Mathematical Modelling of Three Phase Four Leg Converters in Quaternion Space

Typically, AC-DC converters are modeled in two-dimensional space using the dq-coordinates, assuming they are supplied by a balanced three-phase system. However, this space vector model struggles to accurately represent converter behavior under unbalanced conditions. This paper presents the development of a mathematical model for a four-leg converter in quaternion space, offering a higher-dimensional model that captures converter behavior under both balanced and unbalanced input voltage conditions. To validate the proposed model, simulations were conducted, and the results confirm its accuracy.