Linear Approximations to AC Power Flow in Rectangular Coordinates

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

PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations

In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond the traditional DC power flow by capturing reactive power, to convex relaxations, which provide solution quality and runtime performance guarantees. Unfortunately, the sophistication of these emerging methods often presents a significant barrier to evaluating them on a wide variety of power system optimization applications. To address this issue, this work proposes PowerModels, an open-source platform for comparing power flow formulations. From its inception, PowerModels was designed to streamline the process of evaluating different power flow formulations on shared optimization problem specifications. This work provides a brief introduction to the design of PowerModels, validates its implementation, and demonstrates its effectiveness with a proof-of-concept study analyzing five different formulations of the Optimal Power Flow problem