CN107657392B - A Granular Computing Method for Large-scale Economic Dispatching Problems in Power Grids - Google Patents

Abstract

Translated fromChinese

本发明公开了一种针对电网大规模经济调度问题的粒计算方法，包括：1、建立经济调度模型，包括其目标函数和约束条件；2、将电网进行分层粒化；3、参数的等效；4、粒度的划分；5、约束条件的处理；6、采用粒计算方法优化机组出力。本发明的有益效果：考虑因素全面，提高了计算精度；提出分层粒化，应用层次分析法求解问题，大大降低求解时间，提高求解效率；对于大规模电力网络，如果采用合适的机组划分方法和对粒子的参数等效，可以解决收敛难的问题，还能提高计算速度。

The invention discloses a granular computing method for the large-scale economic dispatching problem of power grid, including: 1. establishing an economic dispatching model, including its objective function and constraint conditions; 2. granulating the power grid in layers; 4. The division of granularity; 5. The treatment of constraints; 6. The unit output is optimized by the granular calculation method. Beneficial effects of the invention: considering factors comprehensively, the calculation accuracy is improved; hierarchical granulation is proposed, and the AHP is used to solve the problem, which greatly reduces the solving time and improves the solving efficiency; for large-scale power networks, if a suitable unit division method is adopted Equivalent to the parameters of particles, it can solve the problem of difficult convergence and improve the calculation speed.

Description

Particle calculation method for large-scale economic dispatching problem of power grid

Technical Field

The invention relates to the technical field of economic dispatching of a power system, in particular to a particle calculation method aiming at a large-scale economic dispatching problem.

Background

The economic dispatching takes the lowest power supply cost or energy consumption of the whole network as an objective function, carries out dispatching according to an equal micro-increment rate method and a coordination equation, is an important tool for realizing the economic operation of a power system, is a scientific method in an operation link, and is a dispatching principle generally adopted by various countries in the world so far. At present, the problems mainly encountered in the online economic dispatching research of a large power grid are that the data volume is large, the time period of acquisition and operation is long, and the running condition of the power grid is difficult to reflect in real time, so that the economic dispatching is difficult to realize. The economic dispatching of the power system is a high-dimensional, non-convex and non-linear constrained optimization problem, so that the solution of the problem, particularly the treatment of the mutual coupling constraint condition is very difficult. China power system insists on centralized dispatching for a long time. The centralized scheduling makes the solution of the economic scheduling of the power system more difficult, and an effective method for solving the economic scheduling of the large power grid needs to be found urgently. Therefore, the method has important significance for the research on the problem solving of the large power grid economic dispatching.

Disclosure of Invention

The invention aims to provide a particle computing method for solving the large-scale economic scheduling problem of a power grid, which adopts a layering method to decompose the economic scheduling problem into multiple layers so as to reduce the computational complexity, shorten the computation time and improve the accuracy and efficiency of load flow computation.

In order to realize the purpose, the following technical scheme is adopted: the method comprises the following steps:

step 1, establishing an economic dispatching model, including a target function and constraint conditions thereof;

step 2, layering and granulating the power grid;

step 3, equivalence of parameters;

step 4, dividing the granularity;

step 5, processing constraint conditions;

and 6, optimizing the network load flow by adopting a particle calculation method.

Further, instep 1, the specific process of establishing the economic dispatch model is as follows:

step 1-1, establishing an objective function

Under the condition that constraint conditions are met, the lowest total power generation cost of the generator is taken as an objective function, and the mathematical expression is as follows:

in the formula P_G，iIs the output power of the ith generator; a is_i，b_i，c_iIs the cost factor of the generator set i; n is the number of total generators;

step 1-2, setting constraint conditions of the model, wherein the constraint conditions comprise system power balance constraint and conventional unit output upper and lower limit constraint;

the specific constraint conditions are as follows:

1) system power balance constraints

In the formula P_DTotal load demand; p_LossIs the line loss.

Neglecting line losses, equation (2) is modified to:

2) upper and lower limits of output of conventional unit

In the formula P_i^min，P_i^maxIs the minimum and maximum output power of the generator i.

Further, the specific process ofstep 2 is as follows:

according to a layered quotient space method, granulating a power network, collecting a plurality of fine particles with similar properties to form coarse particles as an equivalent unit, or collecting some coarse particles to form coarse particles as an equivalent unit; all coarse particles are divided into a plurality of layers to form a hierarchical quotient space; the coarse particles are refined into fine particles from the upper layer by layer, the output power of each layer can be obtained after calculation of each layer is completed, the output power is respectively transmitted to the corresponding fine particles to serve as the load requirement of the next layer, and the result of the fine particles of the last layer is the result of economic dispatching.

