The　input-parallel-output-parallel　(IPOP)　dual-active-bridge　(DAB)　converter　is　a　popular　solution　to　be　used　as　a　solid-state-transformer　(SST)　to　increase　current　capacity　for　its　advantages,　including　bidirectional　power　flow,　soft　switching,　and　high　efficiency.　To　reduce　circulating　and　turn-off　currents　under　single-phase-shift　(SPS)　control,　an　IPOP　DAB　converter　with　a　modulated　coupled　inductor　and　the　optimized　modulation　trajectory　are　proposed　in　this　article.　Compared　with　the　previous　modulated　coupled　inductor　solutions,　the　phase-shift　angle　between　two　modules　is　controlled　by　PWM　signals　from　0　degrees　to　180　degrees,　instead　of　just　working　at　two　fixed　values　(0　degrees　and　180　degrees).　Based　on　the　derived　model　of　the　modulated　coupled　inductor　and　analysis　of　converter　working　modes,　the　relationship　between　the　two　phase-shift　angles　and　the　current　stress　of　the　converter　is　analyzed　in　depth.　Consequently,　an　optimized　modulation　trajectory　is　also　proposed　to　achieve　low　turn-off　current　and　rms　current　for　IPOP　DAB　converters　used　for　SST　applications.　The　parameters　design,　including　leakage　inductance　and　coupling　coefficient,　is　introduced.　A　250-kHz,　400-/400-V,　2000-W　IPOP　DAB　prototype　is　built　to　verify　the　effectiveness　of　the　proposed　solution.