New ZVZCT Bidirectional DC-DC Converter Using Coupled Inductors

Abstract

In this study, a novel zero voltage zero current transition (ZVZCT) bidirectional DC-DC converter is proposed by employing coupled inductors. This converter can turn the main switch on at ZVZCT and it can turn it off with zero voltage switching (ZVS) for both the boost and buck modes. These characteristics are obtained by using a simple auxiliary sub-circuit regardless of the power flow direction. In the boost mode, the auxiliary switch achieves zero current switching (ZCS) turn-on and ZVS turn off. Due to the coupling inductors, this converter can make further efficiency improvements because the resonant energy in the capacitor or inductor can be transferred to the load. The main diode operates with ZVT turn-on and ZCS turn-off in the boost mode. For the buck mode, there is a releasing circuit to conduct the currents generated by the magnetic flux leakage to the output. The auxiliary switch turns on with ZCS and it turns off with ZVT. The main diode also turns on with ZVT and turns off with ZCS. The design method and operation principles of the converter are discussed. A 500 W experimental prototype has been built and verified by experimental results.

I. INTRODUCTION

Recently, the research on bidirectional DC-DC converters (BDCs) has become an important topic due to its application in energy recovery and energy storage systems. DC-DC converters are widely applied as such in solar power supplies, electric vehicles, energy storage systems, fuel cell vehicles, etc. [1]-[6]. BDCs can keep storage devices healthy by controlling the discharge and charge [8]. Bi-directional converters have two types: isolated and non-isolated. BDCs are widely applied due to their simple structure and control. A high switching frequency is a good solution to achieve a high-power density in BDCs. Obviously, hard switching (HS) limits the switching frequency, and increases both the electromagnetic interference (EMI) and switching loss. To solve these problems, soft-switching has been developed in BDCs. The task is the challenging since soft switching must be ensured for the both power flow directions. Studies for soft switching have yielded different topologies, and they can be classified into three basic types.

1) The first type of solution adopts the interleaved topology [7]. In some DC-DC converters, parallel connections are used to form interleaved structures. To realizing soft switching, the charge and discharge of the bypass capacitors of the switches can be buffered by the positive and negative flowing of the inductance current. However, too many components, such as double switches and double main inductors, can result in the power density becoming lower, which makes the control algorithm more complex.

2) The second type of solution is to produce an oscillation between the inductors and capacitors, [9]-[12], which makes it possible for zero voltage or zero current to be obtained. In [13], the auxiliary switch is operated two times in one cycle, which increases the complex of the control method. In [14], the circulating current of the auxiliary switchings are reduced by the conduction time reduction. However, when the auxiliary switch turns off, the oscillation between the inductors and snubber capacitors in series results in an undesirable oscillation, which reduces the converter efficiency and increases the voltage stress of the semiconductor elements. In [15], a complicated soft-switching structure is applied to a converter. However, this has relative drawbacks. In [16], a converter is designed with an auxiliary switch operating twice in a switching period. As a result, the switching loss increases, the control strategy becomes more complex, and the switching frequency is limited. In addition, the main switch suffers from high current stress.

In [17], the bi-directional DC-DC converter has the advantage of fewer components, a simple structure and a simple control method. The boost and buck modes share the same resonant circuits. Therefore, the efficiency is high. However, the resonant inductance used to realize ZVS is located in the main circuit of the topology. Thus, the soft switching characteristics of the topology are affected more by the operating state and load of the main circuit. On the other hand, it leads to instability of the main circuit voltage.

3) The third type of solution uses coupled inductors to provide soft-switching of the auxiliary switches [18]-[24]. The coupled inductor is used as a resonant inductor, and all of the magnetic elements are made on a single magnetic core. Therefore, the converter weight and volume are reduced. However, in some converters, the voltage stress of the auxiliary switch exceeds the high voltage side.

In [25], the authors presented a family of snubber active structures using feedback inductors. Although there are more diodes, the feedback inductance is used to transfer the resonant current to the load side to improve efficiency. However, the coupling factor of the feedback inductor is close to 1. Therefore, the topology cannot control the auxiliary switch current stress or reverse recovery current by designing the coupling coefficient.

In this study, a new ZVZCT bidirectional converter using coupled inductors is introduced. For the proposed converter, the soft switch can be implemented for all of the semiconductor components in the entire duty cycle range, regardless of the power flow direction. For this converter, the main switch is easy to control and does not have extra voltage or current stress. In the boost mode, the main switch turns on with ZVZCT and turns off with ZVS. The auxiliary switch turns on with ZCS and turns off at ZVS. In the buck mode, the main switch can be operated with ZVZCT turn-on and ZVS turn-off, and the auxiliary switch can also realize ZCS turn-on and ZVT turn-off.

For this topology, full coupling of the inductors is not necessary. Because the new topology is able to conduct leakage current through the energy release loop, the parasitic oscillation and current rush are eliminated. The coupling inductance is able to deliver resonant power to the output terminal through the coupling effect, and the current stress of the auxiliary switch can be limited, which reduces the conduction loss and improves the efficiency.

In the boost mode, extra resonance energy is transferred to the load side via the coupled inductor. Therefore, the current stress on the auxiliary switch is controllable. When designing the topology, the freewheeling current can be reduced by adjusting the coupling coefficient. As a result, the design flexibility of the topology is improved. On the other hand, when the auxiliary switch is off, the turn-off current and voltage are low. There is no current or voltage spike, which improves the working conditions of the auxiliary switch. With the same components, the load range for ZVZCT realization is expanded.

