;

用于调整越限的粒子，粒子越限时，按照(6)、(7)、(8)、(9)式，根据下列规则对粒子进行调整： It is used to adjust the particles that exceed the limit. When the particle exceeds the limit, according to formulas (6), (7), (8), and (9), the particles are adjusted according to the following rules:

1)根据速度上下限约束对机组出力进行调整，机组越上限时，则将其出力限定在上限，机组越下限时，则将其出力限定在下限；1) Adjust the output of the unit according to the upper and lower limit constraints of the speed. When the unit exceeds the upper limit, its output is limited to the upper limit, and when the unit exceeds the lower limit, its output is limited to the lower limit;

2)根据爬坡约束对机组出力进行调整，机组向上爬坡时，若越限，则将机组出力限定在向上爬坡的上限；机组向下爬坡时，若越限，则将机组出力限定在向下爬坡的下限；2) Adjust the output of the unit according to the climbing constraints. When the unit climbs upward, if it exceeds the limit, the output of the unit is limited to the upper limit of the upward climb; when the unit climbs downward, if it exceeds the limit, the output of the unit is limited at the lower limit of the downward climb;

3)根据调整后的机组出力，重新计算网损；3) Recalculate the network loss according to the adjusted unit output;

4)计算各时段出力的不平衡量，即各时段机组出力之和与负荷之间的差值，将不平衡量根据机组等耗量微增率的大小并结合各个机组的上下限出力约束进行分配。4) Calculate the unbalanced amount of output in each period, that is, the difference between the sum of unit output and the load in each period, and distribute the unbalanced amount according to the small increase rate of the equal consumption of the unit and combined with the upper and lower limit output constraints of each unit.

进一步地，对于粒子速度，将其限定在速度约束范围内，速度约束公式如下：Further, for the particle velocity, it is limited within the range of velocity constraint, and the velocity constraint formula is as follows:

${V V}_{m m}^{k k} [[i i]] [[j j]] = = \{\begin{matrix} {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{max max},, & if if {V V}_{m m}^{k k} [[i i]] [[j j]] > > {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{max max} \\ {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{min min},, & if if {V V}_{m m}^{k k} [[i i]] [[j j]] < < {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{min min} \end{matrix} - - - - - - ((1515));;$

其中：为粒子速度的第i行，第j列的元素，为粒子速度的第i行，第j列的元素中所限定的最大值，为粒子速度的第i行，第j列的元素中所限定的最小值；粒子速度的最大、最小值根据以下表达式设置：in: is the i-th row and the j-th column element of the particle velocity, is the maximum value defined in the elements of the i-th row and j-th column of the particle velocity, is the minimum value defined in the elements of the i-th row and j-th column of the particle velocity; the maximum and minimum values of the particle velocity are set according to the following expressions:

${V V}_{m m}^{k k} {[[i i]]}_{max max} = = (({P P}_{i i}^{max max} - - {P P}_{i i}^{min min})) / / 100100 - - - - - - ((1616));;$

${V V}_{m m}^{k k} {[[i i]]}_{min min} = = (({P P}_{i i}^{min min} - - {P P}_{i i}^{max max})) / / 100100 - - - - - - ((1717));;$

其中：分别为粒子中对应第i台机组速度的上限和下限，将会扩展成与时段相应长度的横向量，即得到粒子第i行的速度上限和下限。in: are respectively the upper limit and lower limit of the speed of the i-th unit in the particle, which will be expanded into a transverse quantity corresponding to the length of the time period, that is, the upper limit and lower limit of the speed of the i-th row of particles are obtained.

进一步地，所述步骤H中，根据步骤E中得到全局最优值，比较前后两次的全局最优值，采用自适应方法，根据两次全局最优值之差的绝对值大小，对粒子速度进行调整，绝对值越大，调整程度越大；执行如下：Further, in the step H, according to the global optimal value obtained in the step E, compare the global optimal value twice before and after, and adopt an adaptive method, according to the absolute value of the difference between the two global optimal values, the particle The speed is adjusted, the greater the absolute value, the greater the adjustment degree; the execution is as follows:

粒子群算法中，随着迭代次数的增加，可能会陷入局部最优，此时粒子的速度会随之减小，故对粒子速度进行调整，即：In the particle swarm optimization algorithm, as the number of iterations increases, it may fall into a local optimum, and the speed of the particles will decrease accordingly, so the particle speed is adjusted, namely:

v₁＝v₀+Δv (18)；v ₁ =v ₀ +Δv (18);

