Probabilistic, robust, and fuzzy wind uncertainty in multistage incentive-based demand response: A novel Stackelberg particle swarm optimization

The increasing wind energy penetration in competitive electricity markets requires demand-side mechanisms that are capable of mitigating renewable uncertainty without compromising economic efficiency or reliability. To address this, a novel Incentive-Based DR (IBDR) approach is proposed to assess the effects of three wind uncertainty models: probabilistic, robust, and fuzzy, on Locational Marginal Prices (LMPs), demand reduction, generation cost, customer profit, and Load Serving Entity (LSE) profit. A hierarchical Stackelberg Game structure is developed to capture market interactions among Independent System Operators (ISOs), LSEs, and consumers, accounting for wind uncertainty. Stackelberg Particle Swarm Optimization (SPSO) is used to reduce the problem’s complexity and achieve equilibrium among all participants. The methodology is tested on the PJM 5-bus system and, to ensure scalability, on the IEEE 118-bus system. Results demonstrate that the probabilistic model performs best, achieving a 29 MW reduction in peak demand, lowering LMPs by 10%-12%, and increasing LSE revenue by 22%. The robust model offered enhanced reliability with a 15% increase in benefits, while the fuzzy model provides a balanced alternative. The proposed SPSO-based structure allows ISO/RTOs to balance cost and operational robustness by supporting probabilistic approaches in competitive markets and robust or fuzzy methods in conservative or data-limited markets. To assess performance, the Monte Carlo (MC) validation approach is used. Various statistical performance measures, such as mean, Standard Deviation (SD), Coefficient of Variation (CV), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE), have been used for performance evaluation and robustness testing. Results show that properly selecting a wind-uncertainty modeling approach is essential, depending on the system’s needs. A demand-side sensitivity analysis further confirms that the comparative model performance remains consistent under demand variation.