Two-stage optimal scheduling for the microgrid considering uncertainties and user endowment effect in demand response

Demand response (DR) can relieve source-load imbalance in microgrids (MGs), but its practical scheduling value is limited by renewable uncertainty and uncertain user response behavior. This paper proposes a coordinated day-ahead/intraday scheduling framework that combines multi-scenario risk scheduling with fuzzy chance-constrained rolling correction. Specifically, an endowment effect based mechanism is modeled to quantify users’ psychological costs caused by breaking habitual electricity consumption in DR regulation. Differentiated uncertainty handling strategies are adopted across timescales: KDE-Gaussian-copula-based multi-scenario stochastic optimization is used to mitigate long-term source-load stochasticity for risk-aware day-ahead scheduling, while fuzzy chance-constrained rolling optimization addresses short-term forecast deviations for efficient intraday correction. Comparative benchmarks include deterministic, stochastic, CVaR-based, fuzzy chance-constrained, robust, and literature endowment-effect models. Numerical results show that the proposed endowment-effect-based DR model reduces the endowment cost from 14,913.86 to 2,346.73 CNY and limits the DR quantity to 3.33 MW, indicating a lighter and more behaviorally plausible response pattern. Relative to independent KDE/MC sampling, the KDE-Gaussian-copula scenario generator reduces autocorrelation RMSE, cross-correlation RMSE, and ramp-rate Wasserstein distance by 67.6%, 43.1%, and 69.8%, respectively; relative to the Gaussian-copula-normal baseline, it reduces Wasserstein and extreme-quantile errors by 53.1% and 34.4%. Intraday comparisons further show that the proposed hybrid framework reduces online computation time by 84.39% compared with the unified multi-scenario model. Compared with the unified fuzzy model, it increases intraday revenue by 642.35 CNY and reduces DR curtailment by 0.4841 MW. These results indicate that the proposed framework improves the balance among revenue, risk exposure, user-side behavioral cost, real-time tractability, renewable utilization, and computational burden.