其中：v₀、v₁分别为调整前后的粒子速度，Δv为调整的速度量，调整时采用自适应算法，自适应算法公式如下：Among them: v ₀ and v ₁ are the particle speeds before and after adjustment, respectively, and Δv is the adjusted speed. The adaptive algorithm is used for adjustment. The formula of the adaptive algorithm is as follows:

$Δv Δv = = \{\begin{matrix} 00,, λ λ > > 0.01 0.01 \\ {v v}_{ini ini} \cdot &Center Dot; {r r}_{33},, 0.001 0.001 < < λ λ \leq \leq 0.01 0.01 \\ {v v}_{ini ini} \cdot \cdot {r r}_{44},, 00 < < λ λ \leq \leq 0.001 0.001 \end{matrix} - - - - - - ((1919));;$

其中：v_ini为粒子群算法中所设置的初始速度，r₃为-0.1到0.1的随机数，r₄为-0.01到0.01的随机数，对于随机数r₃、r₄根据实际需用设定，λ则根据下式计算：Among them: v _ini is the initial velocity set in the particle swarm optimization algorithm, r ₃ is a random number from -0.1 to 0.1, r ₄ is a random number from -0.01 to 0.01, and the random numbers r ₃ and r ₄ are set according to actual needs fixed, λ is calculated according to the following formula:

$λ λ = = \frac{| | {f f}_{best the best}^{k k} - - {f f}_{best the best}^{k k - - 11} | |}{{f f}_{best the best}^{k k}} - - - - - - ((2020));;$

其中：f_best ^k为第k代粒子的全局最优位置，f_best ^k-1第k-1代粒子的全局最优位置λ即为前后两次全局最优值差值相对比例，据此对速度进行提速的调整，避免前后两次全局最优值过于相近，陷于局部最优。Among them: f _best ^k is the global optimal position of particles in the kth generation, and the global optimal position λ of f _best ^k-1 particles in the k-1th generation is the relative ratio of the difference between the two global optimal values before and after. The speed is adjusted to increase the speed, so as to avoid the two global optimal values being too close to the local optimal value.

进一步地，所述步骤I中，根据步骤A已设定的迭代算法，判定迭代次数是否达到：若达到迭代次数C＝500，则停止计算，得到粒子全局最优值即为最终粒子位置，该粒子位置即为各机组在各时段的出力，从而计算出最终结果，最终结果包括各机组各时段的出力水平以及计算经济周期内的机组运行总费用；若没有达到迭代次数，则返回到步骤D，继续计算。Further, in the step I, according to the iterative algorithm set in step A, it is determined whether the number of iterations has reached: if the number of iterations C=500 is reached, the calculation is stopped, and the global optimal value of the particle is obtained as the final particle position. The position of the particle is the output of each unit in each period, so as to calculate the final result. The final result includes the output level of each unit in each period and the total operating cost of the unit in the calculation of the economic cycle; if the number of iterations is not reached, return to step D , to continue the calculation.

与现有技术比，本发明达到的有益效果是：Compared with prior art, the beneficial effect that the present invention reaches is:

本发明提供的基于改进粒子群算法的电力系统动态经济调度方法，其特征在于基于粒子速度约束与经济调度约束条件构成的粒子位置约束对每次迭代得到的粒子速度和粒子位置进行调整。现有粒子群算法，并没有根据适应值的变化对粒子速度进行调整，当对粒子的速度进行调整，在迭代陷入局部搜索时，粒子速度基本变为零，不利于跳出局部搜索，因此本发明中，基于迭代前后两次得到的适应值进行粒子位置调整，对粒子速度进行提速，以跳出局部搜索，在提速过程中，采用自适应方法，保证粒子即能跳出局部搜索，也能保证粒子的小范围搜索功能，而且采用调整速度的方法能更有针对性地去执行搜索，从而更好地在电力系统动态经济调度中进行寻优，以在满足相关物理约束，并考虑网损的情况下，实现发电的最小出力，从而实现发电总费用最小化，达到动态经济调度的目的。The power system dynamic economic scheduling method based on the improved particle swarm algorithm provided by the present invention is characterized in that the particle velocity and particle position obtained in each iteration are adjusted based on the particle position constraint formed by the particle velocity constraint and the economic scheduling constraint condition. The existing particle swarm optimization algorithm does not adjust the particle speed according to the change of the fitness value. When the particle speed is adjusted, when the iteration falls into the local search, the particle speed basically becomes zero, which is not conducive to jumping out of the local search. Therefore, the present invention In this method, the particle position is adjusted based on the fitness value obtained twice before and after the iteration, and the speed of the particle is accelerated to jump out of the local search. Small-scale search function, and the method of adjusting speed can be used to perform search more targetedly, so as to better optimize in the dynamic economic dispatch of the power system, so as to meet the relevant physical constraints and consider the network loss , to achieve the minimum output of power generation, so as to minimize the total cost of power generation and achieve the purpose of dynamic economic dispatch.

