English

Linear Approximations to AC Power Flow in Rectangular Coordinates

Systems and Control 2015-12-23 v1

Abstract

This paper explores solutions to linearized powerflow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active and reactive-power injections.

Keywords

Cite

@article{arxiv.1512.06903,
  title  = {Linear Approximations to AC Power Flow in Rectangular Coordinates},
  author = {Sairaj V. Dhople and Swaroop S. Guggilam and Yu Christine Chen},
  journal= {arXiv preprint arXiv:1512.06903},
  year   = {2015}
}
R2 v1 2026-06-22T12:15:30.770Z