Probability Density Forecasting of Electricity Price Difference in the Spot Market

Probabilistic electricity price forecasting (EPF) is crucial for optimizing decision-making in modern electricity markets. However, most studies focus on forecasting individual market prices, such as day-ahead (DA) or real-time (RT) prices, while neglecting the importance of price difference forecasting in identifying arbitrage opportunities. The strong correlation between DA and RT prices can significantly amplify probabilistic forecasting errors if not properly accounted for. To address the above issue, a novel price difference probabilistic forecasting framework based on joint probability density modeling and numerical integral solutions is proposed. First, the skewed deep auto-regressive recurrent neural network (skewed DeepAR) is proposed to separately forecast the probability densities of DA and RT prices with the consideration of both skewness and kurtosis characteristics. Sklar’s theorem is then applied to model the joint probability density function. Second, we derive the integral relationship between the price difference’s probability density and the joint probability densities of DA and RT prices. Finally, a numerical conditional density projection method is proposed to efficiently project the joint probability density onto the price difference space, offering a flexible approach to calculating complex integrations. Case studies based on PJM electricity market data demonstrate the effectiveness of the proposed method, achieving at least a 10.15% improvement in the overall performance of probabilistic forecasting.