Stochastic two-stage coordination of electric vehicles in distribution networks: A multi-follower bi-level approach

As the number of electric vehicles (EVs) continues to rise, it is essential to consider appropriate management strategies for coordinating EVs connected to different buses in the power networks. In light of this, this paper proposes a stochastic two-stage bi-level model for coordinating EVs in a distribution network with charging stations under alternating current optimal power flow (ACOPF) constraints. The scheduling problem is considered to independently minimize the costs of the distribution system operator (DSO) and EVs parked at different charging stations located at various buses of the network. In the proposed model, the DSO as the leader, and all EVs as independent followers, are individual entities who try to follow their priorities and objectives. The amount and price of exchanged power between the DSO and EVs are optimally determined in the proposed model. The proposed bi-level model has been converted to a single-level model using the Karush- Kuhn-Tucker (KKT) conditions. Afterwards, the Big M method is used to convert the non-linear equations that appear due to utilizing the KKT approach. The scenario-based uncertainty modeling is used to model the uncertainty in input data such as day-ahead and real-time market prices, EVs' initial state of charge (SOC), and arrival/departure time. The centralized unilateral form of the model has also been developed to validate the proposed model. The results indicate that the bi-level model can lead to cost reduction for the EVs.