Conic optimisation for electric vehicle station smart charging with battery voltage constraints

This paper proposes a new convex optimisation strategy for coordinating electric vehicle charging, which accounts for battery voltage rise, and the associated limits on maximum charging power. Optimisation strategies for coordinating electric vehicle charging commonly neglect the increase in battery voltage which occurs as the battery is charged. However, battery voltage rise is an important consideration, since it imposes limits on the maximum charging power. This is particularly relevant for DC fast charging, where the maximum charging power may be severely limited, even at moderate state of charge levels. First, a reduced order battery circuit model is developed, which retains the nonlinear relationship between state of charge and maximum charging power. Using this model, limits on the battery output voltage and battery charging power are formulated as second-order cone constraints. These constraints are integrated with a linearised power flow model for three-phase unbalanced distribution networks. This provides a new multiperiod optimisation strategy for electric vehicle smart charging. The resulting optimisation is a second-order cone program, and thus can be solved in polynomial time by standard solvers. A receding horizon implementation allows the charging schedule to be updated online, without requiring prior information about when vehicles will arrive