Analysis and Implementation of a Hybrid DC Converter with Wide Voltage Variation

Abstract

A new hybrid DC converter is proposed and implemented to have wide voltage variation operation and bidirectional power flow capability for photovoltaic power applications. The hybrid DC converter, including a half- or full-bridge resonant circuit, is adopted to realize the bidirectional power operation and low switching losses. To overcome the wide voltage variation problem (60 V–480 V) from photovoltaic panels due to sunlight intensity, the full-bridge structure or half-bridge structure resonant circuit is used in the presented converter to implement high or low voltage gain under a low or high input voltage condition. Using a pulse frequency modulation (PFM) scheme, the voltage transfer function of the resonant circuit is controlled to regulate the load voltage. Due to the symmetric circuit structures used on the primary and the secondary sides in the proposed converter, the bidirectional power flow can be achieved with the same circuit characteristics. Therefore, the proposed converter can be applied to battery stacks to achieve charger and discharger operations. Finally, a 400 W prototype is implemented, and the performance of the proposed hybrid DC converter is confirmed by the experiments.

1. Introduction

Bidirectional DC converters [1,2,3,4,5,6] have been proposed to interface between the different DC voltage buses for renewable energy sources, battery chargers/dischargers, uninterrupted power supplies, and electric vehicles. For electric vehicle applications [7,8], bidirectional power factor correctors and bidirectional DC converters have been proposed to realize grid-to-vehicle and vehicle-to-grid operations. Phase-shift pulse-width modulation (PWM) converters have been proposed in [9,10] to realize a forward power flow operation with a voltage step-down operation, and achieve reverse power flow with a voltage step-up operation. The main drawbacks of phase-shift PWM converters are a high freewheeling current and hard switching loss at light load conditions. Dual active bridge (DAB) converters have been studied and proposed in [11,12,13,14] to realize bidirectional power flow using a phase-shift PWM technique and duty cycle control. However, two control variables, the phase-shift angle and duty cycle, are more difficult to be calculated and derived compared to the other bidirectional DC converters. Symmetric CLLC converters have been proposed in [15,16] to accomplish forward and reverse power flow operations for DC distribution systems and battery charging/discharging systems. The primary-side and secondary-side have the same circuit structures in CLLC converters. Therefore, the forward and backward voltage transfer functions are identical and the circuit characteristics for both power flows are identical. The power switches can be turned on at soft switching operation due to the circuit characteristics of the resonant converter with frequency modulation. The main drawback of the CLLC converter is a narrow voltage operation range due to its low voltage gain. Therefore, the CLLC converter cannot work well under wide voltage variation conditions, such as solar power applications. To realize wide voltage variation capability, cascade DC converters have been proposed in [17,18], with a buck or boost circuit on the front-stage and a PWM converter on the rear stage. The main problem of cascade DC converters is high conduction loss. PWM converters or resonant converters with serial–parallel circuit structures have been studied in [19,20,21,22] to realize wide input voltage operation (V_in,max/V_in,min < 4). However, only forward power flow can be realized in these circuit topologies.

According to the foregoing studies, a DC hybrid symmetric resonant converter for battery charging and discharging is proposed in this paper. One AC switch and one hybrid half/full-bridge circuit structure are used on both the primary-side and secondary-side to achieve wide voltage input operation and bidirectional power flow operation. The benefits of the proposed converter are as follows: (1) wide voltage operation from 60 V–480 V input; (2) symmetric circuit on both the primary and secondary sides to have the same voltage transfer function for backward and reverse power operations; and (3) soft switching operation on power semiconductors due to resonant circuit characteristics with frequency modulation. The proposed converter can be applied to photovoltaic power applications or battery charging/discharging systems. A 400 W prototype is provided to verify the proposed bidirectional power flow converter. The experimental results demonstrated that the maximum circuit efficiency of the prototype is approximately 93.6%. The circuit diagram of the proposed hybrid DC converter is discussed in Section 2. In Section 3, the principle operations of the converter are provided. The circuit characteristics and a design example are described in Section 4. Experimental results are provided and discussed in Section 5, to verify the feasibility of the theoretical discussions. The conclusions of the proposed circuit are described in Section 6.

