# Constant-Current and Constant-Voltage Output for Single-Switch WPT System with Composite Shielding Structure

^{*}

## Abstract

**:**

## 1. Introduction

_{CC}is the charging current in CC mode, the V

_{CV}is the charging voltage in CV mode, and the I

_{min}is the cut-off charging current. Moreover, I

_{B}is the variation trend of the battery current, and V

_{B}is the variation trend of the battery voltage.

## 2. Analysis Compensation Network

_{p}is the resonant capacitance at the primary-side. The primary side can be regarded as the P compensation network, where U

_{dc}is the input DC voltage, Q is MOSFET, and L

_{p}and L

_{s}are the self-inductances of the transmitting coil and receiving coil, respectively. In addition, M is the mutual inductance between the two coils, D

_{1}– D

_{4}are four diodes to form the rectifier bridge, C

_{o}is the output filter capacitor, and R

_{L}is the DC output load. The secondary-side compensation network can be designed according to the requirements of the output.

_{p}. By applying Thévenin’s and Norton’s theorems, Figure 3a can be simplified as Figure 3b, and L

_{T}= L

_{s}− M

^{2}/L

_{p}is defined.

_{1}is connected to C

_{s1}, the circuit can be regarded as the P-LC compensation with constant-current output characteristics. However, the design freedom of the loosely coupled transformer (LCT) is not high. When S

_{2}is connected to C

_{s2}, the circuit can be regarded as the P-S compensation with constant-voltage output characteristics. In order to improve the design freedom of the loosely coupled transformer, as shown in Figure 4b, the hybrid P-LCC and P-S compensation network is proposed. C

_{s1}and C

_{s2}can be used to adjust the output current in constant-current mode. The secondary side compensation network is changed by two switches S

_{1}and S

_{2}. When both switches are turned on, the circuit is in constant-current mode, and the circuit can be regarded as the P-LCC compensation network. When both switches are turned off, and the circuit is in constant-voltage mode, the circuit can be regarded as the P-S compensation network.

_{1}and S

_{2}are turned on, C

_{s1}and C

_{s2}are connected in parallel, and the equivalent capacitance is defined as C

_{T}. As shown in Figure 5b, L

_{T1}and capacitor C

_{T}are inductive after they are connected in series, and the equivalent inductance is defined as L

_{T1}. In order to achieve the constant-current output, the equivalent inductance L

_{T1}and C

_{s3}resonate at frequency f. In this case, Figure 5b can be simplified as Figure 5c.

_{1}and S

_{2}are turned off, similarly, when the equivalent inductance L

_{T}, L

_{1}, and C

_{s1}resonate at frequency f. In this case, Figure 6a can be simplified as Figure 6b.

_{1}, and the value of C

_{T}can be adjusted to change the output current. In order to make the input impedance Z

_{T}resistive in Figure 5b, the relationship between L

_{1}and C

_{s3}can be expressed as:

_{L}and the peak AC current i

_{o}before rectification is as follows:

_{1}is the fundamental peak value of the equivalent input voltage source. The relationship between the output DC load voltage V

_{L}and the peak AC voltage v

_{o}before rectification is as follows:

_{L}and R

_{eq}is as follows:

## 3. Calculation of Equivalent Input AC Voltage Source

_{p}. However, the voltage waveform of C

_{p}is not a complete square wave. Here, the voltage waveform of C

_{p}is composed of a rectangular wave and half sine wave. It is necessary to calculate the equivalent AC voltage input to the compensation network. The relevant voltage and current waveforms are shown in Figure 7. Here, u

_{gs}is the driving signal of Q, i

_{L}

_{p}is the current of the transmitter, and u

_{Cp}is the voltage of the capacitor C

_{p}. In addition, u

_{ds}is the voltage stress on the switch Q. The voltage waveform of C

_{p}in one operating period can be divided into three stages. During 0 to t

_{2}, it is the conduction time of Q, and u

_{C}

_{p}is equal to the input DC voltage U

_{dc}. During t

_{2}to t

_{6}, it is the blocking period of Q, and u

_{C}

_{p}is determined by the compensation network. As shown in Figure 8a, the waveform of u

_{C}

_{p}can be regarded as the sine wave. During t

_{6}to t

_{7}, there is a current flowing through the anti-parallel diode of Q, which provides conditions for Q to realize ZVS. Moreover, u

_{C}

_{p}is equal to the input DC voltage U

_{dc}, and the margin of ZVS is defined as D

_{1}.

