# Dual-Side Phase-Shift Control for Strongly Coupled Series–Series Compensated Electric Vehicle Wireless Charging Systems

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Synchronous rectification is normally conducted to the secondary-side rectifier of the loosely coupled WPT systems to improve efficiency [9,10]. However, it is found in strongly coupled WPT systems that this will result in the primary-side inverter working in hard switching, leading to decreasing efficiency and potential circuit failures. Additionally, in loosely coupled WPT systems, dual-side phase-shift control is seldomly used to regulate the secondary-side charging current due to the fact that too much reactive power will be introduced if the phase difference between the primary-side and secondary-side voltages is not 90°. However, in strongly coupled WPT systems, since the coupling coefficient is large, the efficiency can still be high even though the phase difference is not 90°. Thus, the secondary-side charging current and even bidirectional power flow can be easily regulated. The contributions of this paper include building the mathematical model of dual-side phase-shift control for strongly coupled WPT systems;
- (2)
- Investigating the performance of dual-side phase-shift control for strongly coupled WPT systems;
- (3)
- Revealing that synchronous rectification is not suitable for strongly coupled WPT system because soft switching can be lost;
- (4)
- Experimentally validating the model and analysis.

## 2. Mathematical Modelling

_{1}–S

_{8}are the active switches. V

_{INV}(V

_{REC}), u

_{1}(u

_{2}), i

_{1}(i

_{2}), L

_{1}(L

_{2}), C

_{1}(C

_{2}), u

_{C1}(u

_{C2}) are the respective primary-side (secondary-side) dc voltage, ac voltage, ac current, self-inductance, capacitance, and capacitor voltage. M is the mutual inductance.

_{V}is defined as

#### 2.1. First Harmonic Approximation

_{1}(U

_{2}) and I

_{1}(I

_{2}) are the fundamental components of the inverter (rectifier) ac voltage and current, respectively. R

_{1}and R

_{2}are the equivalent resistance of the transmitter and receiver, respectively. With 180° phase shift within the legs of the inverter and the rectifier, we have

_{1}and R

_{2}when their voltage drops are significantly smaller than U

_{1}and U

_{2}, we have

_{2}leads U

_{1}, the phasor diagram is plotted in Figure 3 [11]. The rectifier dc current and the output power can be calculated as

_{REC}and P

_{out}change sinusoidally with the dual-side phase-shift angle β.

#### 2.2. Time-Domain Modelling

_{1}is rising, and at t

_{0}, u

_{2}is falling. In the first half cycle, S

_{1}and S

_{4}are on and S

_{2}and S

_{3}are off. In the second half cycle, S

_{1}and S

_{4}are off and S

_{2}and S

_{3}are on. Due to symmetry, only the first half cycle is considered.

_{0}, S

_{1}, S

_{4}, S

_{5}, and S

_{8}are all on, namely u

_{1}and u

_{2}are both positive, the differential equations can be given as

_{0}.

_{0}< t < T/2, S

_{2}, S

_{3}, S

_{5}, and S

_{8}are all on, namely u

_{1}is positive and u

_{2}is negative, the differential equations can be given as

_{0}< t < T/2.

_{0}indicates the phase-shift instant when the secondary-side rectifier is switching. The relationship between t

_{0}and β is

_{2-1}(t

_{0}) = i

_{2-2}(t

_{0}) = 0, which is the natural zero crossing point of the receiver current. By solving this, the phase-shift angle between u

_{2}and the u

_{1}is larger than 90°. In this condition, i

_{1-1}(0) is larger than 0, indicating that soft switching is lost.

#### 2.3. Comparison of FHA and Model Based on Differential Equations

_{2}and u

_{1}, namely β, is plotted in Figure 5. At strong couplings, the rectifier dc currents are larger than the predictions from FHA between the phase-shift angles of 60° and 120°, and smaller at other phase-shift angles. This shows the inaccuracy of FHA at strong couplings.

_{1}and I

_{1}, U

_{2}and I

_{2}) are defined in an associate reference direction. This means that when the active power of the voltage source is positive, the voltage source acts as an actual source and the active power is transferred from the voltage source to the outside circuit; when the active power of the voltage source is negative, the voltage source acts as a sink and the active power is transferred from the outside circuit to the voltage source. Thus, in Figure 3, when U

_{2}leads U

_{1}or β ∈ (0, 180°), active power is transferred from the primary side to the secondary side; when U

_{2}lags behind U

_{1}or β ∈ (−180°, 0), active power is transferred from the secondary side to the primary side. This is also true for strongly coupled cases.

_{1}lags behind U

_{1}, which means the input impedance is inductive. Thus, zero voltage switching (ZVS) can be achieved for both the primary-side inverter and secondary-side rectifier. When 90° < β < 180°, I

_{1}leads U

_{1}, and zero current switching (ZCS) can be achieved for both the primary-side inverter and secondary-side rectifier. When MOSFETs are used, ZVS is preferred, indicating that the dual-side phase-shift angle should be in the range of [0, 90°]. The variations of the rectifier currents or output power with the dual-side phase-shift angle β are plotted in Figure 6.

## 3. Experimental Validation

_{INV}is set to 200 V. Three voltage gains are selected: 0.5, 1.0, and 2.0, with corresponding V

_{REC}of 100 V, 200 V, and 400 V.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 8.**(

**a**) Measured dc-dc efficiency, (

**b**) rectifier current, and (

**c**) output power under three voltage gains.

**Figure 9.**Experimental waveforms with 2.0 voltage gain: (

**a**) synchronous rectification; (

**b**) 90° phase shift.

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

Airgap | 40 mm |

f_{0} | 83.3 kHz |

L_{1} | 169.7 μH |

L_{2} | 169.8 μH |

C_{1} | 21.5 nF |

C_{2} | 21.5 nF |

k | 0.64 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Shen, Z.; Wu, Y.; Wang, H.; Pan, W.
Dual-Side Phase-Shift Control for Strongly Coupled Series–Series Compensated Electric Vehicle Wireless Charging Systems. *World Electr. Veh. J.* **2022**, *13*, 6.
https://doi.org/10.3390/wevj13010006

**AMA Style**

Zhang Y, Shen Z, Wu Y, Wang H, Pan W.
Dual-Side Phase-Shift Control for Strongly Coupled Series–Series Compensated Electric Vehicle Wireless Charging Systems. *World Electric Vehicle Journal*. 2022; 13(1):6.
https://doi.org/10.3390/wevj13010006

**Chicago/Turabian Style**

Zhang, Yiming, Zhiwei Shen, Yuanchao Wu, Hui Wang, and Wenbin Pan.
2022. "Dual-Side Phase-Shift Control for Strongly Coupled Series–Series Compensated Electric Vehicle Wireless Charging Systems" *World Electric Vehicle Journal* 13, no. 1: 6.
https://doi.org/10.3390/wevj13010006