Power system economic dispatching method of distributed hybrid differential evolution algorithm

Abstract

The invention discloses a power system economic dispatching method based on a distributed hybrid differential evolution algorithm, and belongs to the technical field of power systems. In order to solve the problems that a distributed gradient descent algorithm is easy to fall into a local optimal solution and a centralized network framework can cause the problem that the computing power is limited when a large-scale optimization problem is processed, an initial population is randomly generated and is decomposed according to the dimension of the problem, and each sub-population comprises generator information of a single dimension. The distributed gradient descent algorithm is introduced before mutation operation is executed, so that the power generation cost of population individuals is reduced, the search efficiency of the algorithm is effectively improved, and meanwhile, the problem that the distributed gradient descent algorithm is prone to falling into a local optimal solution is solved. A preset time average consistency algorithm is introduced in a selection link, so that the fitness of different generators is averagely consistent within preset time. The method is distributed, the communication cost is saved, the robustness of the network is improved, and the search efficiency of the differential evolution algorithm is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and in particular relates to a power system economic dispatching method based on a distributed hybrid differential evolution algorithm. Background Art

[0002] In recent years, due to the influence of factors such as the accelerated electrification process in various industries, social electricity consumption has increased dramatically, and energy problems have become increasingly serious. Improving energy utilization efficiency is a hot topic in current research. The economic dispatch problem of the power system is to allocate the power generation power of each generator to minimize the total power generation cost under the premise of meeting the power supply needs of users and the upper and lower limits of the generator power. At present, the most widely used algorithm to solve the economic dispatch problem is the intelligent optimization algorithm, such as genetic algorithm, differential evolution algorithm, etc. In order to improve the search efficiency of the intelligent optimization algorithm, some scholars have proposed a hybrid intelligent optimization algorithm. However, this type of method is usually centralized and requires a control center to process the status information of all generator sets. If this control center fails, the entire system will stop running. At the same time, centralized algorithms have high requirements for network communication and computing resources. As the scale of the network expands, centralized algorithms may encounter limitations in computing power and storage capacity, and the scalability of the system is also limited. These problems can be effectively avoided by adopting distributed algorithms. Therefore, many scholars have made research on distributed solutions to economic dispatch problems and proposed a distributed gradient descent algorithm based on consistency theory. Each unit uses the local gradient information of the transfer function with the adjacent units to iteratively update its own state information, so as to find the best power generation solution. However, affected by factors such as the valve point effect, the economic dispatch problem becomes a non-convex optimization problem. When solving this non-convex optimization problem, this type of distributed algorithm is prone to fall into the local minimum and it is difficult to find the optimal solution.

[0003] In summary, the problems of the existing technology are: the economic dispatch problem considering the valve point effect is a non-convex problem, there are multiple local optimal solutions, and the distributed gradient descent algorithm is prone to fall into the local optimal solution. The search time of the intelligent optimization algorithm is long, and the centralized network framework will lead to large network communication volume when processing large-scale optimization problems, and the computing power is limited. Summary of the invention

[0004] In view of the fact that distributed gradient descent algorithms are prone to fall into local optimal solutions and that centralized network frameworks lead to limited computing power when processing large-scale optimization problems, the present invention provides an economic dispatch method for power systems based on a distributed hybrid differential evolution algorithm.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A distributed hybrid differential evolution algorithm for power system economic dispatching method, comprising the following steps:

[0007] Step 1: Construct a mathematical model of the economic dispatch problem with the goal of minimizing the total cost of power generation;

[0008] Furthermore, the specific operations of step 1 are:

[0009] The mathematical model of the economic dispatch problem is constructed in the form of minimizing the total generation cost:

[0010]

[0011] In the formula, C T is the total power generation cost of the unit, C j (p j ) is the power generation cost function of generator j, p j is the power generated by generator j, and n is the total number of generators;

[0012] When the valve point effect is considered, the local power generation cost function is expressed as:

[0013]

[0014] In the formula, α j ,β j ,γ j ,∈ j ,ψ j is the power generation coefficient of generator j, is the minimum power generation of generator j;

