# Linear Approximations to AC Power Flow in Rectangular Coordinates

arXiv: https://arxiv.org/abs/1512.06903 · HTML: https://mlsanity.com/paper/1512.06903/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2015.

## Built on by (most cited first, 2 of 2)

- [Realistic Differentially-Private Transmission Power Flow Data Release](https://mlsanity.com/paper/2103.14036/) (2021)
- [AC Power Flow Contingency Analysis Using a Single Deep Neural Network](https://mlsanity.com/paper/2609.30859/) (2026)

## Abstract (arXiv)

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.