Analysis of a Three-Level Bidirectional ZVS Resonant Converter

: A bidirectional three-level soft switching circuit topology is proposed and implemented for medium voltage applications such as 750 V dc light rail transit, high power converters, or dc microgrid systems. The studied converter is constructed with a three-level diode-clamp circuit topology with the advantage of low voltage rating on the high-voltage side and a full-bridge circuit topology with the advantage of a low current rating on the low-voltage side. Under the forward power ﬂow operation, the three-level converter is operated to regulate load voltage. Under the reverse power ﬂow operation, the full-bridge circuit is operated to control high-side voltage. The proposed LLC resonant circuit is adopted to achieve bidirectional power operation and zero-voltage switching (ZVS). The achievability of the studied bidirectional ZVS converter is established from the experiments.


Introduction
Renewable power to reduce the effect of global warming has been developed by using high efficiency power electronic based converters in local dc nanogrid or microgrid distribution [1][2][3][4][5][6] between renewable energy power and local dc or ac loads. In order to maintain the voltage stability on dc distribution system, energy storage power units are usually demanded between battery banks and dc bus system to save (or restore) excess (or insufficient) energy on the dc bus. Therefore, the bidirectional pulse-width modulation (PWM) converters have been proposed for the battery-based systems [7][8][9][10][11][12][13][14] such as electric vehicles, hybrid electric vehicles, and dc microgrids. In dc microgrids, the unipolar voltage (380 V) or bipolar voltage (±380 V or 760 V) distribution can be adopted on the dc bus voltage. High frequency link medium voltage converters have been used for dc traction power units, three phase industry power supplies and dc microgrids. Three-level dc converters with 600 V MOSFETs or conventional PWM converters with 1200 V IGBTs or SiCs have been presented in medium voltage input applications. The drawback of 1200 V IGBT is low switching frequency and the cost of 1200 V SiC is expensive. Bidirectional PWM converters with dual active bridge (DAB) structure have been studied to realize forward and reverse power transfer. Three-level bidirectional converters or cascaded converters with the high frequency MOSFETs have been developed for high voltage systems such as 760 V input. PWM scheme is widely adopted in bidirectional DAB systems to control power flow and realize soft switching turn-on characteristics. However, the control scheme for generating the PWM signals is complicated and the circulating current under low duty cycle is high. Resonant converters have the benefits of high circuit efficiency and low electromagnetic interference. A full-bridge resonant circuit topology was proposed in [15] to achieve bidirectional power transfer. However, the soft switching characteristics cannot be achieved in backward power flow. Bidirectional Full-bridge resonant converters presented in [16][17][18] have symmetric circuit structure to achieve forward and backward power flow so that power switches can realize zero-voltage switching. However, there is a circulating current on the parallel inductor in primary-side which will result in addition conduction loss during forward power flow. A soft switching three-level resonant converter is developed for high voltage to low voltage conversion. The profits of the developed converter are forward and backward power flow capability and zero-voltage turn-on characteristic. Three-level diode-clamp circuit topology is used on the primary-side and full-bridge circuit topology is adopted on the secondary-side. The LLC circuit tank is employed to control load voltage and achieve zero-voltage switching on active devices. For forward power transfer, the three-level diode-clamp converter is controlled using the pulse-frequency modulation (PFM) to control low-side voltage and active devices of full-bridge converter on the secondary-side are operated as synchronous rectifiers. In order to implement the same resonant circuit structures for bidirectional power flow, an additional inductor is connected on the primary-side during the reverse power flow condition. In reverse power flow operation, the full-bridge converter on the low-voltage side is operated with PFM scheme to control high-side voltage. The proposed converter with bidirectional power flow capability can be applied in local dc nanogrid or microgrid distribution between renewable energy power and local dc or ac loads. The circuit schematic and circuit operation are provided and discussed in Sections 2 and 3. The circuit characteristic and experiments with a 1.44 kW laboratory circuit are demonstrated and discussed to show the