# Bidirectional CLLLC Resonant Converter Based on Frequency-Conversion and Phase-Shift Hybrid Control

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. System Structure and Characteristic Analysis

#### 2.1. Birirectional CLLLC Resonant Converter

_{1}~S

_{4}constitute the primary-side full bridge, and S

_{5}~S

_{8}constitute the secondary-side full bridge. D

_{1}~D

_{8}are the body diodes of S

_{1}~S

_{8}, and C

_{coss1}~C

_{coss8}are the output capacitors of S

_{1}~S

_{8}. The ratio of the transformer is n:1; L

_{m}is the excitation inductance of the transformer; L

_{r1}, L

_{r2}, C

_{r1}, and C

_{r2}are the resonant inductance and resonant capacitance of the primary side and the secondary side, respectively, and the high-frequency transformer is used for electrical isolation. U

_{AB}is the primary voltage, U

_{CD}is the secondary voltage, and C

_{in}and C

_{o}are the filter capacitors. When the converter is working forward, the power is transmitted from U

_{AB}to U

_{CD}. Since the converter operates in the same state when it is working in the forward and reverse operations, only the positive working time is taken as an example for the analysis.

_{1}~S

_{4}obtain the driving signal to realize the inverter and S

_{5}~S

_{8}realize the rectification.

#### 2.2. Working Characteristics of Frequency-Conversion Control

_{AB_FHA(t)}is the square-wave fundamental component of the input DC-bus voltage after the full-bridge inverter. L

_{r2}′ and C

_{r2}′ are the values of the capacitance and inductance converted from L

_{r2}and C

_{r2}to the primary side of the transformer. R

_{eq}is the equivalent load converted to the primary side. The expression is:

_{out}, I

_{out}, and P

_{out}are the output voltage, output current, and output power, respectively.

_{m}is clamped by the output voltage, the corresponding resonant frequency is the first resonant frequency:

_{m}is no longer clamped by the output, the corresponding resonant frequency is the second resonant frequency:

_{1}is the primary-side series-resonant impedance; Z

_{2}is the equivalent secondary series-resonant impedance; Z

_{m}is the excitation inductance impedance; and ${w}_{\mathrm{s}}$ is the switching angular frequency, ${w}_{\mathrm{s}}=2\mathsf{\pi}{f}_{\mathrm{s}}$.

_{m}/L

_{r1}; Q is the quality factor, $Q=\sqrt{{L}_{\mathrm{r}1}/{C}_{\mathrm{r}1}}/{R}_{\mathrm{eq}}$; f

_{n}is the normalized frequency; ${f}_{n}={f}_{\mathrm{s}}/{f}_{\mathrm{r}1}$; and f

_{s}is the actual switching frequency.

_{n}. The main parameters affecting the voltage gain are the inductance coefficient k and quality factor Q, which are analyzed in detail below:

- (1)
- Influence of inductance factor k on voltage gain

_{n}= 1, the resonant frequency is equal to the switching frequency, the system works at the resonant point, and no matter how k changes, the voltage gain is always 1. In the under-resonant region, the smaller the k value, the greater the maximum voltage gain, and the narrower the frequency modulation range, which is conducive to the adjustment of the wide gain range. As the k value increases, the peak value of the converter voltage gain gradually decreases, the normalized frequency corresponding to the maximum gain of the curve gradually decreases, and the frequency modulation range becomes wider. In the over-resonant region, the voltage gain curve becomes smooth and the effect of adjusting the voltage gain by adjusting the switching frequency is very limited. If the gain is expected to remain unchanged in a wide range around the resonance point, then k should take a larger value. However, when the k value is greater than a certain value, the peak voltage gain of the converter will be less than the maximum value required by the design, and the minimum switching frequency is too low.