附图说明Description of drawings

图1是本发明提供的基于改进粒子群算法的电力系统动态经济调度方法的流程图；Fig. 1 is the flow chart of the power system dynamic economic dispatching method based on improved particle swarm algorithm provided by the present invention;

图2是本发明提供的根据(6)、(7)、(8)、(9)式调整粒子位置的分解子步骤。Fig. 2 is the decomposition sub-steps for adjusting particle positions according to equations (6), (7), (8) and (9) provided by the present invention.

具体实施方式Detailed ways

下面结合附图对本发明的具体实施方式作进一步的详细说明。The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings.

本发明提供的基于改进粒子群算法的电力系统动态经济调度方法的流程图如图1所示，包括下述步骤：The flow chart of the method for dynamic economic dispatch of power systems based on the improved particle swarm algorithm provided by the present invention is shown in Figure 1, comprising the following steps:

A、设置粒子群算法所需的各个参数，所述参数包括权重因子、学习因子、粒子群规模数和迭代次数，权重因子取ω_max＝0.9，ω_min＝0.4，学习因子取c₁＝c₂＝3.05，粒子群规模和迭代次数根据实际情况设置，包括设置为粒子群规模数N＝40，迭代次数C＝500。A. Set the various parameters required by the particle swarm optimization algorithm. The parameters include weight factor, learning factor, particle swarm size and number of iterations. The weight factor is ω _max = 0.9, ω _min = 0.4, and the learning factor is c ₁ = c ₂ = 3.05, the particle swarm size and the number of iterations are set according to the actual situation, including setting the particle swarm size N = 40, and the number of iterations C = 500.

B、根据计算期间内各时段的负荷水平随机分摊到各个机组的出力水平，按照粒子群规模数重复该步骤，获得初始粒子群；包括：B. According to the load level of each period in the calculation period, it is randomly allocated to the output level of each unit, and this step is repeated according to the size of the particle swarm to obtain the initial particle swarm; including:

P_i,t＝a_i,t·P_D,t (2)；P _i,t = a _i,t P _D,t (2);

其中：T表示经济调度的时段数，为一天24小时，以每小时为一个段，共24个时段，M表示机组数；a_i,t表示第i台机组第t时段的比例元素，为随机生成，但必须满足(3)式，故(3)式表示对于第t时段所有M台的比例元素之和为1，P_D,t为第t时段的负荷的大小，采用相同方法生成其他粒子。Among them: T represents the number of time slots for economic scheduling, which is 24 hours a day, with each hour as a segment, a total of 24 time slots, _M represents the number of units; Generated, but must satisfy the formula (3), so the formula (3) means that the sum of the proportional elements of all M units in the t-th period is 1, P _D,t is the size of the load in the t-th period, use the same method to generate other particles .

C、设置粒子的速度上下限约束：根据各机组的上下限约束确定各个粒子的速度上下限，粒子速度的上下限根据机组上下限出力之差进行缩减，缩减范围为1％，即粒子速度上限为机组出力上限减去出力下限之差的1％，粒子速度下限为机组出力下限减去出力上限之差的1％。C. Set the upper and lower limit constraints of the particle speed: determine the upper and lower limits of the speed of each particle according to the upper and lower limit constraints of each unit, and the upper and lower limits of the particle speed are reduced according to the difference between the upper and lower limit output of the unit, and the reduction range is 1%, which is the upper limit of the particle speed It is 1% of the difference between the upper limit of unit output minus the lower limit of output, and the lower limit of particle velocity is 1% of the difference between the lower limit of unit output minus the upper limit of output.

D、根据目标函数，计算各粒子的适应值：D. According to the objective function, calculate the fitness value of each particle:

根据步骤B中所获得的初始粒子群，根据电力系统动态经济调度目标函数确定粒子的适应值，电力系统动态经济调度目标函数为：According to the initial particle swarm obtained in step B, the fitness value of the particles is determined according to the objective function of the dynamic economic dispatch of the power system. The objective function of the dynamic economic dispatch of the power system is:

$f f = = {Σ Σ}_{t t}^{T T} {Σ Σ}_{i i}^{M m} (({a a}_{i i} \cdot \cdot {P P}_{i i t t}^{22} + + {b b}_{i i} \cdot \cdot {P P}_{i i t t} + + {c c}_{i i})) - - - - - - ((44));;$