feasibility of the studied bidirectional power converter in Section 4. Finally, a conclusion of the studied converter is given in Section 5. Figure 1a provides the converter schematic of the studied bidirectional converter. There is a three-level diode-clamp circuit topology on the high-voltage side with the benefit of using low voltage rating switches. Clamped diodes D a and D b and capacitor C f are used to balance input voltages V CH1 = V CH2 and reduce the voltage stress on S 1~S4 . Full bridge circuit topology is used on the low-voltage side to achieve full-wave rectification. S ac and L b are series-connection and connect to points a and b in order to achieve LLC circuit operation under backward power flow operation (S ac is ON). For forward power operation from V H (high-side voltage) to V L (low-side voltage), S ac is OFF and L b is disconnected on the primary-side. Figure 1b gives the circuit structure under forward power operation. S 1~S4 are main power devices to control output voltage V L . L r , L m and C r are LLC resonant circuit and Q 1~Q4 are activated as synchronous switches. For reverse power operation from the V L terminal to the V H terminal, S ac is ON and Figure 1c provides the circuit diagram of reverse power operation. Switches Q 1~Q4 are major power switches and L r , L b and C r are resonant circuit. D S1~DS4 are operated as a full-wave diode rectifier. Therefore, LLC resonant characteristics for both power flow are achieved and the turn-on switching loss of major power switches is removed.

Circuit Schematic of the Developed Converter
Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 18 structure to achieve forward and backward power flow so that power switches can realize zerovoltage switching. However, there is a circulating current on the parallel inductor in primary-side which will result in addition conduction loss during forward power flow. A soft switching three-level resonant converter is developed for high voltage to low voltage conversion. The profits of the developed converter are forward and backward power flow capability and zero-voltage turn-on characteristic. Three-level diode-clamp circuit topology is used on the primary-side and full-bridge circuit topology is adopted on the secondary-side. The LLC circuit tank is employed to control load voltage and achieve zero-voltage switching on active devices. For forward power transfer, the three-level diode-clamp converter is controlled using the pulsefrequency modulation (PFM) to control low-side voltage and active devices of full-bridge converter on the secondary-side are operated as synchronous rectifiers. In order to implement the same resonant circuit structures for bidirectional power flow, an additional inductor is connected on the primary-side during the reverse power flow condition. In reverse power flow operation, the fullbridge converter on the low-voltage side is operated with PFM scheme to control high-side voltage. The proposed converter with bidirectional power flow capability can be applied in local dc nanogrid or microgrid distribution between renewable energy power and local dc or ac loads. The circuit schematic and circuit operation are provided and discussed in Sections 2 and 3. The circuit characteristic and experiments with a 1.44 kW laboratory circuit are demonstrated and discussed to show the feasibility of the studied bidirectional power converter in Section 4. Finally, a conclusion of the studied converter is given in Section 5. Figure 1a provides the converter schematic of the studied bidirectional converter. There is a three-level diode-clamp circuit topology on the high-voltage side with the benefit of using low voltage rating switches. Clamped diodes Da and Db and capacitor Cf are used to balance input voltages VCH1 = VCH2 and reduce the voltage stress on S1~S4. Full bridge circuit topology is used on the lowvoltage side to achieve full-wave rectification. Sac and Lb are series-connection and connect to points a and b in order to achieve LLC circuit operation under backward power flow operation (Sac is ON). For forward power operation from VH (high-side voltage) to VL (low-side voltage), Sac is OFF and Lb is disconnected on the primary-side. Figure 1b gives the circuit structure under forward power operation. S1~S4 are main power devices to control output voltage VL. Lr, Lm and Cr are LLC resonant circuit and Q1~Q4 are activated as synchronous switches. For reverse power operation from the VL terminal to the VH terminal, Sac is ON and Figure 1c provides the circuit diagram of reverse power operation. Switches Q1~Q4 are major power switches and Lr, Lb and Cr are resonant circuit. DS1~DS4 are operated as a full-wave diode rectifier. Therefore, LLC resonant characteristics for both power flow are achieved and the turn-on switching loss of major power switches is removed.

