Under the trend of increased power electronics integration in power equipment

waveform distortion of voltage and current exhibits time-variability and randomness. Consequently

discrete frequency-based waveform characterization methods relying on a constant power frequency period and consistent distortion shape are unsuitable for practical engineering. This paper considers the power frequency voltage and current components as operating points. At the same time

waveform distortions are viewed as fluctuations at these points and are characterized by additional amplitude and phase fluctuations of the power frequency. The feasibility of characterizing harmonics

attenuated DC components

attenuated AC components

and their combinations using fluctuations at the operating point is demonstrated. The operating point is determined using a trust-region-reflective (TRR) method

and fluctuations are resolved using a designed Hilbert filter. Simulation results demonstrate that the proposed method achieves high accuracy in estimating power frequency components and amplitude-phase fluctuation parameters

while allowing flexible data length selection. Compared to methods based on Discrete Fourier Transform (DFT) and Wavelet Packet Transform (WPT)

it offers advantages such as independence from synchronized sampling of complete cycles and higher distortion representation accuracy. Moreover

the method exhibits strong noise immunity. This method holds potential applications in analyzing waveform distortion issues at different time scales

such as harmonics and oscillations in the power system.