_{p}and the primary coil L

_{p}are in parallel, u

_{C}

_{p}= u

_{L}

_{p}, u

_{L}

_{p}is the voltage of the primary coil L

_{p}, and the average voltage of inductor is zero in one operating period. As shown in Figure 8, it is the waveform of u

_{L}

_{p}, where E is the maximum resonant voltage of C

_{p}, and the expression of u

_{L}

_{p}in one operating period can be written as follows:

_{1}is the angular frequency of the sinusoidal half wave, and ω

_{1}can be expressed as follows:

_{3}− t

_{2}= t

_{6}− t

_{5}, Δt can be expressed as follows:

_{3}, t

_{5}, and t

_{6}can be expressed as follows:

_{1}represents the yellow area, and S

_{2}represents the blue area, using the principle of volt-second balance, S

_{1}= S

_{2}, S

_{1}and S

_{2}can be expressed as follows:

_{ZVS}= 5%, the duty cycle D is fixed at 0.5. This paper sets the input DC voltage as U

_{dc}= 96 V, f = 85 kHz. Through the Mathcad software, the intersection of S

_{1}and S

_{2}can be obtained using Formula (12). As shown in Figure 9, the intersection of S

_{1}and S

_{2}is 240 V, in other words, E = 240 V. The above analysis provides a theoretical basis for the value of C

_{p}. According to the value of E, the coefficients of Δt, t

_{3}, and t

_{5}can also be obtained.

_{p}and the input DC voltage U

_{dc}, U

_{Q}

_{max}is the peak voltage of Q, which can be expressed as:

_{L}

_{p}(t) can be decomposed by Fourier decomposition to obtain the fundamental amplitude. The expansion of Fourier series of u

_{L}

_{p}(t) can be expressed as follows:

_{0}, a

_{1}, and b

_{1}can be expressed as:

_{L}

_{p}(t) can also be expressed as:

_{0}= a

_{0}, ${E}_{1}=\sqrt{{a}_{1}{}^{2}+{b}_{1}{}^{2}}$, $\phi =\mathrm{arctan}(-{b}_{1}/{a}_{1})$. E

_{1}represents the fundamental amplitude, and E

_{0}represents the DC component.

_{p}are mainly used to adjust the ZVS margin. From Figure 7, when the driving signal of Q turns off at t

_{2}, the C

_{p}, L

_{e}, and R

_{e}will have a zero input response, and the range values of C

_{p}can be determined from the perspective of energy attenuation. The simplified circuit model is shown in Figure 10. Here, the reflected impedances from the secondary to the primary can be expressed as Z

_{T}, Z

_{T}= jωL

_{e}+ R

_{e}.

_{L}

_{p}(t

_{1}) = 0, and the charging time of L

_{p}is equal to D

_{1}T. It should be noted that D

_{1}≤ D. i

_{L}

_{p}(t) can be expressed as:

_{2}, the total energy stored by L

_{p}and C

_{p}can be expressed as:

_{4}, i

_{L}

_{p}= 0, the voltage value of C

_{p}rises to the maximum. The rate of energy attenuation is ${e}^{\frac{-{R}_{\mathrm{e}}}{{L}_{\mathrm{e}}}}$, the time of energy attenuation is $(\frac{1-D-{D}_{\mathrm{ZVS}}}{2})T$.

