Discontinuities and unstable solutions beyond the maximum load point of nonlinear unbalanced distribution systems

Abstract

• Discontinuities in the PV curves are inherent to the power flow formulation of distribution systems. • Discontinuities may change the operational point between two or more PV curves. • Defining if the maximum loading point is not part of a fully unstable curve is challenging. • A false maximum loading point may be used inappropriately when analyzing multiphase distribution systems. • Discontinuities may occur around the loading level that is related to when the eigenvalues of multiple Jacobians are on the same attraction area. Distribution feeders are usually modeled by a set of nonlinear equations that likely leads to multiple solutions on power flow tools if an adequate nonlinear mathematical model for multi-grounded unbalanced feeders is considered. Specifically, this work presents a study about these solutions through the analysis of PV curves obtained by using the multiphase continuation power flow tool. Herein, the paper discloses discontinuities on the PV curves, which are related to the occurrence of multiple Jacobians with several eigenvalues on the same attraction area. The results revealed the possibility of unstable solutions presenting greater maximum loading levels (around 29.5% higher) than the stable solution. Moreover, a power factor variation study has also indicated that unstable solutions might occur for a broad range of reactive power values. Finally, it is shown that, in some distribution systems, the maximum loading point found is not a global one and, most importantly, stable curves can be confused with unstable ones, leading users and researchers to wrong conclusions in their studies.