Circuit Operation
For forward power delivery, the electric power energy is transferred from VH side to VL side and Sac is OFF. S1~S4 are controlled with PFM scheme. Due to PWM signals of S1~S4, there is a square wave with -VH/2 or VH/2 on the leg voltage vab. However, Q1~Q4 are operated as the synchronous switches instead of the rectifier diodes in conventional full-bridge rectifier to reduce conduction loss. The equivalent resonant circuit and PWM waveforms for forward power delivery are provided in Figure  2. To realize the ZVS operation of S1~S4, the input impedance of LLC circuit must be inductive. Figure  3 gives the corresponding equivalent circuits related to six operating steps in a switching period under fr (resonant frequency) > fsw (switching frequency). It is assumed that the Lr represents the external series resonant inductance and the leakage inductance of transformer and Cr represents the external series resonant capacitance and the parasitic capacitance on transformer winding turns. The output capacitances CS1-CS4 are assumed to be identical. In the same manner, CQ1 = … = CQ4. Since the current iCf on Cf is less than iS1 and iS2 in mode 1 and iS3 and iS4 in mode 4, iCf is ignored in PWM waveforms. Therefore, iS1 is equal to iS2 in steps 1-3 and 6 and iS3 is equal to iS4 in steps 3-6.

Circuit Operation
For forward power delivery, the electric power energy is transferred from V H side to V L side and S ac is OFF. S 1~S4 are controlled with PFM scheme. Due to PWM signals of S 1~S4 , there is a square wave with −V H /2 or V H /2 on the leg voltage v ab . However, Q 1~Q4 are operated as the synchronous switches instead of the rectifier diodes in conventional full-bridge rectifier to reduce conduction loss. The equivalent resonant circuit and PWM waveforms for forward power delivery are provided in Figure 2. To realize the ZVS operation of S 1~S4 , the input impedance of LLC circuit must be inductive. Figure 3 gives the corresponding equivalent circuits related to six operating steps in a switching period under f r (resonant frequency) > f sw (switching frequency). It is assumed that the L r represents the external series resonant inductance and the leakage inductance of transformer and C r represents the external series resonant capacitance and the parasitic capacitance on transformer winding turns. The output capacitances C S1 -C S4 are assumed to be identical. In the same manner, C Q1 = . . . = C Q4 . Since the current i Cf on C f is less than i S1 and i S2 in mode 1 and i S3 and i S4 in mode 4, i Cf is ignored in PWM waveforms. Therefore, i S1 is equal to i S2 in steps 1-3 and 6 and i S3 is equal to i S4 in steps 3-6. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 18 v ab     Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 18   Step 1 (t0 ≤ t < t1): At t < t0, iLr < 0. Thus, iLr discharges CS1 and CS2 are discharged. At t0, vCS1=vCS2=0. Thus, DS1 and DS2 are conducting due to iLr < 0. The ZVS operation of S1 and S2 can be achieved after time t0. If iLr < 0, Db is forward biased. The leg voltage vab = vCf = vCS3 = vCS4 = VH/2. Since iLr > iLm, Q1 and Q4 turn on to conduct the secondary-side current. When iLr increases and iLr > 0, Db becomes off. In this step, the magnetizing voltage vLm is equal to nVL, where n = np/ns is the transformer turns ratio, and iLm increases. The ripple current ∆iLm in step 1 is equal to nVL∆t01/Lm where ∆t01 = t1 -t0. The resonant frequency in step 1 is Step 2 (t1 ≤ t < t2): If fsw < fr, iQ1 and iQ4 will decrease to zero ampere at t1. Thus, Q1 and Q4 can turn off after time t1. In step 2, the leg voltage vab=VH/2 and Lr, Lm and Cr are resonant.
