A modified Benders decomposition-robust optimization approach for retailers using game theory considering demand response program

In recent decades, the restructuring of the electricity industry has been implemented in many countries around the world. This has led to the emergence of multiple markets for buying and selling electricity and ancillary services, giving rise to new institutions to manage these processes. One of these entities is electricity retailer, responsible for supplying electric energy to residential, commercial, and small industrial consumers through bilateral contracts and electricity forward markets. Naturally, retailers face uncertainties in purchasing electricity from various markets, particularly in short-term markets, which they need to consider. In addition, the load forecasting of consumers is also subject to uncertainty. Robust optimization (RO) is an efficient approach that deals with the uncertainty in such conditions. This paper examines the optimal strategy for electricity retailers considering uncertainty in day-ahead market prices and load of consumers using robust optimization. Robust optimization serves as a powerful and analytical tool to manage retailer’s decision-making problem concerning purchases from different contracts. Additionally, this study addresses demand response program implementation and modeling, focusing on the electricity purchase issue for retailers. The results demonstrate an increase in retailers’ profits of $14.8, $294.5, and $391.7, respectively, as well as a reduction in peak-hour loads of 7.1%, 8.43%, and 9.57%, which are shifted to off-peak hours, thereby flattening the load curve. Moreover, it explores short-term cooperation among retailers via cooperative games to supply consumers with lower costs. This short-term cooperation has increased retailers’ profit. After solving the problem considering load uncertainties, applying demand response programs, and incorporating cooperation among retailers, the profit increment for retailers 1 to 3 has been calculated as $271.6, $500.8, and $447.2, respectively, with the profit allocation determined through Shapley value assessment.