## 4. Simulation Verification

_{ds}and u

_{C}

_{p}versus C

_{p}values in Saber simulation are shown in Figure 11. It can be seen that with the increasing value of C

_{p}, the maximum value of u

_{ds}decreases gradually, and the ZVS margin D

_{ZVS}decreases until it disappears.

_{p}. When the input DC voltage is 96 V and the switching frequency f is 85 kHz, in order to obtain a 5% ZVS margin, the peak voltage of C

_{p}should be about 240 V. As shown in Figure 11b, when other circuit parameters are determined, the value of C

_{p}is changed continuously in Saber simulation until the value of u

_{C}

_{p}is about 240 V, and C

_{p}= 64.5 nF. When C

_{p}= 64.5 nF, the ZVS margin measured in the simulation is about 5.5%, which is close to the design target of 5%, indicating that the calculation method is reliable in Section 3.

_{P}is set as 64.5 nF in Saber simulation. The fundamental amplitude after Fourier decomposition is 158.3 V by (17). The values of the calculation and the simulation results can match well, and thus, validate the correctness of the theoretical analysis in Section 3.

_{i}(f) at 85 kHz is 0.042, and the voltage gain value G

_{v}(f) at 85 kHz is 0.50. This indicates that when the input DC voltage is 96 V and the driving frequency is 85 kHz, the output current is about 4A, and the output voltage is approximately 48 V.

_{1}has no effect on the output current in constant-current mode, and the values of C

_{T}and C

_{s3}can be used to adjust the output current. Therefore, the design freedom of the loosely coupled transformer is improved.

_{1}are not sensitive to the output voltage in constant-voltage mode.

## 5. Experimental Verification

_{1}and S

_{2}are used to switch the compensation networks to achieve the constant-current output or constant-voltage output.

_{ref}is the critical reference voltage at the conversion point between the CC and CV modes and I

_{min}is the lower limit of the output current. When the sampling voltage u

_{o}is lower than the reference value u

_{ref}, the switching signals are generated to drive the MOSFET (Q), and the system is then in the CC mode.

_{o}is higher than or equal to the reference value u

_{ref}, the CV mode is selected. With the load R

_{L}increasing in CV mode, the output current decreases gradually. Considering the possible problems (high current or high voltage spikes) caused by the transition point, a switching method is proposed here to avoid the problems. A short period of time before and after the mode convention point, the PWM signal of Q is closed. Although it causes a short charging pause, for a few hours of the real charging process, this effect can be ignored.