其中：P_it为第i台机组第t时段的出力，T为动态经济调度的时段数，M为参与动态经济调度的机组数；a_i、b_i、c_i分别表示相应的成本系统，具体根据机组情况而定；Among them: P _it is the output of unit i in time period t, T is the period number of dynamic economic dispatching, M is the number of units participating in dynamic economic dispatching; a _i , bi _, and c _i represent the corresponding cost system respectively. According to the situation of the unit;

相应的适应值为：The corresponding fitness values are:

f_a＝f (5)；f _a = f (5);

${Σ Σ}_{i i = = 11}^{M m} {P P}_{i i t t} = = {P P}_{D D.,, t t} + + {P P}_{loss loss,, t t} - - - - - - ((66));;$

P_loss,t＝P_t ^T*B*P_t (7)；P _loss,t =P _t ^T *B*P _t (7);

P_i ^min≤P_it≤P_i ^max (8)；P _i ^min ≤ P _it ≤ P _i ^max (8);

E、比较各粒子的适应值，确定粒子适应度最高的粒子，找到各个粒子的历史最优值，即局部最优值，和粒子位置，以及全局最优值及粒子位置；若第一次迭代，则找到全局最优值及对应粒子位置；E. Compare the fitness value of each particle, determine the particle with the highest particle fitness, find the historical optimal value of each particle, that is, the local optimal value, and the particle position, as well as the global optimal value and particle position; if the first iteration , then find the global optimal value and the corresponding particle position;

F、根据步骤E所得到的局部最优值和粒子位置，以及全部最优值及粒子位置，根据下述表达式更新粒子的速度与位置：F, according to the local optimal value and particle position obtained in step E, and all optimal values and particle positions, update the speed and position of particles according to the following expressions:

${V V}_{m m}^{k k + + 11} = = ω ω \cdot &Center Dot; {V V}_{m m}^{k k} + + {c c}_{11} \cdot &Center Dot; {r r}_{11} \cdot &Center Dot; (({pbest pbest}_{m m}^{k k} - - {P P}_{m m}^{k k})) + + {c c}_{22} \cdot &Center Dot; {r r}_{22} \cdot &Center Dot; (({gbest gbest}^{k k} - - {P P}_{m m}^{k k})) + + Δ Δ {V V}_{m m}^{k k} - - - - - - ((1212));;$

4)计算各时段出力的不平衡量，即各时段机组出力之和与负荷之间的差值，将不平衡量根据机组等耗量微增率的大小并结合各个机组的上下限出力约束进行分配。等耗量微增率即也就是第i台机组t时段成本对出力的偏导。4) Calculate the unbalanced amount of output in each period, that is, the difference between the sum of unit output and the load in each period, and distribute the unbalanced amount according to the small increase rate of the equal consumption of the unit and combined with the upper and lower limit output constraints of each unit. Equal consumption micro-increase rate is That is, the partial derivative of the cost of the i-th unit to the output during the period t.

G、根据约束条件，以及粒子速度的上下限约束判断粒子的位置和速度是否越限，若越限，将粒子的位置和速度调整至约束范围内。对于粒子速度，将其限定在速度约束范围内，速度约束公式如下：G. According to the constraint conditions and the upper and lower limits of the particle velocity, judge whether the position and velocity of the particle exceed the limit. If it exceeds the limit, adjust the position and velocity of the particle to the constraint range. For the particle speed, it is limited within the speed constraint range, and the speed constraint formula is as follows:

H、根据步骤E中得到全局最优值，比较前后两次的全局最优值，采用自适应方法，根据两次全局最优值之差的绝对值大小，对粒子速度进行调整，绝对值越大，调整程度越大；执行如下：H, obtain the global optimal value according to the step E, compare the global optimal value twice before and after, adopt the self-adaptive method, according to the absolute value size of the difference of the global optimal value twice, adjust the particle speed, the absolute value is more Larger, the greater the degree of adjustment; the execution is as follows:

v₁＝v₀+Δv (18)；v ₁ =v ₀ +Δv (18);

$Δv Δv = = \{\begin{matrix} 00,, λ λ > > 0.01 0.01 \\ {v v}_{ini ini} \cdot &Center Dot; {r r}_{33},, 0.001 0.001 < < λ λ \leq \leq 0.01 0.01 \\ {v v}_{ini ini} \cdot &Center Dot; {r r}_{44},, 00 < < λ λ \leq \leq 0.001 0.001 \end{matrix} - - - - - - ((1919));;$

