K-S变换及其电网超谐波时频分析应用

K-S Transformation and Its Application to Superharmonic Time-Frequency Analysis in Power System

依据FFT→优化窗→IFFT思路,突破线性时频变换的窗函数积分性能桎梏,实现高性能优化窗函数的线性时频变换应用,建立新型时频变换算法——K-S变换.对信号x(t)的FFT频谱向量进行频移处理后,与该频移点下Kaiser优化窗的频谱向量进行Hadamard乘积,再将乘积结果进行FFT逆变换(IFFT),构造出K-S变换复时频矩阵,由此获得x(t)的时间-频率-幅值、时间-频率-相位三维信息;给出逆变换的数学推导与局部性质、线性性质和变分辨率特性;0~150 kHz电网的稳态与时变超谐波信号仿真实验表明,K-S变换的时域、频域分辨能力均优于流行的短时傅里叶变换、S变换,具有优良的变分辨率性能;0~40 kHz超谐波信号的实测证明,基于K-S变换的超谐波电压幅值测量绝对误差均小于0.032 3 V.

According to the idea of FFT(Fast Fourier Transform)→optimization window→IFFT(Inverse Fast Fourier Transform),the performance constraints of window function integration in linear time-frequency transformation are broken through,achieve the application of high-performance optimization window function in linear time-frequency transformation is achieved,and establish a new time-frequency transformation algorithm,K-S transformation is establisged.After frequency shifting for the FFT spectrum vector of signal x(t)is carried out,Hadamard multiplication with the spectrum vector of Kaiser optimization window at the frequency shift point,and then inverse FFT transformation(IFFT)on the product result is performed,the K-S transform complex time-frequency matrix is constructed to obtain three-dimensional time-frequency amplitude and time-frequency phase information of x(t).The mathematical derivation,local properties,linear properties,and variable resolution properties of inverse transformation are given;simulation experiments on steady state and time-varying superharmonic signals from 0~150 kHz power grids show that the K-S transform has better resolution in both time and frequency domains than popular short-time Fourier transform and S-transform,and has excellent variable resolution performance.The actual measurement of 0~40 kHz superharmonic signals proves that the absolute error of superharmonic voltage amplitude measurement based on K-S transformation is less than 0.0323 V.