The rest of this paper is organized as follows. The second section describes the topology and working principle. The third section provides a parameter analysis and the topology design. In the fourth part, experimental results are discussed. The final section gives some conclusions.

II. TOPOLOGY AND WORKING PRINCIPLE

The proposed ZVZCT bidirectional DC-DC converter is shown in Fig. 1(a), and Fig. 1(b) shows an equivalent circuit of this topology. The resonance part includes one resonant capacitor, a coupled-inductor, two diodes and two auxiliary switches, where v_L1, v_La1 and v_Lb1 are the voltages of the inductors; L₁, L_a1 and L_b1 are the inductances; M is the mutual inductance of L_a1 and L_b1; and i_L1, i_La1 and i_Lb1 are the currents of L₁, L_a1 and L_b1.

Fig. 1. The proposed DC/DC converter: (a) Proposed topology; (b) Equivalent circuit.

A. Boost Working Mode

In the boost mode, seven working modes are analyzed in one period. Fig. 2(a) shows each operation mode for the topology. Key waveforms of the boost mode are shown in Fig. 2(b).

Fig. 2. Operations and principles for the boost mode: (a) Operation stages for the boost mode; (b) Key waveforms for the boost mode.

1) Mode 1 (t₀ ≤ t < t₁):

This is the main switch off mode for the traditional boost converter. In this interval, both S₁ and S₂ are off and D_S3 is on. V_S1 is equal to the output voltage. Therefore, there is no voltage stress on it. The converter energy is transfered from the low side to the high side.

2) Mode 2 (t₁ ≤ t < t₂):

The initial conditions at t₁ are v_CS1=V_H, v_Cr2=0, i_S1=0, i_S2=0, i_DS3=I_i and i_La1=i_Lb1=0. The turn-on signal is implemented to S₂, and the resonance begins with L_a1, L_b1, C_S1 and C_S3. This resonance provides S₂ with ZCS turn-on. Meanwhile, the current i_CS3 falls down, and C_r2 is charged. At the end of this mode, the resonance reduces the current of C_S3 to zero. Therefore, S₃ achieves ZCS turn-off, and the capacitor C_r2 voltage rises. The following equations are obtained in this mode by KVL:

\(\left\{\begin{array}{l} C_{s 3} \frac{d v_{C s 3}}{d t}=i_{C s 3} \\ C_{s 1} \frac{d v_{C s 1}}{d t}=i_{C s 1} \\ C_{r 2} \frac{d v_{C r 2}}{d t}=i_{C r 2} \\ -M \frac{d i_{L b 1}}{d t}+L_{a 1} \frac{d i_{L a 1}}{d t}+v_{C s 1}=0 \\ -M \frac{d i_{L a 1}}{d t}+L_{b 1} \frac{d i_{L b 1}}{d t}+v_{C r 2}=0 \\ v_{C s 1}+v_{C s 3}=V_{H} \end{array}\right.\)       (1)

3) Mode 3 (t₂ ≤ t < t₃):

In mode 3, C_S1 and C_S3 have been discharged to zero and separately charged to the output voltage. Thus, S₃ does not suffer from voltage stress. D_S1 is at the turn-on stage, and C_r2 continues the charge. L_a1, L_b1 and C_r2 resonate though the body diode of S₁. Once C_r2 has been completely charged, the voltage of C_r2 is the same as that of C₂. Therefore, this condition provides the body diode of S₄ ZVS turn-on. At the end of mode 3, the voltage of C_r2 reaches V_H. S₄ is turned on with ZVS and the current in L_b1 continues. Thus, the energy transfers from the coupled inductor to the load by the body diode of S₄ in the next mode. The current stress of S₂ is obviously reduced. i_La1= I_La1(t2), i_Lb1=I_Lb1(t2) and u_Lb1=U_Lb1(t2) are the initial conditions. For this resonance, the following equations are:

\(\left\{\begin{array}{l} C_{r 2} \frac{d v_{C r 2}}{d t}=i_{C r 2}=i_{L b 1} \\ M \frac{d i_{L b 1}}{d t}-L_{a 1} \frac{d i_{L a 1}}{d t}=0 \\ M \frac{d i_{L a 1}}{d t}=L_{b 1} \frac{d i_{L b 1}}{d t}+v_{C r 2} \end{array}\right.\)       (2)

Therefore:      \(i_{DS1}=I_i-i_{La1}\)       (3)

\(\begin{array}{l} i_{L b 1}=I_{L b 1(t 2)} \cos \omega_{1(t 2)}\left(t-t_{2}\right)+ \\ \sqrt{\frac{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}{L_{a 1} L_{b 1}^{2}}} U_{L b 1(t 2)} \sin \omega_{1(t 2)}\left(t-t_{2}\right) \end{array}\)       (4)

\(\begin{array}{l} v_{C r 2}=I_{L b 1(t 2)} \sqrt{\frac{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}{L_{a 1}}} \sin \omega_{1(t 2)}\left(t-t_{2}\right) \\ -\frac{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}{L_{a 1} L_{b 1}} U_{L b 1(t 2)} \cos \omega_{1(t 2)}\left(t-t_{2}\right) \end{array}\)       (5)

where      \(\omega_{1(t 2)}=\sqrt{\frac{L_{a 1}}{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}}\)

