We develop a novel decentralized charging control of large populations of plug-in electric vehicles (PEVs) with the so-called Nash certainty equivalence principle (or mean field games) proposed by Huang et. al.
We are concerned with a situation that PEV agents are rational and weakly coupled via their charging operation costs. At an established Nash equilibrium, each of PEV agents reacts optimally with respect to the average charging strategy of the rest of mass PEV agents. The average charging strategies can be approximated by an infinite population limit which is the solution of a particular fixed point problem.
Under certain mild conditions, we show that there exists a unique Nash equilibrium which is a collection of nearly 'valley-fill' charging controls; moreover we specify a sufficient condition under which the system converges to unique Nash equilibrium. The results are demonstrated by numerical examples.
The work is in the context of deterministic and non-stationary finite-horizon control problems.