I、根据步骤A已设定的迭代算法，判定迭代次数是否达到：若达到迭代次数C＝500，则停止计算，得到粒子全局最优值即为最终粒子位置，该粒子位置即为各机组在各时段的出力，从而计算出最终结果，最终结果包括各机组各时段的出力水平以及计算经济周期内的机组运行总费用；若没有达到迭代次数，则返回到步骤D，继续计算。I, according to the iterative algorithm that step A has been set, determine whether the number of iterations has reached: if the number of iterations C=500 is reached, then stop the calculation, and obtain the global optimal value of the particle to be the final particle position, which is the position of each unit at The output of each time period, so as to calculate the final result, the final result includes the output level of each unit in each time period and the total operating cost of the unit in the calculation of the economic cycle; if the number of iterations is not reached, return to step D and continue the calculation.

实施例Example

本发明采用的电力系统算例数据如下，具体负荷数据如表1所示，电源参数如表2所示，一共是6个火力发电机组，本发明计算网损时采用B系数矩阵法，故列B系数矩阵于表3。The example data of the power system used in the present invention are as follows, the specific load data are as shown in Table 1, and the power supply parameters are as shown in Table 2. There are 6 thermal power generating units in total. The B coefficient matrix method is adopted when the present invention calculates the network loss, so it is listed B coefficient matrix is in Table 3.

表1负荷参数Table 1 Load parameters

表2机组参数Table 2 Unit parameters

表3B系数矩阵参数单位：×10^-5 Table 3B coefficient matrix parameter unit: ×10 ^-5

表4各机组各时段出力Table 4 Output of each unit at each time period

表5调度日内的总发电费用Table 5 Total Power Generation Costs in Dispatch Days

表4为采用改进粒子群得到的各机组出力的优化结果。表5分别为常规粒子群算法与采用本发明中的改进自适应粒子群算法获得的该调度日内总的发电量和发电费用。Table 4 shows the optimization results of the output of each unit obtained by using the improved particle swarm. Table 5 respectively shows the total power generation and power generation cost in the scheduling day obtained by the conventional particle swarm optimization algorithm and the improved adaptive particle swarm optimization algorithm in the present invention.

本发明对粒子群算法的迭代公式进行了改进，加入自适应方法，以对粒子速度进行调整，并根据约束条件对粒子进行调整，以保证粒子不越限。采用改进后的粒子群算法对电力系统的动态经济调度进行求解，获得了优化后的各机组各时段的出力水平，通过与常规的粒子群算法对比可以看出，本发明中提出的改进自适应粒子群算法能够获得更好的优化结果。The invention improves the iterative formula of the particle swarm algorithm, adds an adaptive method to adjust the particle speed, and adjusts the particles according to the constraint conditions to ensure that the particles do not exceed the limit. The improved particle swarm optimization algorithm is used to solve the dynamic economic dispatch of the power system, and the optimized output levels of each unit at each time period are obtained. Compared with the conventional particle swarm optimization algorithm, it can be seen that the improved self-adaptive Particle swarm optimization algorithm can obtain better optimization results.

最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，尽管参照上述实施例对本发明进行了详细的说明，所属领域的普通技术人员应当理解：依然可以对本发明的具体实施方式进行修改或者等同替换，而未脱离本发明精神和范围的任何修改或者等同替换，其均应涵盖在本发明的权利要求范围当中。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the present invention can still be Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall be covered by the scope of the claims of the present invention.

Claims

1. A dynamic economic dispatching method for electric power system based on improved particle swarm algorithm, is characterized in that, described method comprises the steps:

A. Set the parameters of the particle swarm optimization algorithm;

B. Generate initial particle swarm;

C. Set the upper and lower limits of the speed of the particles in the dynamic economic dispatch of the power system;

D. Determine the fitness value of the particle;

E. Compare the fitness value of the particles, find out the historical optimal value and its position of each particle, and the particle and its position that reach the global optimal value;

F. Update the position and velocity of each particle according to the local optimum and all optimum values;

G. According to the constraints and the upper and lower limits of the particle velocity, judge whether the position and velocity of the particle exceed the limit. If it exceeds the limit, adjust the position and velocity of the particle to the constraint range;

H, using an adaptive method to adjust the particle position;

I. If the number of iterations is reached, stop the iteration and get the final result.

2. The power system dynamic economic dispatch method according to claim 1, characterized in that, in the step A, the parameters include weight factors of ω _max =0.9 or ω _min =0.4, c ₁ =c ₂ =3.05 The learning factor, the number of particle swarm scale and the number of iterations; the size of particle swarm and the number of iterations are set according to the actual situation, including setting the number of particle swarm size N=40, and the number of iterations C=500.