Further, the specific process ofstep 3 is as follows:

step 3-1, calculating equivalent parameters

In the economic dispatch model, the cost coefficient a_i、b_i、c_iMinimum output power

Maximum output power

Calculations are required, in which they are replaced by equivalent parameters;

in the jth particle, the unit number is assumed to be m, and the equivalent principle is as follows:

(5) in the formula (I), the compound is shown in the specification,

is the equivalent cost coefficient for the jth particle; (6) in the formula P_G，jIs the output power of the jth particle;

the equivalent parameters can be calculated as follows:

in the formula, P_j^eqmin，P_j^eqmaxIs the equivalent minimum and equivalent maximum output power of the jth particle;

however, before the economic scheduling problem is solved, P_G，iIs unknown. But equivalent parameters must be prepared prior to particle computation. An approximate method is therefore proposed to initialize P_G，i。

Step 3-2, initialization procedure

P_G，iThe initialization of (2) is critical to the granularity calculation method, as it determines the equivalent parameters; the closer the initial output power is

The closer to the optimal value, the better the result will be shown; there are three steps to P_G，iAnd (3) initializing:

first, initializing the output power of each unit

P′_G，i＝P_i^min+(P_i^max-P_i^min)/2 (12)

P″_G，i＝σP′_G，i (14)

P′_G，iIs the average output power of unit i; σ is the load level coefficient; p ″)_G，iIs the output power of unit i;

the process enables the output power of each unit to be close to the average power, and the power balance constraint is met;

second, forward migration

λ′_i＝2aiP″_G，i+b_i (15)

P_D′＝αP_D (16)

λ′_iIs the micro-increment rate of the ith unit; α is a positive number; p_D' is load compensation; p'_G，iIs the output power after the migration of the ith unit;

the process makes the unit have smaller lambda'_iObtaining a relatively large positive deviation value;

third, negative migration

(18) In the formula (I), the compound is shown in the specification,

is the initialized output power of the ith unit;

this process gives the unit a greater lambda'_iAnd obtaining a relatively large negative deviation amount; according to the increment principle, the second step and the third step can ensure that the output power is close to the optimal solution;

fourthly, balancing the constraints

The offset adjustment may result in unequal power constraints, so a constraint process is necessary to correct

The correction process is instep 5.

Step 3-3, granularity calculation model

After equivalence, the cost function formula of the granularity calculation is as follows:

(19) wherein M is the number of subparticles of the host particle;

the power balance constraint of the particle calculation is modified as follows:

(20) in the formula, P_GDThe output power of the main particle is the load requirement of the next layer of sub-particles;

the power constraints of the particles are as follows:

P_j^eqmin≤P_G，j≤P_j^eqmax (21)

in the particle size calculation method, one particle is considered as an equivalent unit; particles with one unit (M ═ 1) are called fine particles; the equivalent parameters of the fine particles are equal to the parameters of the unit contained in the fine particles; particles with more than one set of units (M > 1) are called coarse particles.

Further, thestep 4 is as follows:

particle size is an average measurement of particle size; when describing information, granularity is mainly used for measuring the abstraction degree of data information and knowledge; the particle size is determined by the number of units contained in the particles;

the obvious fluctuation point of the micro-increment rate divides the unit into particles, and the calculation formula of the micro-increment rate is as follows:

(22) in the formula, λ_iIs the micro-increment rate of the ith unit;

after calculation, sorting the micro-increment rates of all the units according to the sequence; separating the unit according to the obvious fluctuation point;

(23) in the formula, theta_sIs the point of fluctuation of the micro-increment rate,

is the rank order fractional increase; s is a sequence number with increasing rate;

θ_sreact to

And

the difference in (a); if theta is greater than theta_sIs significantly greater than the other values, then θ_sIs the point of significant fluctuation.

