Novel Bidirectional Isolated DC/DC Converter with High Gain Ratio and Wide Input Voltage for Electric Vehicle Storage Systems

Abstract

This study proposes a novel bidirectional isolated DC/DC converter with a high gain ratio and wide input voltage for electric vehicle (EV) storage systems. The DC bus of an EV can be used to charge its battery, and the battery pack can discharge energy to the DC bus through the bidirectional converter when the DC bus lacks power. The input voltage range of the proposed converter is 24 to 58 V on the low-voltage side, which meets the voltage specifications of most servers and batteries on the market. The proposed topology is verified through design, simulation, and implementation, and voltage gain, voltage stress, and current stress are investigated. The control bidirectional converter is simple. Only one set of complementary signals is required for step-up and step-down modes, which greatly reduces costs. The converter also features a continuous current at the low-voltage side, a leakage inductance function for energy recovery, and zero-voltage switching (ZVS) on certain switches, which can prevent voltage spikes on the switches and increase the efficiency of the proposed converter. A bidirectional converter with a total power of 1 kW is used to verify the topology’s feasibility and practicability. The power at the low-voltage side was 24–58 V, and the maximum efficiency in step-up mode was 94.5%, 96.5%, and 94.8%, respectively; the maximum efficiency in step-down mode was 94.4%, 95.4%, and 93.7%, respectively.

1. Introduction

The public’s awareness of environmental problems is increasing. In response to global warming, renewable energy is gradually replacing power derived from fossil fuels. The burning of fossil fuels causes substantial pollution, such as that from CO₂, SO₂, and particulate matter [1]. These pollutants are detrimental to health and influence climatic conditions. The price of lithium-ion battery pack was around $1100/kWh in 2010, but now it is only $157/kWh in 2021 [2]. Further, MOSFETs, which deliver high current reliably, have been the backbone of converters in recent years [3]. As mentioned above, the development of converters will get better and better.

The application of diverse converters can be divided into three types: AC/DC, DC/DC, and DC/AC converters, as shown in Figure 1. Basic DC/DC converters are broadly divided into two categories: nonisolated converters and isolated converters. Boost converters have been widely applied for maximum power point tracking (MPPT) in solar power systems [4,5,6]. Buck converters, which step down a voltage from its input to its output, are extensively used in consumer electronics such as laptops [7,8,9]. Forward and flyback converters are commonly used in industry settings. The flyback converter is the most popular option for isolated DC/DC converters because of its cost effectiveness and high efficiency. However, leakage inductance energy cannot be released when the converter switch is turned off; the high spike on the switch is also a serious problem [10,11,12].

Rapid advancements have been made in bidirectional DC/DC converter technology. The reliability and efficiency of DC/DC converters must be increased for an improvement in power supply. For cost reductions, fewer components used to obtain increased power output is a main research direction. Ref. [13] presents a nonisolated bidirectional DC/DC converter with ZVS technology; its advantages include achieving ZVS and a clamping circuit, but the converter does not apply galvanic isolation. Ref. [14] presents a switched quasi-Z-source nonisolated bidirectional DC/DC converter; it has a wide voltage gain range in step-up and step-down modes. However, it possesses high switching loss and noise because all switches of this converter are operated with hard switching. Ref. [15] presents an isolated bidirectional converter with Cuk topology; it is suitable for photovoltaic (PV) applications because of the wide input voltage range for supporting a wide variety of DC supply equipment. However, high-voltage stress and high-current stress across switches can damage the circuit. Voltage gain bidirectional LLCL resonant DC/DC converters [16] are among the most popular converters and can be adapted for high-power fields, but their control method is complicated. Bidirectional full-bridge converters [17,18,19] are widely used in EVs, energy storage systems, and uninterruptible power supply (UPS) systems. Such converters contain many components, and their complicated control leads to increased converter costs. An improved current-fed bidirectional DC/DC converter for EVs was developed [20] to achieve ZVS turn-on and ZCS (zero-current switching) turn-off for all power switches, but it only provides 250 W of output power for step-up and step-down modes. This output power is insufficient for EV batteries. Researchers have developed an isolated two-stage bidirectional DC/DC converter for residential energy storage systems [21] and a reactive power elimination bidirectional converter with ripple-free current [22]; these converters have a low output ripple and high voltage gain, but they have two crucial disadvantages: too many components are required and the PWM control signals are complex.