[0015] When considering multiple fuel types, the local power generation cost function is expressed as:

[0016]

[0017] In the formula, α nj ,β nj ,γ nj ,∈ nj ,ψ nj is the power generation coefficient of generator j;

[0018] The constraints include power size constraints and total power constraints, where the power size constraints and total power constraints are:

[0019]

[0020] Where P d is the total power generation requirement of the power system;

[0021] Step 2: Obtain the parameters and power constraints of the generator set and randomly generate the initial population;

[0022] Furthermore, the specific operations of step 2 are:

[0023] Initialize the population size to NP, the i-th individual in the population is represented by (x i1 ,…,x in ), the generation method of the i-th individual is:

[0024]

[0025] In the formula, and are the minimum and maximum power generation of generator j respectively. After randomly generating the initial population, the initial population is divided into n sub-populations, where the j-th sub-population contains the information of the j-th dimension of the initial population, including (x 1j ,…,x NPj ); rand(0,1) means that the returned random number is a uniformly distributed random real number greater than or equal to 0 and less than 1; the number of generators determines the dimension of the problem, and thus determines the number of sub-populations.

[0026] Step 3: Use the distributed hybrid differential evolution algorithm to iterate the generated initial population until the predetermined iteration termination condition is reached;

[0027] Furthermore, the specific operations of step 3 are:

[0028] Step 3.1: Use the distributed gradient descent algorithm for all individuals in the population to generate a new population with low individual power generation cost; the distributed gradient descent algorithm is as follows:

[0029]

[0030] In the formula, y ij (G) is the component of the jth dimension of the ith individual in the new population generated at the Gth iteration, G is the current iteration number, is the outer iteration in the iteration, d>0 is a constant, when k∈N j When jk =1,a jk is the weight connecting the j-th dimension and the k-th dimension; k represents the index of the dimension, and n represents the total number of dimensions;

[0031] Step 3.2: Specify the mutation probability. According to the specified mutation probability, perform mutation operations on the individuals in the new population generated in step 3.1 to generate mutant individuals. The specific mutation strategy is as follows:

[0032] v ij (G) = y aj (G)+F(y bj (G)-y cj(G)

[0033] Where a, b, c are three different integers randomly generated from [0,…, NP], F is a mutation parameter randomly selected from [0,1]; v ij (G) represents the component of the jth dimension of the i-th variant individual generated at the G-th iteration, (y bj (G)-y cj (G)) represents the difference of the j-th dimension components among different individuals;

[0034] Step 3.3: Specify the crossover probability. According to the specified crossover probability, perform a crossover operation on the individuals in the new population generated in step 3.1 and the mutant individuals to generate test individuals. The specific crossover strategy is as follows:

[0035]

[0036] Where CR is a crossover parameter randomly selected from [0,1]; u ij (G) represents the component of the jth dimension of the i-th trial individual generated at the G-th iteration;

[0037] Step 3.4: Use the projection algorithm to make the experimental individuals that do not meet the constraints meet the constraints;

[0038] Step 3.5: Compare the test individuals with the corresponding population individuals, and select individuals with low fitness to form an iterative population;

[0039] The i-th modified experimental individual is (u i1 ,…,u in ), the corresponding population individual is (y i1 ,…,y in ), the generation method of individuals with low fitness is:

[0040]

[0041] In the formula, C j (y ij (k f )) is the average fitness of individual i in the Gth iteration, C j (u ij (k f )) represents the average fitness of the test individual i in the Gth iteration. The method for obtaining the average fitness is as follows:

[0042]

[0043] Where u(l) is the predetermined time control function, k1, k2>0 is a constant, k fis the preset convergence time, which is the inner iteration in the Gth iteration. f The algorithm obtains the average value of individual fitness; C j (u ij (l)) represents the local power generation cost of the jth component of the i-th experimental individual, C k (u ik (l)) represents the local power generation cost of the kth component of the ith test individual, (C k (u ik (l))-C j (u ij (l))) represents the difference between two local power generation costs;

[0044] Step 3.6: If the maximum number of iterations is not met, return to step 3.1; if it is met, terminate the iteration.

