# Design Method of Double-Boost DC/DC Converter with High Voltage Gain for Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Topology and Operating Principle of the Proposed Converter

#### 2.1. Topology of Double-Boost Converter

_{1}, Q

_{2}, two inductors L

_{1}, L

_{2}, three diodes D

_{1}, D

_{2}, D

_{3}and an output filter capacitor C

_{1}. Assuming that the inductors L

_{1}, L

_{2}are the same, the remaining diodes and metal-oxide-semiconductor field-effect transistor (MOSFET) switching also have the same parameters. The two switches in the converter are turned on or off together, and the two operating modes are shown in Figure 2.

_{1}and Q

_{2}are turned on, that is, the converter is in the ON operating mode, the inductors L

_{1}and L

_{2}are charged by the input power source, and the inductors absorb energy; the capacitor C

_{1}supplies energy to the load. The operating mode of the proposed converter is shown in Figure 2.

_{1}is turned on, and diodes D

_{2}and D

_{3}are turned off under reverse voltage. During this stage, there are three loops in the equivalent circuit. The input power U

_{in}charges the inductor L

_{1}through the switch Q

_{1}to form the first loop. The input power U

_{in}charges the inductor L

_{2}through the switch Q

_{2}to form the second loop. The output capacitor C

_{1}provides energy to the load to form the third loop. The voltages across the two inductors L

_{1}and L

_{2}are the voltages U

_{in}of the input voltage power source. The voltage and current on the inductor take the associated reference direction, and set T

_{S}as a Pulse-width modulation (PWM) period, D is the duty cycle of PWM, then the turn-on time of switches Q

_{1}and Q

_{2}is D × T

_{S}in one cycle. Suppose that the currents through the inductors L

_{1}and L

_{2}are I

_{L}

_{1}and I

_{L}

_{2,}respectively. In this stage, the currents of the two inductors are equal, and the energy absorbed by the two inductors in a PWM period is shown in Equation (1).

_{L}represents the energy absorbed by the inductor during the turn-on period of the switch.

_{1}and Q

_{2}are turned off, that is, the equivalent circuit is in the OFF mode, the inductors L

_{1}and L

_{2}are connected in series with the input power source to provide energy to the load and charge the capacitor C

_{1}; the operating mode of the converter is shown in Figure 3.

_{2}and D

_{3}are turned on, and diode D

_{1}is turned off under reverse voltage. During this stage, there is only one loop in the equivalent circuit. The input power source U

_{in}and inductors L

_{1}and L

_{2}are connected in series to provide energy to the load and charge the output capacitor C

_{1}. By ignoring the conduction voltage drop in the diode, the voltage across the two inductors L

_{1}and L

_{2}are the voltage U

_{in}of the input voltage. The voltage and current reference directions on the inductor are uncorrelated, and the energy released by the two inductors in a PWM period is shown in Equation (2).

_{L}’ represents the energy released by the inductor during the turn-off period of the switch.

_{D}of the proposed converter can be obtained as shown in Equation (4).

_{Con}and I

_{Coff}, and the equation is as follows.

_{o}represents the output current and I

_{D3}represents the current flowing through diode D

_{3}. By applying ampere-second balance to the capacitor, the following equation can be obtained as

_{3}can be expressed as:

_{in}and output current I

_{o}can be expressed as follows:

_{1}, Q

_{2}and the diode D

_{1}can be obtained as:

_{Q1}and I

_{Q2}represent the current flowing through switches Q

_{1}and Q

_{2}, respectively, and I

_{D1}represents the current flowing through the diode D

_{1}.

_{2}is equal to that of diode D

_{3}, and it can be described as follows:

_{C}

_{1}of capacitor C

_{1}can be obtained as:

_{L}is the inductor current ripple, ΔU is the output voltage ripple, f is the switching frequency, and D is the duty cycle of the PWM. It can be seen from Table 2 that, although the boost converter has the least number of devices, the stress of the switch device is the largest of the three converters. The performance requirements of the switch device are the highest, and the values of inductance and capacitance are the largest, resulting in the power module cost being high, and it is difficult to meet the requirements of high voltage gain in the DC/DC converter. Although the four-phase interleaved DC/DC converter has low stress on the switch device and the smallest value of inductance and capacitance, the converter adopted many devices, resulting in a higher cost. Although the proposed double-boost converter is simple, the number of devices is small, the voltage stress is low when the voltage gain is the same, and the two switches only need the same PWM signal for control.

#### 2.2. Operating Principle of Double-Boost Converter

_{0}–t

_{1}stage, the switches Q

_{1}and Q

_{2}are turned on, and the diodes D

_{2}and D

_{3}are turned off due to the reverse voltage. Meanwhile, the input power source U

_{in}charges the inductors L

_{1}and L

_{2}, and the inductor current rises linearly. The energy required by the load is provided by the output filter capacitor C

_{1}, and the capacitor is in a discharged state; therefore, and the capacitor voltage U

_{C}

_{1}decreases. Since the parameters of the inductors L

_{1}and L

_{2}are the same, take the inductor L

_{1}as an example for analysis. In this stage, the expression of the inductor current is shown in Equation (14).

