  Electric vehicles (EVs) offer an attractive long-term solution to reduce the
dependence on fossil fuel and greenhouse gas emission. However, a fleet of EVs
with different EV battery charging rate constraints, that is distributed across
a smart power grid network requires a coordinated charging schedule to minimize
the power generation and EV charging costs. In this paper, we study a joint
optimal power flow (OPF) and EV charging problem that augments the OPF problem
with charging EVs over time. While the OPF problem is generally nonconvex and
nonsmooth, it is shown recently that the OPF problem can be solved optimally
for most practical power networks using its convex dual problem. Building on
this zero duality gap result, we study a nested optimization approach to
decompose the joint OPF and EV charging problem. We characterize the optimal
offline EV charging schedule to be a valley-filling profile, which allows us to
develop an optimal offline algorithm with computational complexity that is
significantly lower than centralized interior point solvers. Furthermore, we
propose a decentralized online algorithm that dynamically tracks the
valley-filling profile. Our algorithms are evaluated on the IEEE 14 bus system,
and the simulations show that the online algorithm performs almost near
optimality ($<1%$ relative difference from the offline optimal solution) under
different settings.

Networking and Internet Architecture