  Due to their large power draws and increasing adoption rates, electric
vehicles (EVs) will become a significant challenge for electric distribution
grids. However, with proper charging control strategies, the challenge can be
mitigated without the need for expensive grid reinforcements. This manuscript
presents and analyzes new distributed charging control methods to coordinate EV
charging under nonlinear transformer temperature ratings. Specifically, we
assess the trade-offs between required data communications, computational
efficiency, and optimality guarantees for different control strategies based on
a convex relaxation of the underlying nonlinear transformer temperature
dynamics. Classical distributed control methods such as those based on dual
decomposition and alternating direction method of multipliers (ADMM) are
compared against the new Augmented Lagrangian-based Alternating Direction
Inexact Newton (ALADIN) method and a novel low-information, look-ahead version
of packetized energy management (PEM). These algorithms are implemented and
analyzed for two case studies on residential and commercial EV fleets.
Simulation results validate the new methods and provide insights into key
trade-offs.
