The circuit schematic of the studied dual half-bridge converter is provided in
Figure 1 to realize bidirectional power flow. Two half-bridge circuits are used on both the high- and low-voltage sides and one resonant tank is adopted on the high-voltage side to achieve the soft switching characteristic under frequency control. If power is transferred from high-voltage
V1 to low-voltage
V2 as shown in
Figure 2a, the ac switch
S is open and the dual half-bridge converter is worked under buck mode operation.
Q1 and
Q2 are main power devices and
Q3 and
Q4 are operated as synchronous rectifiers.
Lr,
Cr, and
Lm1 are operated as an
LLC resonant converter to have low switching losses and high circuit efficiency functions. If power is transferred from low-voltage
V2 to high-voltage
V1 as shown in
Figure 2b, the ac switch
S is closed and the dual half-bridge converter is worked under boost mode operation. Under this condition,
Q3 and
Q4 are the main power devices,
Q1 and
Q2 are off, and the antiparallel diodes are worked as the full-wave rectifier.
Lr,
Cr, and
Lm2 are operated as an
LLC resonant converter to give low switching losses and high circuit efficiency functions.
2.1. Forward Power Flow
The studied dual half-bridge converter can achieve bidirectional power flow capability. When power is transferred from high-voltage
V1 to low-voltage
V2, battery banks or super capacitors can be adopted as energy storage units on the low-voltage terminal. The circuit configuration of the adopted dual half-bridge converter under forward power flow is shown in
Figure 2a. The ac switch
S is off under forward power flow.
Q1 and
Q2 are worked as the main switches to generate a square wave voltage on voltage
vab.
Q3 and
Q4 are operated as synchronous rectifiers to lessen conducting losses on the low-voltage side. According to the polarity of the secondary side current, a square wave voltage is generated on voltage
vcd’.
Lm1 is the magnetizing inductance of the transformer;
Lr and
Cr are the resonant inductor and capacitor.
Q1 and
Q2 are controlled by using frequency modulation to regulate load current
I2 or voltage
V2. Due to the resonant operation by
Lr,
Cr, and
Lm1, the soft switching operation of
Q1 and
Q2 can be realized.
Figure 3a demonstrates the basic PWM signals of the studied converter under forward power flow operation. If the series resonant frequency is higher (or lower) than the operating frequency, there are six (or four) operation stages per switching cycle as shown in
Figure 3b–g. The circuit operations of the studied circuit under forward power flow are presented in the following.
Stage 1 (t0~t1): The output voltage of CQ1 is decreased to zero at t0. Therefore, the soft switching characteristic of Q1 can be achieved after t0 due to iQ1 (t0) = iLr (t0) < 0 and DQ1 conducts. Since iLr > iLm1 and iQ3 < 0, Q3 is turned on and the secondary side current flows through MOSFET Q3 turn-on resistor Ron to charge capacitor C3. Due to low turn-on resistance Ron, the conduction losses on the low-voltage side can be reduced compared to using a fast recovery diode. The ac side voltages of the two half-bridge circuits are vab = VC1 = V1/2 and vcd = VC3 = V2/2. Thus, the primary magnetizing voltage vLm1 = vcd’ = nV2/2 and the magnetizing current iLm1 increase with the current slope nV2/(2Lm1). The magnetizing current variation in Stage 1 is about ΔiLm1,1 = nV2Δt10/(2Lm1) where Δt10 is the time interval in Stage 1. Cr and Lr are resonant in Stage 1 under vab = V1/2, vLm1 = nV2/2 and . If fr > fsw, then Tr/2 < Tsw/2. Therefore, the transformer secondary current will decrease to zero before Q1 turns off. The circuit operation goes to Stage 2. If fr < fsw, then Tr/2 > Tsw/2. When Q1 turns off, the secondary winding current is still positive. Then, the circuit operation goes to Stage 3.
Stage 2 (t1~t2): If fr > fsw, the transformer secondary current decreases to zero before Q1 turns off. When iQ3 equals zero at t1, Q3 turns off. iLr flows through Q1, Cr, Lr, Lm1, and C1. Since C1 >> Cr, components Cr, Lr, and Lm1 are resonant under vab = V1/2 and resonant frequency . When t = Tsw/2, switch Q1 turns off and the circuit operation of Stage 2 is completed.