2. Circuit Diagram of the Proposed Hybrid DC Converter

Figure 1a gives the circuit diagram of a hybrid DC converter. The primary and secondary sides of the isolated transformer have the same circuit structure. Full-power switches and one AC switch are used on each side. The AC switches S_ac1 and S_ac2 are implemented by two switches connected back-to-back. On each side, the resonant circuit can be operated at the full-bridge structure (S₁–S₄) or half-bridge structure (S₁, S₂, and S_ac1), related to low or high input voltage range conditions. For forward power flow operation, S₅–S₈ are all inactive. Therefore, the right-hand side circuit operates as a half-wave (S_ac2 is on) or full-wave (S_ac2 is off) diode rectifier. The proposed hybrid converter has three operation modes to achieve wide input voltage variation. In each operation mode, the circuit can achieve two times the input voltage range. Therefore, the wide input voltage range variation V_in,max = 8V_in,min (where V_in,min = 60 V and V_in,max = 480 V) can be implemented in the proposed converter. When V_in,min ≤ V_in < 2V_in,min, the high voltage gain is needed in the proposed converter. Therefore, the full-bridge resonant circuit (S_ac1 is off) is operated on the left-hand side and the half-wave diode rectifier (or voltage doubler rectifier) (S_ac2 is on) is operated on the right-hand side, as shown in Figure 1b, to achieve the maximum voltage gain. When 2V_in,min ≤ V_in < 4V_in,min, the half-bridge resonant circuit (S_ac1 is on and S₃ and S₄ are off) is used on the left-hand side and half-wave diode rectifier (S_ac2 is on) is selected on the right-hand side (Figure 1c) to obtain medium voltage gain. If 4V_in,min ≤ V_in < 8V_in,min, the half-bridge resonant circuit (S_ac1 is on and S₃ and S₄ are off) and full-wave diode rectifier (S_ac2 is off) are selected on the left-hand side and right-hand side, respectively (Figure 1d), to obtain the minimum voltage gain. For backward power flow operation (Figure 1e), S₁–S₄ are off and S_ac1 is on. Thus, the left-hand side circuit operates as a half-wave diode rectifier. S₅–S₈ are controlled with the PFM scheme to deliver power from the V_o terminal to the V_in terminal.

3. Operation Principle

Two main advantages of the proposed converter are wide voltage variation operation and bidirectional power flow operation. Under forward power flow operation, three operations modes, shown in Figure 1b–d, can be operated according to the low, medium and high voltage range inputs. Under backward power flow operation (Figure 1e), power switches on the secondary side are controlled to reverse the power flow from the load side to the input side.

3.1. Low Voltage Range Input (V_in,min ≤ V_in < 2V_in,min) under Forward Power Flow

If the input voltage is in the low voltage range, the full-bridge resonant circuit is used on the primary side and the half-wave diode rectifier is adopted on the secondary side to achieve the maximum voltage gain. Therefore, S_ac1 and S₅–S₈ are off and S_ac2 is on, as shown in Figure 1b. From the pulse-width modulation signals of S₁–S₄, D_S5, and D_S6, one can observe that there are eight switching states (Figure 2a) in every switching cycle if f_sw (switching frequency) < f_r (resonant frequency). The circuit components are assumed as C_r,2 = n²C_r,1 and L_r,2 = L_r,1/n², where n = n_p/n_s, to simplify the circuit analysis. Therefore, the series resonant frequency on the primary and secondary sides are identical, $f_{r,1}=1/(2\pi \sqrt{L_{r,1}{C}_{r,1}})=f_{r,2}=1/(2\pi \sqrt{L_{r,2}{C}_{r,2}})$. The state circuit operations related to the eight switching states are provided in Figure 2b–i.

State 1 [t₀ ≤ t < t₁]: When t = t₀, v_S1,ce = v_S4,ce = 0. i_Lr,1(t₀) < 0 will flow through diodes D_S1 and D_S4. Then, S₁ and S₄ can turn on at zero-voltage switching. The secondary side current i_Lr,2 flows through diode D_S5 to charge capacitor C₃. In this state, i_Lr,1 increases from a negative value to zero ampere.

State 2 [t₁ ≤ t < t₂]: When t > t₁, i_Lr,1 becomes a positive value. Then i_Lr,1 flows through S₁ and S₄. Forward power flow is from V_in to V_o in State 2 operation. The converter leg voltages are V_ab = V_in and V_de = V_C3 = V_o/2. The resonant frequency in State 2 is given as $f_{r,1}=1/(2\pi \sqrt{L_{r,1}{C}_{r,1}})$.

State 3 [t₂ ≤ t < t₃]: When f_sw is less than f_r,1, i_Lr,2 will be decreased to zero at time t₂. The rectifier diode D_S5 becomes off. In State 3, the resonant frequency of i_Lr,1 is $f_{p,1}=1/(2\pi \sqrt{C_{r,1}(L_{m,1}+L_{r,1})})$. No power is transferred to output load in this state.

