Synthesis of Spatial Charging/Discharging Patterns of In-Vehicle Batteries for Provision of Ancillary Service and Mitigation of Voltage Impact

We develop an algorithm for synthesizing a spatial pattern of charging/discharging operations of in-vehicle batteries for provision of ancillary service (AS) in power distribution grids. The algorithm is based on the ordinary differential equation (ODE) model of the distribution voltage that has been recently introduced. In this paper, first, 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 electric vehicle (EV) charging/discharging to the distribution voltage. Second, based on the analytical solutions, we propose an algorithm for determining the values of charging/discharging power (active and reactive) by in-vehicle batteries in the single feeder grid, so that the power demanded as AS (e.g., a regulation signal to the distribution system operator for the primary frequency control reserve) is provided by EVs, and the deviation of the distribution voltage from a nominal value is reduced in the grid. Effectiveness of the algorithm is established with numerical simulations on the single feeder grid and on a realistic feeder grid with multiple bifurcations.