On the existence and uniqueness of load flow solution for radial distribution power networks

On the basis of voltage level, an electric power system can be viewed as consisting of a generation system, a transmission system, and a distribution system. The steady-state operation of a power system requires that the power supply, transmission losses, and load demand be balanced, as described by the load flow equations. The configuration of a transmission network is that of a loop while the configuration of a distributed network is radial. It is well recognized that the number of load flow solutions for transmission networks, if they exist, are multiple. In contrast, it is shown here that a load flow solution with feasible voltage magnitude for radial distribution networks always exists and is unique. These results demonstrate the weak ability of radial distribution networks to meet load demands in the sense that different patterns of load demand require different power supply from the substation.>