Linear Power-Flow Formulation Based on a Voltage-Dependent Load Model

Abstract

The power-flow (PF) solution is a fundamental tool in power system analysis. Standard PF formulations are based on the solution of a system of nonlinear equations which are computationally expensive due to the iterations needed. On the other hand, distribution-system (DS) automation algorithms should be fast enough to meet real-time performance. The conventional load representation, as constant <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Q$</tex></formula> , becomes less accurate as we get closer to the actual load's level. In this paper, a new load model is proposed which represents the loads' voltage dependency. A simple curve-fitting technique is used to derive a voltage-dependent load model which splits the load as a combination of an impedance and a current source. With this representation and some numerical approximations on the imaginary part of the nodal voltages, it is possible to formulate the load-flow problem as a linear power-flow (LPF) solution which does not require iterations. The approximation has been tested in systems up to 3000 nodes with excellent results. The LPF formulation is particularly important in the context of optimization algorithms for automated smart distribution systems. The extension of the technique to unbalanced distribution systems will be presented in future work.