4) Mode 4 (t₃ ≤ t < t₄):

In this mode, S₁ is turned on. Because the current in L_b1 falls to zero slowly, the body diode of S₄ is turned off with ZCS. Meanwhile, the freewheeling current i_La1−I_i in S₁ continues to decrease. At t=t₃, the initial conditions are v_Cr2=V_H, i_La1=I_La1(t3) and i_Lb1=I_Lb1(t3). The following equations are valid:

\(\left\{\begin{array}{l} -M \frac{d i_{L b 1}}{d t}+L_{a 1} \frac{d i_{L a 1}}{d t}=0 \\ L_{b 1} \frac{d i_{L b 1}}{d t}-M \frac{d i_{L a 1}}{d t}=V_{H} \end{array}\right.\)       (6)

\(i_{L a 1}=I_{L a 1(t 3)}-\frac{M}{L_{a 1} L_{b 1}-M^{2}} V_{H}\left(t-t_{3}\right)\)       (7)

\(i_{L b 1}=I_{L b 1(t 3)}-\frac{M}{L_{a 1} L_{b 1}-M^{2}} V_{H}\left(t-t_{3}\right)\)       (8)

The interval before which i_La1−I_i fall to zero provides the ZVZCT turn-on margin for S₁. The signal of S₁ is applied in this margin when the body diode is active.

5) Mode 5 (t₄ ≤ t < t₅):

At the beginning of mode 5, S₂ is turned off. The turn-off current for S₂ is lower than I_i due to the resonance in mode 4. Furthermore, the voltage of S₂ is not directly raised to V_H. The ZVS-off of S₂ is realized due to C_r2. The current in L_b1 and C_r2 resonates. At t=t₄, the initial conditions are i_Lb1=I_Lb1(t4), i_La1=I_La1(t4), v_cr2(t4)=V_H, and v=U _Lb1(t4). The following equations exist:

\(\left\{\begin{array}{l} M \frac{d i_{L b 1}}{d t}-L_{a 1} \frac{d i_{L a 1}}{d t}-v_{c r 2}+V_{H}=0 \\ L_{b 1} \frac{d i_{L b 1}}{d t}-M \frac{d i_{L a 1}}{d t}=v_{C r 2} \\ C_{r 2} \frac{d v_{C r 2}}{d t}=i_{L a 1}-i_{L b 1} \end{array}\right.\)       (9)

Further derivation can be obtained as:

\(\begin{array}{l} i_{L b 1}=\frac{\left(I_{L a 1(t 4)}-I_{L b 1(t 4)}\right)\left(L_{a 1}-M\right)^{2}\left(L_{a 1}+M\right)}{C_{r 2}\left(L_{a 1}+L_{b 1}+2 M\right)\left(L_{a 1} L_{b 1}-M^{2}\right)} \cos \omega_{1(t 4)}\left(t-t_{4}\right)- \\ \sqrt{\frac{\left(L_{a 1}+M\right)\left(M-L_{a 1}\right)}{\left(L_{a 1}+L_{b 1}+2 M\right)^{2}}}\left [\left(L_{a 1}+L_{b 1}+2 M\right) U_{L b 1(t4)}-V_{H}\right] \sin \omega_{1(t 4)}\left(t-t_{4}\right)+ \\ \frac{V_{H}}{L_{a 1}+L_{b 1}+2 M}\left(t-t_{4}\right)+I_{L b1(t 4)}+\frac{\left(L_{a 1}+M\right)\left(L_{a 1}-M\right)^{2}}{L_{a 1}+L_{b 1}+2 M}\left(I_{L b1(t 4)}-I_{L a l(t 4)}\right) \end{array}\)       (10)

where:      \(\omega_{1(t 4)}=\sqrt{\frac{2 M+L_{a 1}+L_{b 1}}{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}}.\)

6) Mode 6 (t₅ ≤ t < t₆):

This is a conventional PWM mode. In this mode, C_r2 is discharged. Therefore, the voltage cross D₂, which is parallel to C_r2, also falls to zero, and D₂ conducts the current with ZVS. The inductor L_b1 current falls to 0.

7) Mode 7 (t₆ ≤ t < t₇):

In this mode, the main switch is off and the capacitors C_S1 and C_S3 are separately charged and discharged. At t=t₆, v_CS1=0 and v_Cs3=V_H.

\(\left\{\begin{array}{l} v_{c s 1}+v_{c s 3}=V_{H} \\ i_{c s 1}+i_{c s 3}=I_{i} \\ i_{c s 1}=C_{s 1} \frac{d v_{c s 1}}{d t} \\ i_{c s 3}=C_{s 3} \frac{d v_{c s 3} }{d t} \end{array}\right.\)       (11)

In addition, the solution can be obtained by the equation group:

\(v_{C s 1}=\frac{I_{i}}{C_{s 1}-C_{s 3}}\left(t-t_{6}\right)\)       (12)

\(v_{C s 3}=V_H-\frac{I_{i}}{C_{s 1}-C_{s 3}}\left(t-t_{6}\right)\)       (13)

B. Buck Working Mode

For the buck mode, each operation stage of this topology is presented in Fig. 3(a). Fig. 3(b) shows the key waveforms of the buck mode. The seven operation stages for one PWM period have been analyzed below.

