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 activeand reactive-power injections.
Assuming complex-valued perturbations around a nominal voltage, LPF can be obtained by neglecting quadratic terms REF .
Linear approximations to AC power flow in rectangular coordinates
2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Computer Science Mathematics