This article proposes a novel stochastic framework based on point estimate method (PEM) and firefly algorithm (FA) for the optimal operation of plug-in electric vehicles (PVs) in the distribution systems. The stochastic problem will consider the uncertainties of active and reactive loads, the number of PVs in the fleets and the departure and arrival time at charging locations. According to the high complexity and severity of the problem, a new version of FA called θ-FA is used to search the solutions in the polar space instead of the traditional Cartesian space. The objective function is to minimize the total cost of the system considering the operation and security constraints. The feasibility and high performance of the propose problem are examined on a standard IEEE test system.
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