Further, the specific process ofstep 5 is as follows:

step 5-1, examining each

All elements are adjusted to satisfy the inequality constraint as follows:

(24) in the formula, if

Or

Then the transition variable T_jSet to 0, otherwise

k is the current number of iterations;

step 5-2, by

Calculating P_RIf | P_RIf | is greater than ε, go to step 5-3, if | P_RIf | ≦ epsilon, go tostep 4, epsilon is the precision requirement;

step 5-3, modification

To satisfy the following equation constraint:

step 5-4, checking all

If the inequality constraint is violated, returning to the step 5-1; if the inequality constraint is not violated, entering step 5-5;

5-5, stopping the constraint processing process;

calculating according to the steps, wherein the initial output power of the equivalent parameter is close to the actual power level, so that the equivalent parameter is more accurate; then hold

Put into equations (7) and (8), substitute for P_G，jTo calculate

And

further, thestep 6 specifically includes:

and 6-1, parameter preparation. The basic parameters of all units need to be input, namely a_i、b_i、c_i、

And

calculating initial output power

Step 6-2, determining the hierarchical structure of the coarse particles and calculating parameters; determining a proper number of layers according to the scale of the power system; although the hierarchical method can improve the search efficiency and reduce the calculation time, the equivalent process causes deviation; accuracy is reduced if there is too much delamination; first layer M¹Number of particles and maximum number of units n of second layer_maxSetting is needed before calculation so as to guide the division process of the unit; when the unit division is completed, calculating equivalent parameters in the next part;

6-3, calculating the output power of the particles; the results are transferred accordingly to their sub-particles as the loading requirements for the next layer;

when the bottom layer particle calculation is completed, a final optimized solution is obtained.

Compared with the prior art, the invention has the following advantages:

1. the factors are considered comprehensively, and the calculation precision is improved;

2. providing a layered quotient space, applying an analytic hierarchy process, and solving the problem in a layered granulation manner, so that the solving time can be reduced, and the solving efficiency can be improved;

3. for a large-scale power network, if a reasonable hierarchical particle calculation method is adopted, the problem of difficult convergence can be solved, and the calculation speed can be increased.

Drawings

FIG. 1 is a 3-layer system configuration of an exemplary 10-unit system of the present invention.

FIG. 2 illustrates the micro-augmentation fluctuation of a 10-unit system according to the present invention.

FIG. 3 is a flow chart of particle computation for the method of the present invention.

Fig. 4 is a flow chart of the method of the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings:

as shown in fig. 4, the method of the present invention includes the following steps:

step 1, establishing an economic dispatching model, including a target function and constraint conditions thereof;

step 1-1, the specific process of establishing the economic dispatching model is as follows:

under the condition that constraint conditions are met, the lowest total power generation cost of the generator is taken as an objective function, and the mathematical expression is as follows:

in the formula P_G，iIs the output power of the ith generator; a is_i，b_i，c_iIs the cost factor of the generator set i; n is the number of total generators;

step 1-2, setting constraint conditions of the model, wherein the constraint conditions comprise system power balance constraint and conventional unit output upper and lower limit constraint;

the specific constraint conditions are as follows:

1) system power balance constraints

In the formula P_DTotal load demand; p_LossIs the line loss;

neglecting line losses, equation (2) is modified to:

2) upper and lower limits of output of conventional unit

In the formula

Is the minimum and maximum output power of the generator i.

Step 2, layering and granulating the power grid;

the specific process of layering and granulating the power grid is as follows:

according to an analytic hierarchy process, a method for establishing a hierarchical quotient space is provided for an economic scheduling problem. To clarify the layered structure, a 10-unit power system is taken as an example. The numbers are #1- # 10. Assuming that the system can be divided into three layers, as shown in fig. 1, the respective characteristics of each layer are as follows:

1) a first layer: there are three coarse particles V₁₁，V₁₂，V₁₃In this layer. V₁₁Comprising four units (#1, #3, #6, #7), as shown in FIG. 1, V₁₂(#2, #9) and V₁₃(#4, #5, #8, #10) and V₁₁As such. V₁₁，V₁₂，V₁₃Are three equivalent units. Thus reducing the warpThe dimensionality of the scheduling problem is saved, and the optimization efficiency is improved. After this layer is calculated, V₁₁，V₁₂，V₁₃Their output power can be derived and delivered to their sub-particles separately as the load demand of the next layer.

2) A second layer: the layer has six particles V₂₁，V₂₂，V₂₃，V₂₄，V₂₅，V₂₆。V₂₁And V₂₂Is V₁₁Are considered to be equivalent sets, and V₂₁And V₂₂From V₁₁A load demand is obtained. Host particle V₁₁Is responsible for calculating V₂₁And V₂₂The power output of (1). Calculation of the other two particles and V₁₁The transformation is similar. As shown in fig. 1, at V₂₃，V₂₄，V₂₆There is only one set, so the results for these three particles are exactly the final power outputs of #9, #2, and #5, respectively. However, V₂₁、V₂₂、V₂₅Can still be divided into several sub-particles in the third layer.

