Planning of optimal daily power generation tolerating prediction uncertainty of demand and photovoltaics

The concern with renewable energy has been growing. Large-scale installation of photovoltaic (PV) generation and electricity storage is expected to be installed into the power system in Japan. In this situation, we need to keep supply-demand balance by systematically using not only traditional power generation systems but also the PV generation and storage equipment. Towards this balancing, a number of prediction methods for PV generation and demand have been developed in literature. However, prediction-based balancing is not necessarily easy. This is because the prediction of PV generation and the demand forecasting inevitably includes some uncertainty. Against this background, we formulate a problem to plan battery charge pattern while minimizing the fuel cost of generators with explicit consideration of prediction uncertainty. In this problem, given as interval quadratic programming, the prediction uncertainty is described as a parameter in constraint condition. Furthermore, we propose a method to find a solution to this problem from the viewpoint of monotonicity analysis. Finally, by numerical analysis based on this problem and its solution method, we discuss the relation between the minimal regulating capacity and the required battery charge/discharge pattern to tolerate a given amount of prediction uncertainty.