Joint Probability Distribution and Correlation Analysis of Wind and Solar Power Forecast Errors in the Western Interconnection

Abstract

Wind and solar power generation differ from conventional power generation because of the variable and uncertain nature of their power output. This can have significant impacts on grid operations. Short-term forecasting of wind and solar power generation is uniquely helpful for planning the balance of supply and demand in the electric power system because it allows for a reduction in the uncertainty associated with their output. As a step toward assessing the simultaneous integration of large amounts of wind and solar power, this article investigates the spatial and temporal correlation between wind and solar power forecast errors. The forecast and actual data analyzed are obtained from one of the world’s largest regional variable generation integration studies to date. Multiple spatial and temporal scales (day ahead, 4 h ahead, and 1 h ahead) of forecast errors for the Western Interconnection in the United States are analyzed. A joint probability distribution of wind and solar power forecast errors is estimated using kernel density estimation. The Pearson’s correlation coefficient and mutual information between wind and solar power forecast errors are also evaluated. The results show that wind and solar power forecast errors are inversely correlated, and the correlation between wind and solar power forecast errors becomes stronger as the geographic size of the analyzed region increases. The absolute value of the correlation coefficient is generally less than 0.1 in the case of small geographic regions, while it is generally between 0.15 and 0.6 in the case of large geographic regions. The forecast errors are less correlated on the day-ahead timescale, which influences economic operations more than reliability, and more correlated on the 4-h-ahead timescale, where reliability is more impacted by the forecasts. It is also found that the correlation between wind and solar power forecast errors in summer (July) is relatively stronger than in winter (January). The inverse correlation implies that in systems with high penetrations of both wind and solar power, reserves that are held to accommodate the variability of wind or solar power can be at least partially shared. In addition, interesting results are found through time and seasonal variation analyses of wind and solar power forecast errors, and these insights may be uniquely useful to operators who maintain the reliability of the electric power system.