Stage 3 (t2~t3): When
t =
t2 =
Tsw/2,
Q1 turns off, and
CQ1 (
CQ2) is charged (discharged) by
iLr. In order to ensure that
Q2 turns on at zero voltage, the zero-voltage condition of
Q2 is calculated using
where
CQ =
CQ1 =
CQ2. The maximum magnetizing current is estimated using Equation (2).
The time interval in Stage 3 can be estimated as follows when
CQ2 is discharged to zero voltage:
where
tdead is the dead time between
Q1 and
Q2. Based on Equation (3), the maximum magnetizing inductance
Lm1 can be calculated using Equation (4).
Stage 4 (t3~t4): The voltage of CQ2 is decreased to zero at t3. The body diode DQ2 conducts due to iLr (t3) > 0 (or iQ2 (t3) < 0). After time t3, the soft switching characteristic of Q2 can achieved. Since the secondary side current iQ4 is negative, Q4 is forced to turn on to decrease conduction loss. Then, the ac side voltage vcd = −V2/2, the magnetizing voltage vLm1 = −nV2/2, and iLm1 decreases. The magnetizing current variation in Stage 2 is about ΔiLm1,4 = nV2Δt34/(2Lm1) where Δt34 is the time interval in Stage 4. In Stage 4, Cr and Lr are resonant under vab = −V1/2, vLm1 = −nV2/2 and . If fr > fsw, the circuit operation goes to Stage 5. If fr < fsw, the circuit operation goes to Stage 6.
Stage 5 (t4~t5): If fr > fsw, iQ4 will go to zero before Q2 turns off. When iQ4 equals zero at t4, Q4 is forced to turn off. In Stage 5, iLr flows through Q2, Cr, Lr, Lm1, and C2. Components Cr, Lr, and Lm1 are resonant under vab = −V1/2 with resonant frequency . When Q2 turns off, the circuit operation goes to Stage 6.
Stage 6 (t5~Tsw + t0): When Q2 turns off at t5, CQ1 (CQ2) is discharged (charged) by iLr (t5) < 0. To ensure that Q1 turns on at zero voltage, the zero-voltage condition of Q1 is the same as that of Q2. The time interval in this stage is short enough to be neglected in state–state analysis. At time Tsw + t0, the voltage of CQ1 decreases to zero voltage and the circuit operation of this stage is completed.
To derive the transfer function of the studied converter under forward power flow, a fundamental frequency approach is adopted to derive the ac voltage gain. According to the on/off states of
Q1~
Q4, the square voltage waveforms are obtained on voltages
vab and
vcd. Since the resonant tank of
Lr,
Cr, and
Lm1 is worked as a band pass filter, the harmonic frequency on
vab and
vcd can be neglected to simplify the characteristic analysis. The root mean square (
rms) values of
vab and
vcd’ at the switching frequency are
and
, respectively. The equivalent resistance at the primary side of transformer can be calculated as
. The equivalent circuit of the adopted resonant tank is shown in
Figure 2a. The effectively fundamental sinusoidal voltage is
vab,f with
rms voltage value
and the resonant tank consists of
Lr,
Cr,
Lm1, and
Rac2. The voltage transfer function between low-voltage
V2 and high-voltage
V1 is derived in Equation (5).
The amplitude of the voltage transfer function in Equation (5) can be obtained using Equation (6):
where
,
,
k = Lm1/
Lr, and
F = fsw/
fr. Based on the input voltage
V1, output voltage
V2, inductor ratio
k, and load resistance
Rac2, the necessary switching frequency can be calculated from Equation (6). The gain curve of the proposed converter under forward power flow is plotted in
Figure 3h under inductor ratio
k = Lm1/
Lr = 7.
2.2. Reverse Power Flow
The power flow of the studied dual half-bridge circuit can also be delivered from low-voltage
V2 to high-voltage
V1 as shown in
Figure 2b. Under this condition, the ac switch
S is turned on,
Q3 and
Q4 are operated as the main power switch to generate a square voltage waveform on voltage
vcd, and the primary voltage
vLm1 ≈
nvcd =
vcd’.
Q1 and
Q2 are off and the antiparallel diodes
DQ1 and
DQ2 are operated as the full-wave rectifiers. According to the polarity of
iQ1 and
iQ2, a square wave voltage is generated on voltage
vab.
Lr,
Cr, and
Lm2 are activated as the resonant tank to realize an inductive load operation. Therefore, the soft switching characteristic of main power devices
Q3 and
Q4 can be achieved.
