Stability properties of nonlinear model predictive control of variable speed hydropower

Abstract

This study presents a method for small-signal analysis of an advanced, multi-variable control system for variable speed hydropower (VSHP) plants. A model predictive controller (MPC) optimises the power plant performance. In parallel, a virtual synchronous generator-type (VSG) converter control ensures that the VSHP contributes to virtual inertia and frequency control of the power system. The aim of the small-signal analysis is to parametrise the cost function of the MPC to minimise oscillatory modes between the VSHP hydraulic system and the power system. A state-space representation of the MPC is developed by assuming a stable steady-state operating point equal to the reference values of the MPC cost function, and that no constraints are active. This state-space representation allows for small-signal analysis of the power system, including the MPC. The results show that the modes between the hydraulic system and the power system are well-damped and negligible when the costs of deviations in the hydraulic system are low compared to the cost of deviations in the VSG power reference. Thus, these modes do not constrain the tuning of the VSG. The VSHP power output can, therefore, be optimised independently through the VSG controller to damp power oscillations and reduce frequency deviations.