_{L}

_{1}is the ΔI

_{L}, dt = D/f, f is the switching frequency. The expression of the voltage change in the capacitor C

_{1}is shown in Equation (15).

_{C}

_{1}= ΔU

_{C}

_{1}, ΔU

_{C}

_{1}is the capacitor voltage fluctuation. From Equations (14)–(16) can be written as:

_{1}–t

_{2}stage, the switches Q

_{1}and Q

_{2}are turned off, and the diode D

_{1}is turned off due to the reverse voltage, and the inductors L

_{1}and L

_{2}are connected in series with the power supply to provide energy to the load and charge capacitor C

_{1}. Therefore, the inductor current is linearly decreasing and the capacitor voltage is increasing. The expression of the inductor current is shown in Equation (17).

_{1}is shown in Equation (18):

## 3. Modeling of Double-Boost Converter

_{1}and Q

_{2}are turned on, the corresponding state equation of the converter in this mode is expressed by Equation (16). When the switches Q

_{1}and Q

_{2}are turned off, the corresponding state equation of the converter in this mode is expressed by Equation (19).

_{C}

_{1}and U

_{in}, are the DC steady-state quantities, and $\widehat{D}$, ${\widehat{U}}_{\mathrm{C}1}$, $\widehat{E}$ and ${\widehat{I}}_{\mathrm{L}1}$ are the AC small-signal components of variables. By taking Equation (21) into (20), and using the average quantity in the state space average equation with Equation (21), the following equation can be obtained:

_{L}

_{1}can be obtained as:

_{L}

_{1}to output voltage Uo is shown in Equation (30).

## 4. Design of the Double-Boost Converter Controller

#### 4.1. Calculation of Inductor and Capacitor of Converter

_{1}and L

_{2}are both 0.35 mH, the value of the capacitor is 47 μF, the type of switch is IFR640N, the type of diode is DFE10I600PM and the switching frequency is 20 kHz [21].

_{L}is the inductor current ripple; taking 20% of the average current as the inductor current ripple, the inductance value of the two inductors can be calculated to be 0.35 mH.

#### 4.2. Design of Feedforward Double Closed-Loop Feedback Controller

_{C1}(s) and G

_{C2}(s) adopt PI control. The control block diagram is shown in Figure 8 and is achieved by the following steps: setting the reference voltage U

_{ref}; comparing the output voltage value U

_{C}

_{1}with the reference voltage to get error signal e1; sending the signal to the PI controller G

_{C1}(s) to obtain the reference current I

_{L}

_{1′}; comparing this with the actual inductor current to get error signal e

_{2}; then, the adjusted duty ratio D can be obtained through the PI controller G

_{C2}(s). Meanwhile, the adjusted output voltage is obtained through the transfer functions G

_{D-IL1}(s) and G

_{IL1-UC1}(s).

_{f}(s). According to Equations (28) and (29), the transfer function of feedforward control can be expressed as:

## 5. Simulation and Experimental Results Analysis

#### 5.1. Simulation Results and Analysis

_{gs}is about 0.67, the output voltage of the proposed converter is 100 V, and a higher voltage gain can be obtained without using the extreme duty cycle, which proves the effectiveness of the proposed converter.

#### 5.2. Experimental Platform Construction

#### 5.3. Function Test of the Prototype

#### 5.4. Control Algorithm Verification

#### 5.5. Efficiency Test of the Prototype

## 6. Conclusions

- (1)
- Considering the voltage gain, device stress, and number of components, the proposed converter has certain advantages over traditional boost converters and four-phase interleaved converters. Compared to four-phase interleaved DC/DC converters, this converter has a simple operating principle and only requires two of the same PWM signals.
- (2)
- For the double-boost converter, the proposed feedforward double closed-loop control is more robust than the feedforward double closed-loop control; when the load and input voltage change suddenly, it can make the output voltage return to stability faster.
- (3)
- This can be obtained through the construction of the experimental prototype of the proposed double-boost converter and by comparison with the four-phase interleaved DC/DC converter and the traditional boost converter. In terms of the actual voltage gain and system efficiency under different conditions, the proposed double converter has obvious advantages. The efficiency is measured and compared from three aspects: different output voltages, different loads and different frequencies: In addition, the output voltage ripple of the proposed double-boost converter is smaller than that of the traditional boost converter. Although it is slightly larger than the four-phase interleaved DC/DC converter, the double-boost converter has the advantages of fewer devices, simple control and high efficiency, making up for the output voltage ripple, which is slightly higher than the four-phase interleaved disadvantages of DC/DC converters.