_{L}is set as 6 Ω, and the ZVS margin is 4.76% when R

_{L}is set as 24 Ω. The design of ZVS margin ensures the ZVS of switch Q.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Mekikis, P.-V.; Antonopoulos, A.; Kartsakli, E.; Lalos, A.S.; Alonso, L.; Verikoukis, C. Information Exchange in Randomly Deployed Dense WSNs With Wireless Energy Harvesting Capabilities. IEEE Trans. Wirel. Commun.
**2016**, 15, 3008–3018. [Google Scholar] [CrossRef] [Green Version] - Ayestarán, R.G.; León, G.; Pino, M.R.; Nepa, P. Wireless power transfer through simultaneous near-field focusing and far-field synthesis. IEEE Trans. Antennas Propag.
**2019**, 67, 5623–5633. [Google Scholar] [CrossRef] - Dai, X.; Wu, J.; Jiang, J.; Gao, R.; Madawala, U.K. An Energy Injection Method to Improve Power Transfer Capability of Bidirectional WPT System with Multiple Pickups. IEEE Trans. Power Electron.
**2021**, 36, 5095–5107. [Google Scholar] [CrossRef] - Sun, Y.; Zhang, H.; Hu, A.P.; Tang, C.; Xiang, L. The Recognition and Control of Nonideal Soft-Switching Frequency for Wireless Power Transfer System Based on Waveform Identification. IEEE Trans. Power Electron.
**2017**, 32, 6617–6627. [Google Scholar] [CrossRef] - Barsari, V.Z.; Thrimawithana, D.J.; Covic, G.A. An Inductive Coupler Array for In-Motion Wireless Charging of Electric Vehicles. IEEE Trans. Power Electron.
**2021**, 36, 9854–9863. [Google Scholar] [CrossRef] - Song, B.; Cui, S.; Li, Y.; Zhu, C. A Fast and General Method to Calculate Mutual Inductance for EV Dynamic Wireless Charging System. IEEE Trans. Power Electron.
**2021**, 36, 2696–2709. [Google Scholar] [CrossRef] - Thai, V.X.; Jang, G.C.; Jeong, S.Y.; Park, J.H.; Kim, Y.S.; Rim, C.T. Symmetric Sensing Coil Design for the Blind-Zone Free Metal Object Detection of a Stationary Wireless Electric Vehicles Charger. IEEE Trans. Power Electron.
**2020**, 35, 3466–3477. [Google Scholar] [CrossRef] - Zhou, J.; Zhang, B.; Xiao, W.; Qiu, D.; Chen, Y. Nonlinear Parity Time Symmetric Model for Constant Efficiency Wireless Power Transfer: Application to a Drone-in-Flight Wireless Charging Platform. IEEE Trans. Ind. Electron.
**2019**, 66, 4097–4107. [Google Scholar] [CrossRef] - Arteaga, J.M.; Aldhaher, S.; Kkelis, G.; Kwan, C.; Yates, D.C.; Mitcheson, P.D. Dynamic Capabilities of Multi-MHz Inductive Power Transfer Systems Demonstrated with Batteryless Drones. IEEE Trans. Power Electron.
**2019**, 34, 5093–5104. [Google Scholar] [CrossRef] - Liu, C.; Jiang, C.; Song, J.; Cha, K.T. An Effective Sandwiched Wireless Power Transfer System for Charging Implantable Cardiac Pacemaker. IEEE Trans. Ind. Electron.
**2019**, 66, 4108–4117. [Google Scholar] [CrossRef] - Sedehi, R.; Budgett, D.; Jiang, J.; Ziyi, X.; Dai, X.; Hu, A.P.; McCormick, D. A Wireless Power Method for Deeply Implanted Biomedical Devices via Capacitively Coupled Conductive Power Transfer. IEEE Trans. Power Electron.
**2021**, 36, 1870–1882. [Google Scholar] [CrossRef] - Hassan, N.U.; Hong, S.-W.; Lee, B. A Robust Multioutput Self-Regulated Rectifier for Wirelessly Powered Biomedical Applications. IEEE Trans. Ind. Electron.
**2021**, 68, 5466–5472. [Google Scholar] [CrossRef] - Lee, Y.-D.; Kim, K.-W.; Moon, G.-W. A Self-Compensated Planar Coil with Integrated Single-Switch Regulator for Wireless Power Transfer (WPT) Systems. IEEE Trans. Power Electron.
**2021**, 36, 10954–10958. [Google Scholar] [CrossRef] - Huang, Y.; Lee, A.T.-L.; Tan, S.-C.; Hui, S.Y. Highly Efficient Wireless Power Transfer System with Single-Switch Step-Up Resonant Inverter. IEEE J. Emerg. Sel. Topics Power Electron.