State 4 [t₃ ≤ t < t₄]: When t = t₃, S₁ and S₄ are turned off. i_Lr,1 discharges C_S2 and C_S3 where C_S2 and C_S3 are the output capacitors of S₂ and S₃, respectively. If the primary current $i_{Lr,1}(t_3)={\widehat{i}}_{Lm,1}>V_{in}\sqrt{2C_{S,p}/L_{r,1}}$, where C_S,p = C_S1 = C_S2 = C_S3 = C_S4 (C_S1–C_S3 are output capacitors of S₁–S₄, respectively) and ${\widehat{i}}_{Lm,1}$ is the peak value of i_Lm,1, then C_S2 and C_S3 can be discharged to zero voltage at time t₄.

State 5 [t₄ ≤ t < t₅]: The capacitor voltages v_CS2 = v_CS3 = 0 (or v_S2,ce = v_S3,ce = 0) at time t₄. Then i_Lr,1(t₄) > 0 will flow through D_S2 and D_S3. The zero-voltage turn-on operation of S₂ and S₃ can be implemented after time t₄. The secondary side current i_Lr,2 will be decreased and D_S6 becomes forward biased. The primary curent i_Lr,1 is decreased and capacitor C₄ is charged in State 5.

State 6 [t₅ ≤ t < t₆]: After t > t₅, i_Lr,1 < 0. Then, D_S2 and D_S3 become reverse biased. i_Lr,1 will flow through S₂ and S₃. In State 6, i_Lr,1 is decreased and C₄ is charged by i_Lr,2. The resonant frequency is $f_{r,1}=1/(2\pi \sqrt{L_{r,1}{C}_{r,1}})$.

State 7 [t₆ ≤ t < t₇]: At t = t₆, the secondary side current i_Lr,2 = 0 and D_S6 becomes reverse biased. The resonant frequency in this state is $f_{p,1}=1/(2\pi \sqrt{C_{r,1}(L_{m,1}+L_{r,1})})$.

State 8 [t₇ ≤ t < T_sw + t₀]: When t = t₇, S₂ and S₃ turn off. i_Lr,1(t₇) < 0 will discharge C_S1 and C_S4. The one switching period ends at time T_sw + t₀.

3.2. Medium Voltage Range Input (2V_in,min ≤ V_in < 4V_in,min) under Forward Power Flow

When a medium voltage range is input to the proposed converter, the half-bridge resonant circuit is operated on the left-hand side (Figure 1c). Since the input voltage of the resonant circuit is ±V_in/2 instead of ±V_in in Figure 1b, the voltage gain in Figure 1c is only 1/2 of the voltage gain in Figure 1b. One can observe in Figure 1c that S_ac1 is on and S₃ and S₄ are off. Only S₁ and S₂ are operated with the PFM scheme. S_ac2 is on and the half-wave diode rectifier or voltage doubler rectifier is operated on the secondary side. Since the half-bridge resonant circuit (Figure 1c) and full-bridge resonant circuit (Figure 1b) have similar operation states, the circuit operations of the proposed converter under a medium voltage range input are neglected in this subsection.

3.3. High Voltage Range Input (4V_in,min ≤ V_in < 8V_in,min) under Forward Power Flow

When the input voltage is in the high voltage range, the half-bridge resonant circuit is operated on the left-hand side and the full-wave diode rectifier (S_ac2 is off) is operated on the right-hand side, as shown in Figure 1d. Comparing Figure 1c,d, the leg voltage v_de is ±V_o in Figure 1d instead of ±V_o/2 in Figure 1c with voltage doubler rectifier structure. Therefore, the converter in the Figure 1d operation has less voltage gain than the Figure 1c operation. From Figure 1b–d, it can be concluded that the Figure 1b circuit is selected to control the load voltage with the maximum voltage gain under a low voltage range input condition, and the Figure 1d circuit is selected to regulate the load voltage with the minimum voltage gain under high voltage range input conditions. The circuit operation in Figure 1d is similar to the circuit operation in Figure 1b,c. Thus, the operation principle of the Figure 1d circuit is neglected in this subsection.

3.4. Backward Power Flow

If the converter is operated at backward power operation, the power flow is transferred from V_o to V_in, as shown in Figure 1e. Since V_in is controlled at 400 V, the half-wave diode rectifier is used on the left-hand side. Therefore, S_ac1 is on. The full-bridge resonant circuit is operated on the right-hand side so that S_ac2 is off and S₅–S₈ are operated with the PFM scheme. Figure 3a provides the switching signals of the converter under backward power flow in every switching cycle. Figure 3b–i show these state equivalent circuits.