3) And a third layer: this layer is the bottom layer, which comprises seven particles, each V₃₁，V₃₂，V₃₃，V₃₄，V₃₅，V₃₆，V₃₇. There is only one unit per particle. The calculation process is similar to the method of the second layer, including V₂₁Is equivalent to V₃₁And V₃₂，V₂₂Is equivalent to V₃₃And V₃₄，V₂₅Is equivalent to V₃₅、V₃₆And V₃₇. When all the calculation processes are completed, V₃₁，V₃₂，V₃₃，V₃₄，V₃₅，V₃₆，V₃₇And V₂₃，V₂₄，V₂₆The result is the final unit output result of 10 units.

In the design of the hierarchical model, a method for finding a reasonable equivalent parameter of the computer set is critical and has a remarkable influence on a final result.

Step 3, equivalence of parameters;

step 3-1, calculating equivalent parameters

In the economic dispatch model, the cost coefficient a_i、b_i、c_iMinimum output power

Maximum output power

Calculations are required, in which they are replaced by equivalent parameters;

in the jth particle, the unit number is assumed to be m, and the equivalent principle is as follows:

(5) in the formula (I), the compound is shown in the specification,

is the equivalent cost coefficient for the jth particle; (6) in the formula P_G，jIs the output power of the jth particle;

the equivalent parameters can be calculated as follows:

in the formula, P_j^eqmin，P_j^eqmaxIs the equivalent minimum and equivalent maximum output power of the jth particle;

step 3-2, initialization procedure

P_G，iThe initialization of (2) is critical to the granularity calculation method, as it determines the equivalent parameters; the closer the initial output power is

The closer to the optimal value, the better the result will be shown; there are three steps to P_G，iAnd (3) initializing:

first, initializing the output power of each unit

P′_G，i＝P_i^min+(P_i^max-P_i^min)/2 (12)

P″_G，i＝σP′_G，i (14)

P′_G，iIs the average output power of unit i; σ is the load level coefficient; p ″)_G，iIs the output power of unit i;

the process enables the output power of each unit to be close to the average power, and the power balance constraint is met;

second, forward migration

λ′_i＝2a_iP″_G，i+b_i (15)

P_D′＝αP_D (16)

λ′_iIs the micro-increment rate of the ith unit; α is a positive number; p_D' is load compensation; p'_G，iIs the output power after the migration of the ith unit;

the process makes the unit have smaller lambda'_iObtaining a relatively large positive deviation value;

third, negative migration

(18) In the formula (I), the compound is shown in the specification,

is the initialized output power of the ith unit;

this process gives the unit a greater lambda'_iAnd obtaining a relatively large negative deviation amount; according to the increment principle, the second step and the third step can ensure that the output power is close to the optimal solution;

fourthly, balancing the constraints

The offset adjustment may result in unequal power constraints, so a constraint process is necessary to correct

Step 3-3, granularity calculation model

After equivalence, the cost function formula of the granularity calculation is as follows:

(19) wherein M is the number of subparticles of the host particle;

the power balance constraint of the particle calculation is modified as follows:

(20) in the formula, P_GDThe output power of the main particle is the load requirement of the next layer of sub-particles;

the power constraints of the particles are as follows:

P_j^eqmin≤P_G，j≤P_j^eqmax (21)

in the particle size calculation method, one particle is considered as an equivalent unit; particles with one unit (M ═ 1) are called fine particles; the equivalent parameters of the fine particles are equal to the parameters of the unit contained in the fine particles; particles with more than one set of units (M > 1) are called coarse particles.

Step 4, dividing the granularity;

particle size is an average measurement of particle size. When describing information, granularity is mainly used to measure the abstraction degree of data information and knowledge. In this context, the particle size is determined by the number of units the particle contains.

The obvious fluctuation point of the micro-increment rate divides the unit into particles, and the calculation formula of the micro-increment rate is as follows:

(22) in the formula, λ_iIs the micro-increment rate of the ith unit.

After the calculation is finished, the micro-increment rates of all the units need to be sorted to be small to large. And separating the unit according to the obvious fluctuation point.

(23) In the formula, theta_sIs the point of fluctuation of the micro-increment rate,

is the rank order fractional increase; s is the sequence number of the increasing rate ascending order.

θ_sReact to

And

the difference in (a). If theta is greater than theta_sIs significantly greater than the other values, then θ_sIs the point of significant fluctuation.

