Solar radiation forecast under convex piecewise linear cost functions

The actual cost function for many decision makers (like balancing authorities (BAs) of the power grid) are usually different from the symmetric cost functions that are commonly used to study renewable energy generation forecasts. While the actual cost function may be difficult to obtain, a convex piecewise linear (CPWL) cost function could be used to approximate and model cost in many practical applications. In this paper we consider three ways to deal with solar forecast under a CPWL cost function. In the simplest approach a constant bias is added to the initial point forecast according to the distribution of errors. A more sophisticated indirect method is using a probabilistic forecast which gives the distribution of future outcome rather than a single value in point forecast. The predictive distribution for each point is used to determine the best biased forecast according to the cost function. Finally the cost function is directly considered in the training phase to create a customized forecast method. Our simulations shows that substantial cost saving is possible through both directly biased method and indirectly biased probabilistic forecast.