Bidirectional DC Converter with Frequency Control: Analysis and Implementation

Abstract

In this paper, a direct current (dc) converter with the abilities of bidirectional power transfer and soft switching characteristics is studied and implemented. The circuit schematic of the developed dc converter is built by a half-bridge converter and a center-tapped rectifier with synchronous rectifier. Under forward power transfer, a half-bridge circuit is controlled to regulate the low-voltage side at a stable value. For backward power transfer, a center-tapped rectifier with synchronous rectifier is regulated to control the high-voltage side at the desired voltage value, and the half-bridge circuit is operated as a voltage doubler rectifier. Active power devices are operated at zero-voltage switching using a series resonant technique on the high-voltage side with frequency modulation and inductive load operation. The practicability of the developed converter is established from experiments with a laboratory prototype circuit.

1. Introduction

To reduce air pollution and climate change, renewable energy sources with power electronic conversion have been demanded and developed in recent years. Bidirectional power converters [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] have been developed for alternating current (ac) to direct current (dc) conversion and dc–dc conversion. In references [1,2,3,4,5,6,7], ac–dc bidirectional power converters are employed between an ac power source and dc bus voltage, and dc–ac bidirectional power converters are widely employed in ac drive systems. Direct current to dc bidirectional power converters [8,9,10,11,12,13] are demanded for battery-based storage systems. Bidirectional power flow dc converters with dual full-bridge circuit topology or half-bridge circuit topology were proposed to deliver power between high-voltage side dc bus and low-voltage side storage devices. Duty cycle control is normally used in dual full-bridge converters to control load voltage and attain soft switching characteristics. The main drawbacks of dual full-bridge converters are complicated control scheme and high conduction losses under low effective duty cycle case with high circulating current. Resonant techniques with a frequency-control scheme have been developed in modern power converters with high circuit efficiency due to wide load range of soft switching characteristics. The dual full-bridge resonant converter in reference [14] achieves soft switching characteristics in forward power transfer. However, the soft switching characteristics were lost in this circuit topology in backward power transfer due to the non-symmetric circuits in both power flow operations. The circuit topologies of dual full-bridge resonant converters in references [15,16,17] are symmetric for both forward and backward power transfer. Therefore, active switches can achieve soft switching at turn-on instant to eliminate switching loss. However, one parallel inductor is used on the high-voltage side. The circulating current in this parallel inductor will result in additional power loss when the circuit is operated under forward power transfer.

A soft switching resonant converter is studied and implemented in this paper to have the benefits of bidirectional power transfer ability, soft switching characteristics and less power devices. The proposed circuit is constructed by a half-bridge circuit on the primary-side and a center-tapped rectifier on the secondary-side. The LLC resonant circuit with frequency control is used on high-voltage side to control secondary-side voltage, reach soft switching turn-on for main power devices. To achieve same LLC resonant characteristics for both forward and backward power transfer, a parallel inductor is connected between half-bridge leg and split input capacitors on the high-voltage side. Under forward power transfer, power switches on half-bridge circuit are controlled by frequency-modulation to generate a square voltage input to the resonant tank and regulate low-side voltage V_L. Power switches on a center-tapped rectifier with synchronous switches are operated as synchronous rectifiers for reducing the conduction losses on the low-voltage side. Under forward power flow, the parallel inductor on the high-voltage side is disconnected (ac power switch is off) to reduce the power loss on this parallel inductor. When the proposed circuit is worked under backward power transfer, the parallel inductor is used on the high-voltage side to achieve LLC resonant characteristics. Power switches on the center-tapped rectifier are controlled to create a square voltage waveform on the primary-side of the isolated transformer and regulate high-side voltage V_H. Finally, experimental results are presented to verify the feasibility of the proposed circuit.

