Bidirectional Resonant Converter with Half-Bridge Circuits: Analysis, Design, and Implementation

Abstract

A soft-switching dc–dc converter with bidirectional power flow capability is studied in this paper for energy storage units or electric vehicle applications. The circuit topology of the studied converter is constructed using a dual half-bridge circuit with split capacitors. A series resonant tank with frequency control modulation is employed in the proposed circuit to realize the soft switching characteristics of active devices. Synchronous-rectifier-based Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFETs) are used on the low-voltage side to lessen conduction loss on the power semiconductors. The benefits of the studied circuit are bidirectional power flow capability, high efficiency, low switching loss, and simple circuit structure. The achievability of the developed converter is demonstrated from test results with a scaled-down laboratory prototype.

1. Introduction

Clean energy sources have been developed to lessen the demand of fossil fuel, reduce environmental air pollution, and decrease climate change. Therefore, power-electronics-based energy conversion has been researched and studied to increase energy conversion efficiency and reduce circuit size. For ac or dc microgrid systems [1,2,3,4,5], dc/dc converters, ac/dc converters, and dc/ac converters are needed to integrate the utility power, wind power, solar power, energy storage units, and residential loads. For electric vehicles [6,7,8,9], ac/dc converters are employed for the battery charger, dc/dc converters are adopted on the dc power distributing system, and dc/ac converters are used for ac motor drives. Bidirectional dc/dc converters [10,11,12,13,14,15] are widely used for battery-based energy storage units in dc microgrid systems and electric vehicles. Normally, bidirectional dc/dc converters are adopted to transfer electric energy between high voltage dc buses and energy storage units. Among the circuit topologies of bidirectional dc/dc converters, the half-bridge topologies and full-bridge topologies are most attractive solutions to realize bidirectional power flow capability. Phase-shift pulse-width modulation (PWM) is usually selected in full-bridge converters. However, high circulating current losses and high switching losses on light load are the main shortcomings. Resonant converters [16,17,18,19] with frequency modulation have been studied to achieve soft switching characteristics and bidirectional power flow capability. However, the circuit characteristics under forward and reverse power flow directions are different. Thus, the design procedures of bidirectional resonant converters are more difficult. In [16], the characteristic of a series resonant converter was achieved in forward power flow (or buck operation). However, the characteristic of a series resonant converter cannot be achieved at the whole load range in reverse power flow (or boost operation) due to the circuit topologies in the buck and boost operations not being symmetric circuits. In [17,18,19], the circuit topologies with half-bridge or full-bridge converters in both power flows are symmetric so that the power devices can be turned on under zero voltage and low switching losses. However, one more inductor is connected to the switching leg so that high circulating current is introduced and conduction losses are increased. Therefore, the circuit efficiency is reduced.

A bidirectional dc/dc converter with a frequency modulation scheme is studied to realize the features of bidirectional power flow capability and zero-voltage switching. A dual half-bridge circuit is used in the studied circuit to realize bidirectional power flow. A series resonant tank is adopted on the high-voltage side to realize the soft switching characteristics for all active devices. Synchronous rectifiers are used on the low-voltage side to further reduce the conduction loss. In order to realize the same resonant characteristics under forward and reverse power flow directions, an ac power switch and parallel inductor are connected to the half-bridge leg on the high-voltage side. The proposed circuit and the conventional bidirectional resonant converters in [17,18,19] have the same resonant component counts. However, the proposed converter has less circulating current loss due to the fact that the parallel inductor is disconnected under forward power flow. The circuit topology of the studied circuit is simple and easy to implement. In Section 2, the circuit configuration, operating stages, and circuit characteristics of the proposed converter are discussed. In Section 3, the design procedures of the developed converter are provided. Experimental waveforms are demonstrated in Section 4, and conclusions are discussed in Section 5.

