Analysis of a Three-Level Bidirectional ZVS Resonant Converter

Abstract

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.

1. 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 Section 2 and Section 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.

2. Circuit Schematic of the Developed Converter

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 S₁~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. S₁~S₄ are main power devices to control output voltage V_L. L_r, L_m and C_r are LLC resonant circuit and Q₁~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 Q₁~Q₄ are major power switches and L_r, L_b and C_r are resonant circuit. D_S1~D_S4 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.

3. 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. S₁~S₄ are controlled with PFM scheme. Due to PWM signals of S₁~S₄, there is a square wave with −V_H/2 or V_H/2 on the leg voltage v_ab. 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 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.

Step 1 (t₀ ≤ t < t₁): At t < t₀, i_Lr < 0. Thus, i_Lr discharges C_S1 and C_S2 are discharged. At t₀, v_CS1 = v_CS2 = 0. Thus, D_S1 and D_S2 are conducting due to i_Lr < 0. The ZVS operation of S₁ and S₂ can be achieved after time t₀. If i_Lr < 0, D_b is forward biased. The leg voltage v_ab = v_Cf = v_CS3 = v_CS4 = V_H/2. Since i_Lr > i_Lm, Q₁ and Q₄ 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 Δi_Lm in step 1 is equal to nV_LΔt₀₁/L_m where Δt₀₁ = t₁ − t₀. The resonant frequency in step 1 is $f_r=1/(2\pi \sqrt{L_r{C}_r})$.

Step 2 (t₁≤t < t₂): If f_sw < f_r, i_Q1 and i_Q4 will decrease to zero ampere at t₁. Thus, Q₁ and Q₄ can turn off after time t₁. In step 2, the leg voltage v_ab = V_H/2 and L_r, L_m and C_r are resonant.

Step 3 (t₂≤t < t₃): At t₂, S₁ and S₂ turn off. The positive current i_Lr(t₂) 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 S₃ and S₄ is expressed in Equation (1).

$$i_{Lm,p}\ge \frac{V_H}{2}\sqrt{\frac{C_S}{L_r}}$$

(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).

$$i_{Lm,p}=\frac{\Delta i_{Lm}}{2}\approx \frac{n{V}_L{T}_{sw}}{4L_m}$$

(2)

The dead time t_d between S₃ and S₁ (or S₄ and S₂) is approximately expressed in Equation (3).

$$t_d>\frac{C_S{V}_H}{i_{Lm,p}}=\frac{4L_m{C}_S{V}_H}{n{V}_L{T}_{sw}}$$

(3)

Therefore, the maximum magnetizing inductance is derived in Equation (4).

$$L_m\le \frac{n{V}_L{t}_d{T}_{sw}}{4C_S{V}_H}$$

(4)

Step 4 (t₃≤t < t₄): At t₃, v_CS3 = v_CS4 = 0. Since i_Lr(t₃) is positive, D_S3 and D_S4 are conducting. Power devices S₃ and S₄ can turn on after t₃ under zero voltage condition. Since i_Lr(t₃) > 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(t₃) < 0 and i_Q3(t₃) < 0. Therefore, Q₂ and Q₃ turn on to conduct the secondary-side current, the primary-side voltage v_Lm = −nV_L and i_Lm decreases.

Step 5 (t₄≤t < t₅): The secondary-side switch currents i_Q2 = i_Q3 = 0 at t₄. Then, Q₂ and Q₃ turn off. In this step, v_ab = −V_H/2 and L_r, L_m and C_r are resonant.

Step 6 (t₅≤t <T_sw+t₀): At t₅, S₃ and S₄ turn off. In this step, i_Lr(t₅) < 0 and v_CS1 and v_CS2 decrease. The ZVS condition of S₂ and S₁ is the same as S₄ and S₃ in Equation (1). The step 6 is ended at time T_sw+t₀.

