Time-Varying Inertia Characterization of DFIG-based Wind Turbines for Power System Frequency Dynamic Analysis

Accurately assessing the inertial response of renewable energy generation (REG) is critical for frequency stability. However, REG represented by doubly-fed induction generator (DFIG)-based wind turbine (WT) exhibits inherent time-varying inertia behavior, fundamentally distinct from synchronous generators (SGs). Prevailing inertia assessment methods predominantly rely on SG-derived time-domain inertia constants, which cannot capture this intrinsic variability. Consequently, the rationality of directly applying these conventional methods to DFIG-based WT lacks theoretical justification. To address this gap, this paper derives an expression for calculating time-varying inertia using the angular momentum theorem. Results demonstrate that inertia in the time domain dynamically varies with disturbances, highlighting the significant limitations of conventional inertia descriptions. Alternatively, a frequency-domain inertia characterization method is investigated to provide a disturbance-independent description of inertia, effectively capturing its intrinsic time-varying nature. Due to the duality between time and frequency domains, this paper mathematically describes the relationship between frequency-domain inertia and time-domain inertia, explicitly clarifying the physical meaning of inertia in the frequency domain. Simulations on an IEEE 39-bus system verify that the frequency-domain inertia method accurately captures inertia dynamics and is suitable for frequency stability analysis. These findings emphasize frequency-domain inertia characterization as an essential method for representing inertia in renewable-rich power systems.