Asymptotic Assessment of Distribution Voltage Profile Using a Nonlinear ODE Model

TL;DR

This paper develops an asymptotic method based on nonlinear ODEs to evaluate how electric vehicle charging impacts the voltage profile along power distribution feeders, providing a rigorous analytical tool.

Contribution

It introduces a mathematically rigorous asymptotic approach to analyze the nonlinear ODE model for distribution voltage profiles affected by EVs.

Findings

Asymptotic characterization accurately predicts voltage profile changes.

Method validated through simulations of simple and practical grid configurations.

Provides a quantitative tool for impact assessment of EV charging on distribution grids.

Abstract

The promising increase of Electric Vehicles (EVs) in our society poses a challenging problem on the impact assessment of their charging/discharging to power distribution grids. This paper addresses the assessment problem in a framework of nonlinear differential equations. Specifically, we address the nonlinear ODE (Ordinary Differential Equation) model for representing the spatial profile of voltage phasor along a distribution feeder, which has been recently introduced in literature. The assessment problem is then formulated as a two-point boundary value problem of the nonlinear ODE model. In this paper we derive an asymptotic charcterisation of solutions of the problem through the standard regular perturbation method. This provides a mathematically-rigor and quantitative method for assessing how the charging/discharging of EVs affects the spatial profile of distribution voltage. Effectiveness of the asymptotic charcterisation is established with simulations of both simple and practical configurations of the power distribution grid.