Q3 and
Q4 are controlled with frequency modulation to regulate current
I1 or voltage
V1.
Figure 4 demonstrates the PWM waveforms and the equivalent circuit of the studied converter under reverse power flow.
Stage 1 (t0~t1): CQ3 is discharged to zero voltage at t0, iLr > 0, and iQ3 < 0. The soft switching characteristic of Q3 is realized when Q3 is turned on after t0. Since −iLr > iLm2 and iQ1 < 0, DQ1 conducts and C1 is charged by −iQ1. In Stage 1, the ac side voltages are vab = VC1 = V1/2 and vcd = VC3 = V2/2. iLm2 increases with the current slope V1/(2Lm2). Cr and Lr are resonant in Stage 1 under vab = V1/2, vLm1 = nV2/2, and . If fr > fsw, the circuit operation goes to the next stage. If fr < fsw, the circuit operation goes to Stage 3. Power is transferred in this stage from V2 to V1 through Q3, T, Lr, Cr, and DQ1.
Stage 2 (t1~t2): When iDQ1 is decreased to zero at t1, DQ1 is reverse biased. iLr flows through S, Cr, Lr, T, and Lm2. Cr, Lr, and Lm2 are resonant under vLm1 = nV2/2 and resonant frequency . When t = t2, Q3 turns off and the circuit operation of Stage 2 is completed.
Stage 3 (t2~t3):Q3 turns off at time
t2. Since
iLr < 0,
CQ3 (
CQ4) is charged (discharged). In order to ensure that
Q4 turns on at zero voltage, the zero-voltage condition of
Q4 is calculated in Equation (7):
where
CQ,s =
CQ3 =
CQ4. The peak values of
iLm1 and
iLm2 can be calculated as
The time interval in Stage 3 can be estimated when
CQ4 is discharged to zero voltage:
where
tdead is the dead time between
Q3 and
Q4.
Stage 4 (t3~t4):CQ4 is discharged to zero at t3. The body diode DQ4 of Q4 conducts due to the fact that iD4 (t3) < 0. Therefore, the soft switching characteristic of Q4 can achieved after time t3. In Stage 4, iQ2 is negative and DQ2 conducts. Therefore, vab = −V1/2 and vcd = −V2/2. Cr and Lr are resonant with resonant frequency . If fr > fsw, the circuit operation goes to Stage 5. If fr < fsw, the circuit operation goes to Stage 6.
Stage 5 (t4~t5): If fr > fsw, iQ2 will go to zero before Q4 is turned off. When iDQ2 equals zero at t4, DQ2 is reverse biased. In Stage 5, iLr flows through Cr, Lr, T, and Lm2. Components Cr, Lr, and Lm2 are resonant under vcd = −V2/2 with resonant frequency . When Q4 turns off at t5, the circuit operation goes to Stage 6.
Stage 6 (t5~Tsw + t0): When Q4 turns off at t5, CQ3 (CQ4) is discharged (charged). The time interval in Stage 6 can be neglected in state–state analysis. At time Tsw + t0, the voltage of CQ3 is decreased to zero and the circuit operation of Stage 6 is completed.
The transfer function of the studied circuit under reverse power flow is similar to that under forward power flow operation.
Q3 and
Q4 are the main active devices and
DQ1 and
DQ2 are worked as the full-wave diode rectifier. The circuit characteristic of
Lr,
Cr, and
Lm2 (instead of
Lm1) is like a band pass filter to filter the harmonic current.
Figure 2b gives the equivalent circuit of the adopted resonant tank. The effectively fundamental sinusoidal voltage is
vcd’,f with rms voltage value
, and the resonant tank consists of
Lr,
Cr,
Lm2, and
Rac1. The equivalent resistance at the high-voltage side is calculated as
. The voltage transfer function between high-voltage
V1 and low-voltage
V2 is derived in Equation (11).
Likewise, the amplitude of the voltage transfer function in Equation (11) can be calculated using Equation (12):
where
,
,
k = Lm2/
Lr, and
F = fsw/
fr. Based on
V1,
V2,
k, and
Rac1, the necessary switching frequency can be obtained from Equation (12). The gain curve of the proposed converter under reverse power flow is plotted in
Figure 4h under inductor ratio
k = Lm2/
Lr = 7.