State 1 [t₀ ≤ t < t₁]: C_S5 and C_S8 are discharged to zero voltage at t₀. i_Lr,2(t₀) is negative so that D_S5 anf D_S8 are forward biased. Active switches S₅ and S₈ can be turned on after t₀ to have soft switching turn-on operation. Since i_Lr,1 > 0, D_S1 is forward biased and C₁ is charged.

State 2 [t₁ ≤ t < t₂]: At t₁, i_Lr,2 > 0. Thus, i_Lr2 flows through S₅ and S₈. Backward power is transferred from V_o to V_in in this state. One can obtain V_ab = V_C1 = V_in/2 and V_de = V_o. The resonant frequency is $f_{r,2}=1/(2\pi \sqrt{L_{r,2}{C}_{r,2}})=1/(2\pi \sqrt{L_{r,1}{C}_{r,1}})=f_{r,1}$.

State 3 [t₂ ≤ t < t₃]: If f_sw < f_r,1, i_Lr,1 = 0 at t₂ and D_S1 is reverse biased. The resonant frequency on right-hand side circuit is $f_{p,2}=1/(2\pi \sqrt{C_{r,2}(L_{m,2}+L_{r,2})})$ and f_p,2 < f_p,1.

State 4 [t₃ ≤ t < t₄]: S₅ and S₈ are off at t₃. Due to i_Lr,2(t₃) > 0, C_S6 and C_S7 are discharged by i_Lr,2.

State 5 [t₄ ≤ t < t₅]: C_S6 and C_S7 are discharged to zero voltage at t₄. Since i_Lr,2(t₄) > 0, i_Lr,2 flows through D_S6 anf D_S7. Then, S₆ and S₇ turn on after t₄ to achieve soft switching turn-on operation. Owing to i_Lr,1 < 0, D_S2 becomes forward biased and C₂ is charged.

State 6 [t₅ ≤ t < t₆]: After t₅, i_Lr,2 < 0 and i_Lr,2 flows through S₆ and S₇. Backward power flow is from V_o to V_in in this state operation.

State 7 [t₆ ≤ t < t₇]: i_Lr,1 = 0 at t₆. Then, D_S2 is off. The resonant frequency on the right-hand side circuit is $f_{p,2}=1/(2\pi \sqrt{C_{r,2}(L_{m,2}+L_{r,2})})$.

State 8 [t₇ ≤ t < T_sw + t₀]: S₆ and S₇ turn off at t₇. Since i_Lr,2(t₇) < 0, i_Lr,2 discharges C_S5 and C_S8. At time T_sw + t₀, C_S5 and C_S8 are discharged to zero voltage.

4. Circuit Characteristics and Design Example

There are four operating modes in the proposed circuit, as shown in Figure 1. In each mode, the PFM scheme is selected to control the active switches so that the voltage gain of the resonant circuit is depended on the switching frequency. The equivalent resonant circuits in Figure 1b–e can be redrawn and is shown in Figure 4. For the forward power flow operation, the leg voltage V_ab is a square-wave voltage with ± V_in (low voltage range input condition) or ± V_in/2 (medium and high voltage range input conditions). The leg voltage V_de on the right-hand side of the converter is a square-wave voltage with ± V_o/2 (low and medium voltage range input conditions) or ±V_o (high voltage range input condition). For the backward power flow operation, the leg voltages V_ab = ± V_in/2 and V_de = ± V_o. According to the Fourier Series Analysis, the square-wave voltage can be expressed as the summation of the fundamental sinewave voltage and the higher-order harmonic components. Since the higher-order harmonic components are less than the fundamental frequency voltage, only the fundamental sinewave voltage is adopted in the following consideration. The analysis of fundamental frequency is used in [23] to analyze the resonant converter and simplify the circuit analysis. Figure 5 provides the resonant circuits with the fundamental frequency analysis method under four operating modes. If the leg voltage V_ab = ± V_in/2 (Figure 4b–d) or ± V_in (Figure 4a), then its fundamental root-mean-square (rms) voltage can be obtained as $V_{ac,f}=\sqrt{2}{V}_{in}/\pi$ (Figure 5b–d) or $2\sqrt{2}{V}_{in}/\pi$ (Figure 5a). Similarly, the rms voltage $V_{de,f}=\sqrt{2}{V}_o/\pi$ (Figure 5a,b) or $2\sqrt{2}{V}_o/\pi$ (Figure 5c,d) if V_de = ± V_o/2 (Figure 4a,b) or ± V_o (Figure 4c,d). In Figure 5, R_o,e,h and R_o,e,f are the fundamental load resistances under the half-wave diode rectifier (Figure 5a,b) and full-wave diode rectifier (Figure 5c) operation with forward power flow operation.

