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 ODE (Ordinary Differential Equation) model of distribution voltage 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. 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 distribution system operator for primary frequency control reserve) is provided by EVs, and the deviation of 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. following a change of frequency is in the ranges of two to three seconds, which is sufficient as the requirement of primary reserve listed in [5]. Regarding this, in this paper we will propose a computationally simple method for determining the values of charging/discharging power by in-vehicle batteries in order to satisfy the power demanded as AS.There are several problems on the provision of AS by EVs. One problem is to manage the impact of charging/discharging of a large number of EVs to a distribution grid. An EV is regarded as an autonomously moving battery in the spatial domain and can conduct the charging and discharging (in principle) anywhere in the grid. Thus, to maintain the nominal distribution voltage while providing the AS by EVs is a challenging subject. In fact, Clement-Nyns et al. [10,11] study the impact of EV charging to the distribution grid using the load-flow analysis and propose optimization-based methods for determining the timing and amount of charging power in order to reduce the voltage deviation. Also, Falahi et al.[12] study the control of reactive power by grid-connected inverters of in-vehicle batteries for the voltage regulation and propose an optimization-based method for determining the reactive power injected to a grid from EVs in order to reduce the voltage deviation.Currently, we are developing methodology and tools for provision of AS under cooperation with an EV-sharing system, as a part of the research project "Integrated Design of Local EMSs 1 and their Aggregation Scenario Considering Energy Consumption Behaviors and Cooperative Use of Decentralized In-Vehicle Batteries [13]." An EV-sharing system has a function of tracking trajectories of EVs to allocate them upon user's request [14,15]. The authors of [16] propose to use the function of EV-sharing system for community-level energy management. This work opens a new possibility ...
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