## Author Contributions

## Funding

## Conflicts of Interest

## Glossary

Electric vehicle | EV |

New energy vehicles | NEVs |

D | Duty cycle of PWM |

T_{S} | A PWM period |

W_{L} | Energy absorbed by inductor during ON state |

W_{L}’ | Energy released by inductor during OFF state |

G_{D} | Voltage gain |

ΔI_{L} | The inductor current ripple |

ΔU | The output voltage ripple |

f | Switching frequency |

$\overline{D}$ | Average value of the duty cycle |

${\overline{I}}_{\mathrm{L}1}$ | Average value inductor current |

${\overline{U}}_{\mathrm{C}1}$ | Average value output voltage |

$\overline{E}$ | Average value input voltage |

$\widehat{D}$ | AC small-signal component of D |

${\widehat{U}}_{\mathrm{C}1}$ | AC small-signal component of U_{C1} |

$\widehat{E}$ | AC small-signal component of E |

${\widehat{I}}_{\mathrm{L}1}$ | AC small-signal component of I_{L1} |

${G}_{D\to {I}_{L1}}\left(\mathrm{s}\right)$ | Transfer function of D to the inductor current I_{L}_{1} |

${G}_{{U}_{\mathrm{in}}\to {I}_{L1}}\left(\mathrm{s}\right)$ | The transfer function from input voltage to inductor current |

${G}_{{I}_{L1}\to {U}_{C1}}\left(\mathrm{s}\right)$ | The transfer function of the inductor current I_{L1} to output voltage |

${G}_{D\to {U}_{{C}_{1}}}(\mathrm{s})$ | The transfer function of duty cycle to output voltage |

G_{C1}(s) | The transfer function of voltage PI controller |

G_{C2}(s) | The transfer function of current PI controller |

G_{f}(s) | The transfer function of feedforward control |

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**Figure 14.**The prototype of proposed converter. (

**a**) The experimental platform of double-boost converter. (

**b**) Experimental prototype of four-phase interleaved DC/DC converter.

**Figure 17.**Output voltage ripple of three converters. (

**a**) Boost converter. (

**b**) Double-boost converter. (

**c**) Four-phase interleaved DC/DC converter.

**Figure 18.**With or without feedforward control effect diagram. (

**a**) Feedforward dual closed-loop control output waveform. (

**b**) Output waveform without feedforward control.

**Figure 21.**Comparison of efficiency of two converters. (

**a**) The efficiency of the proposed converter. (

**b**) Efficiency of four-phase interleaved DC/DC converter efficiency.

Device Name. | Current Stress |
---|---|

Diode D_{1} | I_{o}(1 + D)/2(1 − D) |

Diode D_{2} | I_{o}/(1 − D) |

Diode D_{3} | I_{o}/(1 − D) |

Switch device Q_{1} | I_{o}(1 + D)/2(1 − D) |

Switch device Q_{2} | I_{o}(1 + D)/2(1 − D) |

Output capacitor C_{1} | I_{o}[D/(1 − D)]1/2 |

Converter | Traditional Boost | Four-Phase Interleaving | Double-Boost |
---|---|---|---|

Number of inductors | 1 | 4 | 2 |

Number of capacitors | 1 | 2 | 1 |

Number of switch devices | 1 | 4 | 2 |

Number of diodes | 1 | 4 | 3 |

Total number of devices | 4 | 14 | 8 |

Stress of switch devices | U_{o} | (U_{o} + U_{in})/2 | (U_{o} + U_{in})/2 |

Capacitance | I_{out}D/(ΔU × f) | I_{out}D/2(ΔU × f) | I_{out}D/(ΔU × f) |

Inductance | U_{in}D/(ΔI_{L} × f) | U_{in}D/4(ΔI_{L} × f) | U_{in}D/2(ΔI_{L} × f) |

Theoretical voltage gain | 1/(1 − D) | (1 + D)/(1 − D) | (1 + D)/(1 − D) |

Parameters | Values |
---|---|

Rated power P | 100 W |

Input voltage U_{in} | 20 V |

Rated output Voltage U_{O} | 100 V |

Rated load resistance R_{L} | 100 Ω |

Switching frequency f | 20 kHz |

Inductor L_{1} and L_{2} | 0.35 mH |

Capacitor | 47 μF |

Power switches | IFR640N |

Diodes | DFE10I600PM |

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## Share and Cite

**MDPI and ACS Style**

Liu, Z.; Du, J.; Yu, B.
Design Method of Double-Boost DC/DC Converter with High Voltage Gain for Electric Vehicles. *World Electr. Veh. J.* **2020**, *11*, 64.
https://doi.org/10.3390/wevj11040064

**AMA Style**

Liu Z, Du J, Yu B.
Design Method of Double-Boost DC/DC Converter with High Voltage Gain for Electric Vehicles. *World Electric Vehicle Journal*. 2020; 11(4):64.
https://doi.org/10.3390/wevj11040064

**Chicago/Turabian Style**

Liu, Zhengxin, Jiuyu Du, and Boyang Yu.
2020. "Design Method of Double-Boost DC/DC Converter with High Voltage Gain for Electric Vehicles" *World Electric Vehicle Journal* 11, no. 4: 64.
https://doi.org/10.3390/wevj11040064