Fig. 3. Operations and principles for the buck mode: (a) Operation stages for the buck mode; (b) Key waveforms for the buck mode.

1) Mode 1 (t₀ < t < t₁):

Mode 1 is the PWM standard mode. At t = t₀, the main switch S₃ is off. L₁ and C₁ supply the output through the body-diode of S₁.

2) Mode 2 (t₁ < t < t₂):

At the beginning of mode 2, S₄ is activated. Resonance starts between C_r2, L_a1, L_b1, C_S3 and C_S1. D_S1 is turned off with ZVS because of the bypass capacitor C_S1. S₄ turns on with ZCS due to the coupling inductors. C_S1 is charged to V_H, and C_S3 is discharged. Thus, S₁ does not suffer from voltage stress. The initial conditions are v_Cr2=0, i_La1=i_Lb1=0, v_Cs1(t1)=0, v_Cs3(t1)=V_H and I_L=constant. The following equations are derived as:

\(\left\{\begin{array}{l} \left(L_{a 1}-M\right)\left(C_{s 3}-C_{s 1}\right) \frac{d^{2} i_{L a 1}}{d t^{2}}+\left(L_{b 1}-M\right)\left(C_{s 3}-C_{s 1}\right) \frac{d^{2} i_{L b 1}}{d t^{2}}=i_{L a 1}-I_{L 1} \\ -C_{r 2} M \frac{d^{2} i_{L a 1}}{d t^{2}}+C_{r 2} L_{b 1} \frac{d^{2} i_{L b 1}}{d t^{2}}+i_{L b 1}=I_{L 1} \end{array}\right.\)       (14)

3) Mode 3 (t₂ < t < t₃):

In mode 3, resonance separately charges and discharges C_S1 and C_S3. Later, D_S3 is active with ZVS due to the bypass capacitor C_S3. L_b1, L_a1 and C_r2 continue to resonate through the anti-parallel-diode of S₃. The following initial values are valid: v_Cr2= U_Cr2(t2), i_La1= I_La1(t2), i_Lb1= I_Lb1(t2) and u_Lb1= U_Lb1(t2). The following formulas can be obtained:

\(\left\{\begin{array}{l} -M \frac{d i_{L a 1}}{d t}+L_{b 1} \frac{d i_{L b 1}}{d t}+L_{a 1} \frac{d i_{L a 1}}{d t}-M \frac{d i_{L b 1}}{d t}=0 \\ -M \frac{d i_{L a 1}}{d t}+L_{b 1} \frac{d i_{L b 1}}{d t}=v_{c r 2} \\ i_{C r 2}=C_{r 2} \frac{d v_{C r 2}}{d t} \\ i_{L b 1}+i_{C r 2}=i_{L a 1} \end{array}\right.\)       (15)

The following conclusions are valid:

\(\begin{array}{l} i_{L b 1}=\frac{\sqrt{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}}{\sqrt{L_{a 1}+L_{b 1}-2 M} L_{b 1}} U_{L b 1(t 2)} \sin \omega_{2(t 2)}\left(t-t_{2}\right) \\ -\frac{\left(L_{a 1}-M\right)\left(I_{L a 1(t 2)}-I_{L b 1(t 2)}\right)}{L_{a 1}+L_{b 1}-2 M} \cos \omega_{2(t 2)}\left(t-t_{2}\right) \\ +\frac{L_{a 1}-M}{L_{a 1}+L_{b 1}-2 M} I_{L a 1(t 2)}+\frac{L_{b 1}-M}{L_{a 1}+L_{b 1}-2 M} I_{L b 1(t 2)} \end{array}\)       (16)

where: \(\omega_{2(t 2)}=\sqrt{\frac{L_{a 1}+L_{b 1}-2 M}{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}} .\)

4) Mode 4 (t₃ < t < t₄):

For this mode, C_r2 has been completely charged. The current in L_a1 and L_b1 continues to flow through D_S3. t₄-t₂ are the ZVT interval for S₃. At the end of mode 4, the current in L_a1 and L_b1 decreased to 0. The initial conditions are: v_Cr2= v_Cr2(t3) and i_La1= i_Lb1= I_La1(t3).

\(-M \frac{d i_{L a 1}}{d t}+L_{b 1} \frac{d i_{L b 1}}{d t}+L_{a 1} \frac{d i_{L a 1}}{d t}-M \frac{d i_{L b 1}}{d t}=0\)       (17)

From the differential equation, it can be seen that in this mode, i_Lb1 is close to the constant current I_La1(t3). Then the interval of this mode should not be too long. Otherwise, there are serious circulation losses. This means that once the diode of the auxiliary switch and the main switch are active, the main switch should be turned on as soon as possible.

5) Mode 5 (t₄ < t < t₅):

When this mode starts, the main switch S₃ is turned on. C_r2 starts to discharge, and C_r2 resonates with L_a1 and L_b1. This resonance provides S₄ with ZCS. The active signal is removed when this mode ends. The initial conditions are as follows : v_Cr2= V_H and i_La1= i_Lb1= 0.

