Resiliency-oriented optimal scheduling of microgrids in the presence of demand response programs using a hybrid stochastic-robust optimization approach

•Hybrid optimization approach is considered for normal and resilient operation of MG.•Modeling the risk-based operation of MG in the normal and resilient operation modes.•Modeling the different demand response programs for risk-based operation of microgrid in the normal and resilient operation modes.•Proposing a linear model of the AC power flow and used in the proposed resilient oriented framework. Natural incidents with a low occurrence probability and high impacts like windstorms and earthquakes, threaten the optimal operation of the distribution networks. Hence, some operational solutions are required to improve network resiliency. Microgrids (MGs) provide a proper solution for the resiliency enhancement of distribution networks to reach the optimal resilient operation under such incidents. Also, the inherent uncertainties make the resilience-oriented optimal operation of MGs more critical and should be modelled by efficient uncertainty modelling tools. In this paper, a hybrid stochastic-robust optimization (HSRO) approach is used to get the optimal scheduling of an MG under normal and resilient operation mode. The impact of the upstream grid price uncertainty on the optimal scheduling of MGs is modelled using the robust optimization approach. Other dominant uncertainties, including the wind power, photovoltaic (PV) power, and active/reactive electrical loads, are also modelled by stochastic optimization via generating a set of relevant scenarios. In addition, adjustable and interruptible demand response programs (DRP) are implemented to improve the resilient operation of MG under incidents. The proposed approach tries to improve the MG operation under uncertainties during the resilience and normal mode of network. Furthermore, this paper concentrates on the robust and normal strategies adopted for the resilience-oriented scheduling of MGs. The effectiveness of the proposed framework is evaluated through a large-scale MG test system.