$$R_{o,e,h}=\frac{2n^2}{{\pi }^2}{R}_o.$$

(1)

$$R_{o,e,f}=\frac{8n^2}{{\pi }^2}{R}_o.$$

(2)

Similarly, the fundamental load resistance R_in,e,h (Figure 5d) under backward power flow operation is given in Equation (3).

$$R_{in,e,h}=\frac{2}{{\pi }^2{n}^2}{R}_{in}.$$

(3)

The voltage transfer functions in Figure 5a–d are derived in Equations (4)–(7), where M_ac,F,L, M_ac,F,M, and M_ac,F,H are the voltage transfer functions at the low, medium, and high voltage range inputs under forward power flow operation and M_ac,B is the voltage transfer function under backward power flow operation.

$$\begin{array}{cc}\hfill M_{ac,F,L}\left(s\right)& =\frac{n{V}_{de,f}}{V_{ac,f}}=\frac{\sqrt{2}n{V}_o/\pi }{2\sqrt{2}{V}_{in}/\pi }=\frac{n{V}_o}{2V_{in}}\hfill \\ & =\frac{s{L}_{m,1}//\left(s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,h}\right)}{s{L}_{r,1}+\frac{1}{s{C}_{r,1}}+\left[s{L}_{m,1}//\left(s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,h}\right)\right]}\times \frac{R_{o,e,h}}{s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,h}}\end{array}.$$

(4)

$$\begin{array}{ll}{M}_{ac,F,M}\left(s\right)& =\frac{n{V}_{de,f}}{V_{ac,f}}=\frac{\sqrt{2}n{V}_o/\pi }{\sqrt{2}{V}_{in}/\pi }=\frac{n{V}_o}{V_{in}}\\ & =\frac{s{L}_{m,1}//\left(s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,h}\right)}{s{L}_{r,1}+\frac{1}{s{C}_{r,1}}+\left[s{L}_{m,1}//\left(s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,h}\right)\right]}\times \frac{R_{o,e,h}}{s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,h}}\end{array}.$$

(5)

$$\begin{array}{ll}{M}_{ac,F,H}\left(s\right)& =\frac{n{V}_{de,f}}{V_{ac,f}}=\frac{2\sqrt{2}n{V}_o/\pi }{\sqrt{2}{V}_{in}/\pi }=\frac{2n{V}_o}{V_{in}}\\ & =\frac{s{L}_{m,1}//\left(s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,f}\right)}{s{L}_{r,1}+\frac{1}{s{C}_{r,1}}+\left[s{L}_{m,1}//\left(s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,f}\right)\right]}\times \frac{R_{o,e,f}}{s{n}^2{L}_{r,2}+\frac{n^2}{s{C}_{r,2}}+R_{o,e,f}}\end{array}.$$

(6)

$$\begin{array}{ll}{M}_{ac,B}\left(s\right)& =\frac{V_{ab,f}/n}{V_{de,f}}=\frac{V_{in}}{2n{V}_o}\\ & =\frac{s{L}_{m,2}//\left(s{L}_{r,1}/n^2+\frac{1}{s{n}^2{C}_{r,1}}+R_{in,e,h}\right)}{s{L}_{r,2}+\frac{1}{s{C}_{r,2}}+\left[s{L}_{m,2}//\left(s{L}_{r,1}/n^2+\frac{1}{s{n}^2{C}_{r,1}}+R_{in,e,h}\right)\right]}\times \frac{R_{in,e,h}}{s{L}_{r,1}/n^2+\frac{1}{s{n}^2{C}_{r,1}}+R_{in,e,h}}\end{array}.$$

(7)

The following parameters are defined: $Q_{F,h}=\sqrt{L_{r,1}/C_{r,1}}/R_{o,e,h}$, $Q_{F,f}=\sqrt{L_{r,1}/C_{r,1}}/R_{o,e,f}$,$Q_{B,h}=\sqrt{L_{r,2}/C_{r,2}}/R_{in,e,h}$, $K_F=L_{m,1}/L_{r,1}$, $K_B=L_{m,2}/L_{r,2}=K_F$, $F_F=f_{sw}/f_{r,1}$ and $F_B=f_{sw}/f_{r,2}=F_F$. The voltage gains in the four operation modes in (4)–(7) can be expressed in (8)–(10) for the low, medium, and high voltage range inputs under forward power flow and in (11) for backward power flow operation.