2. Circuit Diagram

Figure 1a shows the circuit schematic of a conventional resonant converter with s center-tapped rectifier on the secondary side. The main drawback in Figure 1a is high conduction loss on secondary-side rectifier diodes for high current output. In order to reduce conduction loss on secondary-side diodes, synchronous switches instead of fast recovery diodes are used on the secondary-side as shown in Figure 1b. For achieving bidirectional power control, Figure 2a demonstrates the circuit structure of the developed bidirectional dc converter. The circuit differences between the proposed converter and conventional unidirectional half-bridge resonant converter shown in Figure 1b are one ac switch S and inductor L_m1 used in the proposed circuit to achieve LLC resonant behavior for both forward and backward power transfer. Therefore, the advantages of a conventional unidirectional LLC resonant converter all exist in the proposed circuit. Half-bridge circuit is employed on the high voltage side to clamp voltage ratings of power semiconductor devices Q₁ and Q₂ at V_H. A center-tapped circuit topology with synchronous rectifier is employed on the secondary-side to reduce the conduction loss on the low-voltage side. An ac switch S is adopted on the primary-side to achieve resonant behavior when the adopted circuit is operated at backward power transfer. Figure 2b demonstrates the equivalent circuit of the developed circuit operated at forward power transfer from V_H to V_L. AC switch S is turned off. C_r, L_r and L_m2 are operated to achieve soft switching turn-on of Q₁ and Q₂. Power devices Q₃ and Q₄ on the low-voltage side operate as the synchronous switches. Therefore, the conduction losses on Q₃ and Q₄ are reduced at the low-voltage and high-current sides. Figure 2c illustrates circuit structure of the studied circuit operated at backward power transfer from V_L to V_H. At backward power transfer condition, power switch S is closed and Q₁ and Q₂ are turned off. L_m1, C_r and L_r are resonant. Thus, main switches Q₃ and Q₄ are turned on under zero-voltage switching.

Table 1. Circuit topologies and component counts between the proposed converter and the other bidirectional dc–dc converters.

	Primary-Side	Secondary-Side	Component Counts	Control Scheme
Proposed converter	Half-bridge circuit	Center-tapped circuit	5 switches, 3 magnetic components, 1 resonant capacitor	Frequency control
Circuit topology in Reference [8]	Full-bridge circuit	Center-tapped circuit	6 switches, 2 magnetic components	Duty cycle control
Circuit topology in Reference [9]	Full-bridge circuit	Full-bridge circuit	8 switches, 2 magnetic components	Duty cycle control
Circuit topology in Reference [10]	Half-bridge circuit	Half-bridge circuit	6 switches, 3 magnetic components, 1 resonant capacitor	Frequency control
Circuit topology in Reference [14]	Full-bridge circuit	Full-bridge circuit	8 switches, 2 magnetic components, 1 resonant capacitor	Frequency control
Circuit topology in Reference [16]	Full-bridge circuit	Full-bridge circuit	8 switches, 3 magnetic components, 2 resonant capacitors	Frequency control

gives the basic comparison between the proposed circuit and the conventional bidirectional dc–dc converters. It can be observed that the proposed converter has less component counts.

3. Principles of Operation

3.1. Forward Power Flow

If the converter is operated at forward power transfer as shown in Figure 2a, the power flow is from V_H terminal to V_L terminal. Power device S is controlled at the OFF state. Power switches Q₁ and Q₂ are regulated with frequency control to create a square voltage v_ab on the high-voltage side. Power switches Q₃ and Q₄ are operated as the synchronous switches to decrease conduction loss compared to the rectifier diodes with high voltage drop when diodes are conducting. The ON/OFF state of the synchronous switches are based on the current direction on the low-voltage side. Then a square voltage waveform can be created on the primary-side of the isolated transformer. L_m2, L_r and C_r are the magnetizing inductance, series resonant inductance and series resonant capacitance, respectively. Due to the inductive impedance of the resonant tank on the high-voltage side, as shown in Figure 3a, the soft switching characteristics of main switches Q₁ and Q₂ are achieved. The basic pulse-width modulation signals for forward power transfer operation are illustrated in Figure 3a. There are six operation modes under f_r (series resonant frequency) > f_sw (switching frequency). On the other hand, four operation modes per switching cycle can be observed if f_sw > f_r. Figure 4 illustrates the equivalent topological circuits for each mode of operation under forward power transfer. The principles of operation are discussed in what follows.