Step 3 (t2 ≤ t < t3): At t2, S1 and S2 turn off. The positive current iLr(t2) will charge CS1 and CS2. On the other hand, CS3 and CS4 are discharged in this step. The ZVS operation of S3 and S4 is expressed in Equation (1).
where iLm,p is the peak current on Lm and CS = CS1 = ... = CS4. The peak current iLm,p is calculated from Equation (2).
The dead time td between S3 and S1 (or S4 and S2) is approximately expressed in Equation (3).
Therefore, the maximum magnetizing inductance is derived in Equation (4).
Step 4 (t3 ≤ t < t4): At t3, vCS3 = vCS4 = 0. Since iLr(t3) is positive, DS3 and DS4 are conducting. Power devices S3 and S4 can turn on after t3 under zero voltage condition. Since iLr(t3) > 0, Da is forward biased. The leg voltage vab=-VH/2 and vCf = vCS1 = vCS2 = VH/2. When iLr decreases and iLr < 0, Da becomes off. On the secondary side, iQ2(t3) < 0 and iQ3(t3) < 0. Therefore, Q2 and Q3 turn on to conduct the secondary-side current, the primary-side voltage vLm = -nVL and iLm decreases. Step 1 (t 0 ≤ t < t 1 ): At t < t 0 , i Lr < 0. Thus, i Lr discharges C S1 and C S2 are discharged. At t 0 , v CS1 = v CS2 = 0. Thus, D S1 and D S2 are conducting due to i Lr < 0. The ZVS operation of S 1 and S 2 can be achieved after time Since i Lr > i Lm , Q 1 and Q 4 turn on to conduct the secondary-side current. When i Lr increases and i Lr > 0, D b becomes off. In this step, the magnetizing voltage v Lm is equal to nV L , where n = n p /n s is the transformer turns ratio, and i Lm increases. The ripple current ∆i Lm in step 1 is equal to and i Q4 will decrease to zero ampere at t 1 . Thus, Q 1 and Q 4 can turn off after time t 1 . In step 2, the leg voltage v ab = V H /2 and L r , L m and C r are resonant.
Step 3 (t 2 ≤ t < t 3 ): At t 2 , S 1 and S 2 turn off. The positive current i Lr (t 2 ) will charge C S1 and C S2 . On the other hand, C S3 and C S4 are discharged in this step. The ZVS operation of S 3 and S 4 is expressed in Equation (1).
where i Lm,p is the peak current on L m and C S = C S1 = . . . = C S4 . The peak current i Lm,p is calculated from Equation (2).
The dead time t d between S 3 and S 1 (or S 4 and S 2 ) is approximately expressed in Equation (3).
Therefore, the maximum magnetizing inductance is derived in Equation (4). Step is positive, D S3 and D S4 are conducting. Power devices S 3 and S 4 can turn on after t 3 under zero voltage condition. Since i Lr (t 3 ) > 0, D a is forward biased. The leg voltage v ab = −V H /2 and v Cf = v CS1 = v CS2 = V H /2. When i Lr decreases and i Lr < 0, D a becomes off. On the secondary side, i Q2 (t 3 ) < 0 and i Q3 (t 3 ) < 0. Therefore, Q 2 and Q 3 turn on to conduct the secondary-side current, the primary-side voltage v Lm = −nV L and i Lm decreases.
Step 5 (t 4 ≤ t < t 5 ): The secondary-side switch currents i Q2 = i Q3 = 0 at t 4 . Then, Q 2 and Q 3 turn off. In this step, v ab = −V H /2 and L r , L m and C r are resonant.
Step 6 (t 5 ≤ t <T sw +t 0 ): At t 5 , S 3 and S 4 turn off. In this step, i Lr (t 5 ) < 0 and v CS1 and v CS2 decrease. The ZVS condition of S 2 and S 1 is the same as S 4 and S 3 in Equation (1). The step 6 is ended at time T sw +t 0 .