\(\left\{\begin{array}{l} v_{C r 2}-M \frac{d i_{L a 1}}{d t}+L_{b 1} \frac{d i_{L b 1}}{d t}=0 \\ i_{C r 2}=C_{r 2} \frac{d v_{C r 2}}{d t} \\ i_{C r 2}=i_{L a 1}+i_{L b 1} \end{array}\right.\)       (18)

Then:

\(\begin{array}{l} i_{L b 1}=\frac{\sqrt{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}}{\sqrt{L_{a 1}+L_{b 1}+2 M} L_{b 1}} U_{L b 1(t 4)} \sin \omega_{2(t 4)}\left(t-t_{4}\right) \\ +\frac{\left(L_{a 1}+M\right)\left(I_{L a 1(t 4)}+I_{L b 1(t 4)}\right)}{L_{a 1}+L_{b 1}+2 M} \cos \omega_{2(t 4)}\left(t-t_{4}\right) \\ +\frac{\left(L_{b 1}+M\right) I_{L b 1(t 4)}-\left(L_{a 1}+M\right) I_{L a 1(t 4)}}{L_{a 1}+L_{b 1}+2 M} \end{array}\)       (19)

where: \(\omega_{2(t 4)}=\sqrt{\frac{L_{a 1}+L_{b 1}+2 M}{C_{r 2}\left(L_{a 1} L_{b 1}-M^{2}\right)}}\)

6) Mode 6 (t₅ < t < t₆):

Mode 6 is the PWM standard mode, where V_H supplies the output through L₁. Meanwhile, C_r2 and L_b1 are oscillating. The initial conditions are as follows: v_Cr2= U_Cr2(t5) and i_Lb1= I_Lb1(t5). The following equations can be obtained:

\(\left\{\begin{array}{l} -v_{C r 2}+L_{b 1} \frac{d i_{L b 1}}{d t}=0 \\ i_{C r 2}=C_{r 2} \frac{d v_{C r 2}}{d t} \\ i_{C r 2}=-i_{L b 1} \end{array}\right.\)       (20)

Then:

\(\begin{array}{l} i_{L b 1}=\sqrt{\frac{C_{r 2}}{L_{b 1}}} U_{L b 1(t 5)} \sin \omega_{2(t 5)}\left(t-t_{5}\right) \\ +I_{L b 1(t 5)} \cos \omega_{2(t 5)}\left(t-t_{5}\right) \end{array}\)       (21)

\(\begin{array}{l} u_{L b 1}=\sqrt{L_{b 1} C_{r 2}} \omega_{2(t 5)} U_{L b 1(t 5)} \cos \omega_{2(t 5)}\left(t-t_{5}\right) \\ -I_{L b 1(t 5)} \omega_{2(t 5)} L_{b 1} \sin \omega_{2(t 5)}\left(t-t_{5}\right) \end{array}\)       (22)

where: \(\omega_{2(t 5)}=\frac{1}{\sqrt{C_{r 2} L_{b 1}}}\)

7) Mode 7 (t₆ < t < t₇):

In this mode, L_b1 releases the rest of the energy. At the same time C_S1 and C_S3 are charged and discharged by the constant current I_L1. When this is completed, one circle is over and the next period starts. The initial conditions for this mode are: v_CS3=0 and v_CS1=V_H.

\(\left\{\begin{array}{l} v_{C s 1}+v_{C s 3}=V_{H} \\ i_{C s 3}+i_{C s 1}=I_{L 1} \\ i_{C s 3}=C_{s 3} \frac{d v_{C s 3}}{d t} \\ i_{C s 1}=C_{s 1} \frac{d v_{C s 1}}{d t} \end{array}\right.\)       (23)

Thus, the solution can be expressed as:

\(v_{C s 1}=\frac{I_{L 1}}{C_{s 1}-C_{s 3}}\left(t-t_{6}\right)\)       (24)

\(v_{C s 3}=V_{H}-\frac{I_{L 1}}{C_{s 1}-C_{s 3}}\left(t-t_{6}\right)\)       (25)

III. PARAMETER ANALYSIS AND TOPOLOGY DESIGN

A. ZVZCT Turn-On Conditions and ZVS Turn-Off Conditions for the Main Switch

The ZVS off condition of S₁ can always be met due to the bypass capacitor C_S1. On the other side, before the activate signal of S₂ is off, C_S1 must be completely discharged in the boost working mode. At this time, the body diode of S₁ starts to conduct current, the driving signal of the main switch (S₁) is activated, and the main switch turns on at ZVZCT. In this case, the discharge interval of C_S1 and C_S3 should not exceed t₃-t₂. Therefore, the following constraints must be implemented for the ZVZCT turn-on of S₁, with consideration of the charge and discharge current of C_S1 and C_S3:

\(i_{L a 1(t 3)}-I_{i} \geq 0\)        (26)

where I_i is the input current, and i_La1(t3) is the current in L_a1 for mode 3.

i_La1 creates the ZVS condition for the main switch. When at a light load, the circulating current is larger, while at a heavy load, the circulating current is smaller. The reason for reserving a current margin in the design is to prevent a soft switch lost in the case of i_La1-I_i<0 due to a system overload. This resonant current and the voltage on i_S1 do not form an overlap. Thus, there is no power loss for this part.

With the consideration above, the load range can be estimated. If the load changes beyond the designed range, soft switching is lost, the main switch goes into the HS mode, and there is a voltage shock at the main switch. Some circuits that do not work properly in the HS conditions can be damaged.

