Scheduling of EV Battery Swapping, I: Centralized Solution
  We formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize total travel distance and generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints and AC power flow equations. To deal with the nonconvexity of power flow equations and the binary nature of station assignments, we propose a solution based on second-order cone programming (SOCP) relaxation of optimal power flow (OPF) and generalized Benders decomposition. When the SOCP relaxation is exact, this approach computes a globally optimal solution. We evaluate the performance of the proposed algorithm through simulations. The algorithm requires global information and is suitable for cases where the distribution network, stations, and EVs are managed centrally by the same operator. In Part II of the paper, we develop distributed solutions for cases where they are operated by different organizations that do not share private information. 
Pengcheng You, Steven H. Low, Wayes Tushar, Guangchao Geng, Chau Yuen,   Zaiyue Yang, Youxian Sun
math.OC