# An Auxiliary Passive Circuit and Control Design for Wireless Power Transfer Systems in DC Microgrids with Zero Voltage Switching and Accurate Output Regulations

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{r}is the resonant frequency. When f < 1/2f

_{r}, the resonator is in the current discontinuous working mode, and the switch tube works under the condition of ZCS. When 1/2f

_{r}< f < f

_{r}, the resonant tank is capacitive. Therefore, the current leads the voltage when the switch is turned off, and the overlap area becomes smaller. However, the current–voltage overlap area becomes more significant when the switch is turned on as hard switching. When f

_{r}< f, the resonant circuit is inductive, and the switch tube is turned on with ZVS, but the hard switching happens when turning off. Series or parallel resonance technology is used in some communication switching power supplies, and the switching frequency ranges from 180 to 450 kHz.

- a new passive auxiliary circuit method for WPT systems in achieving both ZVS and accurate output regulations with conventional phase shift control;
- an investigation of the soft switching for primary-side inverters in WPT systems with a wide range of load conditions;
- a systematic design procedure and parameter selection method for the passive auxiliary circuit.

## 2. Analysis and Control of Wireless Power Transmission Systems

_{1}to Q

_{4}. D

_{1}to D

_{4}are the intrinsic diodes of Q

_{1}to Q

_{4}and C

_{1}to C

_{4}are the corresponding capacitances. The resonant tank circuit adopts the S-S compensation circuit. L

_{p}and L

_{s}represent the inductances on the primary and secondary side coils, respectively, and M is the mutual inductance. C

_{p}and C

_{s}are the compensated capacitances. Meanwhile i

_{p}and i

_{s}denote the currents of the primary and secondary circuits, respectively. D

_{R}

_{1}to D

_{R}

_{4}represent the four diodes in the full-bridge rectifier. C

_{f}is the filter capacitance and R

_{Ld}is the load resistor in the secondary circuit.

_{1}and Q

_{3}are called leading legs, and Q

_{2}and Q

_{4}are called lagging legs. Figure 3 shows a possible switching signal waveform for MOSFETs. $\delta $ is the phase shift angle. Fully compensated resonance occurs at the same operating frequency on both the primary and secondary side of the circuit.

- All switching devices are ideal;
- All capacitances and inductances are ideal regardless of their internal resistance;
- The intrinsic capacitances of the four MOSFETs are all equal in value.

_{1}, Q

_{1}is turned off. The primary current i

_{p}begins to charge C

_{1}and discharge C

_{3}. When the voltage of C

_{1}increases to V

_{in}and the voltage of C

_{3}decreases to 0, this makes D

_{3}conduct at t

_{1}. Then D

_{3}clamps the voltage of C

_{3}at 0. Therefore, Q

_{3}can achieve ZVS. At t

_{2}, Q

_{4}is turned off. The primary current i

_{p}still does not reach 0, charging C

_{4}and discharging C

_{2}. However, when the system is at light load condition, i

_{p}is already very small. Therefore, although i

_{p}can charge and discharge Q

_{2}and Q

_{4}, it cannot complete the charge and discharge process. As a result, Q

_{2}and Q

_{4}cannot achieve ZVS, as shown in Figure 6. At t

_{3}, Q

_{2}is turned on. i

_{p}flows from B to A in reverse.

## 3. Solutions and Analysis to Improve Hard Switching in WPT Systems

_{p}drops to 0 before charging and discharging of the lagging leg is completed. If i

_{p}is large enough to finish the charging and discharging, Q

_{2}can achieve ZVS. Hence it is considered to place a current source at point B, as shown in Figure 7a. The current source is used to increase the charging current for the lagging leg to complete the charging and discharging process, and it is typically modelled with a large inductance. The circuit topology after replacing the current source with an inductance is shown in Figure 7b and L

_{a}is the auxiliary inductance.

- All switching devices are ideal;
- All capacitances and inductances are ideal regardless of their internal resistance;
- The intrinsic capacitances of the MOSFETs are all equal in value.

- 1.

_{1}and Q

_{4}are on. U

_{AB}= V

_{in}. The primary current i

_{p}goes from point A to point B.

- 2.

_{1}, Q

_{1}is turned off. The primary current i

_{p}begins to charge C

_{1}and discharge C

_{3}, as shown in Figure 9b. The voltage of the two capacitances gradually changes. When the voltage of C

_{1}increases to V

_{in}and the voltage of C

_{3}decreases to 0, this makes D

_{3}conduct, clamping the voltage of C

_{3}at 0, as shown in Figure 9c. Therefore, if Q

_{3}turns on after that time, it can achieve ZVS.

- 3.

_{2}, Q

_{4}is turned off. The primary current i

_{p}charges C

_{4}and discharges C

_{2}. Since the primary side of the circuit is now inductive, the time for the current to drop to 0 can be greatly increased, providing additional time for the charging and discharging process. As a result, C

_{2}can successfully end the discharge process until D

_{2}turns on and clamps the voltage of Q

_{2}to 0, as shown in Figure 10. This provides a prerequisite for Q

_{2}to realize ZVS conduction.

