一种混合卷积窗及其在谐波分析中的应用

电力系统稳态信号非同步采样时,利用离散傅里叶变换分析谐波会使各频率成分产生频谱泄漏,增大了谐波参数的测量误差。为进一步抑制频谱泄漏,提高谐波测量的准确度,提出一种由矩形窗和余弦窗经过卷积运算得到的混合卷积窗。定义L阶混合卷积窗并分析了这种新型窗的主瓣宽度和衰减速率。与经典窗函数比较,新型窗具有更高的旁瓣衰减速率,大大减小了频谱泄漏的影响。将所提新型窗应用于谐波分析,推导了基于L阶混合卷积窗的谐波插值算法。仿真结果表明,混合卷积窗具有优良的频谱泄漏抑制性能,能有效地降低各谐波成分间的相互干扰。即使在噪声条件下,本方法的优势也比较明显,适用于电力系统谐波的高准确度测量。

A Kind of Hybrid Convolution Window and Its Application in Harmonic Analysis

When steady waves of electric power system are sampled asynchronously, using discrete Fourier transform to analyze harmonics will generate spectrum leakage and fence effect, which causes measurement errors of harmonic parameters. To further suppress spectral leakage and improve the measurement accuracy of harmonics, a new kind of hybrid convolution windows produced by convolving rectangular windows and cosine windows was proposed. The main lobe width and side lobe attenuation of definedL-order hybrid convolution window were analyzed. Compared with the performance of classical windows, the new windows have faster side lobe attenuation, which can greatly reduce the effects of spectral leakage. The proposed new windows were applied to harmonic analysis, and then the harmonic interpolation algorithm based onL-order hybrid convolution windows was derived. The results show that the new windows have the excellent property of restraining spectral leakage, and the mutual interference between various harmonic components can be reduced effectively. The advantages of this method are also obvious even under noisy conditions. The new algorithm can be used for high-precision measurement of power system harmonics.