Mode 1 [t₀ ~ t₁]: At t₀, v_CQ1 = 0. Since i_Q1(t₀) < 0, D_Q1 conducts. Thus, Q₁ is turned on under zero voltage after t₀. In mode 1, i_Lr > i_Lm2 so that i_Q3 < 0 and D_Q3 conducts. Thus, Q₃ is forced to turn on. Due to low turn-on resistance R_on, the conduction losses on Q₃ are reduced. In this mode, the voltage v_ab = V_CH1 = V_H/2 and v_Lm2 = nV_L. The magnetizing current i_Lm2 will increase with the current slope nV_L/L_m2. In mode 1, the current variation on L_m2 is calculated as Δi_Lm2,1 = nV_LΔt₁₀/L_m2 where Δt₁₀ is time duration in this mode. C_r and L_r are resonant under v_ab = V_H/2, v_Lm2 = nV_L and the series resonant frequency $f_r=1/2\pi \sqrt{C_r{L}_r}$. If f_r > f_sw, then i_DQ3 will fall to zero. Thus, the next mode will go to mode 2. On the other hand, the circuit operation will go to mode 3 if f_r < f_sw.

Mode 2 [t₁ ~ t₂]: At time t₁, i_Q3 falls to zero. Then Q₃ is forced to turn off. i_Lr will flow through Q₁, C_r, L_r, L_m2 and C_H1. Due to C_H1 > C_r, L_r, C_r and L_m2 are resonant in mode 2 with v_ab = V_H/2 and resonant frequency $f_p=1/2\pi \sqrt{C_r(L_r+L_{m2})}$. Mode 2 ends at the half of the switching frequency t = T_sw/2.

Mode 3 [t₂ ~ t₃]: At time t₂, Q₁ turns off and i_Lr(t₂) > 0. After time t₂, v_CQ1 (v_CQ2) is increased (decreased) because C_Q1 (C_Q2) is charged (discharged) by the resonant current i_Lr. The zero-voltage switching condition of power device Q₂ is derived as.

$$i_{Lm2,peak}\ge \frac{V_H}{2}\sqrt{\frac{2C_{eq}}{L_{m2}+L_r}},$$

(1)

where C_eq = C_Q1 = C_Q2. Based on the switching frequency, magnetizing inductance and turn-ratio, the maximum magnetizing current can be calculated as:

$$i_{Lm2,peak}=\frac{\Delta i_{Lm2}}{2}\approx \frac{n{V}_L}{4L_{m2}{f}_{sw}},$$

(2)

From the given dead time, switching frequency, and input and output voltages, the magnetizing inductance L_m2 is obtained as:

$$L_{m2}\le \frac{t_{d}n{V}_L}{8f_{sw}{V}_H{C}_{eq}},$$

(3)

Mode 4 [t₃ ~ t₄]: At t₃, v_CQ2 = 0. Since i_Lr(t₃) > 0, the antiparallel diode D_Q2 is forward biased. Thus, Q₂ will turn on at zero voltage switching. Due to i_Q4(t₃) < 0, Q₄ turns on to reduce the conduction loss on Q₄. In this mode, v_ab = −V_H/2, v_Lm2 = −nV_L/2, and i_Lm2 decreases. The current variation on L_m2 is Δi_Lm2,4 = nV_LΔt₃₄/L_m2 where Δt₃₄ is the time duration in mode 4. L_r and C_r are resonant with v_ab = −V_H/2, v_Lm2 = −nV_L and $f_r=1/2\pi \sqrt{C_r{L}_r}$. If f_r > f_sw, the next step of the circuit operation will go to mode 5. Otherwise, the circuit operation will go to mode 6.

Mode 5 [t₄ ~ t₅]: At time t₄, i_Q4 = 0 and synchronous switch Q₄ turns off. The resonant inductor current i_Lr will flow through Q₂, C_r, L_r, L_m2 and C_H2. L_r, C_r and L_m2 are resonant with input voltage v_ab = −V_H/2.

Mode 6 [t₅ ~ T_sw + t₀]: At t₅, power device Q₂ turns off. Due to i_Lr(t₅) < 0, capacitor C_Q1 (C_Q2) is discharged (charged). The soft switching condition of power device Q₁ is the same as power device Q₂. The charge (discharge) time of C_Q2 (C_Q1) is sufficiently quick and can be ignored. At time T_sw + t₀, v_CQ1 = 0 and the circuit operations of the developed converter are completed.

