Stability analysis and control of hydroelectric generator unit speed regulation systems based on the time-domain describing function method

The speed governing system of a hydroelectric generating unit incorporates dead zone and amplitude limiting elements, classifying it as a typical non-smooth dynamic system. Currently, stability analysis primarily relies on the describing function method, an approximate discrimination technique based on frequency-domain analysis that requires the linear components of the system to exhibit satisfactory low-pass filtering characteristics. However, from a mathematical standpoint, there is no rigorous definition for what constitutes satisfactory low-pass filtering. In an attempt to address this issue, this paper proposes a novel stability analysis method grounded in time-domain state space modeling. This method features a rigorous mathematical basis and builds upon the core principles of the describing function method, it can be regarded as the describing function method within the time-domain state space. The application of this method to the stability analysis and control parameter optimization of the hydroelectric generating unit's speed governing system has been validated through experimental results, demonstrating its effectiveness and superiority.