- 4.

_{3}. If Q

_{2}turns on after t

_{3}, it can achieve ZVS. After t

_{3}, Q

_{2}and Q

_{3}have already turned on. U

_{AB}= −V

_{in}. i

_{p}goes down linearly to 0 and then begins to increase reversely.

- 5.

_{p}still increases during this period. At t

_{6}, Q

_{3}is turned off and the circuit operates similarly to Mode 1, which is the beginning of the second switching period. The second half-switching period is similar to the first half period.

## 4. Simulation Results

#### 4.1. Simulation of WPT Systems without Auxiliary Circuits

_{p}and K

_{I}are the parameters of the PI controller. K

_{p}represents the proportional control coefficient, and K

_{I}represents the integral control coefficient.

_{1}is turned on and off are shown in Figure 12. It can be seen that when Q

_{1}is turned on, there is no overlap area between the voltage and current, indicating that Q

_{1}can realize ZVS conduction and Q

_{1}has no conduction loss. The voltage and current waveform of Q

_{3}is exactly the same as that of Q

_{1}, so there is no hard-switching problem in the leading leg in the WPT system. The upper part of Figure 12 is an overview of the waveforms, and the lower part shows the details of the voltage and current waveforms when Q

_{1}conducts.

_{2}during operation. It can be seen that when Q

_{2}is turned on, the current increases, while the voltage decreases, and the two have an overlapping area. The part covered by the dotted line in the black circle in Figure 13 is the conduction loss generated by Q

_{2}. Q

_{4}works the same as Q

_{2}. The lagging leg cannot achieve soft switching when turning on, resulting in conduction loss. These losses reduce the overall efficiency of the circuit.

#### 4.2. Simulation of WPT Systems with Auxiliary Circuits

_{1}at the turning on stage. Q

_{1}can still achieve soft switching. The voltage and current waveforms of Q

_{3}are the same as those of Q

_{1}. The added auxiliary inductance does not affect the working state of the leading leg.

_{2}is turned on. In the black circle, the current and voltage have no overlapping area. The current of Q

_{2}shows the same trend as Q

_{1}. It increases in the negative direction and then rises again. This is because the discharge current does not decrease to 0 before Q

_{2}turns on. The current direction is opposite to Q

_{2}’s voltage direction, which means that Q

_{2}has completed the discharge process before turning on. Therefore, ZVS can be turned on. The conduction process of Q

_{4}is the same as that of Q

_{2}. The lagging leg can achieve ZVS conduction with the help of the auxiliary inductance.

#### 4.3. Simulation of WPT System with Auxiliary Inductance in Special Cases

## 5. Experimental Verification

#### 5.1. Experimental Setup

#### 5.2. Experiment Results

#### 5.2.1. Experiment of MOSFETs to Realize Soft Switching

_{AB}and i

_{AB}are the current and voltage of the input side of the resonator, respectively. u

_{sed}and i

_{sed}are the current and voltage of the output side of the resonator, respectively.

#### 5.2.2. Experiment to Achieve ZVS with the Maximum Power Factor (PF) of the Circuit

_{AB}and i

_{AB}are the voltage and current waveforms of the primary side; u

_{sed}and i

_{sed}are the voltage and current waveforms of the secondary side. If the current is negative when the voltage jumps from 0 to a positive value, the MOSFETs on the primary side are soft switching, and the circuit on the primary side generates redundant reactive power. The relationship between the voltage and current waveforms is shown in Figure 25. When the voltage suddenly changes and the current is 0 simultaneously, the auxiliary circuit makes the MOSFETs achieve soft switching, while the PF of the circuit is the least. The waveform relationship between the voltage and current at this time is shown in Figure 26.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 7.**Proposed soft-switching circuit. (

**a**) is the topology after adding the current source; (

**b**) is the topology after replacing the current source with an inductance.

**Figure 8.**Waveforms of MOSFETs control signals V

_{AB}, and i

_{p}for the proposed soft-switching circuit.

**Figure 11.**The waveform of output voltage and the phase shift angle in WPT system without optimization.

**Figure 17.**The waveform of output voltage. (

**a**) is the overview waveform; (

**b**) is the detail waveform when the resistor changes; (

**c**) is the detail waveform when the input voltage changes.

**Figure 18.**(

**a**,

**b**) are the waveform diagrams of the current and voltage of Q2 when the output voltage is stable, respectively.

**Figure 20.**Waveforms of the current and voltage on the primary and secondary sides of the resonator without using auxiliary inductance.

**Figure 21.**Waveforms of the current and voltage on the primary and secondary sides of the resonator when using auxiliary inductance.

**Figure 22.**The comparison of the inverter efficiency by adding the auxiliary inductor and without using the auxiliary inductor.

