Stability and dynamic response of primary frequency regulation in pumped storage unit governing system under opening control mode

Abstract

The present study investigates the stability and dynamic response characteristics of pumped storage units (PSU) in a primary frequency regulation (PFR) under opening control mode. A comprehensive nonlinear mathematical model has been developed for the pumped storage unit governing system (PSUGS), incorporating hydraulic-mechanical-electrical coupling dynamics, including explicit representation of the synchronous generator excitation system. Derivation of nonlinear state equations is undertaken in order to characterize multi-energy domain interactions within PSUGS. These state equations serve as the fundamental framework for subsequent stability analysis. Employing Hopf bifurcation theory, the stability boundaries and critical oscillation modes are systematically analyzed under grid frequency disturbances, with numerical simulations validating the theoretical bifurcation thresholds. Further investigation reveals that PSUGS exhibits a dual-frequency oscillation phenomenon during PFR: (1) low-frequency oscillations (LFOs, 0.1–2.5 Hz) governed by generator dynamics and (2) ultra-low-frequency oscillations (ULFOs, <0.1 Hz) dominated by hydraulic transients in the penstock-governor subsystem. It is noteworthy that the Hopf bifurcation boundary consists of two distinct components corresponding to these oscillation modes, thereby demonstrating frequency-dependent instability mechanisms. The process of parametric sensitivity analysis is one of quantifying the regulatory impacts of key factors. These factors include hydraulics, mechanical, and electrical parameters. The results of the study demonstrate that ULFOs are particularly sensitive to hydraulic system configurations, while LFOs are predominantly influenced by electrical grid interactions. The findings of the present study provide a theoretical foundation for the optimization of frequency regulation strategies and the suppression of multi-frequency oscillations in pumped storage systems.