An optimal control approach for EV charging with distribution grid ageing

In smart grids, the expected increase of electrical vehicle (EV) penetration will impose sizeable charging load, which can critically overburden the distribution network (DN) if the delivered power is non-pragmatically aggregated and induce significant impacts on various important existing grid assets. Among them, the residential distribution transformer is considered as one of the most important components in the grid. The ageing of the transformer is closely related to the temporal evolution of the hot-spot temperature (HST), which is induced by the operating load level history. We propose an optimal control approach to obtain a new EV charging algorithm: the novel aspect of this algorithm is that it takes inertial behavior of HST into account, which is the key parameter to capture the ageing. Though our formulation closely resembles to the linear quadratic control problem that includes costs induced from the state of the transformer and its present charging load, the natural constraints which are imposed to the instantaneous charging level (saturation constraints) induces intricate complicacy for the analytical solution. Thus, we follow the Pontryagin maximum principle approach to obtain the optimal charging policy and resort to numerical methods to compute the optimal charging trajectory. Numerical results allow us to evaluate and compare the performance of the proposed algorithm with various existing benchmark charging policies.