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This paper discusses simple methods for forecasting solar irradiation. We use the zenith angle (the angle between sun beam and perpendicular line on horizontal surface) to remove both seasonal and time of day effects. Then we forecast by using least-squares (LS), time-varying least squares (TVLS), exponentially weighted recursive least squares (EWRLS) and one step estimation of second order statistics. For comparison we also consider a standard method of normalizing data by subtracting mean and dividing by deviation (at that time of day, sixty days moving average) and then applying the same signal processing algorithms. Finally, we compare simulation results for different sites and various time of prediction. Simulation results shows that using zenith angle in signal processing methods improves the performance.

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.

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