3. The dynamic economic dispatching method of power system as claimed in claim 1, characterized in that, in said step B, according to the load level of each period in the calculation period, it is randomly assigned to the output level of each unit, and repeated according to the particle swarm scale number This step is to obtain the initial particle swarm; including:

Randomly generate a random array in which the number of rows is the number of units and the number of columns is the number of time periods. The elements of the array are all positive numbers, and the sum of the elements in each column is one; the initial particle is the time period load multiplied by the corresponding column, repeat This operation, that is, to obtain the entire initial particle group, is generated as follows for the mth particle:

{P P}_{m m} = = [\begin{matrix} {P P}_{1,1 1,1} & . . . . . . & {P P}_{11,, t t} & . . . . . . & {P P}_{11,, T T} \\ {P P}_{i i,, 11} & . . . . . . & {P P}_{i i,, t t} & . . . . . . & {P P}_{i i,, T T} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {P P}_{M m,, 11} & . . . . . . & {P P}_{M m,, t t} & . . . . . . & {P P}_{M m,, T T} \end{matrix}] - - - - - - ((11));;

P _i,t = a _i,t P _D,t (2);

a _1,t +a _2,t +...+a _i,t +...a _M,t = 1 (3);

Among them: T represents the number of time slots for economic dispatch, 24 hours a day, with one hour as a segment, a total of 24 time slots, M represents the number of units; a _i,t represents the proportional element of the i-th unit in the t-th time period, which is randomly generated , satisfy the formula (3), so the formula (3) means that the sum of the proportional elements of all M units for the t-th period is 1, P _D,t is the size of the load in the t-th period, and other particles are generated by the same method.

4. The dynamic economic dispatching method of power system according to claim 1, characterized in that, in said step C, the upper and lower limits of the speed of each particle are determined according to the upper and lower limits of each unit, and the particles are reduced according to the difference between the upper and lower limit output of the unit The upper and lower limits of speed, the reduction range is 1%; the upper limit of particle speed is 1% of the difference between the upper limit of unit output minus the lower limit of output, and the lower limit of particle speed is 1% of the difference between the lower limit of unit output minus the upper limit of output.

5. The power system dynamic economic dispatch method as claimed in claim 1, characterized in that, in said step D, according to the initial particle swarm obtained in step B, according to the power system dynamic economics represented by the following (4) formula The scheduling objective function determines the fitness value of the particles:

f f = = {Σ Σ}_{t t}^{T T} {Σ Σ}_{i i}^{M m} (({a a}_{i i} \cdot &Center Dot; {P P}_{i i,, t t}^{22} + + {b b}_{i i} \cdot \cdot {P P}_{i i,, t t} + + {c c}_{i i})) - - - - - - ((44));;

Among them: P _i,t is the output of the i unit in the t period, T is the number of time periods for dynamic economic dispatch, M is the number of units participating in dynamic economic dispatch; a _i , bi _, and c _i represent the corresponding cost system , depending on the situation of the unit;

The corresponding fitness values are:

f _a = f (5);

The calculation result of the objective function of the dynamic economic dispatch of the power system is used as the fitness value of the particle. The smaller the objective function value is, the smaller the fitness value is, and the higher the fitness of the particle is.

6. The dynamic economic dispatching method of electric power system as claimed in claim 5, is characterized in that, the upper and lower limit constraints of dynamic economic dispatching of electric power system comprise the power balance constraint represented by following formula (6), the expression of following formula (8) The upper and lower limit constraints of unit output and the unit climbing constraint represented by the following formula (9);

{Σ Σ}_{i i = = 11}^{M m} {P P}_{i i,, t t} = = {P P}_{D D.,, t t} + + {P P}_{loss loss,, t t} - - - - - - ((66));;

(6) In the formula: P _D,t is the load size of the tth time period, P _loss,t is the network loss size of the tth time period;

The network loss is calculated using the B coefficient method, and the expression is as follows:

P _loss,t =P _t ^T *B*P _t (7);

(7) In the formula: P _t is the column vector of the output of each unit in the tth period, P _t ^T represents the transposition of P _t , and B is the matrix of M×M, which is used to calculate the network loss;

P _i ^min ≤ _{P i,t} ≤ P _i ^max (8);

In the formula (8): P _i ^min and P _i ^max represent the lower limit and upper limit of the output of the i-th unit in the t-th period, respectively;

{R R}_{i i}^{d d} Δt Δt \leq \leq {P P}_{i i,, t t} - - {P P}_{i i,, t t - - 11} \leq \leq {R R}_{i i}^{u u} Δt Δt - - - - - - ((99));;

(9) where: is the downward climbing speed, which is a negative value; is the upward climbing speed, which is a positive value; Δt represents the time interval between two scheduling periods.

