Spatio-Temporal Frequency Distribution Analysis in Systems With Grid-Forming and Grid-Following Inverters: A New Perspective From Frequency Domain

The high penetration of inverter-based resources (IBRs) in power systems has brought challenges to system frequency stability due to reduced inertia. The conventional method for frequency stability assessment uses the center-of-inertia (CoI) frequency as a single indicator to represent the frequency throughout the entire system, which overlooks the spatio-temporal distribution of frequencies among multiple nodes during transients. The frequency distribution is further complicated by the differences in frequency regulation and synchronization of synchronous generators (SGs) and IBRs, either grid-forming (GFM) or grid-following (GFL). To address this challenge, this paper develops a whole-system frequency response matrix in the frequency domain which accommodates the frequency regulation and synchronization dynamics of all apparatuses in a unified framework. Based on this matrix, two frequency-domain metrics, namely spatio-temporal inertia and damping, are introduced to illustrate the frequency distribution characteristics. The spatial distribution is evaluated by using the matrix entries and the temporal distribution is evaluated by using the frequency spectra. The proposed model and metrics are validated via time-domain simulations on two test systems: a modified 4-machine 2-area system and a modified 5-area 68-bus system. The contributions of SGs and IBRs (GFM and GFL) to frequency regulation are examined by comparative analysis using the proposed metrics.