Adaptive Fourier Decomposition-Based Unified Phasor and Waveform Measurement Method for Power System Signals

The frequency-domain phasor and time-domain waveform measurements are the fundamental techniques in power systems, with the former applied to nontransient conditions and the latter to transient processes, where phasor representation becomes inadequate. Synchrophasor measurement relies on Fourier transforms, whereas waveform measurement depends on data compression. The absence of a unified mathematical foundation between these methods hinders seamless technical integration and increases operational costs due to discrete measurement techniques. This study proposes an adaptive Fourier decomposition (AFD) algorithm based on the Takenaka-Malmquist (TM) system for measuring transient and steady-state signals in power systems. A power signal representation model is developed using the TM system, analogous to conventional Fourier-based models, and its mathematical foundation is established. A unified phasor-waveform measurement framework is introduced, leveraging traditional phasors during nonelectromagnetic transient periods and TM phasors during electromagnetic transient periods. The characteristics of TM phasors are examined across various scenarios, and the influence of AFD parameters is analyzed, leading to a unified synchrophasor-waveform measurement method that integrates time- and frequency-domain measurement approaches. Extensive testing, encompassing IEC/IEEE 60255-118-1 standard signals and field fault recording signals, validates that the proposed method meets P-class PMU requirements with tenfold accuracy in most cases and yields the lowest waveform reconstruction root mean square error (RMSE) across diverse transient conditions.