This work develops and validates a generalized mathematical framework for modeling both resonant and non-resonant converters within the multi-active bridge (MAB) topology. As the number of ports in an isolated converter increases, the modeling complexity rises significantly, and becomes further compounded when transformer parasitics are incorporated, leading to a higher-order system. With parasitics included, loss-optimal control variables can deviate substantially from their nominal values in an ideal converter. To address this, we present a generalized analytical framework that models all node voltages and branch currents in any MAB converter and formulates a method to determine the control degrees of freedom in closed-loop systems for minimizing rms current, switching loss, or total loss. This framework in entirety is validated by a full-scale comparison with simulations and experiments of 2-port and 3-port isolated converters inclusive of transformer parasitics, exhibiting an average modeling error of less than 5%.