\(C_{S 1}+C_{S 3} \leq \frac{I_{i}}{V_{o}}\left(t_{3}-t_{2}\right)\)       (27)

The turn-on signal of the main switch should delay the auxiliary switch. The delay time should be limited by the conditions below:

\(\left\{\begin{array}{ll} \left(t_{3}-t_{1}\right)       (28)

where \(t |_{iDs1=0} \), \(t |_{iDs3=0} \) is the moment when i_DS1, i_DS3 decreases to 0, and t₃ is the moment when the voltage of C_S1 and C_S3 resonate to 0.

In the buck mode, to achieve ZVZCT turn-off for S₄, the resonance should satisfy the following constraint:

\(\frac{1}{2} C_{r 2} V_{C r 2(t 4)}^{2} \geq \frac{1}{2} L_{a l} i_{L a 1(t 4)}^{2} \quad \text { in buck mode }\)       (29)

The delay relation between the auxiliary switch and the main switch is related to the load and voltage changes. The main part of the reverse recovery current, i_a-I_i, is the key factor in creating the main switch ZVZCT.

I_i is another important factor that determines the delay time. With the consideration of (16) and (27), the following relation can be obtained:

\(t_{\text {delay}}>\left(t_{3}-t_{1}\right)>\left(t_{3}-t_{2}\right)>\frac{\left(C_{S 1}+C_{S 3}\right) V_{o}}{I_{i}}\)       (30)

If the main switch voltage is unable to fall back to zero due to factors such as signal mismatch, current chock occurs on the main switch.

The duty cycle D of the conventional buck-boost circuit can affect the soft switching. A D satisfying the following conditions can achieve soft switching:

\(\left\{\begin{array}{l} D=\frac{V_{o}-V_{i}}{V_{o}} \\ V_{o} I_{o}=V_{i} I_{i} \\ i_{S 1_{-}\max }-I_{i} \geq 0 \\ \operatorname{Gain}=\frac{V_{o}}{V_{i}} \end{array}, \text { then } \operatorname{Gain} \leq \frac{i_{S 1_{-} \max }}{I_{o}}\right.\)       (31)

Obviously, \(\operatorname{Gain} \geq \frac{T-t_{\text {delay}}}{T}\)

The buck mode has a similar conclusion.

If the coupling inductance is not reset, the diode D₂ works in the hard switching mode. This forces the inductor to reset when there is still a current flow, which is not desirable. Thus, appropriate circuit parameters are needed to avoid this situation.

The time margin of the reset is t_m≈T-t_{on_aux}-t_release>0. Most of the energy in the capacitor C_r2 is transferred to L_b2 and is eventually released through D₂. By the equations below, t_m can be calculated by:

\(t_{release}=\frac{\frac{1}{2} C_{r 2} V^{2}_{Cr2(t4)}}{\left(\frac{1}{2} I_{L b 1(M A X)}\right)^{2} R}=\frac{I_{L b 1(M A X)}-0}{L_{b 1}}\)       (32)

Therefore, \(t_{m} \approx T-t_{o n_{-} a u x}-\sqrt[3]{\frac{2 C_{r 2} V^{2}_{Cr2(t4)}}{R L_{b 1}^{2}}}>0\)       (33)

where, v_{Cr2 (t4)} is the voltage after C_r2 is charged, R is the internal resistance of the loop in mode 6, and t_{on_aux} is the pulse width of the auxiliary switch.

B. Coupled Inductor for Soft-Switching Realization

For the proposed topology, the main loop is quite independent. It can adapt to a wide load range. The coupling inductors enable the main switch to acquire soft switching, and assist the auxiliary switch to achieve ZVS or ZCS. The stress on the auxiliary switch can be well controlled by adjusting the coupling coefficient. Therefore, the design of the coupling inductors for this circuit is needed.

Coupled inductors use high frequency iron core materials, such as MnFe204, ZnFe204, etc. In practice, the coupling coefficient of a ring-type core is difficult to reach 0.95. The coupling coefficient varies with the distance between the two windings. Adjustable coupling coefficients can be obtained by adjusting the distance between the two windings.

The coupling coefficient and the values of L_a1 and L_b1 have a major impact on the circuit. Therefore, in the initial design stage, the magnetic core is an important part. The related parameters are designed as follows.

The initial conditions are: window fill factor: K_o=0.4; core fill factor (ferrite): K_c=1; working flux density of the transformer: B_m≤1/2 B_sat;current density (the value for natural cooling): j=4.2 A/mm²;switching frequency: f_sw=100 kHz; output voltage: V_out=200 V; input voltage: V_in=120 V; and auxiliary switch turn-on interval: T_{on_max}=1 us.

In this design, the OR48X30X15 type is selected. Then A_e = 133 mm², A_w=1.75 mm², L_e=118 mm and V_e=15700 mm³. In addition, the saturation magnetic density of the ferrite core B_sat = 3900 G. Thus, B_m = 1900 G.