[0045] Step 4: Output the optimal solution, that is, the best power generation allocation plan for the current economic dispatch problem.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] Compared with the traditional differential evolution algorithm, the algorithm proposed in the present invention is distributed, effectively avoiding single point failure and reducing communication costs. At the same time, the distributed gradient descent algorithm is used to preprocess the population, which improves the search efficiency of the population, and the predetermined time average consensus algorithm is used to obtain the fitness information required for the selection process, which reduces the running time required by the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of a method for economic dispatching of a power system using a distributed hybrid differential evolution algorithm provided by the present invention;

[0049] Figure 2 is a distributed power grid communication topology diagram provided by an embodiment of the present invention;

[0050] Figure 3 It is a convergence curve diagram of 10 units provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to gain a deeper understanding of the present invention, we will provide a comprehensive and detailed description of the present invention. However, the present invention has multiple implementations and is not limited to the specific examples listed herein. The presentation of these examples is intended to deepen the comprehensive understanding of the disclosure of the present invention.

[0052] A method for economic dispatching of a power system based on a distributed hybrid differential evolution algorithm comprises the following steps:

[0053] Step 1: Construct a mathematical model of the economic dispatch problem with the goal of minimizing the total cost of power generation;

[0054] Furthermore, the specific operations of step 1 are:

[0055] The mathematical model of the economic dispatch problem is constructed in the form of minimizing the total generation cost:

[0056]

[0057] In the formula, C T is the total power generation cost of the unit, C j (p j ) is the power generation cost function of generator j, p j is the power generated by generator j, and n is the total number of generators;

[0058] When the valve point effect is considered, the local power generation cost function is expressed as:

[0059]

[0060] In the formula, α j ,β j ,γ j ,∈ j ,ψ j is the power generation coefficient of generator j, is the minimum power generation of generator j;

[0061] When considering multiple fuel types, the local power generation cost function is expressed as:

[0062]

[0063] In the formula, α nj ,β nj ,γ nj ,∈ nj ,ψ nj is the power generation coefficient of generator j;

[0064] The constraints include power size constraints and total power constraints, where the power size constraints and total power constraints are:

[0065]

[0066] Where P d is the total power generation requirement of the power system.

[0067] Step 2: Obtain the parameters and power constraints of the generator set and randomly generate the initial population;

[0068] Furthermore, the specific operations of step 2 are:

[0069] Initialize the population size to NP, the i-th individual in the population is represented by (x i1 ,…,x in ), the generation method of the i-th individual is:

[0070]

[0071] In the formula, and are the minimum and maximum power generation of generator j respectively. After randomly generating the initial population, the initial population is divided into n sub-populations, where the j-th sub-population contains the information of the j-th dimension of the initial population, including (x 1j ,…,x NPj ); rand(0,1) means that the returned random number is a uniformly distributed random real number greater than or equal to 0 and less than 1.

[0072] Step 3: Use the distributed hybrid differential evolution algorithm to iterate the generated initial population until the predetermined iteration termination condition is reached;

[0073] Furthermore, the specific operations of step 3 are:

[0074] Step 3.1: Use the distributed gradient descent algorithm for all individuals in the population to generate a new population with low individual power generation cost; the distributed gradient descent algorithm is as follows:

[0075]

[0076] In the formula, y ij (G) is the component of the jth dimension of the ith individual in the new population generated at the Gth iteration, G is the current iteration number, is the outer iteration in the iteration, d>0 is a constant, when k∈N j When jk =1,a jk is the weight connecting the j-th dimension and the k-th dimension; k represents the index of the dimension, and n represents the total number of dimensions;

[0077] Step 3.2: Specify the mutation probability. According to the specified mutation probability, perform mutation operations on the individuals in the new population generated in step 3.1 to generate mutant individuals. The specific mutation strategy is as follows:

[0078] v ij (G) = y aj (G)+F(y bj (G)-y cj (G)

