Deriving Loss Function for Value-oriented Renewable Energy Forecasting

Renewable energy forecasting is the workhorse for efficient energy dispatch. However, forecasts with small mean squared errors (MSE) may not necessarily lead to low operation costs. Here, we propose a forecasting approach specifically tailored for operational purposes, by incorporating operational problems into the estimation of forecast models via designing a loss function. We formulate a bilevel program, where the operation problem is at the lower level, and the forecast model estimation is at the upper level. We establish the relationship between the lower-level optimal solutions and forecasts through multiparametric programming. By integrating it into the upper-level objective for minimizing expected operation cost, we convert the bilevel problem to a single-level one and derive the loss function for training the model. It is proved to be piecewise linear, for linear operation problem. Compared to the commonly used loss functions, e.g. MSE, our approach achieves lower operation costs.