Although there are several approaches [18,19,20,21] to generate square voltage waveforms on the ac side of the converter leg, fundamental frequency analysis [22] is the most useful approach to obtain voltage gain of the proposed circuit under different switching frequency. Based on the switching states of power devices, two square voltage signals are observed on high-voltage side v_ab and v_Lm2. C_r, L_r and L_m2 work as a circuit filter to eliminate harmonic signals. Therefore, v_ab and v_Lm2 can be treated as ac voltage’s only fundamental frequency to simplify the circuit analysis. The fundamental root mean square (rms) voltages v_ab,rms and v_Lm2,rms are calculated as $\sqrt{2}{V}_H/\pi$ and $2\sqrt{2}{V}_{L}n/\pi$. The primary-side fundamental resistance is obtained as $R_{ac2}=8n^2{R}_{o,L}/{\pi }^2$ where R_o,L is load resistance on the low-voltage side. The equivalent circuit at the fundamental switching frequency under forward power transfer is shown in Figure 3a. Based on a resonant tank consisting of C_r, L_r, L_m2 and R_ac2, the voltage gain G_H2L(s) and |G_H2L(s)| under different switching frequency are obtained as:

$$G_{H2L}(s)=\frac{v_{Lm2,rms}(s)}{v_{ab,rms}(s)}=\frac{\frac{s{L}_{m2}{R}_{ac2}}{s{L}_{m2}+R_{ac2}}}{s{L}_r+\frac{1}{s{C}_r}+\frac{s{L}_{m2}{R}_{ac2}}{s{L}_{m2}+R_{ac2}}},$$

(4)

$$|G_{H2L}(F)|=\frac{K_1{F}^2}{\sqrt{{[(K_1+1)F^2-1]}^2+{[Q_1{K}_{1}F(F^2-1)]}^2}},$$

(5)

where $Q_1=\sqrt{L_r/C_r}/R_{ac2}$, K₁=L_m2/L_r, F = f_sw/f_r and $f_r=1/(2\pi \sqrt{L_r{C}_r})$. Based on (5), the switching frequency is derived with the given high voltage value V_H, low voltage value V_L, inductor ratio K₁ = L_m2/L_r and equivalent load resistance R_ac2.

3.2. Reverse Power Flow

When the proposed converter is worked as backward power transfer to transfer power from V_L to V_H (Figure 3b), power devices Q₃ and Q₄ on the low-voltage side work as active switches to control primary-side voltage V_H. For having the circuit characteristics of LLC resonant converter, ac switch S is ON so that L_m1 is connected between points a and b. Based on the amplitude of |i_Lr| and |i_Lm1|, the anti-parallel diodes D_Q1 and D_Q2 are ON or OFF and the quasi-square voltage waveform is generated on voltage v_ab. Likewise, a square waveform is also generated on the primary-side voltage v_Lm2 based on the ON/OFF state of Q₃ and Q₄. Under reverse power transfer operation, L_r, C_r and L_m1 are resonant and the input impedance from the low-voltage side should be an inductive load. Then, Q₃ and Q₄ can be operated under zero-voltage condition such that the switching loss is lessened. The key pulse-width modulation signals under backward power transfer operation are demonstrated in Figure 3b. The equivalent topological circuits corresponding to mode operations are demonstrated in Figure 5.

Mode 1 [t₀ ~ t₁]: The voltage on C_Q3 is decreased to zero voltage at time t₀. Since i_Q3 < 0 and i_Lr > 0, the body diode D_Q3 of MOSFET Q₃ conducts so that MOSFET Q₃ turns on after t₀ to realize soft switching. In this mode, i_Lr(t₀) + i_Lm1(t₀) < 0, D_Q1 is conducting, C_H1 is charged by i_DQ1, v_ab = V_CH1 = V_H/2, v_Lm2 = nV_L, i_Lm2 increases with the slope nV_L/L_m2 and i_Lm1 increases with the slope V_H/(2L_m1). L_r and C_r are resonant. Power transfer is from V_L to V_H in this mode through components Q₃, T, L_r, C_r and D_Q1. If f_sw < f_r, the circuit action will go to mode 2. However, the circuit action will go to mode 3.

Mode 2 [t₁ ~ t₂]: If i_DQ1(t₁) = 0, then diode D_Q1 is off. The resonant current i_Lr flows through components S, C_r, L_r, T and L_m2, the components C_r, L_r and L_m1 are resonant with v_Lm2 = nV_L, and the resonant frequency is $f_p=1/2\pi \sqrt{C_r(L_r+L_{m1})}<<f_r$.