$$\begin{array}{ll}\left|M_{ac,F,L}\right(Q_{F,h},K_F,F_F\left)\right|& =\frac{n{V}_o}{2V_{in}}\\ & =\frac{1}{\sqrt{{[1+\frac{1}{K_F}-\frac{1}{K_F{F}_F^2}]}^2+Q_{F,h}^2{[F_F(2+\frac{1}{K_F})-\frac{1}{F_F}(2+\frac{2}{K_F}-\frac{1}{K_F{F}_F^2})]}^2}}\end{array}.$$

(8)

$$\begin{array}{ll}\left|M_{ac,F,M}\right(Q_{F,h},K_F,F_F\left)\right|& =\frac{n{V}_o}{V_{in}}\\ & =\frac{1}{\sqrt{{[1+\frac{1}{K_F}-\frac{1}{K_F{F}_F^2}]}^2+Q_{F,h}^2{[F_F(2+\frac{1}{K_F})-\frac{1}{F_F}(2+\frac{2}{K_F}-\frac{1}{K_F{F}_F^2})]}^2}}\end{array}.$$

(9)

$$\begin{array}{ll}\left|M_{ac,F,H}\right(Q_{F,f},K_F,F_F\left)\right|& =\frac{2n{V}_o}{V_{in}}\\ & =\frac{1}{\sqrt{{[1+\frac{1}{K_F}-\frac{1}{K_F{F}_F^2}]}^2+Q_{F,f}^2{[F_F(2+\frac{1}{K_F})-\frac{1}{F_F}(2+\frac{2}{K_F}-\frac{1}{K_F{F}_F^2})]}^2}}\end{array}.$$

(10)

$$\begin{array}{ll}\left|M_{ac,B}\right(Q_B,K_B,F_B\left)\right|& =\frac{V_{in}}{2n{V}_o}\\ & =\frac{1}{\sqrt{{[1+\frac{1}{K_B}-\frac{1}{K_B{F}_B^2}]}^2+Q_B^2{[F_B(2+\frac{1}{K_B})-\frac{1}{F_B}(2+\frac{2}{K_B}-\frac{1}{K_B{F}_B^2})]}^2}}\end{array}.$$

(11)

It is clear that Equations (8)–(11) have a similar voltage transfer function but different DC voltage gain.

In the following sub-section, a design example of the hybrid DC converter is discussed and presented. For forward power flow, the input and output electric parameters are V_in = 60 V–480 V, V_o = 40 V–52 V, I_o,max = 7.7 A, and f_r,1 = 100 kHz. For the backward power flow operation, the electric parameters are V_o = 42 V–48 V, V_in = 400 V, P_in,max = 400 W, and f_r,2 = 100 kHz. The constant current/constant voltage is adopted to charge the battery under forward power flow operation. If 60 V ≤ V_in < 120 V (low voltage range), then the full-bridge resonant circuit is operated on the left-hand side and the half-wave diode rectifier is used on the right-hand side of the converter, as shown in Figure 1b. If 120 V ≤ V_in < 240 V (medium voltage range), then the half-bridge resonant circuit is operated on the left-hand side and half-wave diode rectifier is used on the right-hand side of the converter, as shown in Figure 1c. If 240 V ≤ V_in ≤ 480 V (high voltage range), then the half-bridge resonant circuit and full-wave diode rectifier are is operated on the left-hand side and right-hand side of the converter, respectively, as shown in Figure 1d. Due to the gains of the four mode operations in (8)–(11) having a similar transfer function, the circuit parameters in the laboratory prototype are obtained from low voltage range input (V_in = 60 V–120 V) under forward power flow. In the prototype design, the minimum voltage gain |M_ac,F,L|_min is set at unity under V_in = 120 V and V_o = 40 V. The turn-ratio n of T is obtained from Equation (8) and given in Equation (12).

$$n=|M_{ac,F,L}{|}_{min}\times \frac{2V_{in,max}}{V_{o,min}}=1\times \frac{2\times 120}{40}=6.$$

(12)

The transformer T is implemented by magnetic core PC40/EE55 with 22 turns on the primary side and 4 turns on the secondary side. Thus, the actual turn-ratio n = 22/4 = 5.5. The maximum and minimum voltage gains at low voltage range input conditions are given in (13) and (14).

