Advanced Dynamic Phasor-Based Modeling and Load-Flow Analysis of Unsymmetrical Two-Phase Induction Machines

This paper presents a dynamic phasor-based modeling approach for unsymmetrical two-phase induction machines, deriving steady-state equations to support initialization and load-flow simulations. The machine formulation reveals coupling between positive and negative sequence components and exhibits stronger nonlinearity compared to the Electromagnetic Transient (EMT) models. The resulting differential equations are discretized using the trapezoidal integration method with critical damping adjustment (CDA) to provide a stable numerical solution. A companion circuit is then constructed using the Modified Augmented Nodal Analysis (MANA). An iterative solution is applied to obtain accurate results. The proposed method is implemented in C++, and both transient and load-flow simulations are validated on the IEEE 13-Bus test system using EMTP®. Results demonstrate high accuracy and robust numerical solutions.