快速傅里叶变换存在较大的误差,无法直接应用于电力系统谐波分析,文中提出了一种基于傅里叶级数模型的神经网络算法.由于该算法模型与电力系统谐波模型匹配,因而有效提高神经网络的收敛速度和计算精度,减小计算量,使之适用于电力系统的准确谐波分析.为了保证该算法的收敛性,提出并证明该算法的收敛性定理,为神经网络学习率的选择提供理论依据;同时为了验证算法的有效性,给出该算法进行谐波分析的仿真实例.计算结果表明,利用该方法可快速获得电力系统基波及各次谐波的高精度幅值和相位,而且不涉及复数运算,因而在电力系统谐波测量中有较大的应用价值.
The FFT has a higher error in the harmonic analysis of the electric power system, especially for the phases. An algorithm of neural network based on Fourier series is presented. Because the algorithm model presented matches with the harmonic model of the electric power system, this algorithm obviously improves the convergence speed and accuracy of the neural network algorithm, so it can be applied to the precision analysis for electrical harmonic. In order to ensure the convergence of algorithm, the convergence theorem of the algorithm is proposed and proved. The theory gist to select learning rate is provided by the convergence theorem. To validate the validity of the algorithm, the simulating examples of harmonic analysis are given. The simulating results show that the high accurate amplitudes and phases of fundamental and various orders of harmonics could be obtained using the algorithm. Furthermore, the algorithm is not involved in operation of the complex number, thus the harmonic analysis method presented has significant value in the field of the power system harmonic measurement.