To solve these problems, this study designed a converter to provide flexible power conversion. It can be installed in EVs to supply energy to servers or batteries. A common voltage of servers and batteries for cloud systems is 48 V, and the voltage of a DC bus is 400 V. Therefore, in the proposed converter, low-side voltage V_L is 48 V, and high-side voltage V_H is 400 V. The proposed converter can convert a battery’s voltage (24–58 V) to that of a DC bus (400 V) to balance grid energy, as shown in Figure 2.

2. Circuit Architecture and Operation Principle

Figure 3 presents the circuit architecture of the proposed bidirectional converter. V_H and V_L are the high-voltage side and low-voltage side power ports, respectively. The transformer consists of leakage inductance L_lk1 and L_lk2, as well as magnetizing inductance L_m1, for which the turn ratio is N₂:N₁. The proposed converter features six switches (S₁ to S₆). Body diodes D_S1 to D_S6 and parasitic capacitances C_S1 to C_S6 are the parasitic elements of switches S₁ to S₆. Capacitors C₁ to C₄ and inductor L₁ are components of the proposed converter.

The operating principles and operation mode of the proposed topology in step-up and step-down modes were analyzed. This section details the operating principles of the proposed topology in step-up and step-down modes. The voltage polarity and current direction of components in the topology are presented in Figure 3. To simplify our analysis of the operating principles, several assumptions were made:

(1)

All internal resistance and parasitic effects were ignored.

(2)

The voltages of the capacitors and the currents of inductors increase and decrease linearly.

(3)

The capacitance values of C1, C2, C3, and C4 are infinite.

(4)

All magnetic components are operated in CCM.

(5)

The turns of N₁ are less than those of N₂, and N₂/N₁ are defined as N.

2.1. Step-Up Mode (Batteries Discharging Mode)

In step-up mode, the complementary PWM signal is composed of two sets of signals, namely, (v_gs1, v_gs3) and (v_gs2, v_gs4). The gate signals of S₁ and S₃ are the complementary waveforms of S₂ and S₄. The signals of S₅ and S₆ are in the OFF state. The theoretical waveforms of the proposed topology in step-up mode are presented in Figure 4. One operating cycle features five operation modes, as shown in Figure 5a–e.

(1) Mode 1 [t₀–t₁]

The equivalent circuit of Mode 1 is presented in Figure 5a. This mode is operated in a deadtime period. All switch signals are in the OFF state. At the beginning of this mode at time t = t₀, the magnetizing currents of inductor L₁ and coupled inductor Lm₁ start rising. The operation of Mode 1 is followed by that of Mode 5. The energy of the inductor L₁ charges C₁, and C₂ recycles energy from leakage inductance L_lk1 at the primary side of coupled inductor. To achieve ZVS, the energy of the parasitic capacitance of S₃ is released to ground, and then the parasitic diode of S₃ is turned on. On the high-voltage side, coupled inductor Lm₁ and capacitor C₃ supply energy to capacitor C₄ and V_H through body diode D_S6 of S₆. Mode 1 ends when S₁ and S₃ turned on.

(2) Mode 2 [t₁–t₂]

The equivalent circuit of Mode 2 is presented in Figure 5b. When S₁ and S₃ are completely turned on at time t = t₁, the low-voltage side V_L supplies energy to inductor L_1, and the capacitor C₁ releases energy to magnetizing inductance L_m1 and leakage inductance L_lk1. The magnetizing currents of inductor L₁ and coupled inductor Lm₁ continue rising. A coupled inductor Lm₁ transmits energy from the primary N₁ to the secondary N₂. Subsequently, the energy of capacitor C₄ and coupled inductor Lm₁ charge V_H and C₃ through the body diode D_S5 of S₅.

(3) Mode 3 [t₂–t₃]

The equivalent circuit of Mode 3 is indicated in Figure 5c. This mode is operated in a deadtime period. All switch signals are in the OFF state. At the start of this mode’s operation, at time t = t₂, the magnetizing currents of inductor L₁ and coupled inductor Lm₁ start falling. The energy of the inductor L₁ charges the capacitor C₁. To achieve ZVS, the energy of the S₄ parasitic capacitance is absorbed into leakage inductance L_lk1, and then the parasitic diode S₄ is turned on. Capacitor C₂ transmits energy to the coupled inductor Lm₁ through the parasitic diode S₄. On the high-voltage side, Mode 3 operates in the same manner as Mode 2. Mode 3 ends when S₂ and S₄ are completely turned on.

(4) Mode 4 [t₃–t₄]

The equivalent circuit of Mode 4 is presented in Figure 5d. When S₂ and S₄ are completely turned on at time t = t₃, inductor L₁ supplies energy to capacitor C₁, and capacitor C₂ recycles the energy of leakage inductance L_lk1 on the low-voltage side. The magnetizing currents of inductor L₁ and coupled inductor Lm₁ continue falling. On the high-voltage side, Mode 4 operates in the same manner as Mode 5 and Mode 1. Mode 4 ends when inductance i_Llk1 drops to zero.