According to simulations: P_o=0.000375 W and I_{La1_max}=12 A. Then:

\(L_{a 1} \approx \frac{V_{\text {in }} \times T_{o n}}{I_{L a 1_{-} \max } \times f_{s w}}=\frac{120 \times 0.1}{12 \times 10^{5}}=10 u H\)       (34)

\(N_{p}=\frac{V_{\min } \times t_{o n \max }}{A_{e} \times B_{m}}=\frac{120 \times 10}{133 \times 2}=4.5\)       (35)

Due to topology design requirements: L_a1≤8 uH, it is necessary to take 4 turns. Since the coupling inductance does not want to introduce a higher output voltage (stress), the parameters could be determined according to the features of the circuit topology: L_b1≈L_a1. Thus, L_b1=6 uH.

\(\begin{array}{l} A P_{p}=\frac{P_{o} \times 10^{6}}{2 \eta \times K_{o} \times K_{c} \times f_{s} \times B_{m} \times j} \\ =\frac{370 \times 10^{-6} \times 10^{6}}{2 \times 0.8 \times 0.4 \times 1 \times 100000 \times 1900 \times 4.2} \mathrm{cm}^{4} \end{array}\)       (36)

\(A P=A_{w} \times A_{e}=1.33 \mathrm{cm}^{2} \times 0.0175 \mathrm{cm}^{2}\)       (37)

AP>AP_p. The design meets the requirements.

The coupling coefficient has a great influence as: 1) the magnitude of the resonant circulation, 2) the realization of the ZVS boundary. It is observed from Fig. 4(a), that once the coupling coefficient exceeds 0.9, S₂ and S₄ suffer from unacceptable peak currents in both the boost and buck modes. If the coupling coefficient is less than 0.5, the ZVZCT in S₄ is lost in the buck mode. Therefore, the best choice is: the maximum current in S₂. In addition, S₄ and ZVZCT of S₄ should both be considered in the buck mode.

Consequently, the following equations become available:

\(\left\{\begin{array}{l} i_{L a 1}-I_{i}=I_{L a 1(t 3)}-\frac{M}{L_{a 1} L_{b 1}-M^{2}} V_{H}\left(t-t_{3}\right)-I_{i} \geq 0 \\ k \in[0.5,0.9] \\ k=\frac{M}{\sqrt{L_{a 1} L_{b 1}}} \end{array}\right.\)       (38)

Most of the parameters need to be adjusted in the process of experiments. However, some of the parameters can be estimated by the analysis. Considering that the resonance among C_S1, C_S3, the coupled inductor and C_r1 occurs in mode 2 of the boost case, C_r2 needs to choose a value with the same level (1-10nF). With equation (15), L_a1 can be estimated with the assumption of V_Cr2(t4)=V_H (200 V), i_La1(t4)=I_i (the reverse current cannot be too large) and C_r1=5 nF, the relation can be calculated as L_a1≤8 uH. Therefore, L_b1 should choose the same level (1-10 uH). On the other hand, the coupled inductor has the dotted terminals connected together, and the coefficient k choses the value of 0.8 with consideration of Fig. 4.

Fig. 4. Coupling effect for the circuit and the proposed DC/D Cconverter: (a) Coefficient effect on S₂ and S₄; (b) Proposed converter.

With the equation 15, (t₃-t₂) should be larger than 272 ns with the assumption of V_o=200 V and I_i=5 A. Therefore, with consideration of t_delay > (t₃-t₁) > (t₃-t₂), the parasitic capacitance and the switch characteristics, t_delay=1 us. In this coupling inductor design, the value of the coupling inductance is determined first. Then the turn ratio is determined. Therefore, it can meet the soft switching requirement in terms of bidirectional resonance. In addition, the turn ratio of the coupling inductor can also be decided.

C. Switching Loss Distribution

Based on the circuit parameters determined above, it is possible to theoretically estimate the main power distribution of the converter as shown in Fig. 5 below.

Fig. 5. Switching loss comparison: (a) Boost mode at full load; (b) Buck mode at full load.

Thus, the converter loss comes mainly from the switching devices, and the switch loss comes mainly from the turn-on/turn-off moment. Theoretically, it can be seen that the power cost advantage of soft switching is obvious.

IV. EXPERIMENTAL RESULTS

In order to verify the above analysis, a prototype of the proposed converter has been established. Table I lists the components and circuit parameters of the converter.

 TABLE I EXPERIMENTAL CONDITIONS AND CIRCUIT PARAMETERS

A photo of the proposed converter prototype is shown in Fig. 4(b). This converter is composed of a main inductor (L₁), the coupled inductors, the capacitor C_r2, and four transistors with body diodes. The output capacitance is 560 uF. The switching frequency of the converter is 100 kHz. The low and high voltages are 120 V and 200 V, respectively. The test power is 500 W.

In the boost mode, control signals are presented in Fig. 6(a), and the processes of the turn-on and turn-off of the main switch are shown in Fig. 6(b). In this figure, v_S1 is reduced to zero, and the enable signal is applied to S₁. Then the current reverses, and increases from zero. Thus, the S₁ ZVZCT turn-on is realized. Once the disable signal is applied, i_S1 is rapidly reduced to zero, and v_S1 increases. Therefore, S₁ also realizes ZVS during the turn-off process.

Fig. 6. Voltage and current for S₁, S₂ and S₃ in the boost mode(switching frequency100 kHz, 120/200 V, 500 W): (a) Drive signals of the main and auxiliary switches; (b) Voltage and current of S₁; (c) voltage and current of S₂; (d) Voltage and current of S₃.

