基于傅里叶变换的精确频率测量算法

An Accurate Frequency Measuring Algorithm for Power Systems Based on Fourier Transform

传统的傅里叶频率测量算法,通过傅里叶算法求出相邻2个周期的相位,采用相位差对采样频率进行修正和迭代,计算量大而精度差。文中根据严格推导得到傅里叶算法计算值的准确数学形式,通过对相位差的三角函数进行分解展开,代入傅里叶算法计算值,即可在不需要计算相位的情况下得到相邻2个周期相位差的准确值,从而得到真实的信号频率。仿真分析结果表明,该算法精度高,计算量小,实现简单,完全适合于微机保护测控类装置的实际应用。

In the conventional frequency measuring algorithm, first the phases of two adjacent periods are obtained using Fourier transform, then the phase difference is used to perform modification and iteration for the sampling frequency. This algorithm asks for a lot of calculation but is inaccurate. Based on strict mathematical deduction, this paper presents an accurate mathematical expression using Fourier transform, which is composed of the cosine function for the phase difference. Then after trigonometric function decomposition, the cosine function for the phase difference can be expressed with the Fourier transform results. Hence, the real signal frequency can be obtained without calculating the precise phases of the two periods. Simulation results show that the new algorithm is suitable for application in microcomputer-based monitoring and protective devices for its high accuracy, low calculating workload and easy implementation.