(5) Mode 5 [t₄–t₅]

The equivalent circuit of Mode 5 is presented in Figure 5e. At time t = t₄, the switch signals are the same as those in the previous mode during this time interval. Mode 5 operates in a similar manner to Mode 4, but in this mode, capacitor C₂ releases energy to magnetizing inductance L_m1 and leakage inductance L_lk1. Coupled inductor Lm₁ transmits energy from the primary N₁ to the secondary N₂.

2.2. Step-Down Mode (Batteries Charging Mode)

In step-down mode, the complementary PWM signal is composed of two sets of signals: (1) v_gs1, v_gs3, and v_gs5 and (2) v_gs2, v_gs4, and v_gs6. The gate signals of S₁, S₃, and S₅ are complementary waveforms of S₂, S₄, and S₆. The theoretical waveforms of the proposed topology in step-up mode are detailed in Figure 6. One operating cycle features five operation modes, as shown in Figure 7a–e.

(1) Mode 1 [t0–t1]

The equivalent circuit of Mode 1 is illustrated in Figure 7a. This mode operates in a deadtime period. All switch signals are in the OFF state. On the high-voltage side, V_H charges the capacitor C₃. To achieve ZVS, the energy of parasitic capacitance S₅ is absorbed into capacitor C₃, and then the parasitic diode S₅ is turned on. Capacitor C₄ charges the coupled inductor L_m1 until the end of this mode’s operation at time t = t0. Mode 1 is followed by Mode 5. C₁ continuously charges inductor L₁, and C₂ recycles the energy of leakage inductance L_lk1. Mode 1 ends when S₁, S₃, and S₅ are completely turned on.

(2) Mode 2 [t₁–t₂]

The equivalent circuit of Mode 2 is presented in Figure 7b. When S₁, S₃, and S₅ are completely turned on at time t = t₁, V_H and C₃ charge capacitor C₄ via N2 at the high-voltage side. The magnetizing currents of inductor L₁ and coupled inductor Lm1 continue falling. Coupled inductor L_m1 transmits energy to C₂. Inductor L₁ supplies energy to V_L on the low-voltage side.

(3) Mode 3 [t₂–t₃]

The equivalent circuit of Mode 3 is presented in Figure 7c. This mode operates during a deadtime period. All switch signals are in the OFF state. At the beginning of this mode’s operation at time t = t₂, on the high-voltage side, V_H and C₃ charge C₄ and L_m1. The magnetizing currents of L₁ and L_m1 start rising. To achieve ZVS, the energy of parasitic capacitance S₆ is absorbed into leakage inductance L_lk2, and then parasitic diode S₆ is turned on. C₃ charges L_m1 until the end of this mode at time t = t_3. L₁ continuously supplies energy to V_L. C₂ charges L_m1 on the low-voltage side. Mode 3 ends when S₂, S₄, and S₆ are completely turned on.

(4) Mode 4 [t₃–t₄]

The equivalent circuit of Mode 4 is illustrated in Figure 7d. When S₁, S₃, and S₅ are completely turned on at time t = t₃, V_H charges C₃. Capacitor C₄ supplies energy to Lm₁ on the high-voltage side. The magnetizing currents of L₁ and L_m1 continue rising. C₂ continuously charges coupled inductor L_m1, and C₁ releases energy to L₁ on the low-voltage side. Mode 4 ends when current of leakage inductance i_Llk1 drops to zero.

(5) Mode 5 [t₄–t₅]

The equivalent circuit of Mode 5 is presented in Figure 7e. At time t = t₄, the switch signals are the same as those in the previous mode. Mode 5 operates in a similar manner to Mode 4, but in this mode, C₂ recycles the energy of leakage inductance L_lk1.

3. Steady-State Analysis

In step-up mode, the complementary PWM signal is composed of two sets of signals. The switching period is D₁T_S. v_gs1 and v_gs3 are turned ON, and v_gs2 and v_gs4 are turned ON for time (1-D₁)T_S.

In step-down mode, the complementary PWM signal is composed of two sets of signals. v_gs1, v_gs3, and v_gs5 are turned ON for time D₆T_S, and v_gs2, v_gs4, and v_gs6 are turned OFF for time (1-D₆)T_S. Our steady-state analysis of the proposed topology is based on the following assumptions:

(1)

All internal resistance and parasitic effects are ignored.