The LLC resonant circuit is controlled to achieve ZVS operation and the bidirectional power operation. The resonant circuit is based on the fundamental frequency analysis to achieve load voltage regulation. According to the switching status of power devices S 1~S4 and Q 1~Q4 , the voltage values V H /2 and −V H /2 are observed on v ab , and the other voltage values nV L and −nV L are generated on the magnetizing inductor voltage v Lm . L r , C r , L m and R ac,L operate as a filter to suppress the high order harmonics. The root mean square (rms) voltages at the fundamental frequency for input and output sides are v ab,rms = √ 2V H /π and v Lm,rms = 2 √ 2nV L /π. Based on the power balance between the primary-side and the secondary-side of transformer, the primary-side load resistance is expressed as R ac,L = 8n 2 R L /π 2 . The transfer function G H_L (s) between the output and input sides in Figure 2a is obtained as: where From the given input voltage V H , the output voltage V L and the circuit parameters L r , C r , L m and R L , the switching frequency is obtained from Equation (6).
For reverse power flow shown in Figure 1c, the developed converter transfers power from V L terminal to V H terminal. S ac is turned on and L b , L r and C r are operated as a series resonant circuit to achieve voltage V H regulation. Power devices Q 1~Q4 are controlled with PFM scheme and D S1~DS4 work as a full-wave rectifier. When |i Lr |>|i Lb |, D S1 and D S2 or D S3 and D S4 are conducting. Since the LLC resonant circuit by L r , C r and L b is operated at the inductive load, power devices Q 1~Q4 are operated at the zero-voltage turn-on switching. Figure 4a shows the ac equivalent resonant circuit at reverse power flow operation. L b and R ac,H are the parallel inductance and ac equivalent resistance. Figure 4b gives the main PWM waveforms and Figure 5 demonstrates the corresponding equivalent circuits at the reverse power flow operation.
operation. The resonant circuit is based on the fundamental frequency analysis to achieve load voltage regulation. According to the switching status of power devices S1~S4 and Q1~Q4, the voltage values VH/2 and -VH/2 are observed on vab, and the other voltage values nVL and -nVL are generated on the magnetizing inductor voltage vLm. Lr, Cr, Lm and Rac,L operate as a filter to suppress the high order harmonics. The root mean square (rms) voltages at the fundamental frequency for input and output sides are π / 2 , H rms ab Based on the power balance between the primary-side and the secondary-side of transformer, the primary-side load resistance is expressed as where F=fsw/fr, . From the given input voltage VH, the output voltage VL and the circuit parameters Lr, Cr, Lm and RL, the switching frequency is obtained from Equation (6).
For reverse power flow shown in Figure 1c, the developed converter transfers power from VL terminal to VH terminal. Sac is turned on and Lb, Lr and Cr are operated as a series resonant circuit to achieve voltage VH regulation. Power devices Q1~Q4 are controlled with PFM scheme and DS1~DS4 work as a full-wave rectifier. When |iLr|>|iLb|, DS1 and DS2 or DS3 and DS4 are conducting. Since the LLC resonant circuit by Lr, Cr and Lb is operated at the inductive load, power devices Q1~Q4 are operated at the zero-voltage turn-on switching. Figure 4a shows the ac equivalent resonant circuit at reverse power flow operation. Lb and Rac,H are the parallel inductance and ac equivalent resistance. Figure 4b gives the main PWM waveforms and Figure 5 demonstrates the corresponding equivalent circuits at the reverse power flow operation.            Step 1 (t 0 ≤ t < t 1 ): This step starts at t 0 when v CQ4 = v CQ1 = 0. Then, the D Q4 and D Q1 conduct and v Q2,ds = v Q3,ds = V L . Due to D Q1 and D Q4 are conducting, v Q4,ds and v Q1,ds = 0 and Q 1 and Q 4 can turn on under zero voltage. Due to i Lr (t 0 ) + i Lb (t 0 )<0, D S1 and D S2 are forward biased, C H1 is charged, v Lm = nV L , v ab = V H /2 and i Lm and i Lb both increase. Before switches Q 1 and Q 4 turn off, i DS1 and i DS2 will decrease to zero if f sw < f r = 1/2π √ C r L r .
