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This paper proposes two parametric probabilistic forecast methods using beta and two-sided power distributions to predict solar irradiance. It also evaluates their performance. To improve their performance metrics a hybrid procedure based on the beta transformed linear opinion pool is utilized. Our simulations show that these methods – despite their simple structure – can effectively forecast solar irradiance and accurately describe its stochastic characteristics. The proposed approach is flexible and could be extended to many different point forecast methods which otherwise minimize RMSE or MSE. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]