(2)

The currents of the inductors and voltages of the capacitors increase and decrease linearly.

(3)

N₂/N₁ are defined as N.

(4)

All magnetic components are operated in CCM.

(5)

The capacitance values of C₁, C₂, C₃, and C₄ are infinite.

3.1. Step-Up Mode (Batteries Discharging Mode)

(1) Voltage Gain Analysis

On the basis of the voltage–second balance for an inductor, the relationship between V_C1, V_C2, V_C3, V_C4, and V_L can be expressed as follows:

$$V_{C1}=\frac{1}{1-D_1}{V}_L$$

(1)

$$V_{C3}=N{V}_{C1}$$

(2)

These equations are solved simultaneously, where V_C3 is given by

$$V_{C3}=\frac{N}{1-D_1}{V}_L$$

(3)

Equation (1) is substituted into (4)

$$V_{C4}=\frac{N{D}_1}{1-D_1}{V}_{C1}$$

(4)

where V_C4 is given by

$$V_{C4}=\frac{N{D}_1}{{(1-D_1)}^2}{V}_L$$

(5)

Equation (1) is substituted into (6)

$$V_{C4}=N{V}_{C2}$$

(6)

where V_C2 is given by

$$V_{C2}=\frac{D_1}{{(1-D_1)}^2}{V}_L$$

(7)

In accordance with the Mode 2 of step-up mode, the relationships between V_H, V_C1, and V_C3 can be expressed as follows:

$$V_H=N{V}_{C1}+V_{C4}$$

(8)

By substituting (1) and (7) into (8), we can obtain the voltage gain in step-up mode G_step-up as follows:

$$G_{step-up}=\frac{V_H}{V_L}=\frac{N}{{(1-D_1)}^2}$$

(9)

Figure 8 presents the relationship between voltage gain and duty cycle in step-up mode.

(2) Voltage Stress Analysis of Components

On the basis of the equivalent circuit during D₁T_S, the voltage across S₂ is V_C1, and the voltage across S₄ is the sum of V_C1 and V_Lm1. The voltage stress on S₆ is V_H. The voltage stresses on the switch are as follows:

$$V_{S2,stress}=V_{C1}=\frac{1-D_1}{N}{V}_H=\frac{1}{1-D_1}{V}_L$$

(10)

$$V_{S4,stress}=V_{C1}+V_{C2}=\frac{1}{N}{V}_H=\frac{1}{{(1-D_1)}^2}{V}_L$$

(11)

$$V_{S6,stress}=V_H=\frac{N}{{(1-D_1)}^2}{V}_L$$

(12)

On the basis of the equivalent circuit during (1−D₁)T_S, the voltage stress on S₁ is V_C1. The voltage across S₃ is V_C2, and the voltage across S₅ is V_H. The voltage stresses on the switches are as follows:

$$V_{S1,stress}=V_{C1}=\frac{1-D_1}{N}{V}_H=\frac{1}{1-D_1}{V}_L$$

(13)

$$V_{S3,stress}=V_{C2}=\frac{D_1}{N}{V}_H=\frac{D_1}{{(1-D_1)}^2}{V}_L$$

(14)

$$V_{S5,stress}=V_H=\frac{N}{{(1-D_1)}^2}{V}_L$$

(15)

The voltage stresses of the capacitor are as follows:

$$V_{C1,stress}=\frac{\left(1-D_1\right)}{N}{V}_H=\frac{1}{\left(1-D_1\right)}{V}_L$$

(16)

$$V_{C2,stress}=\frac{D_1}{N}{V}_H=\frac{D_1}{{(1-D_1)}^2}{V}_L$$

(17)

$$V_{C3,stress}=\left(1-D_1\right)V_H=\frac{N}{\left(1-D_1\right)}{V}_L$$

(18)

$$V_{C4,stress}=D_1{V}_H=\frac{N{D}_1}{{(1-D_1)}^2}{V}_L$$

(19)

(3) Current Stress Analysis of Components

On the basis of the equivalent circuit during D₁T_S, the induced current of the coupled inductor Lm₁ and i_C4 flows through the parasitic diode of S₅ to release energy to C₃ and i_H. On the low-voltage side, no current flows to C₂. C₁ releases energy to Lm₁. According to Kirchhoff’s current law, the currents of i_C3, i_C4, i_C2, and i_C1 can be expressed as follows:

$$i_{C3}=i_{ds5}+i_H$$

(20)

$$i_{C4}=-i_H$$

(21)

$$i_{C2}=0$$

(22)

$$i_{C1}=i_{Lm1}+N{i}_{ds5}$$

(23)

