An Approach to Determine a Pair of Power-Flow Solutions Related to the Voltage Stability of Unbalanced Three-Phase Networks

This paper proposes an approach to determine a pair of power-flow solutions associated with the voltage stability of unbalanced three-phase networks. The approach is derived from the observations of the multiple three-phase power-flow solutions of a two-bus network. It is found that there are two pairs of solutions at the load bus. The plot of the voltage magnitude of each pair against the power demand at the load bus shows that two possible PV curves can be constructed for each phase. Each of the two curves is a combination of the two pairs of solutions. One of these curves is associated with the voltage stability of the system whereas the other is associated with the imbalance of the three-phase network. Based on the above observations, a constant impedance load model is utilized to calculate the solution associated with the voltage stability of the study system. Then the equivalent complex power load demand is used to calculate the two pairs of solutions, i.e., the multiple three-phase power-flow solutions. Simulation studies have been carried out for the multiple solutions. The results show that there is a point which is directly proportional to the imbalance in the power demand at the load bus. This point is used to set a criterion to differentiate between the two PV curves. Hence, the PV curve which is related to the voltage stability can be determined without the assumption of the linear load model at the start of the study.