Asymptotic assessment of distribution voltage profile using a nonlinear ODE model

This paper addresses a problem of assessment of voltage phasors in AC power distribution grids. This problem is motivated by the promising increase of Distributed Energy Resources (DERs) such as Electric Vehicles (EVs) and its impact to the power grids. 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 characterization of solutions of the problem through the standard regular perturbation method. This enables a quantitative and physically interpretable approach to assessing how the introduction of DERs, e.g., charging/discharging of EVs, affects the spatial profile of distribution voltage. Effectiveness of the asymptotic characterization is established with simulations of both simple and practical configurations of the power distribution grid.

Automated summary

This paper addresses the problem of assessing voltage phasors in AC power distribution grids. The authors derive an asymptotic characterization of the solutions through regular perturbation method, enabling a quantitative and physically interpretable approach to assess the impact of DERs on the spatial profile of distribution voltage.