Step 2 (t 1 ≤ t < t 2 ): At time t 1 , i DS2 = i DS1 = 0 and D S2 and D S1 are off. L r , L b , and C r are series resonant at frequency f p = 1/2π C r (L b + L r ).
Step 3 (t 2 ≤ t < t 3 ): Q 4 and Q 1 turn off at t 2 . C Q2 and C Q3 are discharged in step 3. The ZVS condition of Q 3 and Q 2 are obtained in Equation (7). where The time interval ∆t 23 is expressed in Equation (8).
where t d is dead time between Q 4 and Q 3 or Q 2 and Q 1 .
Step 4 (t 3 ≤ t < t 4 ): Step 4 starts at t 3 when v CQ2 = v CQ3 = 0. Therefore, D Q3 and D Q2 conduct and Q 3 and Q 2 can turn on under zero voltage. In step 4, D S3 and D S4 conduct, v ab = −V H /2, v Lm = −nV L , and i Lm and i Lb both decrease.
Step 5 (t 4 ≤ t < t 5 ): i DS3 = i DS4 = 0 at t 4 . In this step, Q 2 and Q 3 are still in the on state so that v Lm = −nV L . L b , C r and L r are series resonant.
Step 6 (t 5 ≤ t < T sw +t 0 ): Q 2 and Q 3 turn off at t 5 . Then, C Q1 and C Q4 are discharged and v CQ1 = v CQ4 = 0 at t sw + t 0 .
The proposed converter has the similar operation principle for both forward and reverse power operation. For the reverse power operation, Q 1~Q4 are controlled as main power switches. D S1~DS4 are operated as diode rectifier to regulate voltage V H . The resonant circuit including L b , L r and C r is operated as a filter to suppress high order harmonics. The input rms voltage at fundamental frequency ( Figure 4a) is calculated as v Lm,rms = 2 √ 2nV L /π and the ac equivalent resistance at high voltage side is R ac,H = 2R H /π 2 . The rms voltage on v ab is expressed as v ab,rms = √ 2V H /π. Components R ac,H , L b , L r and C r are resonant. The transfer function G L_H (s) and gain |G L_H (s)| are calculated in Equations (9) and (10), respectively.
where F = f sw /f r , f r = 1/(2π √ L r C r ), K 2 = L b /L r and Q 2 = √ L r /C r /R ac,H . From the given input voltage V H , output voltage V L and the circuit parameters L r , C r , L b and R H , the switching frequency is obtained from Equation (10).

Circuit Parameters and Test Results
For forward power transfer, the input and output voltages are V H = 750 V to 800 V and V L = 48 V. The rated power is 1440 W (v L = 48 V and I L = 30 A). For reverse power transfer, the input and output voltages are V L = 36 V to 52 V and V H = 800 V. The transfer functions in Equations (6) and (10) for forward and backward power transfer operations are similar. Thus, the circuit parameters design operated at forward power flow is presented in this section. The dc voltage gain under V H = 800 V input and V L,max = 52 V output is designed to be unity. The transformer turns ratio is calculated in Equation (11).
In the prototype circuit, the selected primary and secondary turns are n H = 48 and n L = 6. Thus, the actual transformer turns ratio is n = n H /n L = 8. With the adopted turns ratio, the actual maximum and minimum voltage gains at V L,nom = 48 V condition are given in Equations (12) and (13).
The control parameters K 1 and Q 1 can be selected at full load P L,full and minimum input voltage V H,min conditions. To reduce circulating current, the inductor ratio K 1 =10 is used in this prototype circuit. For Q 1 = 0.38 and K 1 = 10, it can obtain the peak gain of |G H_L (s)| is 1.13. The ac equivalent resistance R ac,L at the rated power is obtained in Equation (14).
