基于DFT和群组谐波能量回收理论的谐波与间谐波检测算法

采用离散傅里叶变换(DFT)检测含有频率相近的谐波与间谐波的电网信号时，信号的非同步采样会引起频谱泄露和混叠现象，严重影响了检测精度。针对以上问题，提出一种基于DFT和群组谐波能量回收理论的谐波与间谐波检测算法。首先根据DFT对谐波/间谐波的频谱分析结果判别谐波/间谐波分量数。然后基于群组能量回收理论通过频率偏移量自动调整取样窗口的长度，依次对主要谐波/间谐波周围的溃散能量进行迭代收集。最后通过主要谐波/间谐波周围溃散总能量值将其幅值与频率恢复为原貌，即可得到各分量幅值和频率的精确值。Matlab仿真算例表明，该算法能有效减小因频谱泄露而引起的测量误差，准确测量出邻近谐波与间谐波分量的幅值和频率。

A harmonic and interharmonic detection algorithm based on DFT and group harmonic energy recovery theory

When a discrete Fourier transform (DFT) is used to detect a grid signal containing harmonics and interharmonics with similar frequency, the non-synchronous sampling of the signal causes spectrum leakage and aliasing, which seriously affect the detection accuracy. In order to improve this, a harmonic and interharmonic detection algorithm based on DFT and group harmonic energy recovery theory is proposed. First, from a spectrum analysis of the harmonic / interharmonic by DFT, the number of harmonic and interharmonic components is determined. Then based on group energy recovery theory, the length of the sampling window is automatically adjusted by the frequency offset, and the collapse energy around the main harmonic / interharmonic is collected iteratively. Finally, the amplitude and frequency are restored to their original state by total collapse energy value around the main harmonic / interharmonic, and the accurate values of the amplitude and frequency of each component can be obtained. Simulation in Matlab shows that the proposed algorithm can effectively reduce the measurement error caused by spectrum leaks, and accurately measure the amplitude and frequency of adjacent harmonic and interharmonic components. This work is supported by the Natural Science Foundation of Shaanxi Province (No. 2021JM-393).