Caputo derivative applied to very short time photovoltaic power forecasting

Intra-hour photovoltaic power forecasting provides essential information for real time optimal control of microgrids. At this purpose, a critical issue is the selection of the forecasting method. The choice of a forecasting method depends on many factors such as the availability of historical data, the time horizon, the lag period, and the time available for the forecast. Persistence based methods are particularly tailored for real time forecasting which require fast information and are typically a good trade-off choice when dealing with real time operation of microgrids. Their accuracy, however, could be not satisfactory in some cases such as when it appears critical to consider the trend of the power output in the last few minutes rather than only the last measured value. Derivatives help reach this goal, but fractional derivatives seem to be a more accurate choice in order to take into account the history of the variable to be forecasted as they are a promising tool for describing memory phenomena. In this paper, a novel intra-hour forecasting method is proposed based on the Caputo derivative. Numerical applications are carried out to show the efficacy of the proposed approach. Also, the accuracy of the proposed approach is tested through comparison with three models namely, persistence, derivative-persistence and auto regressive moving average models. The strength of the proposed forecasting tool is strictly related to its low computational burden without compromising accuracy. This makes of it an interesting means for real time grid operation strategies and can be of interest for the grid operators especially in vision of the changes distribution grids are witnessing with the transition to the smart grid paradigm.