Intantaneous Complex Frequency of Three-Phase AC Systems: Concept and Analysis

In modern three-phase AC systems with high penetration of power electronic converters, the amplitudes and frequencies of electrical quantities such as voltage and current change dynamically over time. The increasing use of new energy sources threatens the stability of system, thereby increasing the demand for dynamic analysis. The traditional frequency concept could be insufficient to accurately describe the dynamic behavior of a strongly time-varying system. Besides, the differential equations derived in stationary or synchronous reference frames are inconvenient to characterize the dynamic behavior of instantaneous amplitude and frequency. Therefore, this paper develops the concept of instantaneous complex frequency (ICF), from the complex phase angle concept, offering a new mathematical tool for analyzing the dynamic behavior of the three-phase AC systems. The ICF characteristics of passive components are analyzed based on the definition of ICF, and are verified by simulation results.