2. Proposed Converter

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. L_r, C_r, and L_m1 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. L_r, C_r, and L_m2 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 v_ab. 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 v_cd’. L_m1 is the magnetizing inductance of the transformer; L_r and C_r 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 L_r, C_r, and L_m1, 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 C_Q1 is decreased to zero at t₀. Therefore, the soft switching characteristic of Q₁ can be achieved after t₀ due to i_Q1 (t₀) = i_Lr (t₀) < 0 and D_Q1 conducts. Since i_Lr > i_Lm1 and i_Q3 < 0, Q₃ is turned on and the secondary side current flows through MOSFET Q₃ turn-on resistor R_on to charge capacitor C₃. Due to low turn-on resistance R_on, 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 v_ab = V_C1 = V₁/2 and v_cd = V_C3 = V₂/2. Thus, the primary magnetizing voltage v_Lm1 = v_cd’ = nV₂/2 and the magnetizing current i_Lm1 increase with the current slope nV₂/(2L_m1). The magnetizing current variation in Stage 1 is about Δi_Lm1,1 = nV₂Δt₁₀/(2L_m1) where Δt₁₀ is the time interval in Stage 1. C_r and L_r are resonant in Stage 1 under v_ab = V₁/2, v_Lm1 = nV₂/2 and $f_r=1/2\pi \sqrt{C_r{L}_r}$. If f_r > f_sw, then T_r/2 < T_sw/2. Therefore, the transformer secondary current will decrease to zero before Q₁ turns off. The circuit operation goes to Stage 2. If f_r < f_sw, then T_r/2 > T_sw/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 f_r > f_sw, the transformer secondary current decreases to zero before Q₁ turns off. When i_Q3 equals zero at t₁, Q₃ turns off. i_Lr flows through Q₁, C_r, L_r, L_m1, and C₁. Since C₁ >> C_r, components C_r, L_r, and L_m1 are resonant under v_ab = V₁/2 and resonant frequency $f_p=1/2\pi \sqrt{C_r(L_r+L_{m1})}$. When t = T_sw/2, switch Q₁ turns off and the circuit operation of Stage 2 is completed.

Stage 3 (t₂~t₃): When t = t₂ = T_sw/2, Q₁ turns off, and C_Q1 (C_Q2) is charged (discharged) by i_Lr. In order to ensure that Q₂ turns on at zero voltage, the zero-voltage condition of Q₂ is calculated using

$$i_{Lm1,peak}\ge \frac{V_1}{2}\sqrt{\frac{2C_Q}{L_{m1}+L_r}}$$

(1)

where C_Q = C_Q1 = C_Q2. The maximum magnetizing current is estimated using Equation (2).

$$i_{Lm1,peak}=\frac{\Delta i_{Lm}}{2}\approx \frac{n{V}_2}{8L_{m1}{f}_{sw}}$$

(2)

The time interval in Stage 3 can be estimated as follows when C_Q2 is discharged to zero voltage:

$$\Delta t_{23}=\frac{2V_1{C}_Q}{i_{Lr}(t_2)}\approx \frac{2V_1{C}_Q}{i_{Lm1,peak}}=\frac{16L_{m1}{f}_{sw}{V}_1{C}_Q}{n{V}_2}\le t_{dead}$$

(3)

where t_dead is the dead time between Q₁ and Q₂. Based on Equation (3), the maximum magnetizing inductance L_m1 can be calculated using Equation (4).

$$L_{m1}\le \frac{t_{dead}n{V}_2}{16f_{sw}{V}_1{C}_Q}$$

(4)

Stage 4 (t₃~t₄): The voltage of C_Q2 is decreased to zero at t₃. The body diode D_Q2 conducts due to i_Lr (t₃) > 0 (or i_Q2 (t₃) < 0). After time t₃, the soft switching characteristic of Q₂ can achieved. Since the secondary side current i_Q4 is negative, Q₄ is forced to turn on to decrease conduction loss. Then, the ac side voltage v_cd = −V₂/2, the magnetizing voltage v_Lm1 = −nV₂/2, and i_Lm1 decreases. The magnetizing current variation in Stage 2 is about Δi_Lm1,4 = nV₂Δt₃₄/(2L_m1) where Δt₃₄ is the time interval in Stage 4. In Stage 4, C_r and L_r are resonant under v_ab = −V₁/2, v_Lm1 = −nV₂/2 and $f_r=1/2\pi \sqrt{C_r{L}_r}$. If f_r > f_sw, the circuit operation goes to Stage 5. If f_r < f_sw, the circuit operation goes to Stage 6.

Stage 5 (t₄~t₅): If f_r > f_sw, i_Q4 will go to zero before Q₂ turns off. When i_Q4 equals zero at t₄, Q₄ is forced to turn off. In Stage 5, i_Lr flows through Q₂, C_r, L_r, L_m1, and C₂. Components C_r, L_r, and L_m1 are resonant under v_ab = −V₁/2 with resonant frequency $f_p=1/2\pi \sqrt{C_r(L_r+L_{m1})}$. When Q₂ turns off, the circuit operation goes to Stage 6.