$$|G_{ac,F,L}{|}_{max}=\frac{n{V}_{o,max}}{2V_{in,min}}=\frac{5.5\times 52}{2\times 60}\approx 2.38.$$

(13)

$$|G_{ac,F,L}{|}_{min}=\frac{n{V}_{o,min}}{2V_{in,max}}=\frac{5.5\times 40}{2\times 120}\approx 0.92.$$

(14)

The gain curves of the transfer function at the low voltage range input condition under K_F = 5 are plotted in Figure 6. Since the maximum voltage gain at V_in = 60 V and V_o = 52 V is 2.38 in (13), the quality factor Q_F,h = 0.2 is selected to have a peak voltage gain (= 2.5), which is greater than |G_ac,F,L|_max = 2.38. Therefore, the switching frequency index F_F is created and obtained under V_in = 60 V–120 V and V_o = 40 V–52 V. Then, the equivalent resistance R_o,e,h at full load is obtained as

$$R_{o,e,h}=\frac{2n^2}{{\pi }^2}{R}_o=\frac{2\times {5.5}^2}{{3.14159}^2}\times \frac{52}{7.7}\approx 41.4 \Omega .$$

(15)

The resonant components on the primary-side of the converter are calculated in Equations (16) and (17).

$$C_{r,1}=1/(2\pi Q_{F,h}{f}_{r,1}{R}_{o,e,h})\approx 192 \mathrm{nF}.$$

(16)

$$L_{r,1}=Q_{F,h}{R}_{o,e,h}/(2\pi f_{r,1})\approx 13 \mathsf{\mu }\mathrm{H}.$$

(17)

Since K_F = 5, the magnetizing inductance L_m,1 = K_FL_r,1 = 65 µH. The resonant components on the secondary-side of the converter are L_r,2 = L_r,1/n² ≈ 0.43 µH and C_r,2 = n²C_r,1 ≈ 5.8 µF. Magnetic cores PC40/EER35 are used to implement L_r,1 and L_r,2. S₁–S₄ and S_ac1 are implemented by power switches FGH60N60 with a 600 V/60 A rating. S₅–S₈ and S_ac2 are implemented by power switches P80NF12 with a 120 V/80 A rating. The capacitances are C₁ = C₂ = 560 μF/400 V, C₃ = C₄ = 220 μF/100 V, and C_o = 660 μF/100 V.

Table 1. Circuit parameters used in the prototype circuit.

Items	Parameter
C1, C2	560 μF/400 V
C3, C4	220 μF/100 V
Cr,1	192 nF
Cr,2	5.8 µF
Lr,1	13 μH
Lr,2	0.43 μH
Lm,1	65 μH
S1–S4, Sac1	FGH60N60 (600 V/60 A)
S5–S8, Sac2	P80NF12 (120 V/80 A)
Co	660 μH/100 V
Transformer np:ns	22:4

gives the circuit parameters used in the prototype circuit.

5. Experimental Results

Figure 7 shows the measured input voltage V_in and the switch signals S_ac1 and S_ac2. It is clear that S_ac1 is off and S_ac2 is on when 60 V ≤ V_in < 120 V. The converter is operated at a low voltage range input, shown in Figure 1b. If 120 V ≤ V_in < 240 V, then S_ac1 and S_ac2 are both on, and the converter is operated at the medium voltage range input conditions, shown in Figure 1c. If 240 V ≤ V_in ≤ 480 V, then S_ac1 is on and S_ac2 is off and the converter is operated at the high voltage range input conditions, shown in Figure 1d. For forward power flow operation (battery charge), the constant current control (I_o = 7.8 A) is selected to charge the battery (or load) from V_o = 40 V to 52 V. When the battery voltage reaches 52 V, then the constant voltage control (V_o = 52 V) is selected to charge battery. Figure 8a gives the measured load current, load voltage, and input voltage under V_in = 60 V and the forward power flow operation. When V_o is increased from 40 V and V_o ≤ 52 V, the load current I_o is controlled at 7.8 A. If the load voltage is reached at 52 V, then the load voltage V_o is controlled at 52 V and the load current is redecreased from 7.8 A. Therefore, the maximum load power is at V_o = 52 V and I_o = 7.8 A. Figure 8b–e show the measured results of the converter under V_in = 60 V, I_o = 7.8 A, and V_o = 40 V conditions. The gate signals of S₁–S₄ are provided in Figure 8b. The switching frequency is about 55 kHz. The measured voltage and current of switch S₁ are provided in Figure 8c. It is clear that S₁ is turned on at zero-voltage switching. The experimental waveforms on the primary-side of the converter are given in Figure 8d. The leg voltage v_ab = ±V_in = ±60 V. Figure 8e shows the measured results of the resonant current and voltage on the secondary-side of the converter. When i_Lr,2 is positive (or negative), the voltage v_Cr,2 is increased (or negative). If i_Lr,2 = 0, then v_Cr,2 is kept at a constant value. Similarly, the measured results of the converter under V_in = 60 V, I_o = 7.8 A, and V_o = 52 V (maximum power) conditions are given in Figure 8f–i.

