An ODE-Based design of spatial charging/discharging patterns of in-vehicle batteries for provision of ancillary service

We develop a framework for designing a spatial pattern of charging/discharging operations of in-vehicle batteries for provision of Ancillary Service (AS) in a rudimentary power distribution grid. The method is based on the ODE (Ordinary Differential Equation) model of distribution voltage profile that has been recently introduced. In this paper, firstly, we derive analytical solutions of the ODE model for a single straight-line feeder through a partial linearization, thereby providing a physical insight to the impact of spatial EV charging/discharging to the distribution voltage profile. Second, based on the analytical solutions, we propose an algorithm for determining values of charging/discharging power by in-vehicle batteries in the single feeder grid, so that power demanded as AS (e.g. regulation signal for primary and secondary frequency controls) is provided by EVs, and the deviation of distribution voltage from a nominal value is reduced in the grid. Effectiveness of the analytical solution and algorithm is established with numerical simulations.