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 S₁~S₄ and Q₁~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 $v_{ab,rms}=\sqrt{2}{V}_H/\pi$ and $v_{Lm,rms}=2\sqrt{2}n{V}_L/\pi$. Based on the power balance between the primary-side and the secondary-side of transformer, the primary-side load resistance is expressed as $R_{ac,L}=8n^2{R}_L/{\pi }^2$. The transfer function G_{H_L}(s) between the output and input sides in Figure 2a is obtained as:

$$G_{H\_L}(s)=\frac{v_{Lm,rms}(s)}{v_{ab,rms}(s)}=\frac{\frac{s{L}_m{R}_{ac,L}}{s{L}_m+R_{ac,L}}}{\frac{s{L}_m{R}_{ac,L}}{s{L}_m+R_{ac,L}}+s{L}_r+\frac{1}{s{C}_r}}$$

(5)

$$|G_{H\_L}(F)|=\frac{K_1{F}^2}{\sqrt{{[F^2(K_1+1)-1]}^2+{[Q_1{K}_{1}F(F^2-1)]}^2}}$$

(6)

where F = f_sw/f_r, $f_r=1/(2\pi \sqrt{L_r{C}_r})$, K₁ = L_m/L_r and $Q_1=\sqrt{L_r/C_r}/R_{ac,L}$. 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 Q₁~Q₄ are controlled with PFM scheme and D_S1~D_S4 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 Q₁~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.

Step 1 (t₀ ≤ t < t₁): This step starts at t₀ 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 Q₁ and Q₄ can turn on under zero voltage. Due to i_Lr(t₀) + i_Lb(t₀)<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 Q₁ and Q₄ turn off, i_DS1 and i_DS2 will decrease to zero if f_sw < $f_r=1/2\pi \sqrt{C_r{L}_r}$.

Step 2 (t₁≤t < t₂): At time t₁, 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 $f_p=1/2\pi \sqrt{C_r(L_b+L_r)}$.

Step 3 (t₂≤t < t₃):Q₄ and Q₁ turn off at t₂. C_Q2 and C_Q3 are discharged in step 3. The ZVS condition of Q₃ and Q₂ are obtained in Equation (7).

$$(L_b+L_r)i_{Lb,p}^2+L_m{i}_{Lm,p}^2\ge 2C_Q{V}_L^2$$

(7)

where C_Q = C_Q1 =..= C_Q4, $i_{Lm,p}\approx n{V}_L/(4L_m{f}_{sw})$ and $i_{Lb,p}\approx V_H/(8L_b{f}_{sw})$. At t_3, v_CQ3(t₃) = v_CQ2(t₃) = 0. The time interval Δt₂₃ is expressed in Equation (8).

$$\Delta t_{23}\approx \frac{2V_L{C}_Q}{n[i_{Lm,p}+i_{Lb,p}]}=\frac{16L_m{L}_b{f}_{sw}{V}_L{C}_Q}{n(2n{L}_b{V}_L+L_m{V}_H)}\le t_d$$

(8)

where t_d is dead time between Q₄ and Q₃ or Q₂ and Q₁.

Step 4 (t₃≤t < t₄): Step 4 starts at t₃ when v_CQ2 = v_CQ3 = 0. Therefore, D_Q3 and D_Q2 conduct and Q₃ and Q₂ 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 (t₄≤t < t₅):i_DS3 = i_DS4 = 0 at t₄. In this step, Q₂ and Q₃ are still in the on state so that v_Lm = −nV_L. L_b, C_r and L_r are series resonant.

Step 6 (t₅≤t < T_sw+t₀):Q₂ and Q₃ turn off at t₅. Then, C_Q1 and C_Q4 are discharged and v_CQ1 = v_CQ4 = 0 at t_sw + t₀.

The proposed converter has the similar operation principle for both forward and reverse power operation. For the reverse power operation, Q₁~Q₄ are controlled as main power switches. D_S1~D_S4 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 $v_{Lm,rms}=2\sqrt{2}n{V}_L/\pi$ and the ac equivalent resistance at high voltage side is $R_{ac,H}=2R_H/{\pi }^2$. The rms voltage on v_ab is expressed as $v_{ab,rms}=\sqrt{2}{V}_H/\pi$. 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.

$$G_{L\_H}(s)=\frac{v_{ab,rms}(s)}{v_{Lm,rms}(s)}=\frac{\frac{s{L}_b{R}_{ac,H}}{s{L}_b+R_{ac,H}}}{\frac{s{L}_b{R}_{ac,H}}{s{L}_b+R_{ac,H}}+\frac{1}{s{C}_r}+s{L}_r}$$

(9)

$$|G_{L\_H}(F)|=\frac{K_2{F}^2}{\sqrt{{[(F^2-1)Q_2{K}_{2}F]}^2+{[F^2(K_2+1)-1]}^2}}$$

(10)

where F = f_sw/f_r, $f_r=1/(2\pi \sqrt{L_r{C}_r})$, K₂ = L_b/L_r and $Q_2=\sqrt{L_r/C_r}/R_{ac,H}$. 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).

