Linear Approximations to AC Power Flow in Rectangular Coordinates
For power system engineers, this provides a more accurate linear power flow approximation that includes ZIP loads, improving upon the widely used DC power flow.
This paper develops linear approximations to AC power flow in rectangular coordinates by neglecting quadratic terms, proving that for lossless networks the resulting voltage profile satisfies active-power balance. The method improves over DC power flow by including ZIP loads, achieving a linear relationship between voltage and load components in distribution networks.
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.