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This paper presents the design of new high-frequency transformer isolated bidirectional dc-dc converter modules connected in input-series-output-parallel (ISOP) for 20-kVA-solid-state transformer. The ISOP modular structure enables the use of low-voltage MOSFETs, featuring low on-state resistance and resulted conduction losses, to address medium-voltage input. A phase-shift dual-half-bridge (DHB) converter is employed to achieve high-frequency galvanic isolation, bidirectional power flow, and zero voltage switching (ZVS) of all switching devices, which leads to low switching losses even with high-frequency operation. Furthermore, an adaptive inductor is proposed as the main energy transfer element of a phase-shift DHB converter so that the circulating energy can be optimized to maintain ZVS at light load and minimize the conduction losses at heavy load as well. As a result, high efficiency over wide load range and high power density can be achieved. In addition, current stress of switching devices can be reduced. A planar transformer adopting printed-circuit-board windings arranged in an interleaved structure is designed to obtain low core and winding loss, solid isolation, and identical parameters in multiple modules. Moreover, the modular structure along with a distributed control provides plug-and-play capability and possible high-level fault tolerance. The experimental results on 1 kW DHB converter modules switching at 50 kHz are presented to validate the theoretical analysis.