4. 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).

$$n=\left|G_{H\_L}\right|\times \frac{V_{H,\max }}{2V_{L,\max }}\approx 7.7$$

(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).

$$|G_{H\_L}{|}_{\max }=\frac{2n{V}_{L,nom}}{V_{H,\min }}\approx 1.024$$

(12)

$$|G_{H\_L}{|}_{\min }=\frac{2n{V}_{L,nom}}{V_{H,\max }}\approx 0.96$$

(13)

The control parameters K₁ and Q₁ can be selected at full load P_L,full and minimum input voltage V_H,min conditions. To reduce circulating current, the inductor ratio K₁=10 is used in this prototype circuit. For Q₁ = 0.38 and K₁ = 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).

$$R_{ac,L}=\frac{8n^2}{{\pi }^2}{R}_L=\frac{8\times {(48/6)}^2}{{3.14159}^2}\times \frac{48}{30}\approx 83\mathrm{\Omega }$$

(14)

The circuit parameters $C_r=1/2\pi Q_1{f}_r{R}_{ac,L}\approx 50 \mathrm{nF}$ and $L_r=1/{(2\pi f_r)}^2{C}_r\approx 50 \mathsf{\mu }\mathrm{H}$ 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 $L_m=K_1{L}_r=540 \mathsf{\mu }\mathrm{H}$. The theoretical primary rms current is calculated as:

$$I_{pri,rms}=\frac{\pi I_o}{2\sqrt{2}n}\approx 4.2 \mathrm{A}$$

(15)

The theoretical minimum switching frequency is obtained as $f_{sw,\min }=1/2\pi \sqrt{C_r(L_r+L_m)}\approx 30 \mathrm{kHz}$. The minimum switching frequency will result in the maximum rms magnetizing current.

$$I_{Lm,rms}=\frac{1}{2\sqrt{3}}\frac{n{V}_L}{4f_{sw,\min }{L}_m}\approx 1.7 \mathrm{A}$$

(16)

Therefore, the rms resonant inductor current is obtained in Equation (17).

$$I_{Lr,rms}=\sqrt{I_{Lm,rms}^2+I_{pri,rms}^2}\approx 4.53 \mathrm{A}$$

(17)

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 $I_{S1,rms}=..=I_{S4,rms}\approx I_{Lr,rms}/\sqrt{2}\approx 3.2 \mathrm{A}$ and $I_{Q1,rms}=..=I_{Q4,rms}\approx \pi I_o/4\approx 23.6 \mathrm{A}$. Power devices S₁~S₄ are implemented using IRG4PC40W with 600 V/20 A rating. Power switches Q₁~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 K₂ = 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. Parameters and specifications of the presented converter.

Items	Parameter
High voltage VH	750 V~800 V
Low voltage VL	48 V
Rated power Po	1440 W
Resonant frequency fr	100 kHz
High-side capacitances CH1, CH2	330 µF/400 V
Low-side capacitance CL	4400 µF/100 V
Resonant capacitance Cr	47 nF
Flying capacitance Cf	2.2 µF
Resonant inductance Lr	54 µH
Parallel inductance Lb	230 µH
Power switches S1~S4	IRG4PC40W (600 V/20 A)
Power switches Q1~Q4	IRFB3307 (75 V/150 A)
Power switch Sac	G20N50C (500 V/20 A)
Clamp diodes Da, Db	HFA15TB60PBF (600 V/15 A)
Winding turns of T: nH, nL	48, 6
Magnetizing inductance Lm	540 µH

.

Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 provide the test results for forward power operation and Figure 11, Figure 12, Figure 13 and Figure 14 provide the measured waveforms for reverse power operation. The PWM signals of S₁–S₄ at 100% load are presented in Figure 6. S₁ (S₃) and S₂ (S₄) 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 Q₁–Q₄ at 100% load. Figure 10 illustrates the PWM waveforms of S₁–S₄ at 20% load. It can observe that S₁–S₄ all turn on under ZVS at 20% load. Figure 11 gives the PWM signals of Q₁~Q₄ under backward power operation and different input voltages. Power devices Q₁ (Q₂) and Q₄ (Q₃) 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 Q₁~Q₄ under 20% load. It can observe that Q₁–Q₄ 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.

5. 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.