Initialization of unbalanced radial distribution systems for small signal stability analysis

This paper investigates the application of sweeping method in initializing the state variables of an unbalanced radial distribution system for small signal analysis. The unbalance is caused by a single-phase PV system. The system is composed of a three-phase induction machine (IM), a single-phase PV, a load, and a power factor correction (PFC) unit. The IM is modeled in positive-, negative-, and zero- sequence dynamic phasors and then converted into in a abc dynamic phasors frame. The PV, load and PFC and radial network are all modeled in phase-based dynamic phasors. The sweeping method along with embedded Newton-Raphson iterations is implemented to find the equilibrium point for initialization. The iterative procedures are illustrated and demonstrated by case studies. A dynamic simulation case study is also presented.