Probabilistic Forecasting for Multi-Stage Nonlinear Model Predictive Control*

This study proposes a general forecast and control framework for constrained stochastic nonlinear optimal control of isolated gas-renewable energy systems with energy storage. Typically, these systems require control strategies that can handle significant uncertainties in produced renewable energy due to forecast uncertainty from meteorological forecasts. To address the uncertainty in meteorological forecasts, data-driven stochastic grey-box models of the renewable energy source are modelled and probabilistically forecast (PF) with stochastic differential equations (SDEs). The PF scheme improves upon the meteorological forecasts by forming a probability distribution in time with the meteorological forecasts and past data as input. Based on these distributions, a multi-stage (MS) nonlinear model predictive control (NMPC) formulation is utilised, resulting in a tractable control formulation. The proposed framework is validated in simulation with real-life data for a hybrid gas-wind energy system, which shows that the proposed method is real-time capable despite using standard solvers and outperforms standard methods, such as certaintyequivalent NMPC when relying on meteorological forecasts. Though motivated by the energy sector, the proposed method can be extended to any stochastic system since SDEs are a general class of stochastic processes.