Two alternative robust optimization models for flexible power management of electric vehicles in distribution networks

This paper presents a robust optimization problem of the flexible bidirectional power management of a smart distribution network and harmonic compensation of nonlinear loads using electric vehicles (EVs) equipped with bidirectional chargers. The base deterministic model of the proposed problem is as mixed-integer nonlinear programming (MINLP), having the objective function to minimize the economic and technical indices subject to harmonic load flow equations, EVs constraints, system operation and harmonic indices limits. This model is converted to a mixed-integer linear programming (MILP) model in the next step. In the proposed MILP model, the active, reactive and apparent loads, electrical energy, reactive power and harmonic current prices, as well as EVs characteristics, are considered uncertain parameters. Accordingly, two alternative robust optimization approaches have been implemented for the conditions of having both the probability distribution function or the bounded uncertainty in the proposed MILP problem model. The proposed model is tested on distribution networks to demonstrate its efficiency and performance. The results show that the MINLP model can be substituted by the proposed high-speed MILP model. In addition, the capacity of the injecting power of EVs is reduced in the worst-case scenario with respect to the scenario that is used in the deterministic model, while the consumed power of loads and EVs and energy price increases in this scenario. Finally, the payment of EV owners is reduced by considering EVs power and harmonic control.