The switching process of S₂ is shown in Fig. 6(c). The S₂ current increases slowly when the active signal of S₂ is applied. The coupling inductors are helpful for transferring power to the output side of the converter. Due to the coupling effect, S₂ decreases rapidly. Therefore, the smaller average current of S₂ reduces the circulating loss when compared with the common inductor. It can also be observed in Fig. 6(c), that when the switching signal of S2 is removed, the ZVS and the lower i_S2 and v_S2 make S₂ have a good turning off.

As shown in Fig. 6(d), the main diode (body diode of S₃) in the boost mode operates for soft switching. Therefore, the boost efficiency is improved.

As can be seen in Fig. 7(b), v_S3 reduces to “0” before the activation signal of S₃ is applied. Then the current of S₃ reverses and increases from “0”. Therefore, S₃ is able to turn on with ZVZCT. When the signal for S₃ is turned off, the zero voltage switch is realized during the turn-off process. In Fig. 7(b), there exists a small overlap in the turn-off, because C_S3 only includes the S₃ parasitic capacitor. Therefore, the voltage raises quickly. However, this does not get the voltage shock, and it does not significantly increase the power loss. If C_S3 increases, this overlap can be avoided. Therefore, choosing a switch component with a larger C_S3 may be a solution, while getting an additional parallel capacitor is not recommended.

Fig. 7. Voltage and current for S₃, S₄ and S₁ in the buck mode(switching frequency100 kHz, 120/200 V, 500 W): (a) Drive signals of main and auxiliary switches; (b) Voltage and current of S₃; (c) voltage and current of S₄; (d) Voltage and current of S₁.

The turn-on and turn-off processes for S₄ are shown in Fig. 7(c). The current of S₄ increases slowly when the active signal of S₄ is on. Therefore, S₄ turns on with ZCS. Due to the coupling effect, before the signal is removed, the current of S₄ resonates to zero and ZVZCT is realized.

In Fig. 7(d) a fly-back diode (body diode of S₁) in the buck mode operates under soft switching.

Fig. 8(a) shows that main switch turns on with ZVZCT and turns off with ZVS in the boost mode at a low power level.

Fig. 8. Voltage and current for S₁, S₂ and S₃ in the boost mode(switching frequency100 kHz, 120/200 V, 150 W): (a) Voltage and current of S₁; (b) Voltage and current of S₂; (c) Voltage and current of S₃.

In Fig. 8(b), the auxiliary switches turn on with ZCS and turn off with ZVS in the boost mode at a low power level.

As shown in Fig. 8(c), the body diode of S₃ is in the soft switching state in the boost mode at a low power level.

It can be seen from Fig. 9(a), that S₃ turns on with ZVZCT and turns off with ZVS in the buck mode at a low power level.

Fig. 9. Voltage and current for S₃, S₄ and S₁ in the buck mode(switching frequency100 kHz, 120/200 V, 150 W): (a) Voltage and current of S₃; (b) Voltage and current of S₄; (c) Voltage and current of S₁.

The switch S₄ in Fig. 9(b) is turned on with ZCS and turned off with ZVZCT in the buck mode at a low power level.

It is shown in Fig. 8(c) that soft switching for the body diode of S₁ is obtained for a light load.

The efficiency of the proposed bi-directional converter is tested by a power analyzer (WT-1800) in the boost and buck modes. Efficiency comparison curves for the proposed converter, hard switching and another topology are shown in Fig. 10(a) and (b). These figures show that a high efficiency can be achieved at a full load.

Fig. 10. Efficiency comparisons for: (a) Boost mode; (b) Buck mode.

At a full load, the peak efficiency reaches 97% and 96.4% in the boost and buck mode for the proposed converter. That is consistent with the fact that the energy in the resonance tank can be delivered to the output and reduce the auxiliary switch average conduction current, due to the coupling inductors.

In [26], the topology is designed for coupling with a main inductor. The resonance inductor is coupled with the main inductor which leads to a large reverse current. Furthermore, an unnecessary oscillation that is not from parasites or stray parameters occurs in the main circuit. This oscillation may cross zero at a low power level. These problems are caused by the resonance and main circuit coupling. For the above reasons, the efficiency at a low power level is not very good.

Another problem with [26], is that the design margin of the coupling inductance parameters is narrow. The soft-switching conditions is depended on a temporary equivalent electromotive force generated by the coupling effect to release the bypass capacitor of the switch. This electromotive force is a function of the main circuit current changing rate, which means that a large ripple must exist in the main circuit to ensure soft switching. Therefore, the ripple rate and soft switch is a pair of contradictions that cannot both occur.

Table II compares a number of topologies including [26]. From this comparison, it is easier to find the features and application scope of each topology.

TABLE II TOPOLOGY FEATURES AND COMPARISON OF OTHER CONVERTERS

V. CONCLUSION

For this study, a new bi-directional ZVZCT soft-switching converter is proposed. The converter provides the main switch with ZVZCT during the turn-on process and ZVS during the turn-off process, regardless the power flow direction. In addition, the auxiliary switches operate at soft switching due to the coupled inductor. The main diodes can work with soft switching. The main switch does not suffer from additional voltage and current stresses. Furthermore, for the auxiliary switch, the current stress is limited to an acceptable level. A prototype is built, and experimental results verify the realization of the soft switch. This is in accordance with the theoretical analysis derived in this paper.