This paper introduces a two-stage two-level optimization method for optimal day-ahead and real-time scheduling of multicarrier energy distribution systems and microgrids. The model considers the incentive-based and price-based demand response programs to encourage microgrids to transact electrical, heating, and cooling energy carriers with the energy distribution system, which is named hereafter as the energy system. Further, the model formulates the resilient operation of the energy system considering the energy transactions with the electrical, heating, and cooling markets. The main contribution of this paper is the integration of demand response procedures of microgrids in energy transactions with the energy system considering the switching of electrical switches and heating and cooling control valves. The optimization process is another contribution of this paper that is decomposed into two stages that consist of day-ahead and real-time horizons. The first stage is also decomposed into two levels that determine the optimal scheduling of the energy system and microgrids in day-ahead markets. The second stage is comprised of two levels that commit the energy system and microgrids resources. A resiliency index is proposed to assess the resiliency of the energy system in shock conditions. The proposed method was simulated for the 123-bus test system. Different types of microgrids, incentive-based and price-based demand response processes were considered. Simulation results confirmed that the proposed method can reduce the costs of residential, industrial, and commercial microgrids by about 4.47%, 3.88%, and 5.47% concerning only the real-time pricing process. Further, the model can increase the aggregated benefits of the energy system in the day-ahead and real-time markets by about 0.608 Million Monetary Units (MMUs) and 1.10 MMUs, respectively.
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