According to the equivalent circuit during (1−D₁)T_S, the induced current of the coupled inductor iLm₁ and i_C3 flows through the parasitic diode of S₆ to release energy to C₄ and i_H. On the low-voltage side, no current flows to C₂ and S₄ because leakage inductance is neglected. L₁ releases energy to C₁.

$$i_{C3}=-i_{H }$$

(24)

$$i_{C4}=i_{ds6}+i_H$$

(25)

$$i_{C2}=0=i_{ds4}$$

(26)

$$i_{C1}=i_{L1}$$

(27)

According to the ampere–second balance of a capacitor, the average current through a capacitor for steady-state operation is zero. The relationships between i_ds4, i_ds5, i_ds6 and i_H can be expressed as follows:

$$i_{ds4}=0$$

(28)

$$i_{ds5}=\frac{i_H}{D_5}$$

(29)

$$i_{ds6}=\frac{i_H}{1-D_5}$$

(30)

On the basis of the Mode 2 of step-up mode, the relationship between i_ds1 and i_ds3 can be expressed as follows:

$$i_{ds1}=\frac{N}{D_1{(1-D_1)}^2}{i}_H$$

(31)

$$i_{ds3}=\frac{N}{D_1\left(1-D_1\right)}{i}_H$$

(32)

On the basis of the Mode 4 of step-up mode, the i_ds2 can be expressed as follows:

$$i_{ds1}=-\frac{N}{D_1{(1-D_1)}^2}{i}_H$$

(33)

3.2. Step-down Mode (Batteries Charging Mode)

(1) Voltage GainAnalysis

On the basis of the voltage–second balance of an inductor, the relationships between V_C1, V_C2, V_C3, V_C4, and V_H can be expressed as follows:

$$V_{C1}=\frac{1-D_5}{N{D}_5}{V}_{C4}$$

(34)

$$V_{C4}=D_5{V}_H$$

(35)

where V_C1 is given by

$$V_{C1}=\frac{1-D_5}{N}{V}_H$$

(36)

Substituting (35) into (37) provides the following equation:

$$V_{C2}=\frac{1}{N}{V}_{C4}$$

(37)

where V_C2 is given by

$$V_{C2}=\frac{D_5}{N}{V}_H$$

(38)

where V_C3 is given by

$$V_{C3}=(1-D_5)V_H$$

(39)

On the basis of the voltage–second balance of an inductor, the relationship between V_C1 and V_L can be expressed as follows:

$$V_{C1}=\frac{1}{1-D_5}{V}_L$$

(40)

By substituting (1) into (2), we can obtain the voltage gain in step-up mode G_step-down as follows:

$$G_{step-down}=\frac{V_L}{V_H}=\frac{{(1-D_5)}^2}{N}$$

(41)

Figure 9 presents the relationship between voltage gain and duty cycle operated in step-down mode.

(2) Voltage Stress Analysis of Components

On the basis of the equivalent circuit during D₅T_S, the voltage across S₂ is V_C1, and the voltage across S₄ is V_C2. The voltage stress on S₆ is V_H. The voltage stresses on the switches are as follows:

$$V_{S2,stress}=V_{C1}=\frac{1-D_5}{N}{V}_H=\frac{1}{1-D_5}{V}_L$$

(42)

$$V_{S4,stress}=V_{C1}+V_{C2}=\frac{1}{N}{V}_H=\frac{1}{{(1-D_5)}^2}{V}_L$$

(43)

$$V_{S6,stress}=V_H=\frac{N}{{(1-D_5)}^2}{V}_L$$

(44)

On the basis of the equivalent circuit during (1−D₅)T_S, the voltage across S₁ is V_C1. The voltage across S₃ is V_C2. The voltage stress on S₅ is V_H. The voltage stresses of the switches are as follows:

$$V_{S1,stress}=V_{C1}=\frac{1-D_5}{N}{V}_H=\frac{1}{1-D_5}{V}_L$$

(45)

$$V_{S3,stress}=V_{C2}=\frac{D_5}{N}{V}_H=\frac{D_5}{{(1-D_5)}^2}{V}_L$$

(46)

$$V_{S5,stress}=V_H=\frac{N}{{(1-D_5)}^2}{V}_L$$

(47)

