PID Regulation Enabling Multi-Bifurcation Instability of a Hydroelectric Power Generation System in the Infinite-Bus Power System

The integration of new energy into the grid has significantly intensified power grid operational pressure, posing higher demands on hydropower system regulation. As a key unit for power grid load tracking and stability maintenance, parameter mismatch of the PID governor is prone to inducing system bifurcation, thus leading to oscillatory instability, which has emerged as a critical challenge affecting the reliable consumption and sustainable supply of new energy. To address this challenge, a hydroelectric power generation system (HPGS) model in the infinite-bus power system is established. Bifurcation analysis is employed to quantitatively identify the critical thresholds of PID parameters that cause HPGS instability. Based on this, system dynamic response processes under critical thresholds are clarified using time-domain analysis. Furthermore, the potential oscillation instability mechanism is revealed using eigenvalue analysis, and suggestions for PID parameter selection are provided. Key quantitative results indicate that variations in proportional gain, kp, induce five limit point bifurcations. The system enters an unstable region when k p exceeds 2.467, whereas operation within the range below 0.891 is conducive to system stability. A supercritical Hopf bifurcation arises when integral gain k i reaches 0.925, so strict restrictions should be imposed on k i to avoid operating around this critical value. Two supercritical Hopf bifurcations that may trigger system oscillatory instability are identified during differential gain k d changing, and it should be regulated to a level below 5.188 to ensure system stability. By integrating bifurcation analysis, time-domain analysis, and eigenvalue analysis, this study effectively improves the accuracy of characterizing system dynamic behaviors, providing a clear quantitative basis for PID parameter optimization and bifurcation suppression, as well as laying a theoretical foundation for hydropower system stable operation and the efficient absorption of new energy.