Accurate and Fast Feature Extraction Method of Power Quality Disturbances Based on Modified S-Transform of Optimal Bohman Window
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摘要: 针对传统S变换存在时频分辨率低且计算量大的问题，该文提出一种基于最优Bohman窗的改进S变换。该方法通过直接控制窗长获得最优时频分辨率，同时只针对主要频率点进行时频分析，实现对各类扰动信号特征的精确快速提取。首先根据所提评价标准确定最优长度参数；其次将采样信号进行快速傅里叶变换得到FFT频谱，再通过基于极大值包络的动态测度快速算法确定主要频率点；然后根据主要频率点所处频段选择对应最优长度参数进行计算处理；最后根据模时频矩阵计算时频幅值向量完成时频特征提取。仿真分析和实验结果表明，所提方法相较于传统S变换具有更高的时频分辨率和更短的计算时间，适用于电能质量扰动信号特征的精确快速提取。Abstract: Focusing on the problems of low time-frequency resolution and large amount of calculation in the traditional S-Transform, a modified S-Transform based on the optimal Bohman window is proposed. In order to extract accurately and quickly the characteristics of all kinds of disturbance signals, this method obtains the optimal time-frequency resolution by controlling directly the window length and carries out time-frequency analysis only for the main frequency points. Firstly, the optimal length parameter is determined according to the proposed evaluation criteria. Secondly, the sampled signal spectrum is obtained through fast Fourier transform, and then the main frequency points are determined by the dynamic measurement fast algorithm based on the maximum envelope; Then the corresponding optimal length parameter is selected according to the frequency band of the main frequency point for calculation and processing; Finally, the time-frequency feature extraction is completed by calculating the time-frequency amplitude vector based on modulus time-frequency matrix. Simulation analysis and experimental results show that the proposed method has higher time-frequency resolution and shorter calculation time than the traditional S-Transform, and is suitable for the accurate and fast extraction of power quality disturbance signal features.
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表 1 计算量和时间复杂度对比
算法 计算量 时间复杂度 复数加法 复数乘法 SMST $\dfrac{N}{2}(N{\log _2}N)$ $\dfrac{N}{2}(N + \dfrac{N}{2}{\log _2}N)$ $ O({N^2}{\log _{\text{2}}}N) $ OST $\dfrac{N}{2}(N{\log _2}N)$ $\dfrac{N}{2}(N + \dfrac{N}{2}{\log _2}N)$ $ O({N^2}{\log _{\text{2}}}N) $ FBST $ m(N{\log _{\text{2}}}N) $ $\dfrac{m}{2}(N + \dfrac{N}{2}{\log _{\text{2} } }N)$ $ O(N{\log _{\text{2}}}N) $ 
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表 3 谐波与暂态振荡信号相对误差对比
扰动 幅值相对误差(×10–5) 频率相对误差(Hz) SMST OST FBST SMST OST FBST 3次谐波 0 0 0 0 0 0 5次谐波 0 0 0 0 0 0 7次谐波 0 0 0 0 0 0 9次谐波 1 0 0 0 0 0 11次谐波 12 0 0 0 0 0 13次谐波 33 0 0 0 0 0 15次谐波 150 1 0 3.3 0 0 17次谐波 195 1 0 6.7 0 0 19次谐波 393 3 0 – 0 0 21次谐波 337 4 0 3.3 0 0 23次谐波 1132 16 0 – 0 0 25次谐波 871 16 0 26.7 0 0 27次谐波 1537 34 0 – 0 0 29次谐波 853 21 0 – 3.3 0 暂态振荡 98 120 101 0 0 0
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表 5 实测信号相对幅值误差(10–5)
扰动 SMST OST FBST C0暂升 6270 2850 1230 C1暂降 5020 2440 1000 C2中断 12590 6025 2529 C3闪变 3710 1970 1300 C4谐波 8412 153 100 C5暂态振荡 481 543 500 C6暂升+谐波 7400 4170 1790 C7暂降+谐波 8950 7100 4130 C8中断+谐波 22570 17805 10464
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