7. The dynamic economic dispatching method of electric power system as claimed in claim 1, is characterized in that, in described step E, compares the fitness value of each particle, determines the particle with the highest particle fitness, finds the historical optimal value of each particle, That is, the local optimal value, and particle position, as well as the global optimal value and particle position; if it is the first iteration, find the global optimal value and the corresponding particle position;

In the PSO algorithm, the population number of the particle swarm is the number of particles contained, and each individual in the population is called a particle; each feasible solution is a particle in the population, and each particle has two attributes, Both displacement and velocity are expressed as a matrix vector, as shown in the following formula:

{P P}_{m m} = = [\begin{matrix} {P P}_{1,1 1,1} & . . . . . . & {P P}_{11,, t t} & . . . . . . & {P P}_{11,, T T} \\ {P P}_{i i,, 11} & . . . . . . & {P P}_{i i,, t t} & . . . . . . & {P P}_{i i,, T T} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {P P}_{M m,, 11} & . . . . . . & {P P}_{M m,, t t} & . . . . . . & {P P}_{M m,, T T} \end{matrix}] - - - - - - ((1010));;

{V V}_{m m} = = [\begin{matrix} {V V}_{1,1 1,1} & . . . . . . & {V V}_{11,, t t} & . . . . . . & {V V}_{11,, T T} \\ {V V}_{i i,, 11} & . . . . . . & {V V}_{i i,, t t} & . . . . . . & {V V}_{i i,, T T} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {V V}_{M m,, 11} & . . . . . . & {V V}_{M m,, t t} & . . . . . . & {V V}_{M m,, T T} \end{matrix}] - - - - - - ((1111));;

Among them: P _m is the displacement of the m-th particle, P _i,t is the output force of the i-th unit in the t-period, that is, the position of the particle; V _m is the velocity of the V _m -th particle, and V _i,t is the corresponding The correction amount of the output of the i unit in t period; T is the period number of dynamic economic dispatch; M is the number of units participating in dynamic economic dispatch; in the dynamic economic dispatch of power system, the position of the particle represents the output of each unit in each period , the number of rows represents the number of units, and the number of columns represents the number of time periods.

8. The dynamic economic dispatching method of power system as claimed in claim 1, characterized in that, in said step F, according to the local optimal value and particle position obtained in step E, and all optimal values and particle positions, according to The following expression updates the particle's velocity and position:

{V V}_{m m}^{k k + + 11} = = ω ω \cdot \cdot {V V}_{m m}^{k k} + + {c c}_{11} \cdot &Center Dot; {r r}_{11} \cdot \cdot (({pbest pbest}_{m m}^{k k} - - {P P}_{m m}^{k k})) + + {c c}_{22} \cdot &Center Dot; {r r}_{22} \cdot &Center Dot; (({gbest gbest}^{k k} - - {P P}_{m m}^{k k})) + + Δ Δ {V V}_{m m}^{k k} - - - - - - ((1212));;

{P P}_{m m}^{k k + + 11} = = {P P}_{m m}^{k k} + + {V V}_{m m}^{k k + + 11} + + Δ Δ {P P}_{m m}^{k k} - - - - - - ((1313));;

in: Respectively represent the adjustment amount of speed and position; is the velocity of the kth generation of the mth particle, The velocity of the k+1th generation of the mth particle; is the k+1th generation of m particles; is the historical optimal value of the m-th particle, gbest ^k is the global optimal value of the k-th iteration; ω is the inertia factor, which is used to weigh the global search and local search capabilities of the particle swarm optimization algorithm; the larger the value of ω, the easier the algorithm Increase the search space, the smaller the value, the easier it is to perform local optimization, and adopt the method of adaptively adjusting the inertia factor, namely:

ω ω = = {ω ω}_{max max} - - \frac{{ω ω}_{max max} - - {ω ω}_{min min}}{C C} k k - - - - - - ((1414));;

Among them: ω _max is set to 0.9, ω _min is set to 0.4, C is the maximum number of iterations, k is the current number of iterations; c ₁ and c ₂ are learning factors, which control the particle to fly to the individual optimal position and the global optimal position respectively. Maximum step size; take c ₁ =c ₂ =3.05;

It is used to adjust the particles that exceed the limit. When the particle exceeds the limit, according to formulas (6), (7), (8), and (9), the particles are adjusted according to the following rules:

