A stochastic short-term scheduling of virtual power plants with electric vehicles under competitive markets

This paper presents a risk-averse stochastic framework for short-term scheduling of virtual power plants (VPPs) in a competitive environment considering the potential of activating electric vehicles (EVs) and smart buildings in demand response (DR) programs. In this framework, a number of EV Parking Lots (PLs) which are under the jurisdiction of the VPP and its rivals are considered that compete to attract EVs through competitive offering strategies. On the other hand, EVs' owners try to choose a cheaper PL for EVs' charging to reduce payment costs. Therefore, the objective of EVs owners can be in conflict with the objective of PLs that provide services for EVs under each VPP. In this regard, the decision-making problem from the VPP's viewpoint should be formulated as a bi-level optimization model, in which in the upper-level, the VPP profit should be maximized and in the lower-level, procurement costs of EVs and other responsive loads should be minimized, simultaneously. To solve the proposed bi-level problem, it is transformed into a traceable mixed-integer linear programming (MILP) problem using duality theory and Karush-Kahn-Tucker (KKT) optimality conditions. The proposed model is tested on a practical system and several sensitivity analyses are carried out to confirm the capability of the proposed bi-level decision-making framework.