The voltage stresses of the capacitor are as follows:

$$V_{C1,stress}=\frac{1-D_5}{N}{V}_H=\frac{1}{1-D_5}{V}_L$$

(48)

$$V_{C2,stress}=\frac{D_5}{N}{V}_H=\frac{D_5}{{(1-D_5)}^2}{V}_L$$

(49)

$$V_{C3,stress}=D_1{V}_H=\frac{N{D}_1}{{(1-D_1)}^2}{V}_L$$

(50)

$$V_{C4,stress}=\left(1-D_1\right)V_H=\frac{N}{\left(1-D_1\right)}{V}_L$$

(51)

(3) Current Stress Analysis of Components

On the basis of the equivalent circuit during D₅T_S, V_H charges C₄. C₃ transmits energy to C₁ through Lm₁, S₁, and S₃. C₂ has no current. The inductor L₁ releases energy to V_L. According to Kirchhoff’s current law, the currents flowing to C₁-C₄ can be represented as follows:

$$i_{C1}=-i_{ds1}+i_{L1}=-i_{ds3}$$

(52)

$$i_{C2}=0$$

(53)

$$i_{C3}=i_H-i_{ds5}$$

(54)

$$i_{C4}=i_H$$

(55)

On the basis of the equivalent circuit during (1−D₅)T_S, V_H charges capacitor C₃. C₄ transmits energy to Lm₁. C₂ and S₄ still have no current at this time because leakage inductance is neglected. C₁ releases energy to L₁ through S₂. According to Kirchhoff’s current law, the currents of i_C1, i_C2, i_C3, and i_C4 can be expressed as follows:

$$i_{C1}=i_{L1}=-i_{ds2}$$

(56)

$$i_{C2}=0=i_{ds4}$$

(57)

$$i_{C3}=i_H$$

(58)

$$i_{C4}=i_H-i_{ds6}$$

(59)

On the basis of the ampere–second balance of a capacitor, the average current through a capacitor for steady-state operation is zero. The relationships between i_ds4, i_ds5, i_ds6 and i_H can be expressed as follows:

$$i_{ds1}=i_{L1}$$

(60)

$$i_{ds2}=-\left(1-D_5\right)i_{L1}$$

(61)

$$i_{ds3}=\left(1-D_5\right)i_{L1}$$

(62)

$$i_{ds4}=0$$

(63)

$$i_{ds5}=-\frac{{(1-D_5)}^2}{N{D}_5}{i}_{L1}$$

(64)

$$i_{ds6}=-\frac{1-D_5}{N}{i}_{L1}$$

(65)

3.3. Magnetic Component Design

The magnetic components of the proposed converter are designed in CCM, and the maximum currents of L₁ and L_m1 are determined as follows:

$$i_{L1,max}=I_{L1,avg}+\frac{\Delta i_{L1}}{2}$$

(66)

$$i_{Lm1,max}=I_{Lm1,avg}+\frac{\Delta i_{Lm1}}{2}$$

(67)

The minimum currents of L₁ and L_m1 are as follows:

$$i_{L1,min}=I_{L1,avg}-\frac{\Delta i_{L1}}{2}$$

(68)

$$i_{Lm1,min}=i_{Lm1,avg}-\frac{\Delta i_{Lm1}}{2}$$

(69)

When the switch S₁ is turned off, the current Δi_L1 and Δi_Lm1 are as follows:

$$\Delta i_{L1}=\frac{V_{L1}}{L_1}{D}_1{T}_S$$

(70)

$$\Delta i_{Lm1}=\frac{V_{Lm1}}{L_{m1}}{D}_1{T}_S$$

(71)

While the magnetic components are operated in the boundary conduction mode (BCM; Figure 10 and Figure 11), currents i_{L1, min} and i_{Lm1, min} are equal to zero. The i_{L1, min} current can be expressed as follows:

$$i_{L1,min}=0=\frac{N}{{(1-D_1)}^2}{i}_H-\frac{{(1-D_1)}^2{D}_1{T}_s}{2L_{1}N}{V}_H$$

(72)

Similarly, the i_{Lm1, min} currents can be expressed as follows:

$$i_{Lm1,min}=0=\frac{N}{1-D_1}{i}_H-\frac{\left(1-D_1\right)D_1}{2L_{m1}{f}_{s}N}{V}_H$$

(73)

After (24) and (25) are simplified, L_1,BCM and L_m1,BCM can be obtained as follows:

$$L_{L1,BCM}=\frac{{(1-D_1)}^4{D}_1}{2f_s{N}^2}\frac{V_H}{i_{H,BCM}}$$

(74)

$$L_{m1,BCM}=\frac{{(1-D_1)}^2{D}_1}{2f_s{N}^2}\frac{V_H}{i_{H,BCM}}$$

(75)

4. Experimental Results

The measured waveforms were used to verify the correctness and feasibility of the proposed topology. The key waveforms in step-up and step-down modes were measured separately and compared with the simulated waveforms. Finally, the conversion efficiency levels of step-up and step-down modes were measured.

