In this paper, a decision-making framework is proposed for a virtual power plant (VPP) to participate in day-ahead (DA) and regulating market (RM) considering internal demand response (IDR) flexibility. In the proposed model, a DR exchange market (DRXM) is also introduced to cover deviations of uncertain resources and decrease VPP's imbalance penalties in the RM. The VPP can optimize its procurement expenditures by providing DR services from both IDR providers and DRXM. A market inefficiency index (MII) is defined to analyze the effect of trading energy in the DRXM on the market power of the VPP. The proposed model is formulated as a bi-level problem, in which at the upper level, the VPP maximizes its profit while at the lower level, the distribution system operator (DSO) strives to clear both DA and RM markets to maximize social welfare. The proposed problem is nonlinear and converted into a linear single-level problem through Karush-Kuhn-Tucker (KKT) optimality conditions and duality theory. The simulation results show that in high external demand response (EDR) participants, the expected profit of the VPP augments about 3% which is a substantial value for the one-day scheduling horizon. Furthermore, by providing EDR services, MII reduces which implies the EDRs preserve their economic surplus.
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