Modeling and Simulation of a Single-Phase Linear Multi-Winding Transformer in the d-q Frame

Exploring the fundamental principles of system modeling in electrical engineering, this study delves into the transformative power of the d-q transformation, highlighting its pivotal role in rendering time-varying systems into a coherent steady-state representation. Departing from conventional approaches, the study carefully navigates the complexities of single-phase transformer configurations, utilizing the Clarke and Park transformations to seamlessly transition between electrical coordinates and the d-q frame. Through extensive derivations, dynamic equations are formulated in both α-β and d-q coordinates, providing a detailed understanding of system dynamics under specific loads. In addition, the study extends the analysis to a generalized multi-winding transformer model that accommodates a wide range of transformer setups. With detailed mathematical derivations, insightful visual aids, and clear state-space representations, this work attempt to be a resource for researchers, engineers, and practitioners seeking to unravel the intricacies of electrical system modeling and analysis.