- (2)
- Influence of quality factor Q on voltage gain

_{n}= 1, the resonant frequency is equal to the switching frequency, and the system works at the resonant point; no matter how Q changes, the voltage gain is always 1. When the converter is at a light load, that is, the Q value is small, the gain of the converter can be greatly improved when the switching frequency is reduced in the under-resonant region. In the over-resonant region, when the switching frequency increases, the converter gain will only decrease slightly, and the frequency adjustment effect is low. To achieve the effect of voltage regulation, a high frequency is required, and the switching loss increases. Therefore, the selection of the Q value needs to ensure that the converter can meet the requirements of a minimum voltage gain at a light load and that the maximum switching frequency cannot be too high. As the Q value increases, the load becomes heavier and heavier. In the over-resonant region, the gain of the converter changes with the switching frequency. However, when the load is too heavy, the peak value of the maximum gain of the converter decreases in the under-resonant region. To obtain the maximum voltage gain, the switching frequency needs to be reduced to broaden the frequency modulation. The voltage gain curve has two peak points, which are not conducive to the stability of the converter and the design of the control system. Therefore, the selection of the Q value should also be compromised.

_{Lr}flowing through the resonant circuit, which can discharge and charge the parasitic capacitance C

_{oss}of the switching tube. It is assumed that the current flowing through the switching tube remains unchanged as i

_{Lr}within the dead time t

_{d}, and the parasitic capacitance C

_{oss}of the switching tube is equal. To achieve ZVS conditions, i

_{Lr}must be greater than the minimum current for charging and discharging C

_{oss}during the dead time, that is:

#### 2.3. Working Characteristics of Phase-Shift Control

_{AB}changes from a square wave with a duty cycle of 50% to a square wave with a duty cycle of less than 50% and a zero level. From the fundamental equivalent model and Fourier analysis shown in Figure 2, the fundamental component of the input voltage square wave under phase-shift control is expressed as:

_{m2}two-terminal voltage is U

_{2}. From ${U}_{\mathrm{Lm}2}={L}_{\mathrm{m}2}(d{i}_{{}_{\mathrm{Lm}2}}/dt)$ and Equation (7), it is necessary to ensure that the voltage at both ends of C

_{oss}meets ${\mathrm{U}}_{\mathrm{Cos}\mathrm{s}}{>\mathrm{U}}_{2}$ in the dead time td to achieve soft switching. Further, the conditions for soft switching under phase-shift control are:

## 3. Resonant Network Parameter Design

- (1)
- Turn ratio of transformer n

- (2)
- Transformer normalized voltage gain M

- (3)
- Parameter design of inductance coefficient k and quality factor Q

- (4)
- Design of resonant inductor and resonant capacitor

## 4. Frequency-Conversion and Phase-Shift Hybrid Control Strategy

_{n}(under frequency-conversion control) and the phase-shift ratio D (under phase-shift control) can be obtained, as shown in Figure 5. After the quality factor is selected as 0.3, when the bidirectional CLLLC resonant converter is controlled by frequency conversion alone, the voltage gain range is narrow in the step-down mode, and the switching frequency needs to change greatly to change the voltage gain. When phase-shift control is used alone, the maximum voltage gain is only 1, which can only be realized in the step-down mode. The minimum voltage gain in the phase-shift mode is much smaller than the minimum voltage gain under frequency-conversion control. Therefore, this paper proposes a method of frequency-conversion and phase-shift hybrid control applied to a bidirectional CLLLC resonant converter to broaden the voltage gain range. At the resonance point, the working conditions of frequency-conversion control and phase-shift control are the same. Setting this as a switching point can achieve a seamless connection of the voltage gain; that is, frequency-conversion control is adopted when M > 1, and phase-shift control is adopted when M < 1.

_{ref}, the constant-current-control mode is selected when the battery voltage is less than the set value U

_{ref}, and the constant-voltage-control mode is selected when the battery voltage reaches the set value U

_{ref}. When working in the reverse direction, the voltage and current double-closed-loop control method are adopted to output the electric energy in the battery to the primary side through the resonant cavity to obtain a stable 400 V voltage.