[0079] Where a, b, c are three different integers randomly generated from [0,…, NP], F is a mutation parameter randomly selected from [0,1]; vij (G) represents the component of the jth dimension of the i-th variant individual generated at the G-th iteration, (y bj (G)-y cj (G)) represents the difference of the j-th dimension components among different individuals;

[0080] Step 3.3: Specify the crossover probability. According to the specified crossover probability, perform a crossover operation on the individuals in the new population generated in step 3.1 and the mutant individuals to generate test individuals. The specific crossover strategy is as follows:

[0081]

[0082] Where CR is a crossover parameter randomly selected from [0,1]; u ij (G) represents the component of the jth dimension of the i-th trial individual generated at the G-th iteration;

[0083] Step 3.4: Use the projection algorithm to make the experimental individuals that do not meet the constraints meet the constraints;

[0084] Step 3.5: Compare the test individuals with the corresponding population individuals, and select individuals with low fitness to form an iterative population;

[0085] The i-th modified experimental individual is (u i1 ,…,u in ), the corresponding population individual is (y i1 ,…,y in ), the generation method of individuals with low fitness is:

[0086]

[0087] In the formula, C j (y ij (k f )) is the average fitness of individual i in the Gth iteration, C j (u ij (k f )) represents the average fitness of the test individual i in the Gth iteration. The method for obtaining the average fitness is as follows:

[0088]

[0089] Where u(l) is the predetermined time control function, k1, k2>0 is a constant, k f is the preset convergence time, which is the inner iteration in the Gth iteration. f The algorithm obtains the average value of individual fitness; C j (u ij(l)) represents the local power generation cost of the jth component of the i-th experimental individual, C k (u ik (l)) represents the local power generation cost of the kth component of the ith test individual, (C k (u ik (l))-C j (u ij (l))) represents the difference between two local power generation costs;

[0090] Step 3.6: If the maximum number of iterations is not met, return to step 3.1; if it is met, terminate the iteration.

[0091] Step 4: Output the optimal solution, that is, the best power generation allocation plan for the current economic dispatch problem.

[0092] The application effect of the present invention is described in detail below in conjunction with simulation.

[0093] The proposed distributed hybrid differential evolution algorithm is numerically simulated using the IEEE 10-unit power system as an example to solve the economic dispatch problem with the introduction of valve point effect and multi-fuel effect, and compared with the distributed auction algorithm and the distributed continuous convex approximation algorithm. Considering the randomness of the algorithm, the three algorithms are independently executed 100 times, and the results are shown in Table 1. Compared with other distributed and centralized algorithms, the DDEDGD algorithm has better search results. Figure 3 It represents the convergence curve of the algorithm, which shows that the algorithm can complete convergence quickly.

[0094] Table 1 Comparison of results of 10 units

[0095]

[0096] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in the field. Although the illustrative specific embodiments of the present invention are described above to facilitate the understanding of the present invention by the technical personnel in the field, it should be clear that the present invention is not limited to the scope of the specific embodiments. For the ordinary technical personnel in the field, as long as various changes are within the spirit and scope of the present invention defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A distributed hybrid differential evolution algorithm for power system economic dispatching method, characterized in that: The following steps are involved: Step 1: Construct a mathematical model of the economic dispatch problem with the goal of minimizing the total cost of power generation; Step 2: Obtain the parameters and power constraints of the generator set and randomly generate the initial population; Step 3: Use the distributed hybrid differential evolution algorithm to iterate the generated initial population until the predetermined iteration termination condition is reached; Step 4: Output the optimal solution, that is, the best power generation allocation plan for the current economic dispatch problem.