Stage 6 (t₅~T_sw + t₀): When Q₂ turns off at t₅, C_Q1 (C_Q2) is discharged (charged) by i_Lr (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 T_sw + t₀, the voltage of C_Q1 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 v_ab and v_cd. Since the resonant tank of L_r, C_r, and L_m1 is worked as a band pass filter, the harmonic frequency on v_ab and v_cd can be neglected to simplify the characteristic analysis. The root mean square (rms) values of v_ab and v_cd’ at the switching frequency are $\sqrt{2}{V}_1/\pi$ and $\sqrt{2}{V}_{2}n/\pi$, respectively. The equivalent resistance at the primary side of transformer can be calculated as $R_{ac2}=2n^2{R}_o/{\pi }^2$. The equivalent circuit of the adopted resonant tank is shown in Figure 2a. The effectively fundamental sinusoidal voltage is v_ab,f with rms voltage value $\sqrt{2}{V}_1/\pi$ and the resonant tank consists of L_r, C_r, L_m1, and R_ac2. The voltage transfer function between low-voltage V₂ and high-voltage V₁ is derived in Equation (5).

$$G_{1,2}(s)|=\frac{v_{R_{ac2}}(s)}{v_{ab,f}(s)}=\frac{\frac{s{L}_{m1}{R}_{ac2}}{s{L}_{m1}+R_{ac2}}}{\frac{1}{s{C}_r}+s{L}_r+\frac{s{L}_{m1}{R}_{ac2}}{s{L}_{m1}+R_{ac2}}}$$

(5)

The amplitude of the voltage transfer function in Equation (5) can be obtained using Equation (6):

$$|G_{1,2}(f_{sw})|=\frac{k{F}^2}{\sqrt{{[(k+1)F^2-1]}^2+{[QkF(F^2-1)]}^2}}$$

(6)

where $f_r=1/(2\pi \sqrt{L_r{C}_r})$, $Q=\sqrt{L_r/C_r}/R_{ac2}$, k = L_m1/L_r, and F = f_sw/f_r. Based on the input voltage V₁, output voltage V₂, inductor ratio k, and load resistance R_ac2, 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 = L_m1/L_r = 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 v_cd, and the primary voltage v_Lm1 ≈ nv_cd = v_cd’. Q₁ and Q₂ are off and the antiparallel diodes D_Q1 and D_Q2 are operated as the full-wave rectifiers. According to the polarity of i_Q1 and i_Q2, a square wave voltage is generated on voltage v_ab. L_r, C_r, and L_m2 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): C_Q3 is discharged to zero voltage at t₀, i_Lr > 0, and i_Q3 < 0. The soft switching characteristic of Q₃ is realized when Q₃ is turned on after t₀. Since −i_Lr > i_Lm2 and i_Q1 < 0, D_Q1 conducts and C₁ is charged by −i_Q1. In Stage 1, the ac side voltages are v_ab = V_C1 = V₁/2 and v_cd = V_C3 = V₂/2. i_Lm2 increases with the current slope V₁/(2L_m2). C_r and L_r are resonant in Stage 1 under v_ab = V₁/2, v_Lm1 = nV₂/2, and $f_r=1/2\pi \sqrt{C_r{L}_r}$. If f_r > f_sw, the circuit operation goes to the next stage. If f_r < f_sw, the circuit operation goes to Stage 3. Power is transferred in this stage from V₂ to V₁ through Q₃, T, L_r, C_r, and D_Q1.

Stage 2 (t₁~t₂): When i_DQ1 is decreased to zero at t₁, D_Q1 is reverse biased. i_Lr flows through S, C_r, L_r, T, and L_m2. C_r, L_r, and L_m2 are resonant under v_Lm1 = nV₂/2 and resonant frequency $f_p=1/2\pi \sqrt{C_r(L_r+L_{m2})}$. 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 i_Lr < 0, C_Q3 (C_Q4) 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):

$$i_{Lm2,peak}\ge \frac{V_2}{2}\sqrt{\frac{2C_{Q,s}}{L_{m2}+L_r}}$$

(7)

where C_Q,s = C_Q3 = C_Q4. The peak values of i_Lm1 and i_Lm2 can be calculated as

$$i_{Lm1,peak}=\frac{\Delta i_{Lm1}}{2}\approx \frac{V_2}{8L_{m1}{f}_{sw}}$$

(8)

$$i_{Lm2,peak}=\frac{\Delta i_{Lm2}}{2}\approx \frac{V_1}{8L_{m2}{f}_{sw}}.$$

(9)