The granularity division of a 10-unit system is listed in table 1, the power system division scheme of the 10 units is listed, and the fluctuation graph of the ordered growth rate is shown in fig. 2, which shows how the significant fluctuation point fluctuates.

TABLE 1

1) Dividing a first layer:

in FIG. 2, we observe θ₅And theta₇Significantly greater than the average, which means that the growth rates of #9 and #4 are significantly different from the units before them, and then these units are divided into three groups to form (V)₁₁，V₁₂，V₁₃) Three particles.

In a practical example, θ_sNeed to be listed in descending order. Then, according to the number M of particles arranged in the first layer¹M before picking¹-a point of 1. If there are too many particles, the efficiency of the calculation is reduced. Thus M¹The range of (1) is 2 to 9.

2) And second layer division:

at V₁₁In, theta₃Is a significant point of fluctuation, and V₁₁Is divided into V₂₁And V₂₂. Likewise, V₁₂And V₁₃Are also divided into V₂₃，V₂₄，V₂₅，V₂₆Which constitute the second layer shown in figure 1.

In practical applications, the division of the layer is implemented independently in each host particle. In the jth main particle of the layer, the number of sub-particles

Is set by setting the maximum number n of units_maxDetermined, the formula is as follows:

in the formula, m_jIs the total unit number of the jth main particle.

Then according to the previous

The fluctuation point of (a) divides the jth particle into

And (4) sub-particles. If the total unit number ratio n of one main particle_maxSmall, this host particle cannot be divided into sub-particles. Such as n_maxIf it is too small, this will have too many sub-particles, which will increase the dimensionality of the GrC method and will reduce the computational efficiency. If n is_maxToo large, this will not reduce the time-efficient sub-particles of the GrC process. Thus n is_maxThe range of (1) is 10 to 30.

In the first-layer and second-layer division, if only one unique unit set exists in the particles, the particles are combined with the previous particles to improve the global search capability of the GrC method.

3) Bottom layer partitioning:

in this layer, all coarse particles must be broken down into fine particles to obtain the final power output of each unit.

Step 5, processing constraint conditions;

step 5-1, examining each

Adjust all elementsThe elements satisfy the inequality constraint as follows:

(24) in the formula, if

Or

Then the transition variable T_jSet to 0, otherwise

k is the current number of iterations;

step 5-2, by

Calculating P_RIf | P_RIf | is greater than ε, go to step 5-3, if | P_RIf | ≦ epsilon, go tostep 4, epsilon is the precision requirement;

step 5-3, modification

To satisfy the following equation constraint:

step 5-4, checking all

If the inequality constraint is violated, returning to the step 5-1; if the inequality constraint is not violated, entering step 5-5;

5-5, stopping the constraint processing process;

calculating according to the steps, wherein the initial output power of the equivalent parameter is close to the actual power level, so that the equivalent parameter is more accurate; then hold

Put into equations (7) and (8), substitute for P_G，jTo calculate

And

and 6, optimizing the network load flow by adopting a particle calculation method, wherein a flow chart of a particle calculation process is shown in fig. 3.

And 6-1, parameter preparation. The basic parameters of all units need to be input, namely a_i、b_i、c_i、

And

calculating initial output power

And 6-2, determining the hierarchical structure of the coarse particles and calculating parameters. The appropriate number of tiers is determined based on the size of the power system. Although the hierarchical approach can improve search efficiency and reduce computation time, the equivalent process can cause bias. Accuracy is reduced if there is too much delamination. First layer M¹Number of particles and maximum number of units n of second layer_maxBefore calculation, setting is needed to guide the division process of the unit. When the crew division is complete, the next part is to calculate the equivalent parameters.

And 6-3, calculating the output power of the particles. A new intelligent optimization algorithm can be applied to the output power of the optimized particles and the results are transferred to their sub-particles accordingly as the load demand of the next layer.

When the bottom layer particle calculation is completed, a final optimized solution is obtained.

In order to verify the effectiveness of the invention more completely, the comparison between the particle swarm algorithm and the mean variance mapping method shows that the invention can provide a satisfactory global optimal solution and has better time benefit. The two results are compared as follows:

TABLE 2 comparison of Power Generation cost versus time results for two algorithms

Obviously, the advantages of the power generation cost of the invention are not obvious, but the efficiency is greatly improved for the calculation time, and the superiority of the particle calculation is more obvious as the scale of the power grid is enlarged. The above results demonstrate the superiority of the present invention.

