  A key assumption made in this paper is that electric vehicle (EV) battery
charging profiles are rectangular. This requires a specific and new formulation
of the charging problem, involving discrete action sets for the EVs in
particular. The considered cost function comprises of three components: the
distribution transformer aging, the distribution energy losses, and a component
inherent to the EV itself (e.g., the battery charging monetary cost). Charging
start times are determined by the proposed distributed algorithm, whose
analysis is conducted by using game-theoretic tools such as ordinal potential
games. Convergence of the proposed algorithm is shown to be guaranteed for some
important special cases. Remarkably, the performance loss w.r.t. the
centralized solution is shown to be small. Simulations, based on realistic
public data, allow one to gain further insights on the issues of convergence
and optimality loss and provide clear messages about the tradeoff associated
with the presence of the three components in the considered cost function.
While simulations show that the proposed charging policy performs quite
similarly to existing (continuous) charging policies such as
valley-filling-type solutions when the non-EV demand forecast is perfect, they
reveal an additional asset of rectangular profiles in presence of forecasting
errors.
