Short-term reliability and economic evaluation of resilient microgrids under incentive-based demand response programs

•A stochastic bi-level optimization problem is proposed for scheduling of resilient microgrids (MGs).•The proposed stochastic framework handles the prevailing uncertainties of islanding duration, component contingency, market prices and wind generation.•To assess the effect of demand response on the reliability, two new reliability-based indices are defined to compare the MG operation in normal operation and resilient condition.•The impacts of the operator behavior and incentive price factor on economy and reliability indices are investigated via a sensitivity analysis.