Table 1. Electrical specifications of proposed topology.

Parameter	Specification
High-side power PH	1000 W
Low-side power PL	1000 W
High-side voltage VH	400 V
Low-side voltage VL	24–58 V
Switching frequency fs	40 kHz
Power switches S1, S2, and S3	IRFP4568PbF
Power switch S4	IRFP4768PbF
Power switches S5 and S6	IXFH50N50P3
Inductor L1	47 μH
Magnetizing inductance Lm1	190 μH
Leakage inductance Llk1	2.4 μH
Capacitor C1	100 μF
Capacitor C2	70 μF
Capacitor C3 and C4	220 μF
Turns ratio N	2.2

shows the electrical specifications and component parameters of proposed topology. A photograph of the proposed bidirectional isolated DC/DC converter with a microcontroller (MCU) is presented in Figure 12.

A proportional–integral–derivative (PID) controller is used to control the proposed converter and presented in Figure 13. The overall control function is:

$$K_{\mathrm{p}}e\left(t\right)+K_{\mathrm{i}}{{\displaystyle \int }}_0^{t}e\left(\tau \right)\mathrm{d}\tau +K_{\mathrm{d}}\frac{\mathrm{d}e\left(t\right)}{\mathrm{d}t}$$

(76)

In both modes, by receiving voltage feedback from a voltage divider circuit at the other voltage side, the MCU generates PWM signals to control the duty cycle of switches to achieve stable output voltage. The PID parameters are Kp = 0.3, Ki = 0.04, and Kd = 0.001, respectively. In step-down mode, to alter the input voltage (24–58 V), the MCU generates PWM signals to control the duty of switches to achieve stable output voltages. The PID parameters are Kp = −0.275, Ki = −0.1, and Kd = −0.01, respectively.

During measurement, V_L was maintained at 24–58 V, and the high-voltage side V_H was maintained at 400 V. Figure 14, Figure 15 and Figure 16 present the measured waveforms of the low-voltage side at 24, 48, and 58 V at full load in step-up mode.

The images of waveforms are magnified to reveal the ZVS performance. Before ZVS turn-on, the v_ds of S₃ and S₄ dropped to zero, as shown in Figure 17.

Figure 18 presents an analysis of the losses of the proposed converter at V_L = 24 V in step-up mode and under full load. The switching loss and conduction loss of all power switches account for a large proportion of the overall loss.

During measurement, V_L was maintained at 24–58 V, and the high-voltage side V_H was maintained at 400 V. Figure 19, Figure 20 and Figure 21 present the measured waveforms of the low-voltage side at 24, 48, and 58 V at full load in step-down mode.

The magnified images of waveforms are presented to reveal the ZVS performance. Before ZVS turn-on, the v_ds of S₅ and S₆ dropped to zero, as shown in Figure 22.

Figure 23 presents the results from analyzing the losses of the proposed topology at V_L = 48 V in step-down mode at full load. The switching loss and conduction loss of all switches account for a large proportion of the overall loss.

Figure 24 shows the conversion efficiency of the proposed converter in step-up mode. When V_L is 24 V, the highest efficiency is 95.1% at 200 W, and the full-load conversion efficiency is 88%. When V_L is 48 V, the maximum efficiency is moved to 300 W, which is 96.55%, and the full-load conversion efficiency is 92.9%. When V_L is 58 V, the highest efficiency is also 94.8% at 300 W, and the full-load conversion efficiency is 93.3%.

Figure 25 shows the conversion efficiency of the proposed converter in step-down mode. When V_L is 24 V, the highest efficiency is 94.4% at 400 W, and the full-load conversion efficiency is 88.2%. When V_L is 48 V, the highest efficiency is 95.48% at 400 W, and the full-load conversion efficiency is 92.1%. When V_L is 58 V, the highest efficiency point is moved to 500 W, which is 93.7%, and the conversion efficiency at full load is 92.4%.

Figure 26 presents the measured waveforms for step variations in output load. When the output power was changed from half load to full load, the transient voltage fluctuation in the proposed converter was sufficiently small so as to be neglected, output voltage V_H was stable at 400 V in step-up mode, and output voltage V_L was stable at 24 V in step-down mode.

Table 2. Comparison between the proposed converter and related bidirectional converters.