## 5. Simulation Analysis

#### 5.1. Forward Simulation

_{1}and S

_{2}, and S

_{4}and S

_{3}, or adjusting the switching frequency of S

_{1}, S

_{2}, S

_{3}, and S

_{4}. In Figure 9, Figure 10 and Figure 11, V

_{gs}and V

_{ds}represent the driving signal and drain-source voltage of the corresponding switching tube, respectively. i

_{D}represents the forward current of the rectifier diode D, V

_{AB}is the resonant slot input voltage, i

_{Lr}is the resonant current, and i

_{Lm}is the excitation inductance current.

_{o}and the output current I

_{o}are 250 V/7.67 A in the constant current mode. At this time, the output power P

_{o}= 1917.5 W, which is the lightest working point of the converter during the constant current operation. It can be seen from Figure 9a that the converter operates in phase-shift mode, and the output voltage is controlled by adjusting the phase-shift angle between S

_{1}and S

_{4}, and S

_{2}and S

_{3}. It can be seen from Figure 9b that the drain voltage V

_{ds4}of S

_{4}has been reduced to zero before the arrival of the driving signal V

_{gs4}of the switching tube S

_{4}. It can be seen that the primary-side switch can achieve ZVS. Before the arrival of i

_{D5}and i

_{D8}, i

_{D6}and i

_{D7}have been reduced to zero. Similarly, before the arrival of i

_{D6}and i

_{D7}, i

_{D5}and i

_{D8}have also been reduced to zero, so the secondary rectifier diode can achieve ZCS.

_{o}and the output current I

_{o}are 320 V/7.67 A. At this time, the output power P

_{o}= 2454.4 W. As can be seen from Figure 10a, the converter works in the frequency-conversion mode, the switching frequency is 100 kHz, and the primary-side resonant current changes in the form of a sine wave. At this time, the converter works at the rated operating point and is in a quasi-resonant state. It can be seen from Figure 10b that before the arrival of the driving signal V

_{gs4}of the switching tube S

_{4}, the drain voltage V

_{ds4}of S

_{4}has dropped to zero, which shows that the primary-side switching tube can achieve ZVS. Since the resonant current and the excitation current are equal only for a moment, i

_{D6}and i

_{D7}are generated at the moment i

_{D5}and i

_{D8}are reduced to zero. Similarly, i

_{D5}and i

_{D8}are generated at the moment when i

_{D6}and i

_{D7}are reduced to zero, so the secondary rectifier diode can achieve ZCS.

_{o}and the output current I

_{o}are 430 V/7.67 A. At this time, the output power P

_{o}= 3300 W. It can be seen from Figure 11a that the converter works in the frequency-conversion mode, and the switching frequency is 67 kHz. At this time, the converter works in an under-resonant state. It can be seen from Figure 11b that the primary-side switch can achieve ZVS, and the secondary-side rectifier diode can achieve ZCS.

#### 5.2. Reverse Simulation

_{m}/n

^{2}= 60.03 $\mathsf{\mu}\mathrm{H}$.

_{gs5}of the switching tube S

_{5}, the drain voltage V

_{ds5}of the S

_{5}has been reduced to zero, which shows that the switching tube S

_{5}can achieve ZVS. Before the arrival of i

_{D1}and i

_{D4}, i

_{D2}and i

_{D3}have been reduced to zero. Similarly, before the arrival of i

_{D2}and i

_{D3}, i

_{D1}and i

_{D4}have also been reduced to zero, so the rectifier diode on the primary side can achieve ZCS. It can be seen from Figure 14b that the output voltage is stable at 400 V after 8 ms, indicating that the reverse frequency-conversion boost of the bidirectional CLLLC resonant converter can work normally.

_{gs5}of the switching tube S

_{5}, the drain voltage V

_{ds5}of the S

_{5}has been reduced to zero, which shows that the switching tube S

_{5}can achieve ZVS. Before the arrival of i

_{D1}and i

_{D4}, i

_{D2}and i

_{D3}have been reduced to zero. Similarly, before the arrival of i

_{D2}and i

_{D3}, i

_{D1}and i

_{D4}have also been reduced to zero, so the rectifier diode on the primary side can achieve ZCS. From Figure 15b, it can be seen that the output voltage is stable at 400 V after 2.9 ms, indicating that the reverse phase-shift buck of the bidirectional CLLLC resonant converter can work normally.

