  Electric vehicles (EVs) and particularly plug-in hybrid electric vehicles
(PHEVs) are foreseen to become popular in the near future. Not only are they
much more environmentally friendly than conventional internal combustion engine
(ICE) vehicles, their fuel can also be catered from diverse energy sources and
resources. However, they add significant load on the power grid as they become
widespread. The characteristics of this extra load follow the patterns of
people's driving behaviours. In particular, random parameters such as arrival
time and driven distance of the vehicles determine their expected demand
profile from the power grid. In this paper, we first present a model for
uncoordinated charging power demand of PHEVs based on a stochastic process and
accordingly we characterize the EV's expected daily power demand profile. Next,
we adopt different distributions for the EV's charging time following some
available empirical research data in the literature. Simulation results show
that the EV's expected daily power demand profiles obtained under the uniform,
Gaussian with positive support and Rician distributions for charging time are
identical when the first and second order statistics of these distributions are
the same. This gives us useful insights into the long-term planning for
upgrading power systems' infrastructure to accommodate PHEVs. In addition, the
results from this modelling can be incorporated into designing demand response
(DR) algorithms and evaluating the available DR techniques more accurately.