The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.

Claims (6)

Translated fromChinese

1.一种针对电网大规模经济调度问题的粒计算方法，其特征在于，所述方法包括如下步骤：1. a granular computing method for the large-scale economic dispatch problem of power grid, is characterized in that, described method comprises the steps:步骤1，建立经济调度模型，包括其目标函数和约束条件；Step 1, establish an economic dispatch model, including its objective function and constraints;步骤2，将电网进行分层粒化；Step 2, the power grid is layered and granulated;根据分层商空间方法，把电力网络进行粒化，收集若干性质相似的细粒子，形成粗粒子作为等效机组，或者收集一些粗粒子以形成较粗的粒子作为等效机组；所有的粗粒子被分成多个层构成一个分层商空间；粗粒子由上层逐层细化为细粒子，每层计算完后能得出他们的输出功率并且分别传递给他们相应的细粒子作为下一层的负荷需求，最后一层的细粒子的结果就是经济调度的结果；According to the hierarchical quotient space method, the power network is granulated, and several fine particles with similar properties are collected to form coarse particles as equivalent units, or some coarse particles are collected to form coarser particles as equivalent units; all coarse particles It is divided into multiple layers to form a layered quotient space; coarse particles are refined layer by layer into fine particles from the upper layer. After each layer is calculated, their output power can be obtained and passed to their corresponding fine particles as the next layer. Load demand, the result of the last layer of fine particles is the result of economic dispatch;步骤3，参数的等效；Step 3, the equivalence of parameters;步骤4，粒度的划分；Step 4, the division of granularity;步骤5，约束条件的处理；Step 5, processing of constraints;步骤6，采用粒计算方法优化网络潮流。Step 6, using the granular computing method to optimize the network flow.2.根据权利要求1所述的一种针对电网大规模经济调度问题的粒计算方法，其特征在于，步骤1中，建立经济调度模型的具体过程如下：2. a kind of granular computing method for the large-scale economic dispatch problem of power grid according to claim 1, is characterized in that, in step 1, the concrete process of establishing economic dispatch model is as follows:步骤1-1，建立目标函数Step 1-1, establish the objective function在满足约束条件的情况下，以发电机的总发电成本最低为目标函数，其数学表达式具体如下：In the case of satisfying the constraints, the objective function is to take the lowest total power generation cost of the generator as the objective function, and its mathematical expression is as follows:

式中P_G，i是第i台发电机的输出功率；a_i，b_i，c_i是发电机组i的费用系数；N是全部发电机的数量；where P_{G, i} is the output power of the_ith generator; a_i , bi , c_i are the cost coefficients of generator set i; N is the number of all generators;步骤1-2，设置模型的约束条件，约束条件包括系统功率平衡约束、常规机组出力上下限约束；Step 1-2, set the constraints of the model, the constraints include system power balance constraints, conventional unit output upper and lower limit constraints;具体约束条件为：The specific constraints are:1)系统功率平衡约束1) System power balance constraints

式中P_D总的负荷需求；P_Loss是线路损耗；where P_D is the total load demand; P_Loss is the line loss;忽略线路损耗，公式(2)修改为：Ignoring line loss, formula (2) is modified as:

2)常规机组出力上下限2) The upper and lower limits of conventional unit output

式中

是发电机i的最小和最大的输出功率。in the formula

are the minimum and maximum output power of generator i.3.根据权利要求1所述的一种针对电网大规模经济调度问题的粒计算方法，其特征在于，所述步骤3的具体过程如下：3. a kind of granular computing method for the large-scale economic dispatch problem of power grid according to claim 1, is characterized in that, the concrete process of described step 3 is as follows:步骤3-1，等效参数计算Step 3-1, Equivalent Parameter Calculation在经济调度模型中，费用系数a_i、b_i、c_i最小输出功率

最大输出功率

需要计算，在粒计算中，他们被等效参数替代；In the economic dispatch model, the cost coefficients a_i , b_i , c_i minimum output power

maximum output power

Calculations are required, and in granular computing, they are replaced by equivalent parameters;在第j个粒子中假设机组号是m，其等效原理为：Assuming that the unit number is m in the jth particle, the equivalent principle is:

(5)式中，

是第j个粒子的等效成本系数；(6)式中P_G，j是第j个粒子的输出功率；In formula (5),

is the equivalent cost coefficient of the jth particle; (6) where P_{G, j} is the output power of the jth particle;等效参数计算如下：The equivalent parameters are calculated as follows:

