Three-Phase Modeling for Transient Stability of Large Scale Unbalanced Distribution Systems

The transient stability of a distribution system containing rotating machines is usually evaluated by considering a symmetrical disturbance applied to a balanced network. Hence, most, if not all, available algorithms and stability programs use the bus admittance matrix for the positive sequence only. However, a typical distribution system may contain untransposed feeders, single-and/or three-phase unbalanced static shunt loads, single-and/or three-phase dynamic loads (such as induction motors), co-generators, transformers and capacitor banks. Furthermore, even if the network is balanced, unsymmetrical faults introduce unbalance. The effects of unbalances on the transient behavior of a single induction motor in a two-bus system using simultaneous nodal voltage equations has been recently investigated. It was concluded that a significant error may occur by replacing an unbalanced shunt load by an averaged balanced load and by assuming an unbalanced feeder to be an equivalent balanced feeder. This paper extends the previous investigation to large scale networks using a generalized three-phase bus admittance matrix [Ybus] method which takes care of the unbalances referred to above. Developing the three-phase [Ybus] itself is not new, but the novelty of the proposed method lies in the combination of the three-phase [Ybus] with the dynamics of rotating machines in transient stability studies of large networks using step-by-step integration of nonlinear differential equations. The method utilizes phase frame representation of network and machine elements. In order to be general, the computer program allows the user to include synchronous generators, induction motors, transformers, feeders and static loads.