Analytical Method to Aggregate Multi-Machine SFR Model With Applications in Power System Dynamic Studies

TLDR

The system frequency response (SFR) model captures the average network frequency response after a disturbance and is widely used in dynamic studies, yet existing literature lacks a generic analytical method for aggregating its parameters across multiple generators, relying instead on simulations or operator experience. This paper proposes an analytical method to aggregate a multi‑machine SFR model into a single‑machine representation. The method analytically combines multi‑machine SFR parameters into a single‑machine model and is applied to system frequency control, frequency stability, and dynamic model reduction. Verification and simulation studies confirm that the aggregated SFR model accurately reproduces the multi‑machine response and the average frequency response of large systems, demonstrating its promise for broad applications.

Abstract

The system frequency response (SFR) model describes the average network frequency response after a disturbance and has been applied to a wide variety of dynamic studies. However, the traditional literature does not provide a generic, analytical method for obtaining the SFR model parameters when the system contains multiple generators; instead, a numerical simulation-based approach or the operators' experience is the common practice to obtain an aggregated model. In this paper, an analytical method is proposed for aggregating the multi-machine SFR model into a single-machine model. The verification study indicates that the proposed aggregated SFR model can accurately represent the multi-machine SFR model. Furthermore, the detailed system simulation illustrates that the SFR model can also accurately represent the average frequency response of large systems for power system dynamic studies. Finally, three applications of the proposed method are explored, with system frequency control, frequency stability, and dynamic model reduction. The results show the method is promising with broad potential applications.