## 6. Conclusions

- (1)
- Due to its complete symmetrical and good soft-switching characteristics, the bidirectional CLLLC resonant converter solves the problem where the traditional LLC resonant converter has different resonant states during the forward and reverse operations, and cannot achieve soft switching at the same time and is difficult to control.
- (2)
- The hybrid control method of frequency conversion and phase shift adopts frequency-conversion control at a higher voltage gain and phase-shift control at a lower voltage gain. It solves the problem of low voltage gain of the single frequency-conversion control method in the step-down mode, effectively broadens the output voltage range of the bidirectional CLLLC converter, and is suitable for wide-range output occasions. At the same time, it achieves zero-voltage switching and zero-current switching in the full load range, and has a high operating efficiency. This control method is convenient and easy to implement.
- (3)
- The control method proposed in this paper is superior to the traditional control method in reducing the switching frequency-conversion range and improving the efficiency of the converter, which is helpful in the popularization and application of the high-efficiency and high-power bidirectional DC/DC converter in the distributed new energy generation.
- (4)
- In the actual debugging process, it is difficult to establish an accurate model of a bidirectional CLLLC circuit. In the later stage, it is necessary to further analyze the circuit model to design more appropriate closed-loop control parameters and test how well it actually works.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**The simulated waveform of V

_{o}and I

_{o}is 250 V/7.67 A: (

**a**) main working waveform; and (

**b**) ZVS and ZCS.

**Figure 10.**The simulated waveform of V

_{o}and I

_{o}is 320 V/7.67 A: (

**a**) main working waveform; and (

**b**) ZVS and ZCS.

**Figure 11.**The simulated waveform of V

_{o}and I

_{o}is 430 V/7.67 A: (

**a**) main working waveform; and (

**b**) ZVS and ZCS.

**Figure 14.**Simulation results when the reverse input voltage is 250 V: (

**a**) main working waveform; and (

**b**) output voltage.

**Figure 15.**Simulation results when the reverse input voltage is 430 V: (

**a**) main working waveform; and (

**b**) output voltage.

Main Indicator | Parameter |
---|---|

input voltage range | 390–410 V |

rated input voltage | 400 V |

output voltage range | 250–430 V |

rated output voltage | 320 V |

maximal output power | 3.3 kW |

resonant frequency | 100 kHz |

Main Indicator | Parameter |
---|---|

primary-side resonant inductor (L_{r1}) | 18.76 $\mathsf{\mu}\mathrm{H}$ |

primary-side resonant capacitor (C_{r1}) | 135.02 $\mathrm{nF}$ |

secondary-side resonant inductance (L_{r2}) | 12.01 $\mathsf{\mu}\mathrm{H}$ |

secondary-side resonant capacitor (C_{r2}) | 210.97 $\mathrm{nF}$ |

magnetizing inductance (L_{m}) | 93.80 $\mathsf{\mu}\mathrm{H}$ |

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## Share and Cite

**MDPI and ACS Style**

Jin, N.-Z.; Feng, Y.; Chen, Z.-Y.; Wu, X.-G. Bidirectional CLLLC Resonant Converter Based on Frequency-Conversion and Phase-Shift Hybrid Control. *Electronics* **2023**, *12*, 1605.
https://doi.org/10.3390/electronics12071605

**AMA Style**

Jin N-Z, Feng Y, Chen Z-Y, Wu X-G. Bidirectional CLLLC Resonant Converter Based on Frequency-Conversion and Phase-Shift Hybrid Control. *Electronics*. 2023; 12(7):1605.
https://doi.org/10.3390/electronics12071605

**Chicago/Turabian Style**

Jin, Ning-Zhi, Yu Feng, Ze-Yu Chen, and Xiao-Gang Wu. 2023. "Bidirectional CLLLC Resonant Converter Based on Frequency-Conversion and Phase-Shift Hybrid Control" *Electronics* 12, no. 7: 1605.
https://doi.org/10.3390/electronics12071605