Linear Approximations to AC Power Flow in Rectangular Coordinates

TL;DR

This paper introduces a linear approximation method for AC power flow in rectangular coordinates, improving upon traditional DC models by including ZIP loads and providing better accuracy for distribution networks.

Contribution

It develops a linearized power flow model in rectangular coordinates that accounts for ZIP loads and active-power balance, offering a more accurate approximation than conventional DC methods.

Findings

For lossless networks, the voltage profile with suppressed real perturbation satisfies active-power balance.

The model provides a linear relationship between voltage and load components in distribution networks.

The approach improves power flow approximation accuracy over traditional DC methods.

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.