The time interval in Stage 3 can be estimated when C_Q4 is discharged to zero voltage:

$$\Delta t_{23}=\frac{2V_2{C}_{Q,s}}{n[i_{Lm1}(t_2)+i_{Lm2}(t_2)]}\approx \frac{2V_2{C}_{Q,s}}{n[i_{Lm1,peak}+i_{Lm2,peak}]}=\frac{16L_{m1}{L}_{m2}{f}_{sw}{V}_2{C}_{Q,s}}{n(L_{m2}{V}_2+L_{m1}{V}_1)}\le t_{dead}$$

(10)

where t_dead is the dead time between Q₃ and Q₄.

Stage 4 (t₃~t₄):C_Q4 is discharged to zero at t₃. The body diode D_Q4 of Q₄ conducts due to the fact that i_D4 (t₃) < 0. Therefore, the soft switching characteristic of Q₄ can achieved after time t₃. In Stage 4, i_Q2 is negative and D_Q2 conducts. Therefore, v_ab = −V₁/2 and v_cd = −V₂/2. C_r and L_r are resonant with resonant frequency $f_r=1/2\pi \sqrt{C_r{L}_r}$. If f_r > f_sw, the circuit operation goes to Stage 5. If f_r < f_sw, the circuit operation goes to Stage 6.

Stage 5 (t₄~t₅): If f_r > f_sw, i_Q2 will go to zero before Q₄ is turned off. When i_DQ2 equals zero at t₄, D_Q2 is reverse biased. In Stage 5, i_Lr flows through C_r, L_r, T, and L_m2. Components C_r, L_r, and L_m2 are resonant under v_cd = −V₂/2 with resonant frequency $f_p=1/2\pi \sqrt{C_r(L_r+L_{m2})}$. When Q₄ turns off at t₅, the circuit operation goes to Stage 6.

Stage 6 (t₅~T_sw + t₀): When Q₄ turns off at t₅, C_Q3 (C_Q4) is discharged (charged). The time interval in Stage 6 can be neglected in state–state analysis. At time T_sw + t₀, the voltage of C_Q3 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 D_Q1 and D_Q2 are worked as the full-wave diode rectifier. The circuit characteristic of L_r, C_r, and L_m2 (instead of L_m1) 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 v_cd’,f with rms voltage value $\sqrt{2}{V}_{2}n/\pi$, and the resonant tank consists of L_r, C_r, L_m2, and R_ac1. The equivalent resistance at the high-voltage side is calculated as $R_{ac1}=2R_o/{\pi }^2$. The voltage transfer function between high-voltage V₁ and low-voltage V₂ is derived in Equation (11).

$$G_{2,1}(s)|=\frac{v_{R_{ac1}}(s)}{v_{cd\prime ,f}(s)}=\frac{\frac{s{L}_{m2}{R}_{ac1}}{s{L}_{m2}+R_{ac1}}}{\frac{1}{s{C}_r}+s{L}_r+\frac{s{L}_{m2}{R}_{ac1}}{s{L}_{m2}+R_{ac1}}}$$

(11)

Likewise, the amplitude of the voltage transfer function in Equation (11) can be calculated using Equation (12):

$$|G_{2,1}(f_{sw})|=\frac{k{F}^2}{\sqrt{{[(k+1)F^2-1]}^2+{[QkF(F^2-1)]}^2}}$$

(12)

where $f_r=1/(2\pi \sqrt{L_r{C}_r})$, $Q=\sqrt{L_r/C_r}/R_{ac1}$, k = L_m2/L_r, and F = f_sw/f_r. Based on V₁, V₂, k, and R_ac1, 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 = L_m2/L_r = 7.