式中，P_j^eqmin，P_j^eqmax是第j个粒子的等效最小和等效最大输出功率；where P_j^eqmin and P_j^eqmax are the equivalent minimum and equivalent maximum output power of the jth particle;步骤3-2，初始化过程Step 3-2, initialization processP_G，i的初始化对粒度计算方法是关键，因为它决定了等效参数；初始输出功率越接近

就越接近最优值，就会表现出更好的结果；有三步对P_G，i进行初始化：The initialization of P_G,i is critical to the granularity calculation method because it determines the equivalent parameters; the closer the initial output power is

The closer to the optimal value, the better the result will be shown; there are three steps to initialize_PG,i :第一步，初始化每个机组的输出功率The first step is to initialize the output power of each unit

P″_G，i＝σP′_G，i (14)P″_G,i =σP′_G,i (14)P′_G，i是机组i的平均输出功率；σ是负荷水平系数；P″_G，i是机组i的输出功率；P′_{G, i} is the average output power of unit i; σ is the load level coefficient; P″_{G, i} is the output power of unit i;该过程使各机组的输出功率接近平均功率，满足功率平衡约束；This process makes the output power of each unit close to the average power and satisfies the power balance constraint;第二步，正向迁移The second step, forward migrationλ′_i＝2a_iP″_G，i+b_i (15)λ′_i = 2a_i P″_{G, i} +b_i (15)P_D′＝αP_D (16)P_D ′=αP_D (16)

λ′_i是第i个机组的微增率；α是一个正数；P_D′是负荷补偿；P″′_G，i是第i个机组迁移后的输出功率；λ′_i is the slight increase rate of the i-th unit; α is a positive number; P_D ′ is the load compensation; P″′_{G, i} is the output power of the i-th unit after migration;上述过程使机组具有更小的λ′_i，得到相对较大的正偏差量；The above process makes the unit have a smaller λ′_i , and obtains a relatively large positive deviation;第三步，负向迁移The third step, negative transfer

(18)式中，

是第i个机组的初始化输出功率；In formula (18),

is the initialized output power of the i-th unit;这个过程使机组具有更大的λ′_i和得到一个相对较大的负偏差量；根据增量原理，第二步和第三步能够保证输出功率接近最优解；This process enables the unit to have a larger λ′_i and a relatively large negative deviation; according to the incremental principle, the second and third steps can ensure that the output power is close to the optimal solution;第四步，平衡约束Step 4: Balancing Constraints上述偏移调整导致不平等的功率约束，约束处理过程来修正

The above offset adjustment results in unequal power constraints, which are corrected by the constraint processing

步骤3-3，粒度计算模型Step 3-3, particle size calculation model等价后，粒度计算的成本函数公式如下：After equivalence, the cost function formula of granularity calculation is as follows:

(19)式中，M是主粒子的亚粒子数量；(19) where M is the number of sub-particles of the main particle;粒计算的功率平衡约束修正如下：The power balance constraint of granular computing is modified as follows:

(20)式中，P_GD主粒子的输出功率，是下一层亚粒子的负荷需求；(20), the output power of the_PGD main particle is the load demand of the next layer of sub-particles;粒子的功率约束如下：The power constraints of the particles are as follows:P_j^eqmin≤P_G，j≤P_j^eqmax (21)P_j^{eqmin ≤P}_{G, j ≤} P_j^eqmax (21)在粒度计算方法中，一个粒子被认为是一个等效的机组；带有一个机组的粒子M＝1叫做细粒子；细粒子的等效参数等于它所包含的机组的参数；带有不止一个机组的粒子M＞1称为粗粒子。In the particle size calculation method, a particle is considered as an equivalent unit; a particle with one unit M=1 is called a fine particle; the equivalent parameter of a fine particle is equal to the parameter of the unit it contains; with more than one unit Particles with M > 1 are called coarse particles.4.根据权利要求1所述的一种针对电网大规模经济调度问题的粒计算方法，其特征在于，所述步骤4如下：4. a kind of granular computing method for the large-scale economic dispatch problem of power grid according to claim 1, is characterized in that, described step 4 is as follows:粒度是一个粒尺寸的平均测量值；当描述信息时，粒度用来衡量数据信息和知识的抽象程度；粒度由粒子包含的机组数量决定；Particle size is an average measure of particle size; when describing information, particle size is used to measure the abstraction of data information and knowledge; particle size is determined by the number of units the particle contains;微增率的显著波动点把机组分成粒子，微增率的计算公式是：The significant fluctuation point of the micro-increase rate divides the unit into particles. The calculation formula of the micro-increase rate is:

