用加Hanning窗插值高阶正弦拟合法测介损角

电力系统频率偏离50Hz时常规的傅立叶变换用于频谱分析时易产生频谱泄漏和栅栏效应,使介损角计算产生误差。高阶正弦拟合法以信号的基波频率、谐波幅值和相角作为变量对信号进行拟合,该法能有效减轻谐波存在和频率波动的影响,精确测量电气设备的介损角。高阶正弦拟合法的关键是最小二乘的计算,通常使用傅立叶变换结果作为最小二乘法的初始值,当频率偏离50Hz较多时,傅立叶变换结果与谐波分析的真实值相差较大,将其作为初值的最小二乘计算量大,影响了高阶正弦拟合法的实时性。加Hanning窗插值谐波分析法通过加窗和插值能有效减轻频率偏离50Hz时的频谱泄漏和栅栏效应,且有快速算法较之傅立叶变换增加的计算量很少。为提高高阶正弦拟合法计算介损角时的实时性,将加Hanning窗插值谐波分析法的结果作为高阶正弦拟合法的初始值,所得初始值与精确值的差值减少,最小二乘法的迭代次数从2次减到1次,容性设备仿真信号的计算时间从约0.82ms减到约0.45ms,结果表明所提出的方法能有效减少介损角的计算时间,提高介损角测量的实时性。

Application of Higher-order Sine Fitting Algorithm with Hanning-windowed Interpolated in Dielectric Loss Angle Measurement

If power frequency deviates from 50 Hz, ordinary Fourier transform is easy to generate spectral leakage and fence effect when it is used for spectral analysis, and it will cause the error of dielectric loss angle measurement. The higher-order sine fitting algorithm takes fundamental harmonic frequency, harmonic amplitude and initial phase angle as variables to fit signal, so that the influence of harmonic and frequency fluctuation can be alleviated. The key step of the high-order sine fitting algorithm is least square algorithm, generally, the results of Fourier transform are taken as the initial values of the least square of the higher-order sine fitting algorithm, if signal frequency has a large deviation from 50 Hz, the error of harmonic analysis by Fourier transform is remarkable and causes the increase in the calculation quantity of the least square method, and the real-time performance of the high-order sine fitting algorithm is lowered. The Hanning windowed interpolated algorithm uses windowing and interpolation to alleviate spectral leakage and fence effect effectively when the signal frequency deviates from 50 Hz, and the fast algorithm has more calculation quantity than Fourier transform algorithm has. For improving the real-time performance of the high-order sine fitting algorithm, the results of Hanning-windowed interpolated harmonic analysis algorithm are taken as initial values of the least square, the initial values has less deviation form accuracy values, iteration times of least square algorithm is decreased from twice to once, and the calculation time of simulation signal of capacitive equipments is decreased from about 0.82ms to about 0.45ms, indicating that the calculation time of dielectric loss angle can be decreased effectively by the proposal algorithm, and the performance of real-time is improved.