The electrical coupling effect on the behavior of the load flow solutions for voltage collapse purposes

This work analyzes the electrical coupling effect on the behavior of the load flow solutions for electrical power systems. Due to the nonlinarities, the load flow equations does not have a unique solution. The normal power system operating point corresponds to the high voltage solution (HVS) of the load flow equations. There is also a set of load flow solutions that present a low voltage level at one or more load buses. These are called the low voltage solutions (LVS). The number of LVS that may exist depends, basically, of dimensions of the power system as well as of its load level. There is a common agreement that the number of LVS decreases as the system is loaded, in such a way that at the voltage collapse point neighborhood, there is only one remaining LVS. In case the load continues to increase, the high voltage solution bifurcates with this last LVS, producing the voltage collapse. This work shows that the existence of a single LVS at the collapse neighborhood may not be always true. It is shown that the existence of weakly coupled buses may cause the existence of more than one LVS at the collapse point neighborhood. The effects of the electrical coupling are initially analyzed for a simple 3-bus test system. As the coupling between the two load buses is reduced, the load flow solutions tends to bifurcate at the same time. Moreover, it is proven for that 3-bus test system, that all the load flow solutions must bifurcate at the same time, if the two load buses are totally uncoupled. Finally, the paper presents some simulations with the 118 buses, showing the existence of more than just one LVS at the voltage collapse neighborhood.