Mode 3 [t₂ ~ t₃]: At t₂, power device Q₃ turns off. Since i_Q3 > 0 and i_Q4 < 0, C_Q3 is charged and C_Q4 is discharged. The zero-voltage switching condition of Q₄ is obtained as:

$$(L_{m1}+L_r)i_{{}_{Lm1,peak}}^2+L_{m2}{i}_{{}_{Lm2,peak}}^2\ge 2C_{Q,s}{V}_L^2,$$

(6)

where C_Q,s = C_Q3 = C_Q4, $i_{Lm2,peak}\approx n{V}_L/(4L_{m2}{f}_{sw})$ and $i_{Lm1,peak}\approx V_H/(8L_{m1}{f}_{sw})$. The time duration in this mode is calculated when v_CQ4 is decreased to zero voltage.

$$\Delta t_{23}\approx \frac{2V_L{C}_{Q,s}}{n[i_{Lm1,peak}+i_{Lm2,peak}]}=\frac{16L_{m1}{L}_{m2}{f}_{sw}{V}_L{C}_{Q,s}}{n(L_{m2}{V}_H+2n{L}_{m1}{V}_L)}\le t_d,$$

(7)

where t_d is a dead time.

Mode 4 [t₃ ~ t₄]: At time t₃, v_CQ4 = 0. Then, D_Q4 becomes forward biased. Since i_Q4(t₃) is negative, Q₄ can be turned on at this instant without turn-on switching loss. In this mode, D_Q2 is forward biased, Q₄ is turned on, v_ab = v_Lm1 = −V_H/2, v_Lm2 = −nV_L, and C_r and L_r are resonant. If f_sw < f_r, the next operating mode will go to mode 5. Otherwise, the next operating mode is mode 6.

Mode 5 [t₄ ~ t₅]: If f_sw < f_r, i_DQ2 = 0 before active device Q₄ turns off. At time t₄, i_DQ2 = 0 and D_Q2 is reverse biased. Therefore, the resonant inductor current i_Lr flows through L_m1, C_r, L_r and T. L_m1, C_r and L_r are resonant under v_Lm2 = −nV_L.

Mode 6 [t₅ ~ T_sw + t₀]: Q₄ is turned off at t₅. Then, C_Q3 and C_Q4 are discharged and charged, respectively. At time T_sw + t₀, v_CQ3 = 0. Then the circuit operation will go to mode 1 for next switching period.

The operation of the proposed converter at reverse power transfer is like the forward power transfer. Q₃ and Q₄ are controlled by frequency-mode operation. The resonant tank included L_r, C_r and L_m1 and is operated as a band-pass filter to eliminate harmonics. In Figure 3b, the input fundamental rms voltage $v_{Lm2,rms}=2\sqrt{2}n{V}_L/\pi$. The resonant tank includes R_ac1, L_m1, C_r and L_r. The equivalent resistance $R_{ac1}=2R_{o,H}/{\pi }^2$. The voltage gains $G_{L2H}(s)$ and $|G_{L2H}(s)|$ under reverse power transfer are calculated as:

$$G_{L2H}(s)=\frac{v_{Lm1,rms}(s)}{v_{Lm2,rms}(s)}=\frac{\frac{s{L}_{m1}{R}_{ac1}}{s{L}_{m1}+R_{ac1}}}{\frac{1}{s{C}_r}+s{L}_r+\frac{s{L}_{m1}{R}_{ac1}}{s{L}_{m1}+R_{ac1}}},$$

(8)

$$|G_{L2H}(F)|=\frac{K_2{F}^2}{\sqrt{{[(K_2+1)F^2-1]}^2+{[Q_2{K}_{2}F(F^2-1)]}^2}},$$

(9)

where $f_r=1/(2\pi \sqrt{L_r{C}_r})$, $Q_2=\sqrt{L_r/C_r}/R_{ac1}$, K₂ = L_m1/L_r and F = f_sw/f_r. Based on Equation (9), the necessary switching frequency f_sw is calculated from the given parameters V_H, V_L, K₂ = L_m1/L_r and R_ac1.

