Optimal planning of slow-ramping power production in energy systems with renewables forecasts and limited storage

We address the cost-efficient operation of an energy production system under renewables uncertainty. We develop an MDP model for an idealized system with the following features: (1) perfectly predictable power demand, (2) a renewable power source subject to uncertain forecast, (3) limited energy storage, (4) an unlimited fast-ramping power source, and (5) a slow-ramping power source which requires (optimal) planning. A finite-horizon stochastic optimization problem is introduced to minimize the overall cost of operating the system, and then solved numerically using standard approaches (based on backward induction) and available data. In contrast with the unit commitment problem which is traditionally optimized for a single planning frame, we show in simple scenarios that it may be beneficial to optimize over a few planning frames, and that there is no benefit to considering longer (e.g., infinite) horizons. We discretize the state space in an attempt to mitigate the curse of dimensionality usually associated with numerically solving MDPs. We note that few discretization states already yield a significant decrease in the total cost.