3. Design Procedure of the Studied Converter

The design procedure with a laboratory prototype is discussed and presented in this section to demonstrate the practicability of the studied bidirectional dual half-bridge converter. The voltage range at high voltage is from 350 V to 400 V and the voltage range at the low-voltage side is from 38 V to 52 V. The rated power of the prototype circuit is 480 W. When the proposed circuit is worked under forward power flow, V₂ is controlled at 48 V. If the proposed circuit is worked under reverse power flow, V₁ is controlled at 400 V. Since the circuit characteristics of the proposed converter under forward and reverse power flow are similar, only the design procedure of the prototype circuit under forward power flow is discussed in the following. The transformer turn ratio is calculated using Equation (13) under maximum input and output voltages and G_1,2 = 1.

$$n=|G_{1,2}|\times \frac{V_{1,\max }}{V_{2,\max }}=1\times \frac{400}{52}\approx 7.7$$

(13)

The actual primary and secondary winding turns are 24 turns and 3 turns, respectively. Therefore, the minimum and maximum dc gains are determined using Equations (14) and (15), respectively, under nominal output voltage.

$$|G_{1,2}{|}_{dc,\min }=n\times \frac{V_{2,nom}}{V_{1,\max }}=\frac{24}{3}\times \frac{48}{400}\approx 0.96$$

(14)

$$|G_{1,2}{|}_{dc,\max }=n\times \frac{V_{2,nom}}{V_{1,\min }}=\frac{24}{3}\times \frac{48}{350}\approx 1.097$$

(15)

The select inductor ratio k and quality factor Q are based on the necessary maximum dc gain |G_1,2|_dc,max= 1.097. The maximum gain of the proposed converter under the selected k = 7 and Q = 0.6 is about 1.35, which is greater than |G_1,2|_dc,max= 1.097. Based on the selected turn ratio, the equivalent resistance R_ac2 at full load is determined from Equation (16).

$$R_{ac2}=\frac{2n^2}{{\pi }^2}{R}_o=\frac{2\times {(24/3)}^2}{{3.14159}^2}\times \frac{48}{10}\approx 62.25\Omega$$

(16)

The resonant parameters C_r and L_r are calculated from Equations (17) and (18) under the series resonant frequency f_r = 100 kHz and full load.

$$C_r=\frac{1}{2\pi Q{f}_r{R}_{ac2}}=\frac{1}{2\pi \times 0.6\times 100\times {10}^3\times 62.25}\approx 42.6\mathrm{nF}$$

(17)

$$L_r=\frac{1}{{(2\pi f_r)}^2{C}_r}=\frac{1}{{(2\pi \times 100\times {10}^3)}^2\times 42.6\times {10}^{-9}}\approx 59.5\mathsf{\mu }\mathrm{H}$$

(18)

The actual resonant parameters used in the prototype are C_r = 42 nF and L_r = 60 μH. The magnetizing inductance L_m1 is determined from Equation (19).

$$L_{m1}=k{L}_r=7\times 60=420\mathsf{\mu }\mathrm{H}$$

(19)

The primary side rms load current is calculated in Equation (20).

$$I_{rms,p}=\frac{\pi I_o}{\sqrt{2}n}=\frac{\pi \times 10}{\sqrt{2}\times (24/3)}=2.777\mathrm{A}$$

(20)

The minimum switching frequency is determined in Equation (21).

$$f_{sw,\min }=f_p=\frac{1}{2\pi \sqrt{C_r(L_r+L_{m1})}}=\frac{1}{2\pi \sqrt{42\times {10}^{-9}\times (60+420)\times {10}^{-6}}}\approx 35.45\mathrm{kHz}$$

(21)

The rms magnetizing current of transformer T at f_sw,min under minimum switching frequency is calculated in Equation (22).

$$I_{Lm1,rms}=\frac{1}{2\sqrt{3}}\frac{n{V}_2}{4f_{sw,\min }{L}_{m1}}=\frac{1}{2\sqrt{3}}\times \frac{(24/3)\times 48}{4\times 35.45\times {10}^3\times 420\times {10}^{-6}}\approx 1.86\mathrm{A}$$

(22)

The rms values of the resonant inductor current I_Lr,rms and the primary winding current I_pri,T under minimum switching frequency and full load are calculated and expressed in Equation (23).

$$I_{pri,T}=I_{Lr,rms}=\sqrt{I_{Lm1,rms}^2+I_{rms,p}^2}=\sqrt{{1.86}^2+{2.77}^2}\approx 3.34\mathrm{A}$$

(23)

The rms value of the secondary winding current I_sec,T is given as

$$I_{\sec ,T}=n{i}_{rms,p}=(24/3)\times 2.777=22.21\mathrm{A}.$$

(24)

The peak voltage of the resonant capacitor C_r under minimum switching frequency and full load is calculated in Equation (25).

