Frequency-Domain Modeling and Integrated Power Decoupling of the Cross-Coupled Powers in MAB Converters Using a Full-Order Impedance Matrix

The multi-active bridge (MAB) converter has gained widespread adoption due to its multidirectional power flow via a galvanically isolated multi-winding magnetic structure. However, the mutually-shared magnetic link and inter-port phase-shifts induce the cross-coupled power flow which hinders independent port-wise operation. This work presents an analytical framework that combines port-equivalent models derived from a full-order$n \times n$impedance matrix ($\bf {Z}$-matrix) with generalized harmonic analysis (GHA), to accurately capture the cross-coupled power flow in MAB converters. An experimental method based on steady-state tests is developed to characterize the cross-coupled active powers by isolating the inter-port power interactions. Thereafter, a control-integrated power decoupling (iPD) algorithm with feedforward compensation is developed to achieve port-wise decoupling by suppressing voltage fluctuations during transients. The required port-equivalent model parameters are obtained from the experimentally extracted$\bf {Z}$-matrix of the high-frequency magnetic link (HFML) via a proposed single-port impedance measurement scheme. The cross-coupling and decoupling frameworks are validated on a 2.4 kW SiC-based four-port MAB prototype. Transient experiments featuring both voltage- and load-step variations are used to verify the effectiveness and improved decoupling performance of the proposed$\bf {Z}$-matrix iPD strategy, relative to the uncompensated PI controller baseline, and the reduced-order$Y$-$\Delta$(star-delta) feedforward scheme.