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Based on PSO, considering the harmonic influence, the optimal configuration of compensation capacitors

[Abstract] a reasonable capacitor configuration of power distribution can not only effectively improve the voltage level of electricity, reduce the active power loss of the system, but also avoid harmonic resonance or current amplification. In this paper, the constraints of voltage harmonic distortion rate are considered when establishing the nonlinear integer programming model of capacitor optimal configuration, so as to ensure that the total harmonic distortion rate of voltage at each node under the optimization scheme is controlled within the specified limit. Particle swarm optimization (PSO), a simple and effective evolutionary algorithm with good convergence, is applied to solve the problem. The advantages of the algorithm are analyzed from five aspects: coding mode, operation process, objective function selection, parameter adjustment and information sharing mechanism, and the specific solving steps of the algorithm used in the optimal configuration of capacitors are given. Two IEEE tests of different scales show that the optimization calculation of the system shows that the particle swarm optimization algorithm can obtain the global optimal solution of the optimal capacitor configuration problem

introduction

the optimal configuration of compensation capacitors in power distribution involves how to optimally determine the installation location, capacity and type of capacitors. Reasonable capacitor configuration can effectively improve the voltage level of electricity, reduce the active power loss of the system, and avoid harmonic resonance or current amplification at the same time. For a long time, the optimal configuration of capacitors has been a research topic of common concern in engineering and academia. At present, when studying this problem, many literatures only consider the constraints of system power flow and the upper and lower limits of node voltage, and ignore the influence of harmonics in electricity [1~3]. However, with the increasingly extensive application of power electronic devices, the harmonic pollution caused by this is becoming more and more serious. Unreasonable capacitor configuration may lead to harmonic resonance or current amplification at a certain frequency or several times, thus endangering the safe operation of the capacitor itself and other electrical equipment. In order to avoid harmonic resonance or amplification, it is necessary to consider the influence of harmonic on capacitor configuration scheme in optimization calculation. The main index to judge whether there is harmonic amplification in electricity and measure the severity of electrical distortion is total harmonic distortion (THD). Various countries have made clear limits on the harmonic distortion rate under different voltage levels. Therefore, when establishing the planning model of capacitor optimal configuration, this paper considers the constraints of voltage distortion rate of all nodes in electricity, Thus, the total harmonic distortion rate of each node voltage under the planning scheme can be controlled within the specified limit

the capacitor configuration optimization problem is a nonlinear integer optimization problem, and its objective function and constraint conditions are nonlinear functions of discrete control variables. Therefore, it is difficult to accurately solve the problem using traditional programming methods in the drop weight impact experiment of coherent experimental materials. In recent years, the development of evolutionary computing technology represented by genetic algorithms (GA) provides a new way to solve this kind of optimization problems. This paper uses a new evolutionary computing method particle swarm optimization (PSO) to solve the above problems. PSO algorithm is an evolutionary computing method based on swarm intelligence proposed by Dr. Kennedy in 1995 [4,5]. Its idea originally came from the simulation of the foraging process of birds. It was inspired by the behavior model of this simple social system, so as to establish the development foundation of the algorithm, and finally developed into an effective optimization tool. Similar to GA, PSO is also a random search algorithm based on iteration, but the two have the following differences: ① PSO can generally customize various experimental data processing software and experimental AIDS according to domestic and international standards provided by users at the same time, and adopt real number coding instead of binary coding of variables like GA (or adopt genetic operation for real numbers); ② In the iteration process of PSO algorithm, genetic operations such as crossover and mutation are not needed, but the search path is determined according to the speed of particles; ③ PSO directly takes the objective function itself as the fitness function, and performs iterative search according to the value of the objective function (that is, the fitness value), while GA needs to complete the transformation from the objective function to the fitness function when solving the minimum problem; ④ Few parameters need to be adjusted by PSO, especially after the introduction of convergence factor [6], the algorithm can set parameters according to empirical values to obtain better convergence. When using GA to optimize the optimization problem, how to select the appropriate selection rate, crossover rate, mutation rate, retention rate and many other control parameters needs to be tested and compared many times according to the actual situation. The convergence effect of the algorithm depends on the selection of these parameters to a great extent; ⑤ * the information sharing mechanism of the above two is different. In genetic algorithm, each chromosome shares information with each other, so the whole population moves to the optimal region more evenly. In PSO, only the current optimal particles in the group provide information to other particles, which belongs to a one-way information flow. The whole search and update process follows the current optimal solution. Compared with GA, in most cases, all particles converge to the optimal solution faster. Based on these advantages, particle swarm optimization algorithm can not only be used in all fields where genetic algorithm can be applied, but also converge to the global optimal solution faster than genetic algorithm in most cases. At present, PSO algorithm has been applied to power system optimization. In paper [6], particle swarm optimization algorithm is used to solve reactive power optimization. The correctness and effectiveness of the algorithm are proved by several test systems of different scales

in this paper, a nonlinear integer programming model of capacitor optimal allocation considering the influence of harmonics is established, and the particle swarm optimization algorithm is applied to solve it. The algorithm is discretized according to the discrete control quantity in the problem, and the problem of PSO algorithm for integer optimization or mixed integer optimization is solved. The IEEE 9-bus system and IEEE 69 bus system are calculated respectively. The results show that the algorithm is correct and effective, and the global optimal solution of the capacitor optimal configuration problem can be obtained

2 particle swarm optimization algorithm

2.1 standard PSO algorithm

as mentioned above, particle swarm optimization algorithm is developed on the basis of simulating the predatory behavior of birds. Every possible solution of the optimization problem is a "bird" in the search space, which is called "particle" in the algorithm. According to the adaptability to the environment, the individuals (particles) in the group are moved to a good area. These particles fly at a certain speed in the search space according to their own and their partners' flight experience

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