Magnitude-Phase Characteristics Analysis of Inertia for DFIG-Based Wind Turbines

The magnitude of inertia is often used to assess the ability to withstand frequency perturbations. However, the inertia of wind turbines (WTs) is time-varying, equipped with magnitude-phase characteristics. Existing studies have only focused on the magnitude characteristic of WT's inertia but rarely on phase characteristic, which is a limited understanding of WT's inertial response and hard to reveal its effect on system frequency dynamics. Therefore, this article is the first to study the inertial response mechanism of WTs from the perspective of magnitude-phase characteristics. First, the equivalent inertia model of WT is extracted, considering multiple-loop dynamics. Then, the relationship among magnitude-phase characteristics of WT's inertia, active power, and frequency dynamics is revealed according to the definition of equivalent inertia. Furthermore, the extended system frequency response model including the inertia of WT is established and the effect of WT's inertia on system frequency metrics is analyzed. Subsequently, the effects of phase-locked-loop, speed, and reactive power controller parameters on the magnitude-phase characteristics of WT's inertia and frequency metrics are analyzed. Finally, the analysis is verified by hardware-in-loop experiments.