On the relationship between multiple power-flow solutions and the voltage stability problem in unbalanced three-phase networks

This paper investigates the relationship between the multiple power-flow solutions and the voltage stability of unbalanced networks. An analysis of an unbalanced two bus network shows that a pair of solutions for the voltage at the neutral point exists at the neutral node. This is two pair of solutions for the terminal voltages at the load bus. One of the interesting findings is that two possible nose curves or PV curves can be constructed for each phase. Each of these curves is a combination of the multiple solutions. Simulation studies have been carried out for the multiple solutions using two-bus network model. Firstly, a constant impedance load model has been utilized to calculate the solution associated with the voltage stability of the study system. Then, its equivalent complex power load is used to calculate the multiple power-flow solutions. The results show that there is a unique point which is directly proportional to the imbalance in the power demand at the load bus. This point is the key to construct the two PV curves. It is used to set a criterion to differentiate between the two PV curves and hence to find out the PV curve related to the voltage stability problem.