**2021**, 9, 1157–1168. [Google Scholar] [CrossRef] - Huang, X.; Kong, Y.; Ouyang, Z.; Chen, W.; Lin, S. Analysis and Comparison of Push–Pull Class-E Inverters with Magnetic Integration for Megahertz Wireless Power Transfer. IEEE Trans. Power Electron.
**2020**, 35, 565–577. [Google Scholar] [CrossRef] [Green Version] - Tebianian, H.; Salami, Y.; Jeyasurya, B.; Quaicoe, J.E. A 13.56-MHz Full-Bridge Class-D ZVS Inverter with Dynamic Dead-Time Control for Wireless Power Transfer Systems. IEEE Trans. Ind. Electron.
**2020**, 67, 1487–1497. [Google Scholar] [CrossRef] - Li, H.; Wang, K.; Fang, J.; Tang, Y. Pulse Density Modulated ZVS Full-Bridge Converters for Wireless Power Transfer Systems. IEEE Trans. Power Electron.
**2019**, 34, 369–377. [Google Scholar] [CrossRef] - Samanta, S.; Rathore, A.K.; Thrimawithana, D.J. Bidirectional Current-Fed Half-Bridge (C) (LC)–(LC) Configuration for Inductive Wireless Power Transfer System. IEEE Trans. Ind. Appl.
**2017**, 53, 4053–4062. [Google Scholar] [CrossRef] - Trung, N.K.; Ogata, T.; Tanaka, S.; Akatsu, K. Attenuate Influence of Parasitic Elements in 13.56-MHz Inverter for Wireless Power Transfer Systems. IEEE Trans. Power Electron.
**2018**, 33, 3218–3231. [Google Scholar] [CrossRef] - Vu, V.; Tran, D.; Choi, W. Implementation of the Constant Current and Constant Voltage Charge of Inductive Power Transfer Systems with the Double-Sided LCC Compensation Topology for Electric Vehicle Battery Charge Applications. IEEE Trans. Power Electron.
**2018**, 33, 7398–7410. [Google Scholar] [CrossRef] [Green Version] - Chen, Y.; Li, M.; Yang, B.; Chen, S.; Li, Q.; He, Z.; Mai, R. Variable-Parameter T-Circuit-Based IPT System Charging Battery with Constant Current or Constant Voltage Output. IEEE Trans. Power Electron.
**2020**, 35, 1672–1684. [Google Scholar] [CrossRef] - Ahn, D.; Kim, S.; Moon, J.; Cho, I. Wireless Power Transfer with Automatic Feedback Control of Load Resistance Transformation. IEEE Trans. Power Electron.
**2016**, 31, 7876–7886. [Google Scholar] [CrossRef] - Buja, G.; Bertoluzzo, M.; Mude, K.N. Design and Experimentation of WPT Charger for Electric City Car. IEEE Trans. Ind. Electron.
**2015**, 62, 7436–7447. [Google Scholar] [CrossRef] - Qu, X.; Chu, H.; Wong, S.; Tse, C.K. An IPT Battery Charger with Near Unity Power Factor and Load-Independent Constant Output Combating Design Constraints of Input Voltage and Transformer Parameters. IEEE Trans. Power Electron.
**2019**, 34, 7719–7727. [Google Scholar] [CrossRef] - Yue, R.; Wang, C.; Li, H.; Liu, Y. Constant-Voltage and Constant-Current Output Using P-CLCL Compensation Circuit for Single-Switch Inductive Power Transfer. IEEE Trans. Power Electron.
**2021**, 36, 5181–5190. [Google Scholar] [CrossRef] - Wang, D.; Qu, X.; Yao, Y.; Yang, P. Hybrid Inductive-Power-Transfer Battery Chargers for Electric Vehicle Onboard Charging with Configurable Charging Profile. IEEE Trans. Intell. Transp. Syst.
**2021**, 22, 592–599. [Google Scholar] [CrossRef] - Chen, Y.; Zhang, H.; Park, S.; Kim, D. A Switching Hybrid LCC-S Compensation Topology for Constant Current/Voltage EV Wireless Charging. IEEE Access
**2019**, 7, 133924–133935. [Google Scholar] [CrossRef] - Li, Y.; Hu, J.; Liu, M.; Chen, Y.; Chan, K.W.; He, Z.; Mai, R. Reconfigurable Intermediate Resonant Circuit Based WPT System with Load-Independent Constant Output Current and Voltage for Charging Battery. IEEE Trans. Power Electron.
**2019**, 34, 1988–1992. [Google Scholar] [CrossRef]

