Online and batch methods for solar radiation forecast under asymmetric cost functions


Asymmetric cost functions are used for solar radiation forecasting.

Fair comparisons are made between directly biased methods and indirectly biased methods.

Both online and batch learning algorithms are discussed.

Directly biased methods give significant cost savings.

The use of LinEx and CPWL cost function is recommended for solar radiation forecasting for power system operators.


In electric power grids, generation must equal load at all times. Since wind and solar power are intermittent, system operators must predict renewable generation and allocate operating reserves to mitigate imbalances. If they overestimate the renewable generation during scheduling, insufficient generation will be available during operation, which can be very costly. However, if they underestimate the renewable generation, usually they will only face the cost of keeping some generation capacity online and idle. Therefore overestimation of renewable generation resources usually presents a more serious problem than underestimation. Many researchers train their solar radiation forecast algorithms using symmetric criteria like RMSE or MAE, and then a bias is applied to the forecast later to reflect the asymmetric cost faced by the system operator – a technique we call indirectly biased forecasting. We investigate solar radiation forecasts using asymmetric cost functions (convex piecewise linear (CPWL) and LinEx) and optimize directly in the forecast training stage. We use linear programming and a gradient descent algorithm to find a directly biased solution and compare it with the best indirectly biased solution. We also modify the LMS algorithm according to the cost functions to create an online forecast method. Simulation results show substantial cost savings using these methods.


  • Asymmetric cost functions;
  • Convex piecewise linear cost function;
  • LinEx;
  • Solar radiation forecast;
  • Reserve allocation

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