  The main objective of this paper is to design electric vehicle (EV) charging
policies which minimize the impact of charging on the electricity distribution
network (DN). More precisely, the considered cost function results from a
linear combination of two parts: a cost with memory and a memoryless cost. In
this paper, the first component is identified to be the transformer ageing
while the second one corresponds to distribution Joule losses. First, we
formulate the problem as a non-trivial discrete-time optimal control problem
with finite time horizon. It is non-trivial because of the presence of
saturation constraints and a non-quadratic cost. It turns out that the system
state, which is the transformer hot-spot (HS) temperature here, can be
expressed as a function of the sequence of control variables; the cost function
is then seen to be convex in the control for typical values for the model
parameters. The problem of interest thus becomes a standard optimization
problem. While the corresponding problem can be solved by using available
numerical routines, three distributed charging policies are provided. The
motivation is threefold: to decrease the computational complexity; to model the
important scenario where the charging profile is chosen by the EV itself; to
circumvent the allocation problem which arises with the proposed formulation.
Remarkably, the performance loss induced by decentralization is verified to be
small through simulations. Numerical results show the importance of the choice
of the charging policies. For instance, the gain in terms of transformer
lifetime can be very significant when implementing advanced charging policies
instead of plug-and-charge policies. The impact of the accuracy of the non-EV
demand forecasting is equally assessed.