The circuit parameters C r = 1/2πQ 1 f r R ac,L ≈ 50 nF and L r = 1/(2π f r ) 2 C r ≈ 50 µH under f r = 100 kHz. The actual resonant inductance and capacitance are C r = 47 nF and L r = 54 µH and the magnetizing inductance L m = K 1 L r = 540 µH. The theoretical primary rms current is calculated as: The theoretical minimum switching frequency is obtained as f sw,min = 1/2π C r (L r + L m ) ≈ 30 kHz. The minimum switching frequency will result in the maximum rms magnetizing current.
Therefore, the rms resonant inductor current is obtained in Equation (17).
I Lr,rms = I 2 Lm,rms + I 2 pri,rms ≈ 4.53 A The flying capacitor C f is used to realize voltage balance of C H1 and C H2 so that V CH1 = V CH2 = V H /2. The theoretical voltage stresses of power semiconductors can be calculated as v S1,stress = .. = v S4,stress = V H,max /2 = 400 V and v Q1,stress = .. = v Q4,stress = V L,max = 52 V. The switch currents approximate I S1,rms = .. = I S4,rms ≈ I Lr,rms / √ 2 ≈ 3.2 A and I Q1,rms = .. = I Q4,rms ≈ πI o /4 ≈ 23.6 A. Power devices S 1~S4 are implemented using IRG4PC40W with 600 V/20 A rating. Power switches Q 1~Q4 are implemented using IRFB3307 with 75 V/150 A rating. S ac is implemented using two G20N50C with 500 V/20 A rating. The parallel inductor L b is selected as 230 µH and K 2 = L b /L r = 4.25 under reverse power flow operation. The clamp diodes D a and D b are implemented with ultrafast recovery diodes HFA15TB60PBF with 600 V/15 A rating. The other circuit parameters used in the prototype are C H1 = C H2 = 330 µF/400 V, C f = 2.2 µF/630 V and C L = 4400 µF/100 V. The parameters and specifications used in the laboratory prototype are given in Table 1.   Figure 6. S 1 (S 3 ) and S 2 (S 4 ) have the same gate-to-source voltage signals. The converter at V H = 750 V input has less switching frequency than V H = 800 V input condition. Figure 7 gives the experimental results of leg voltage v ab , i Lr and v Cr at 100% load. It can be seen that the measured waveforms i Lr and v Cr are almost the sinusoidal waves due to f sw close to f r for both 750 V and 800 V inputs. Figure 8 shows the experimental results of V CH1 , V CH2 , V Cf , V Da and V Db . The dc voltage differences between V CH1 , V CH2 and V Cf are about 5V. Figure 9 demonstrates the switch currents of Q 1 -Q 4 at 100% load. Figure 10 illustrates the PWM waveforms of S 1 -S 4 at 20% load. It can observe that S 1 -S 4 all turn on under ZVS at 20% load. Figure 11 gives the PWM signals of Q 1~Q4 under backward power operation and different input voltages. Power devices Q 1 (Q 2 ) and Q 4 (Q 3 ) have the same gate-to-source voltage signals. Figure 12 illustrates the measured results of i Lr , i Lb and v Cr under for reverse power operation. The parallel inductor current i Lb is similar to the magnetizing current on conventional LLC resonant converter to achieve voltage step-up capability. Figure 13 shows the measured capacitor voltages V Cf , V CH1 and V CH2 on the high voltage side. These three voltages V CH1 , V CH2 and V Cf are almost balanced with about 7 V voltage difference. Figure 14 gives the measured PWM waveforms of Q 1~Q4 under 20% load. It can observe that Q 1 -Q 4 can turn on under zero voltage at 20% load. For forward power operation (buck mode), the measured circuit efficiencies are 89.7% at 20% load, 92.1% at 50% load and 91.8% at 100% load under 800 V input. For reverse power operation (boost mode), the measured circuit efficiencies are 86.3% at 20% load, 89.4% at 50% load and 88.9% at 100% load under 40 V input case. Figure 15a gives the picture of the prototype circuit and the experimental setup is given in Figure 15b.         Figure 10. Measured PWM waveforms of S1-S4 at 20% load (a) S1 waveforms (b) S2 waveform (c) S3 waveform (d) S4 waveform (vS1,g-vS4,g: 10 V/div; vS1,d-vS4,d: 200 V/div; iS1~iS4: 2 A/div; time: 1 μs).   Figure 10. Measured PWM waveforms of S1-S4 at 20% load (a) S1 waveforms (b) S2 waveform (c) S3 waveform (d) S4 waveform (vS1,g-vS4,g: 10 V/div; vS1,d-vS4,d: 200 V/div; iS1~iS4: 2 A/div; time: 1 μs). Figure 10. Measured PWM waveforms of S 1 -S 4 at 20% load (a) S 1 waveforms (b) S 2 waveform (c) S 3 waveform (d) S 4 waveform (v S1,g -v S4,g : 10 V/div; v S1,d -v S4,d : 200 V/div; i S1~iS4 : 2 A/div; time: 1 µs).