The measured results of the converter operated at V_in = 118 V and the maximum power (I_o = 7.8 A and V_o = 52 V) condition are provided in Figure 9. From Figure 8 and Figure 9, one can observe that the converter has less voltage gain at V_in = 118 V so that the switching frequency of the converter at the V_in = 118 V condition is higher than the switching frequency at the V_in = 60 V condition. According to Figure 8c,g and Figure 9b, power switch S₁ is turned on at zero-voltage switching for both the V_in = 60 V and 118 V cases.

Figure 10 gives the test results of the converter under V_in = 238 V and the maximum power conditions. The half-bridge resonant circuit and half-wave diode rectifier are used in the converter (Figure 1c) under V_in = 238 V input. Only switches S₁ and S₂ are controlled on the left-hand side. Figure 10a gives the gate voltages and resonant current and voltage on the input side. The resonant current and voltage on the output side are provided in Figure 10b. The switch voltage and current of S₁ are provided in Figure 10c. The switching frequency of the converter at V_in = 238 V input and full power condition is about 96 kHz, which is close to the resonant frequency (100 kHz). The resonant currents i_Lr,1 and i_Lr,2 are quasi-sinusoidal waveforms. Power switch S₁ is also turned on at zero-voltage switching under the V_in = 238 V condition (Figure 10c).

Figure 11 provides the experimental waveforms under V_in = 480 V and the maximum power conditions. The half-bridge resonant circuit and full-wave diode rectifier are used on the left-hanf side and right-hand side of the converter (Figure 1d) under the V_in = 480 V input. The waveforms v_S1,g, v_S2,g, i_Lr,1, and –v_Cr,1 are given in Figure 11a. The waveforms i_Lr,2 and –v_Cr,2 are provided in Figure 11b. The waveforms v_S1,g, v_S1,ce, and i_S1 are shown in Figure 11c. The switching frequency of the converter at the V_in = 480 V input and maximum power condition is about 114 kHz. From the test results in Figure 11c, S₁ is also turned on at zero-voltage switching under V_in = 480 V. For the backward power flow operation (from V_o to V_in), V_o = 52 V and V_in is controlled at 400 V. Therefore, S₅–S₈ are controlled on the right-hand side and the half-wave diode rectifier is operated on the left-hand side (Figure 1e). Figure 12 provides the experimental results under the backward power flow condition. Figure 12a shows the experimental waveforms v_S5,g–v_S8,g and the resonant currents and voltages are provided in Figure 12b. Figure 12c gives the test results of the switch current and voltage of S₅. From the test results in Figure 12, the proposed converter can achieve reverse power flow operation well and switch S₅ on the right-hand side can turn on at zero-voltage switching. The measured circuit efficiencies of the converter are 87.1%, 90.3%, 92.8%, and 93.6% at the V_in = 60 V, 118 V, 238 V, and 480 V inputs and maximum power conditions.

6. Conclusions

In this paper, a hybrid resonant converter is presented and implemented to have wide voltage operation and forward/backward power flow operation for photovoltaic power or battery base applications. The symmetric resonant circuits with a half/full-bridge circuit structure are used on the primary and secondary side to achieve wide voltage operation, such as wide voltage variation on photovoltaic solar panel applications. By selecting the different circuit structures, such as half/full-bridge circuits, the converter can achieve different voltage gain under the input voltage condition. Thus, the drawback of conventional bidirectional resonant converters, such as a narrow voltage range operation, can be improved in the proposed converter. Owing to the resonant circuits on both the primary and secondary sides having the same resonant frequency, the bidirectional power flow can be easily implemented by using a pulse frequency modulation approach. In this paper, the basic circuit structure is presented and discussed in detail. The circuit operation and characteristics are also analyzed and provided. The circuit components of the laboratory prototype were designed, and the experiments are provided to show the benefits of the proposed converter.