4. Experimental Waveforms

In this section, a design procedure of the studied circuit is discussed and the experiments are demonstrated. For forward power operation, the high-side voltage V_H = 350 V ~ 400 V and the low-side voltage V_L = 48 V. For reverse power transfer, the low-voltage V_L varies from 38 V to 52 V and V_H = 400 V. The power rating P_o,rated = 480 W. Based on Equations (5) and (9), the voltage transfer functions for both forward power operation and reverse power operation are alike. To simplify the circuit design, only the forward power transfer is discussed. The voltage gain |G_H2L(s)| under V_H = 400 V is set to one. Then, the turn-ratio n of power transformer T is calculated as $n=|G_{H2L}|\times \frac{V_{H,\max }}{2V_{L,\max }}=1\times \frac{400}{2\times 52}\approx 3.85$. In this prototype, the selected primary turns and secondary turns are 23 and 6, respectively. According to turn-ratio n, the dc gains are derived under 48 V output voltage.

$$|G_{H2L}{|}_{dc,\min }=\frac{2n{V}_{L,nom}}{V_{H,\max }}=\frac{2\times (23/6)\times 48}{400}\approx 0.92,$$

(10)

$$|G_{H2L}{|}_{dc,\max }=\frac{2n{V}_{L,nom}}{V_{H,\min }}=\frac{2\times (23/6)\times 48}{350}\approx 1.05,$$

(11)

Since the maximum gain of |G_H2L(s)| is 1.05, the select inductor ratio K₁ and quality factor Q₁ should be selected under the full load and minimum input voltage case. The larger K₁ can reduce circulating current loss and the smaller K₁ can increase voltage gain. Since the maximum voltage gain of |G_H2L(s)| is 1.05, K₁ = 13 is selected in the prototype to lessen the circulating current loss. The maximum gain of |G_H2L(s)| under K₁ = 13 and Q₁ = 0.35 is close to 1.18. Since n = 23/6, R_ac2 at rated power can be obtained as:

$$R_{ac2}=\frac{8n^2}{{\pi }^2}{R}_{o,L}=\frac{8\times {(23/6)}^2}{{3.14159}^2}\times \frac{48}{10}\approx 57.17\mathsf{\Omega },$$

(12)

Since f_r is selected as 100 kHz, C_r and L_r are calculated as $C_r=1/2\pi Q_1{f}_r{R}_{ac2}\approx 79.5\mathrm{nF}$ and $L_r=1/{(2\pi f_r)}^2{C}_r\approx 31.86\mathsf{\mu }\mathrm{H}$. The selected components are C_r = 78 nF, L_r = 32 µH and ${\mathrm{L}}_{\mathrm{m}2}={\mathrm{K}}_1{\mathrm{L}}_{\mathrm{r}}=13\times 32=416\mathsf{\mu }\mathrm{H}$. The secondary-side rms current reflected to the primary-side is obtained as $I_{rms,p}=\frac{\pi I_o}{2\sqrt{2}n}\approx 2.9\mathrm{A}$. The minimum switching frequency of the prototype circuit is obtained as $f_{sw,\min }=1/2\pi \sqrt{C_r(L_r+L_{m2})}\approx 27\mathrm{kHz}$. The maximum rms magnetizing current occurs at minimum switching frequency f_sw,min and can be expressed as $I_{Lm2,rms}=\frac{1}{2\sqrt{3}}\frac{n{V}_L}{4f_{sw,\min }{L}_{m2}}\approx 1.18\mathrm{A}$. The rms current of L_r is obtained as $I_{Lr,rms}=\sqrt{I_{Lm2,rms}^2+I_{rms,p}^2}\approx 3.13\mathrm{A}$. The maximum peak voltage on capacitor C_r is derived as $v_{Cr,peak}=\frac{\sqrt{2}{I}_{Lr,rms}}{2\pi f_{sw,\min }{C}_r}\approx 334.5V$. The theoretical voltage ratings of Q₁ ~ Q₄ are v_Q1,stress = v_Q2,stress = 400 V and v_Q3,stress = v_Q4,stress = 104V. The rms switch currents are $I_{Q1,rms}=I_{Q2,rms}=I_{Lr,rms}/\sqrt{2}\approx 2.21\mathrm{A}$ and $I_{Q3,rms}=I_{Q4,rms}=n{I}_{\sec ,p}/\sqrt{2}\approx 7.85\mathrm{A}$. Power devices Q₁ and Q₂ are implemented using IRG4PC40W with 600 V/20 A rating, and power devices Q₃ and Q₄ are implemented using IRFB4321PbF with 150 V/85 A rating. Two SiHG20N50C with 500 V/20 A rating with back-to-back connection is adopted to implement ac switch S. The selected inductor L_m1 = 224 µH means the inductor ratio K₂ = L_m1/L_r = 7 at reverse power transfer condition. In the prototype circuit, the input and output capacitances are C_H1 = C_H2 = 180 µF/400 V and C_L = 2200 µF/100 V.