(22)式中，λ_i是第i个机组的微增率；(22) where λ_i is the slight increase rate of the i-th unit;计算后，所有机组的微增率需要小到大进行排序；根据显著波动点对机组进行分离；After calculation, the micro-increase rates of all units need to be sorted from small to large; the units are separated according to significant fluctuation points;

(23)式中，θ_s是微增率波动点，

是排序微增率；s是微增率升序排列的序列号；(23), θ_s is the fluctuation point of the micro-increase rate,

is the sorting increment rate; s is the serial number in ascending order of increment rate;θ_s反应了

和

的差别；如果θ_s的值明显地大于其他值，那么θ_s就是显著波动点。θ_s reacted

and

If the value of θ_s is significantly larger than other values, then θ_s is a significant fluctuation point.5.根据权利要求1所述的一种针对电网大规模经济调度问题的粒计算方法，其特征在于，所述步骤5的具体过程如下：5. A kind of granular computing method for large-scale economic dispatch problem of power grid according to claim 1, is characterized in that, the concrete process of described step 5 is as follows:步骤5-1，检查每个

调整所有元素以满足不等式约束如下：Step 5-1, check each

All elements are adjusted to satisfy the inequality constraints as follows:

(24)式中，如果

或者

则过渡变量T_j设置成0，否则

k是当前的迭代次数；(24), if

or

Then the transition variable T_j is set to 0, otherwise

k is the current number of iterations;步骤5-2，通过

计算P_R，如果|P_R|＞ε，转到步骤5-3，如果|P_R|≤ε，则转到步骤4，ε是精度要求；Step 5-2, pass

Calculate P_R , if |P_R |>ε, go to step 5-3, if |P_R |≤ε, go to step 4, ε is the precision requirement;步骤5-3，修改

的值以满足一下等式约束：Step 5-3, modify

The value of satisfies the following equality constraints:

步骤5-4，检查所有

的修正值，如果违反不等式约束，回到步骤5-1；如果不违反不等式约束则进入步骤5-5；Steps 5-4, check all

If it violates the inequality constraint, go back to step 5-1; if it does not violate the inequality constraint, go to step 5-5;步骤5-5，停止约束处理过程；Step 5-5, stop the constraint processing;按以上步骤计算，等效参数的初始输出功率接近实际功率水平，使等效参数更精确；然后把

放到公式(7)和(8)中，替代P_G，j来计算

和

Calculated according to the above steps, the initial output power of the equivalent parameters is close to the actual power level, so that the equivalent parameters are more accurate;

Put it into formulas (7) and (8), replace P_{G, j} to calculate

and

6.根据权利要求1所述的一种针对电网大规模经济调度问题的粒计算方法，其特征在于，所述步骤6具体如下：6. A kind of granular computing method for large-scale economic dispatch problem of power grid according to claim 1, is characterized in that, described step 6 is as follows:步骤6-1，参数准备；所有机组的基本参数需要输入，即a_i、b_i、c_i、

和

计算初始输出功率

Step 6-1, parameter preparation; the basic parameters of all units need to be input, namely a_i , b_i , c_i ,

and

Calculate the initial output power

步骤6-2，确定粗粒子的分层结构和参数计算；根据电力系统规模确定合适的分层数量；尽管分层的方法能够提高搜索效率和减少计算时间，但是等效的过程会造成偏差；如果分层太多会降低准确性；第一层M¹的粒子数量和第二层最大机组数量n_max在计算前需要设置，以指导机组的划分过程；当完成机组划分时，下一部分是计算等效参数；Step 6-2, determine the layered structure of the coarse particles and calculate the parameters; determine the appropriate number of layers according to the scale of the power system; although the layered method can improve the search efficiency and reduce the calculation time, the equivalent process will cause deviations; If there are too many layers, the accuracy will be reduced; the number of particles in the first layer M¹ and the maximum number of units in the second layer n_max need to be set before calculation to guide the unit division process; when the unit division is completed, the next part is the calculation Equivalent parameters;步骤6-3，计算粒子的输出功率；将结果相应地转移到他们的亚粒子作为下一层的负荷需求；当底层粒子计算完成时，将得到最终的优化解。Step 6-3, calculate the output power of the particles; transfer the results to their sub-particles accordingly as the load requirements of the next layer; when the underlying particle calculation is completed, the final optimized solution will be obtained.

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