Monotonicity Analysis of the Optimal Operation Schedule Taking into Acount Power Network Structure

We consider a day-ahead scheduling problem for resources based on photovoltaic (PV) generation and demand profile predictions. Because the predicted profiles contain uncertainty, the set of profiles is represented as a confidence interval. Giving the predicted profile as a confidence interval, we consider the problem of obtaining ranges for the optimal operating profiles of storage batteries and thermal power plants. This corresponds to finding the region of possible solutions for all parameters representing PV/demand predictions. In order to find the exact solution region efficiently, we focus on the monotonicity of the solution. In particular, we aim to clarify what kind of optimization problem possesses monotonicity. As a first step, we have performed monotonicity analysis in various settings so far. In this study, we show that the problem, where the network structure is taken into account, has monotonicity under conditions with a theoretical proof. We also confirm its practical significance with a numerical example.