Saddle-node bifurcation in three-phase unbalanced distribution networks with distributed generators

This paper presents a method to compute the saddle-node bifurcation points (SNB) of distribution networks and verifies the existence of saddle-node bifurcations in 3-phase distribution networks with distributed generators (DGs). Numerical studies were performed on the IEEE 13-bus distribution test feeder and on a practical 1123-nodes distribution system. These numerical results indicate that SNB occurs due to load variation and the penetration of DGs. Physically speaking, the SNB indicates the limitation of power delivery capability of distribution networks in delivering power from DGs and substation to loads.