2. The method for economic dispatch of power system based on a distributed hybrid differential evolution algorithm according to claim 1, characterized in that: The specific operation of step 1 to construct a mathematical model for the economic dispatch problem with the goal of minimizing the total cost of power generation is: The mathematical model of the economic dispatch problem is constructed in the form of minimizing the total generation cost: In the formula, C T is the total power generation cost of the unit, C j (p j ) is the power generation cost function of generator j, p j is the power generated by generator j, and n is the total number of generators; When the valve point effect is considered, the local power generation cost function is expressed as: In the formula, α j ,β j ,γ j ,∈ j ,ψ j is the power generation coefficient of generator j, is the minimum power generation of generator j; When considering multiple fuel types, the local power generation cost function is expressed as: In the formula, α nj ,β nj ,γ nj ,∈ nj ,ψ nj is the power generation coefficient of generator j; The constraints include power size constraints and total power constraints, where the power size constraints and total power constraints are: Where P d is the total power generation requirement of the power system.

3. The method for economic dispatch of power system based on a distributed hybrid differential evolution algorithm according to claim 2, characterized in that: The specific operation of obtaining the parameters and power constraints of the generator set and randomly generating the initial population in step 2 is: Initialize the population size to NP, the i-th individual in the population is represented by (x i1 , …, x in ), the generation method of the i-th individual is: In the formula, and are the minimum and maximum power generation of generator j respectively. After randomly generating the initial population, the initial population is divided into n sub-populations, where the j-th sub-population contains the information of the j-th dimension of the initial population, including (x 1j , …, x NPj ); rand(0, 1) means that the returned random number is a uniformly distributed random real number greater than or equal to 0 and less than 1.

4. The method for economic dispatch of power system based on a distributed hybrid differential evolution algorithm according to claim 3 is characterized in that: The specific operation of step 3: iterating the generated initial population using the distributed hybrid differential evolution algorithm until the predetermined iteration termination condition is reached is: Step 3.1: Use the distributed gradient descent algorithm for all individuals in the population to generate a new population with low individual power generation cost; the distributed gradient descent algorithm is as follows: In the formula, y ij (G) is the component of the jth dimension of the ith individual in the new population generated at the Gth iteration, G is the current iteration number, is the outer iteration in the iteration, d>0 is a constant, when k∈N j When jk =1,a jk is the weight connecting the j-th dimension and the k-th dimension; k represents the index of the dimension, and n represents the total number of dimensions; Step 3.2: Specify the mutation probability. According to the specified mutation probability, perform mutation operations on the individuals in the new population generated in step 3.1 to generate mutant individuals. The specific mutation strategy is as follows: v ij (G)=y aj (G)+F(y bj (G)-y cj (G)) Where a, b, c are three different integers randomly generated from [0, ..., NP], F is a mutation parameter randomly selected from [0, 1]; v ij (G) represents the component of the jth dimension of the i-th variant individual generated at the G-th iteration, (y bj (G)-y cj (G)) represents the difference of the j-th dimension components among different individuals; Step 3.3: Specify the crossover probability. According to the specified crossover probability, perform a crossover operation on the individuals in the new population generated in step 3.1 and the mutant individuals to generate test individuals. The specific crossover strategy is as follows: Where CR is a crossover parameter randomly selected from [0, 1]; u ij (G) represents the component of the jth dimension of the i-th trial individual generated at the G-th iteration; Step 3.4: Use the projection algorithm to make the experimental individuals that do not meet the constraints meet the constraints; Step 3.5: Compare the test individuals with the corresponding population individuals, and select individuals with low fitness to form an iterative population; The i-th modified experimental individual is (u i1 ,…,u in ), the corresponding population individual is (y i1 , …, y in ), the generation method of individuals with low fitness is: In the formula, C j (y ij (k f )) is the average fitness of individual i in the Gth iteration, C j (u ij (k f )) represents the average fitness of the test individual i in the Gth iteration. The method for obtaining the average fitness is as follows: Where u(l) is the predetermined time control function, k1, k2>0 are constants, and k f is the preset convergence time, which is the inner iteration in the Gth iteration. f The algorithm obtains the average value of individual fitness; C j (u ij (l)) represents the local power generation cost of the jth component of the i-th experimental individual, C k (u ik (l)) represents the local power generation cost of the kth component of the ith test individual, (C k (u ik (l))-C j (u ij (l))) represents the difference between two local power generation costs; Step 3.6: If the maximum number of iterations is not met, return to step 3.1; if it is met, terminate the iteration.

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