３．The operating states of the respective modes

　The operating mode of the high-frequency AC link DC-AC converter has inverter mode and rectifier mode. The steady state of rectifier mode can be classified into 12 Mode. But we will explain the operations at steady state from Mode 1 to Mode 6 by using the operating waveform shown in Fig.4, because the operation of that interval makes no difference with from Mode 7 to Mode 12. The equivalent circuits corresponding to the times (t0 to t6) and modes (M1 to M6) of Fig.4 are shown in Fig.5. For simplicity, the power devices are ideal switches that have zero switching time and switch on and off instantaneously. The circuit is also assumed ideal, with no internal resistances and stray capacitances. However, the leakage inductances of the high-frequency transformer are considered in order to utilize them in ZCS operation on the secondary side.

●Mode 1 : power regeneration interval　 (t0≦t＜t1)
　 At this time, S1,D1,S4,D4,S6(D6),S7(D7) are on, and the power regenerated from secondary side to primary side via D1,D4,S6(D6),S7(D7). Only very small resonance current of resonant pole flows on S1 and S4. This state will continue until switch S5 is turned off at any time t1.

●Mode 2 : ZCS commutation interval　(t1≦t＜t2)
　At time t1, when S5 is on, Io begins commutation from D6 to D5, since D5 becomes forward bias and D6
becomes reverse bias. At this point, hard-switching or sudden commutation due to the leakage inductances of the high-frequency transformer will not occur, and S5 will be turned on by soft-switching of the ZCS mode, in which this current gradually commutates. Since S6 will be turned off after D6 will be completely turned off, it will be turned off by ZVS and ZCS.

●Mode 3 : single circulation interval　 (t2≦t＜t3)
　 When S5 will become on completely, load current Io flows via S5(D5),S7(D7), resulting in a single circulation interval. In this interval, since the primary and the secondary are separated in circuit terms, there active power of load will be processed on the only secondary side. At that time, the power does not regenerate forward to the primary side. At this point, only resonance current continuously flow on S1,S4 in primary side. In practice, exciting current of high-frequency transformer will flow in i1, but since its value is essentially very small, its effect will not present a problem. Secondary phase-shifted PWM control scheme controls the output voltage to sinusoidal wave of cycloconverter by controlling this interval.

●Mode 4 : ZCS commutation(ZVS preparation)　 interval (t3≦t＜t4)
　At any time t4, for S1,S4 turn off easily, there is need to flow on S1,S4 in a slight term. And then, S8 will turn on at t3. When S8 will be turned on, since D7 will become a reverse bias, load current Io is commutated from D7 to S8(D8) by ZCS similarly to Mode 2, and S7 will be turned off by ZVS and ZCS.

●Mode 5 : power supply interval　(t4≦t＜t5)
　When S8 are on, this converter operates as power supply interval in an instant, since direction of i1 turns over and it flows via S1 and S4. At this point, since S1,S4 are already on, ia and ib flows. So that, di/dt is relaxed because i1 dose not suddenly flow in. And after that, at time t5, S1,S4 will turn off. Let me add, since this interval is very short in one period, its effect of regenerating operation will not influence in particular. When S1,S4 will turn off without this interval, since i1 will be regenerated via D1, D4, it flows in the direction which is such as to demote the charge of C1, C4. In this case, for reliable ZVS, there is need to flow the resonance current which is larger than regenerated current i1 on resonant pole part. This resonance current had been become a factor increasing fixed loss. However, in the proposed scheme, since i1 flows to S1,S4 once by preparing this interval, i1 flow forward to a direction which is such as to promote the charge of C1, C4. That is there is no need of large resonance current. Hence, the effect of reduced fixed loss of secondary phase-shifted control will not ruin.

●Mode 6 : ZVS commutation (quasi-resonant) interval　(t5≦t＜t6)
　At time t5, when S1,S4 are off, a quasi-resonant state occur and C1,C4(C2,C3) start to charge(discharge). Vc1 and Vc4 increase linearly, and when they reach the dc source voltage E, i1 commutates to D2,D3. Therefore S1,S4 will be turned off by ZVS. S2,S3 will turn on, during i1,ia,ib will flow via D2,D3. And the half cycle is completed here.
Thus, by operating the proposed switching pattern, the soft-switching operations of ZVS or ZCS, or ZVS and ZCS. In addition, the proposed scheme can be realized in all switching with no loss of the features of the secondary phase-shifted control scheme. Moreover, it can be reduced fixed loss and conduction loss.

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