$$v_{Cr,peak}=\sqrt{2}{I}_{Lr,rms}{X}_{Cr}=\frac{\sqrt{2}{I}_{Lr,rms}}{2\pi f_{sw,\min }{C}_r}=\frac{\sqrt{2}\times 3.34}{2\pi \times 35.45\times {10}^3\times 42\times {10}^{-9}}\approx 505V$$

(25)

The voltage stresses of Q₁ and Q₂ are equal to V₁ = 400 V, and the voltage stresses of Q₃ and Q₄ are equal to V_2,max = 52 V. The current stresses of Q₁~Q₄ are calculated in Equations (26) and (27).

$$I_{Q1,rms}=I_{Q2,rms}=I_{Lr,rms}/\sqrt{2}=3.34/\sqrt{2}\approx 2.36\mathrm{A}$$

(26)

$$I_{Q3,rms}=I_{Q4,rms}=I_{\sec ,T}/\sqrt{2}=22.21/\sqrt{2}\approx 15.7\mathrm{A}$$

(27)

The insulated gate bipolar transistor (IGBT) IRG4PC40W with 600 V/20 A rating with less switching losses and higher switching frequency operation were adopted for switches Q₁ and Q₂ and MOSFETs IRFB4321PbF with 150 V/85 A rating were adopted for switches Q₃ and Q₄. The ac switch S was implemented using two MOSFETs SiHG20N50C with 500 V/20 A rating with back-to-back connection. The selected inductor L_m2 = 180 μH gives inductor ratio k = L_m2/L_r = 3 under reverse power flow operation from V₂ to V₁. The adopted input and output capacitances are C₁ = C₂ = 180 μF/400 V and C₃ = C₄ = 2200 μF/100 V.

4. Experimental Results

Based on the circuit parameters derived from the previous section, a 480 W prototype circuit was tested to validate the practicability of the studied converter. Figure 5, Figure 6, Figure 7 and Figure 8 demonstrate the test results under forward power flow operation. Figure 5 shows the test results of Q₁ at 20% load and full load. The test results show that Q₁ turns on at zero voltage for both 20% and 100% loads. Likewise, Figure 6 demonstrates test results of Q₂ under different load conditions. It is observed that the soft switching turn-on characteristics of Q₂ are also achieved. Figure 7 demonstrates the measured waveforms of the resonant voltage and resonant current. The test results show that the switching frequency is close to the series resonant frequency under 400 V input. Thus, the resonant current is close to a sinusoidal waveform. On the other hand, the series resonant frequency is greater than the switching frequency under the 350 V input case. Figure 8 demonstrates the test results of the secondary side currents and capacitor voltages. The output capacitor voltages V_C3 and V_C4 are balanced and the switch currents −i_Q3 and −i_Q4 are also balanced. Figure 9, Figure 10 and Figure 11 demonstrates test results of the studied converter under reverse power flow. The soft switching characteristics of Q₃ and Q₄ are given in Figure 9 and Figure 10 and the resonant voltage and current are demonstrated in Figure 11. Figure 12 shows the measured circuit efficiencies of the studied circuit. The efficiencies of the proposed converter under forward power flow and V₁ = 400 V are 95.2%, 95.7%, and 93.6% under 20%, 50%, and 100% loads, respectively. The efficiencies of the proposed converter under reverse power flow and V₂ = 52 V are 89.7%, 91.5%, and 91.2% under 20%, 50%, and 100% loads, respectively. The proposed converter has better circuit efficiency under forward power flow due to the fact that MOSFETs are used on the low-voltage side to reduce the conduction losses. The measured switching frequencies of the proposed converter under forward power flow are 138 kHz (or 84 kHz), 114 kHz (or 79 kHz), and 99 kHz (or 71 kHz) under 400 V (or 350 V) input and 20% load, 50% load, and 100% load output, respectively. Lower input voltage results in low switching frequency and the switching frequency is increased when the dc load is decreased. Figure 13 gives a picture of the experimental setup and a photo of the proposed converter in the laboratory test.

5. Conclusions

This paper studied a resonant converter constructed using a dual half-bridge circuit to realize bidirectional power flow. Two half-bridge circuits were used on the high- and low-voltage sides to clamp the voltage rating of the active devices at input and output voltages. A series resonant tank was adopted on the primary side of the isolated transformer to realize soft switching characteristics of the power devices. A frequency control scheme was adopted to control the switching frequency so that the voltage gain of the resonant tank is adjustable and the load voltage can be controlled. A laboratory prototype of the design was built and the test results demonstrated the feasibility of the studied circuit.