Assessing multiple operationally-stable power flow solutions in unbalanced impedance-grounded systems: initialization procedure and analysis

The power flow is usually formulated by nonlinear equations and may present multiple solutions. However, most of these solutions do not represent a practical situation but are mathematical findings. Remarkably, in unbalanced multiphase systems with impedance-grounded loads, a phenomenon can occur where two or more solutions may especially show practical significance. These solutions are called operationally-stable solutions (solutions which for a given loading level the nodal voltages, currents, and losses are feasible) and may be obtained in Distribution Systems (DS). In this paper, some relevant aspects regarding the multiple solutions in unbalanced grounded systems are explored: (i) the development of a simple analytical model considering the feeder and loads to analyze the multiple solutions generically; (ii) a direct procedure for initializing neutral voltages to find possible operationally-stable solutions or reduce the number of iterations to achieve convergence; (iii) a study on multiple solutions using the continuation power flow to analyze their behavior and verify their impacts on DS. The proposed assumptions have been confirmed with numerical experiments over IEEE 123, Simple NEV, and IEEE 8500 test feeders.