Conclusion
A new three-level resonant converter is proposed, analyzed, and discussed to realize bidirectional power transfer and soft switching operation capability. A three-level diode clamp series resonant converter is used on the high-voltage side to have low voltage rating on active devices. For forward power operation, the conventional LLC circuit is selected to have ZVS operation on all power switches. Full-wave rectifier with synchronous switches is adopted on the low-voltage side to reduce conduction loss on power semiconductors. To overcome the low voltage gain problem on conventional LLC converter under reverse power operation, a parallel inductor is connected to the leg terminal of three-level diode-clamp resonant converter. Thus, the proposed converter can achieve voltage step-up and step-down for forward and reverse power operation by using PFM scheme. Compared to the bidirectional LLC circuit [15], the proposed converter can achieve ZVS operation for

Conclusion
A new three-level resonant converter is proposed, analyzed, and discussed to realize bidirectional power transfer and soft switching operation capability. A three-level diode clamp series resonant converter is used on the high-voltage side to have low voltage rating on active devices. For forward power operation, the conventional LLC circuit is selected to have ZVS operation on all power switches. Full-wave rectifier with synchronous switches is adopted on the low-voltage side to reduce conduction loss on power semiconductors. To overcome the low voltage gain problem on conventional LLC converter under reverse power operation, a parallel inductor is connected to the leg terminal of three-level diode-clamp resonant converter. Thus, the proposed converter can achieve voltage step-up and step-down for forward and reverse power operation by using PFM scheme. Compared to the bidirectional LLC circuit [15], the proposed converter can achieve ZVS operation for

Conclusions
A new three-level resonant converter is proposed, analyzed, and discussed to realize bidirectional power transfer and soft switching operation capability. A three-level diode clamp series resonant converter is used on the high-voltage side to have low voltage rating on active devices. For forward power operation, the conventional LLC circuit is selected to have ZVS operation on all power switches. Full-wave rectifier with synchronous switches is adopted on the low-voltage side to reduce conduction loss on power semiconductors. To overcome the low voltage gain problem on conventional LLC converter under reverse power operation, a parallel inductor is connected to the leg terminal of three-level diode-clamp resonant converter. Thus, the proposed converter can achieve voltage step-up and step-down for forward and reverse power operation by using PFM scheme. Compared to the bidirectional LLC circuit [15], the proposed converter can achieve ZVS operation for both power flow directions. Compared to the symmetric LLC converters in [16][17][18], the proposed LLC converter has less freewheeling current on primary-side for forward power operation. However, one ac switch is needed in the studied circuit compared to conventional bidirectional LLC circuit topology. Finally, the theoretical analysis is confirmed by experiments with a laboratory prototype.