  In Part I of this paper 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 a weighted sum of 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. We propose there a centralized solution based on the second-order
cone programming (SOCP) relaxation of optimal power flow (OPF) and generalized
Benders decomposition that is suitable when global information is available. In
this paper we propose two distributed solutions based on the alternating
direction method of multipliers (ADMM) and dual decomposition respectively that
are suitable for cases where the distribution grid, battery stations and EVs
are managed by separate entities. Our algorithms allow these entities to make
individual decisions but coordinate through privacy-preserving information
exchanges to jointly solve an approximate version of the joint battery swapping
scheduling and OPF problem. We evaluate our algorithms through simulations.