	Converter in [20]	Converter in [21]	Converter in [23]	Converter in [24]	Converter in [25]	Converter in [26]	Converter in [27]	Proposed Converter
Voltage gain in step-up mode $\frac{V_H}{V_L}$	$\frac{1}{\left(1-D\right) }‧2N$	$\frac{N}{D_1‧D_2‧D_3}$	$\frac{N+1}{1-D}$	$\frac{N}{{\left(1-D\right)}^2}$	$\frac{1+D\left(N+Na\right)}{1-D}$	$\frac{2N+2}{1-D}$	$\frac{2\left(N+1\right)}{1-D}$	$\frac{N}{{\left(1-D\right)}^2}$
Voltage gain in step-down mode $\frac{V_L}{V_H}$	$\frac{D}{2N}$	$\frac{D_1‧D_2‧D_3}{N}$	$\frac{D}{N+1}$	$\frac{{\left(1-D\right)}^2}{N}$	$\frac{D}{1+\left(1-D\right)\left(N+Na\right)}$	$\frac{D}{2N+2}$	$\frac{D}{2\left(N+1\right)}$	$\frac{{\left(1-D\right)}^2}{N}$
Vin	24–48 V	35–50 V	40 V	24–55 V	48 V	48 V	48 V	24–58 V
Vo	360 V	400 V	400 V	400 V	380 V	384 V	400 V	400 V
Switches	4	10	4	6	3	6	4	6
Inductors	1	2	0	1	0	0	0	1
Coupled inductor	1	1	1	1	1	1	2	1
Capacitors	6	3	2	3	1	4	3	4
Diodes	0	0	0	0	0	0	3	0
Output power	250 W	1000 W	300 W	500 W	300 W	250 W	400 W	1000 W
Efficiency of step-up mode	94%	94%	94%	96%	94%	96%	95%	96%
Efficiency of step-down mode	93%	94%	94%	94%	95%	96%	95%	95%
PWM Control Signals	Normal	Complex	Normal	Normal	Normal	Normal	complex	Normal
Isolated	Yes	Yes	No	Yes	No	No	No	Yes

presents a comparison of the proposed converter with those in [20,21] and [23,24,25,26,27]. The proposed converter has larger power output, higher efficiency, and higher voltage gain, meaning that it can be widely used in numerous industries. In addition, related equipment can be operated safely under galvanic isolation. Comparisons of the voltage gain in step-up and step-down modes are presented in Figure 27 and Figure 28, respectively. The duty variation influences the voltage gain of the converter, and the proposed converter possesses a wider voltage gain than do other bidirectional converters through duty cycle control. When the duty ratio exceeds 0.6, the proposed converter has the highest voltage gain.

Figure 29 and Figure 30 present conversion efficiency comparisons between the proposed converter and the converters proposed in [20,21] and [23,24,25,26,27] operated in step-up and step-down modes, respectively. In the converter described in [20], the conversion efficiency was not high, and the output power of the converter was insufficient. Of all the converters, the converter in [21] has the highest switching frequency; this can greatly reduce converter size, but too many components lead to increased costs. In the converter described in [25], all switches have ZVS, but the efficiency is mediocre. The overall conversion efficiency is the highest in the converter described in [26], but the output power of this converter is insufficient for storage systems. In the converter described in [27], the PWM control signals are too complex.

In summary, the overall conversion efficiency of the proposed converter is high, and the converter has substantial power in both step-up and step-down modes. In addition, this converter has the widest input range of all the converters.

5. Conclusions

This study proposed a novel bidirectional isolated DC/DC converter with a high gain ratio and wide input voltage for EV storage systems. This converter only requires one complementary PWM output to control step-up and step-down modes. Partial switches achieve ZVS, which can increase efficiency. The topology proposed in this paper was demonstrated to be feasible through theoretical analysis and experimentation. When the power on the low-voltage side was 24, 48, and 58 V, the maximum efficiency in step-up mode was 95.1%, 96.5%, and 94.8%, respectively, and the maximum efficiency in step-down mode was 94.4%, 95.4%, and 93.6%, respectively.

The advantages of the proposed converter are as follows: (1) The circuit structure is simple. (2) The converter only requires one complementary PWM output. (3) The converter achieves a wide voltage gain and high voltage gain. (4) Galvanic isolation separates the input and output power supplies. (5) The current of the low-voltage side is continuous in CCM. (6) ZVS technology is used in specific switches to reduce switching loss.

Future research directions include: (1) The proposed topology can be designed for three-stage charging, which are bulk charge, absorption, and float charge to extend battery life effectively by adding current sensor. (2) Modularize the proposed topology to achieve multiple groups of bidirectional energy transmission in parallel to deal with the application of greater power. (3) Implement greater practical power.