Data-driven surrogate modeling and automatic PID tuning of hydropower governors for low-inertia power systems

This paper addresses proportional–integral–derivative (PID) governor tuning for high-head hydropower units that provide fast frequency and ramping services in power systems with high shares of variable renewable energy (VRE). Strong hydraulic–mechanical–electrical couplings and long waterways make traditional trial-and-error tuning slow, labor-intensive and difficult to repeat, especially when water-hammer constraints must be respected. We develop a reproducible surrogate-assisted workflow that formulates the mapping from PID gains to transient performance as a tabular regression problem. A high-fidelity hydraulic–mechanical–electrical simulation based on the method of characteristics (MOC) is used to generate time-domain responses for systematically sampled PID parameters, and the sum of squared speed errors (SSE) is adopted as a unified performance index across the considered disturbance scenarios. Four representative tabular models — a multi-layer perceptron (MLP), FT-Transformer, TabTransformer and TabNet — are trained under a unified data split and random-search protocol. TabNet achieves the lowest validation and test root mean squared error (RMSE) and is therefore selected as the surrogate. The surrogate is then coupled with gray wolf optimization (GWO) to explore PID gains on the learned response surface, after which candidate settings are validated again in the high-fidelity environment. For a representative load-disturbance case, the optimized parameters significantly reduce speed overshoot and oscillation duration while satisfying all water-hammer safety limits, with close agreement between surrogate predictions and high-fidelity simulations near the optimum. From an energy-system perspective, the proposed digital-twin-plus-artificial intelligence (AI) workflow shortens the effective tuning time for a hydropower governor from tens of minutes and many field tests to sub-second surrogate evaluations, thereby enhancing the flexibility, frequency-support capability and safe operating range of hydropower plants in low-inertia, renewable-rich power systems. • Surrogate-assisted PID tuning framework for hydropower frequency control. • TabNet surrogate reduces expensive water-hammer simulations to offline training. • Gray wolf optimization finds PID gains that satisfy water-hammer safety limits. • Results improve speed regulation while supporting stability in low-inertia grids.