**Figure 3.**Analysis of equivalent circuit. (

**a**) Equivalent circuit model; (

**b**) simplified circuit model.

**Figure 4.**Hybrid topology of single-switch circuit. (

**a**) The hybrid P-LC or P-S compensation network; (

**b**) the proposed hybrid P-LCC or P-S compensation network.

**Figure 5.**Equivalent model in CC mode. (

**a**) Equivalent compensation network; (

**b**) Simplified compensation network; (

**c**) Equivalent current source model.

**Figure 6.**Equivalent model in CV mode. (

**a**) Equivalent compensation network; (

**b**) Equivalent voltage source model.

**Figure 8.**The waveform of u

_{L}

_{p}. (

**a**) The waveform of u

_{L}

_{p}in normal operation; (

**b**) the waveform of u

_{L}

_{p}in one operating period.

**Figure 11.**The waveforms of u

_{ds}and u

_{C}

_{p}versus C

_{p}values in Saber simulation. (

**a**) The waveforms of u

_{ds}versus C

_{p}values; (

**b**) the waveforms of u

_{C}

_{p}versus C

_{p}values.

**Figure 14.**Normalized output with varying normalized parameters. (

**a**) The curves in CC mode; (

**b**) the curves in CV mode.

**Figure 16.**Cross-sectional magnetic flux density cloud images of different shielding structures. (

**a**) Single-layer shielding structure; (

**b**) double-layer shielding structure; (

**c**) composite shielding structure.

**Figure 20.**ZVS waveforms under the minimum and maximum load conditions. (

**a**) ZVS waveform of Q when R

_{L}= 6 Ω; (

**b**) ZVS waveform of Q when R

_{L}= 24 Ω.

**Figure 21.**Dynamic performance of the proposed WPT system. (

**a**) In CC mode, when the load changes from 6 to 12 Ω; (

**b**) in CV mode, when the load changes from 12 to 24 Ω.

Magnetic Coupler | Parameter | Value |
---|---|---|

single shield magnetic coupler | Thickness of ferrite | 2.5 mm |

double shield magnetic coupler | Thickness of ferrite | 2.5 mm |

Thickness of aluminium plate | 2 mm | |

composite shield magnetic coupler | Thickness of ferrite | 1 mm |

Thickness of aluminium foil | 0.1 mm | |

Thickness of nanocrystalline strips | 26 µm |

Symbol | Definition | Value |
---|---|---|

U_{dc} | Input DC voltage | 96 V |

C_{p} | Resonant capacitance at the primary-side | 64.5 nF |

L_{p} | Inductance of the transmitter coil | 29.6 µH |

L_{s} | Inductance of the receiving coil | 29.6 µH |

M | Mutual inductance between L_{p} and L_{s} | 11.53 µH |

C_{s1} | Resonant capacitance at the secondary-side | 86.6 nF |

C_{s2} | Resonant capacitance at the secondary-side | 363.4 nF |

C_{s3} | Resonant capacitance at the secondary-side | 202.4 nF |

L_{1} | Resonant inductance at the secondary-side | 17.3 µH |

f | Operating frequency | 85 kHz |

D | Duty cycle | 0.5 |

D_{ZVS} | ZVS margin | 0.05 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Q.; Wang, C.; Yang, L.; Guo, Z.
Constant-Current and Constant-Voltage Output for Single-Switch WPT System with Composite Shielding Structure. *World Electr. Veh. J.* **2022**, *13*, 13.
https://doi.org/10.3390/wevj13010013

**AMA Style**

Zhang Q, Wang C, Yang L, Guo Z.
Constant-Current and Constant-Voltage Output for Single-Switch WPT System with Composite Shielding Structure. *World Electric Vehicle Journal*. 2022; 13(1):13.
https://doi.org/10.3390/wevj13010013

**Chicago/Turabian Style**

Zhang, Quanlei, Chunfang Wang, Lingyun Yang, and Zhihao Guo.
2022. "Constant-Current and Constant-Voltage Output for Single-Switch WPT System with Composite Shielding Structure" *World Electric Vehicle Journal* 13, no. 1: 13.
https://doi.org/10.3390/wevj13010013