Based on the circuit values calculated in design procedure, a prototype circuit was implemented, and the experiments are provided to verify the effectiveness of the developed circuit. Figure 6 gives the photograph of the proposed prototype. The test results of the developed converter operated at forward power transfer are shown in Figure 7, Figure 8, Figure 9 and Figure 10. Likewise, Figure 11, Figure 12, Figure 13 and Figure 14 show the test results under backward power transfer. Figure 7 gives the test results of the developed circuit under 100% load and V_H = 350 V case. Since f_sw is less than f_r, the secondary-side currents are decreased to zero before active device is turned off. Similarly, Figure 8 illustrates the experimental results under 100% rated power and V_H = 400 V case. It is clear that f_sw (switching frequency) is close to f_r (resonant frequency) so that i_Lr and v_Cr are close to sinusoidal waveforms. Figure 9 and Figure 10 demonstrate the test waveforms of the power devices Q₁ and Q₂ under different input voltage and load situations. It is observed that zero-voltage turn-on switching of Q₁ and Q₂ are achieved from 20 to 100% of rated power. The switching frequency at V_H = 350 V case is less than the switching frequency at V_H = 400 V case. For forward power transfer, the circuit efficiencies are 94.73% (90%), 94.8% (93.2%) and 93.9% (92.3%) at 20%, 50% and 100% rated power, respectively, under 400 V (350 V) input. The measured switching frequencies are 151.3 kHz (67.4 kHz), 114.3 kHz (60 kHz) and 97.6 kHz (52.85 kHz) at 20%, 50% and 100% rated power, respectively, under 400 V (350 V) input. Figure 11 and Figure 12 give the test results of main voltage and current waveforms under backward power transfer at input voltage V_L = 38 V and 52 V cases. Based on test results, the switching frequencies f_sw under these cases are all less than f_r (resonant frequency). Therefore, the reverse recovery current loss on D_Q1 and D_Q2 is improved. Figure 13 and Figure 14 demonstrate the measured waveforms of power devices Q₃ and Q₄ at different load and voltage cases. The soft switching characteristics of Q₃ and Q₄ are realized from 20% of rated power. Based on test results shown in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14, the experimental waveforms are agreed with the theoretical waveforms in the system analysis. For backward power transfer, the circuit efficiencies are 88.2% (87.1%), 91.1% (90.4%) and 90.2% (90.1%) at 20%, 50% and 100% rated power, respectively, under 52V (38V) input. The measured switching frequencies are 72.5 kHz (62.8 kHz), 60.2 kHz (53.4 kHz) and 53.5 kHz (48.8 kHz) at 20%, 50% and 100% rated power, respectively, under 52 V (38 V) input. Because of low voltage and high current input at the low voltage side under backward power transfer, more conduction loss will be introduced on power switches at the low voltage side. Thus, the circuit efficiency under backward power operation is less than the circuit efficiency under forward power operation.

5. Conclusions

A bidirectional resonant converter is studied and implemented to achieve bidirectional power transfer capability. To achieve the dual symmetric resonant behavior for both forward power operation and backward power operation and reduce the circulating current loss under forward power transfer, an ac switch and a parallel inductor is used on the high voltage side. The input impedance of the proposed circuit is regulated with the frequency-modulation scheme. The soft switching of active devices is realized. The forward and backward power transfers have the same LLC circuit characteristics. The parallel inductor on the primary-side is disconnected under forward power transfer in order to improve the circulating current loss. Finally, experimental waveforms are provided to demonstrate the achievability of the developed converter. The main drawback of the proposed converter is more conduction loss on magnetizing inductor during the backward power transfer, because the low-side voltage will introduce a magnetizing current, and this is an additional power loss on low-side power devices and transformers. Therefore, the circuit efficiency at the backward power transfer is less than forward power transfer. In order to overcome low circuit efficiency at backward power flow in the proposed converter, the symmetric resonant circuit, such as CLLLC or CLLC, instead of using half-bridge or full-bridge circuit topology, may be researched and studied in future work.