This article presents the synthesis and implementation of a switching-network loss-reduced, soft-switching-enabled PWM modulation scheme for an isolated bidirectional triple-active bridge (TAB) dc-dc converter that dynamically varies the five phase-duty control variables. Due to the power coupling among each TAB port, circuit analysis of TAB's operational modes becomes complex, posing a challenge to implementing a computationally intensive PWM strategy derived from the established frequency domain-based circuit analysis approach. In this work, we first develop the time-domain analytical model of the TAB converter, drawing on the working principles of the dual active bridge (DAB) converter and the linear superposition theorem. This model simplifies the calculation of switching transient currents in a TAB converter, which significantly influences soft-switching operation and overall switching loss in the high-frequency H-bridges. Second, a rigorous effort is made to decipher the zero-voltage-switching (ZVS) process of the TAB converter considering the influence of voltage-dependent junction capacitances, and the critical ZVS current requirements are correctly identified. Using the proposed TAB circuit model, associated loss models, and identified ZVS criteria, the design optimization of the TAB port inductances is further carried out. Subsequently, we propose a simplified penta-phase shift modulation scheme for the TAB converter, ensuring the soft-switching of the H-bridges. This proposed modulation solution is easier to implement, computationally stress-free, features all-ZVS, and exhibits low switching and conduction loss characteristics. The proposed modulation solution is also implemented, validated, and benchmarked in a 2.4-kW/100-kHz GaN-based TAB converter proof-of-concept, tailored for space power supply applications. The converter achieves a peak efficiency of 96.8%, and its average efficiency at 20% loading condition is benchmarked at 94.82%, representing a similar to 4% improvement over the traditional phase-shift modulation-operated TAB.