**Figure 24.**Waveforms of the current and voltage on the primary and secondary sides when the MOSFETs work in hard-switching state.

**Figure 25.**Waveforms of the current and voltage on the primary and secondary sides when the MOSFETs work in soft-switching state with redundant reactive power.

**Figure 26.**Waveforms of the current and voltage on the primary and secondary sides when the auxiliary circuit can just make the MOSFETs achieve soft switching.

**Figure 27.**The curve of the maximum value of the load resistance, after five groups of auxiliary capacitors are connected in parallel.

**Figure 28.**The curve of the distance of the coupled coil, after five groups of auxiliary capacitors are connected in parallel.

Time | Name | Application |
---|---|---|

1970s | Series resonant converters, SRCs and series parallel converters, PRCs | Half-bridge or full-bridge converters |

Early 1980s | Active clamp technology | Mainly single-ended converters |

Mid 1980s | Quasi-resonant converters, QRCs and multi-resonant converters, MRCs | Single-ended or bridge converter |

Late 1980s | ZVS PWM and ZCS PWM | Single-ended or bridge converter |

Late 1980s | Phase-shifted zero-voltage-switching PWM DC/DC full-bridge converter, PS ZVS FB converter | Full-bridge converter over 250 W |

Name | Value |
---|---|

Conducting resistance R_{ds} (ON) | 0.075 Ω |

Diode threshold voltage | 200 V |

Diode resistance | 0.01 Ω |

MOSFET parallel capacitance C_{oss} | 315 pF |

Name | Value |
---|---|

Input voltage (V_{in}) | 380 V |

Reference output voltage (V_{0}) | 48 V |

Primary side resonant capacitance (C_{p}) | 42 nF |

Secondary side resonant capacitance (C_{s}) | 41.6 nF |

Primary side resonant inductance (L_{p}) | 60.9 μH |

Secondary side resonant inductance (L_{s}) | 60.8 μH |

Mutual inductance (L_{m}) | 12.17 μH |

Primary leakage resistance (R_{p}) | 0.15 Ω |

Secondary leakage resistance (R_{s}) | 0.15 Ω |

Coupling coefficient K | 0.2 |

Load resistor R_{0} (light load condition) | 120 Ω |

Switching frequency | 100 kHz |

Filter capacitance (C_{f}) | 100 pF |

Filter capacitance resistance (R_{f}) | 0.005 Ω |

Name | Value |
---|---|

K_{p} | 0.5 |

K_{I} | 50 |

Reference voltage (V_{ref}) | 48 V |

Name | Value |
---|---|

Input voltage (V_{in}) | 6 V |

Reference output voltage (V_{0}) | 500 mV |

Primary side resonant capacitance (C_{p}) | 42 nF |

Secondary side resonant capacitance (C_{s}) | 41.6 nF |

Primary side resonant inductance (L_{p}) | 60.9 μH |

Secondary side resonant inductance (L_{s}) | 60.8 μH |

Mutual inductance (L_{m}) | 12.17 μH |

Primary leakage resistance (R_{p}) | 0.15 Ω |

Secondary leakage resistance (R_{s}) | 0.15 Ω |

Coupling coefficient K | 0.2 |

Load resistance (R_{0}) | 5 Ω/10 Ω/15 Ω |

Switch frequency | 100 kHz |

Filter capacitance (C_{f}) | 100 pF |

Filter capacitance resistance (R_{f}) | 0.005 Ω |

Auxiliary inductance (L_{a}) | 20 μH |

Name | Value |
---|---|

Input voltage (V_{in}) | 6 V |

Reference output voltage (V_{0}) | 500 mV |

Primary side resonant capacitance (C_{p}) | 42 nF |

Secondary side resonant capacitance (C_{s}) | 41.6 nF |

Primary side resonant inductance (L_{p}) | 60.9 μH |

Secondary side resonant inductance (L_{s}) | 60.8 μH |

Switch frequency | 100 kHz |

Filter capacitance (C_{f}) | 100 μF |

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**MDPI and ACS Style**

Xiong, H.; Xiang, B.; Mao, Y.
An Auxiliary Passive Circuit and Control Design for Wireless Power Transfer Systems in DC Microgrids with Zero Voltage Switching and Accurate Output Regulations. *Energies* **2023**, *16*, 694.
https://doi.org/10.3390/en16020694

**AMA Style**

Xiong H, Xiang B, Mao Y.
An Auxiliary Passive Circuit and Control Design for Wireless Power Transfer Systems in DC Microgrids with Zero Voltage Switching and Accurate Output Regulations. *Energies*. 2023; 16(2):694.
https://doi.org/10.3390/en16020694

**Chicago/Turabian Style**

Xiong, Hu, Bin Xiang, and Yuan Mao.
2023. "An Auxiliary Passive Circuit and Control Design for Wireless Power Transfer Systems in DC Microgrids with Zero Voltage Switching and Accurate Output Regulations" *Energies* 16, no. 2: 694.
https://doi.org/10.3390/en16020694