Summary In this paper, a stochastic model for scheduling of AC security‐constrained unit commitment associated with demand response (DR) actions is developed in an islanded residential microgrid. The proposed model maximizes the expected profit of microgrid operator and minimizes the total customers' payments for electricity consumption under load and renewable energy sources uncertainties. In this regard, a stochastic dispatch model for responsive load is developed in order to investigate the effect of price‐based DR programs in a microgrid environment. In this scheme, customers are able to participate in real‐time price program with shifting and curtailing their responsive loads. A multi‐segment AC‐optimal power flow, which allows the voltage and reactive power to be considered directly, is also used to study the effects of DR participation on microgrid operation. The proposed AC security‐constrained unit commitment and DR scheduling problem is modeled as a mixed‐integer programming problem and is solved using the CPLEX solver in the general algebraic modeling system.