Application of Improved Multi-Fractal Trend Removing Wave Model in the Analysis of Multi-Fractal Characteristics of Harmonic Signals

Accurate identification and quantification of harmonic signals are crucial in ensuring the stable operation of the power grid and improving power quality in power system analysis. However, traditional single fractal analysis is difficult to accurately capture the multi-fractal local characteristics of harmonic signals. To address this challenge, this paper constructs a novel method for analyzing the multi-fractal features of harmonic signals by integrating multi-fractal detrended fluctuation models, wavelet transform, and empirical mode decomposition techniques. Experiments have shown that the harmonic signals collected by the research belong to the type of low frequency and weak signal strength, and their frequency distribution is mainly concentrated in the range of 0Hz to 210Hz. The second harmonic (100Hz) and the fourth harmonic (200Hz) are the main harmonic components. As the number of decomposition layers increases, the frequency of the signal will gradually decrease and the fluctuations will gradually level off, which helps to clearly identify the low-frequency features in the signal, including the trend and periodic changes. And the amplitude of the high-frequency component will gradually decrease, indicating that the higher frequency components of the signal are gradually extracted. When the sampling frequency was set to 1kHz, the maximum bandwidth of the harmonic signal was 500Hz. Compared with other methods, the performance of the research method has been improved by 5% to 10%. In the analysis of even harmonics, the computational efficiency, resource consumption, stability, and parameter sensitivity of the research method were 96.6%, 31.2%, 93.7%, and 98.7%. In odd harmonic analysis, these indicators were 95.3%, 30.8%, 94.1%, and 97.9%. In contrast, the performance of the proposed method has enhanced by about 5% to 10%. These data indicate that the proposed method is innovative in technology and demonstrates excellent performance in practical utilization, providing an efficient, stable, and resource efficient solution for the multi fractal feature analysis of harmonic signals.