1) Adjust the output of the unit according to the upper and lower limit constraints of the speed. When the unit exceeds the upper limit, its output is limited to the upper limit, and when the unit exceeds the lower limit, its output is limited to the lower limit;

2) Adjust the output of the unit according to the climbing constraints. When the unit climbs upward, if it exceeds the limit, the output of the unit is limited to the upper limit of the upward climb; when the unit climbs downward, if it exceeds the limit, the output of the unit is limited at the lower limit of the downward climb;

3) Recalculate the network loss according to the adjusted unit output;

4) Calculate the unbalanced amount of output in each period, that is, the difference between the sum of unit output and the load in each period, and distribute the unbalanced amount according to the small increase rate of the equal consumption of the unit and combined with the upper and lower limit output constraints of each unit.

9. The dynamic economic dispatching method of electric power system as claimed in claim 1, is characterized in that, for particle speed, it is limited in the range of speed constraint, and speed constraint formula is as follows:

{V V}_{m m}^{k k} [[i i]] [[j j]] = = \{\begin{matrix} {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{max max},, & if if {V V}_{m m}^{k k} [[i i]] [[j j]] > > {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{max max} \\ {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{min min},, & if if {V V}_{m m}^{k k} [[i i]] [[j j]] < < {V V}_{m m}^{k k} [[i i]] {[[j j]]}_{min min} \end{matrix} - - - - - - ((1515));;

(15) where: is the i-th row and the j-th column element of the particle velocity, is the maximum value defined in the elements of the i-th row and j-th column of the particle velocity, is the minimum value defined in the elements of the i-th row and j-th column of the particle velocity; the maximum and minimum values of the particle velocity are set according to the following expressions:

{V V}_{m m}^{k k} {[[i i]]}_{max max} = = (({P P}_{i i}^{max max} - - {P P}_{i i}^{min min})) / / 100100 - - - - - - ((1616));;

{V V}_{m m}^{k k} {[[i i]]}_{min min} = = (({P P}_{i i}^{min min} - - {P P}_{i i}^{max max})) / / 100100 - - - - - - ((1717));;

(16) and (17) where: are respectively the upper limit and lower limit of the speed of the i-th unit in the particle, which will be expanded into a transverse quantity corresponding to the length of the time period, that is, the upper limit and lower limit of the speed of the i-th row of particles are obtained.

10. The dynamic economic dispatching method of electric power system as claimed in claim 1, characterized in that, in the step H, according to the global optimal value obtained in the step E, comparing the global optimal value twice before and after, adopting an adaptive method , according to the absolute value of the difference between the two global optimal values, the particle speed is adjusted. The larger the absolute value, the greater the adjustment degree; the execution is as follows:

Adjust the particle speed, that is:

v ₁ =v ₀ +Δv (18);

In formula (18), v ₀ and v ₁ are the particle speeds before and after adjustment respectively, and Δv is the adjusted speed, and the self-adaptive algorithm is used for the adjustment, and the formula of the self-adaptive algorithm is as follows:

Δv Δv = = \{\begin{matrix} 00,, λ λ > > 0.01 0.01 \\ {v v}_{ini ini} \cdot &Center Dot; {r r}_{33},, 0.001 0.001 < < λ λ \leq \leq 0.01 0.01 \\ {v v}_{ini ini} \cdot &Center Dot; {r r}_{44},, 00 < < λ λ \leq \leq 0.001 0.001 \end{matrix} - - - - - - ((1919));;

(19) where: v _ini is the initial velocity set in the particle swarm optimization algorithm, r ₃ is a random number from -0.1 to 0.1, r ₄ is a random number from -0.01 to 0.01, and the random numbers r ₃ and r ₄ are based on The actual setting is required, and λ is calculated according to the following formula:

λ λ = = \frac{| | {f f}_{best the best}^{k k} - - {f f}_{best the best}^{k k - - 11} | |}{{f f}_{best the best}^{k k}} - - - - - - ((2020));;

In the formula (20): f _best ^k is the global optimal position of the k-th generation particle, f _best ^k-1 the global optimal position λ of the k-1 generation particle is the relative difference between the two global optimal values before and after Proportion.

11. The dynamic economic dispatching method of electric power system as claimed in claim 1, is characterized in that, in the described step 1, according to the iterative algorithm that step A has been set, whether it is judged that the number of iterations reaches: if reaching the number of iterations C=500, Then the calculation is stopped, and the global optimal value of the particle is obtained as the final particle position. The particle position is the output of each unit at each time period, and the final result is calculated. The final result includes the output level of each unit at each time period and the calculated economic period. The total operating cost of the unit; if the number of iterations is not reached, return to step C and continue the calculation.