# Research and Design of LC Series Resonant Wireless Power Transfer System with Modulation Control Method for Supercapacitor Charging in Linear Motion Systems

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## Abstract

**:**

## 1. Introduction

## 2. Configuration of the Proposed WPT Charging System

_{p}and L

_{s}, respectively. The resonant capacitors of the primary and secondary coils are expressed by C

_{p}and C

_{s}, respectively.

_{p}, while on the secondary side, the four-switch buck-boost input voltage and inductance current controls are used to control the transfer power.

#### 2.1. Coupling Tank Analysis

_{p}and C

_{p}indicate the primary resonant inductance and capacitor, respectively. L

_{s}and C

_{s}indicate the secondary resonant inductance and capacitor, respectively. U

_{p}is the voltage on the resonant tank, U

_{s}is the output voltage on load R

_{L}, and I

_{p}and I

_{s}represent the input current and output current, respectively. M is the magnetic inductance between the primary coil and the secondary coil.

_{r}is the angular speed of the current.

_{p}and I

_{s}is determined by the switching frequency, which should satisfy Equation (2), then I

_{p}and I

_{s}will have the relationship shown in Equation (3).

_{max}) can be approximated as Equation (4).

_{L}.

#### 2.2. Coil Current Constant Characteristics

_{in}is shown in Figure 4. L

_{p}and C

_{p}indicate the primary resonant inductance and capacitor, respectively. L

_{s}and C

_{s}indicate the secondary resonant inductance and capacitor, respectively. u

_{p}(t) is the voltage on the resonant tank, u

_{s}(t) is the input voltage of the rectifier, and i

_{p}(t), i

_{s}(t) represent the input current and output current, respectively. M is the magnetic inductance between the primary coil and the secondary coil. R

_{L}represents the equivalent load.

_{p}and L

_{s}is k, the DC input voltage is E, the system frequency equals the resonant frequency ω

_{0}, the resonant frequency can be obtained as the equation: ${\omega}_{0}=2\pi \sqrt{{L}_{p}{L}_{s}}$. The magnetic inductance between the primary coil and secondary coil can be expressed as Equation (5). K is the coupling factor in the equation.

_{p}(t) and u

_{s}(t) can be obtained as Equations (6) and (7), respectively.

_{p}and R

_{s}can be ignored; thus, based on the resonant theory, Equation (10) can be obtained.

_{in}; once V

_{in}is controlled, the current will be determined; (2) the secondary coil current is only determined by the input voltage of the inverter (power supply voltage), independent of the load.

## 3. Control System Design

#### 3.1. Primary Coil RMS Current Control

_{i}

_{1}(s) is the conventional PI controller, which generates the phase shift angle for the PWM generator to drive the power stage full-bridge inverter, and H(s) is the feedback current transfer function, which is combined by the RMS current sensor with a low pass filter.

#### 3.2. Secondary Side Power Regulation Control

_{vin}(s) is the voltage loop controller, while C

_{i}(s) is the inner current loop controller. Both controllers are conventional PI controllers, formed as Equation (16).

_{vo}(s) is the overcharge protection controller, which will work only when the voltage of the supercapacitor is higher than reference V

_{oref}, then the duty of PWM will be limited by d

_{2}, otherwise, the PWM duty is controlled by d

_{1}. G

_{vod}(s) is the transfer function between the output voltage of the four-switch buck-boost converter and PWM duty, while G

_{vind}(s) indicates the relationship between the output voltage and input voltage of the converter, and G

_{id}(s) represents the transfer function between the inductance current and PWM duty. Through the small-signal modeling method, the transfer functions can be obtained as Equations (16)–(18), respectively.

## 4. System Simulation Results

#### 4.1. Open-Loop System Simulation Results

#### 4.2. Closed-Loop Simulation Results

_{p}= 0.7 and K

_{I}= 400. As shown in the results, the system was working under resonant conditions, and the RMS coil current was successfully controlled.

## 5. Supercapacitor Wireless Charging Experiment

#### 5.1. Start-Up Estimation Experiments

#### 5.2. Primary Coil RMS Current Control Results

#### 5.3. Secondary Side Constant Input Voltage Control Results

#### 5.4. System Stability to Changes in the Supercapacitor Voltage Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Wang, S. Research on a New Lithium Battery Applied in Onboard Energy Storage Device of Light Rail Vehicle. In Proceedings of the 2018 2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Xi’an, China, 25–27 May 2018. [Google Scholar]
- Castaings, A.; Caron, H.; Kharrat, H.; Ovalle, A.; Vulturescu, B. Energy Storage System based on Supercapacitors for a 750 V DC railway power supply. In Proceedings of the 2018 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Nottingham, UK, 7–9 November 2018; pp. 1–5. [Google Scholar]
- Ayad, M.Y.; Becherif, M.; Henni, A.; Aboubou, A.; Wack, M. Sliding mode control and Unit Power Factor applied to embarked supercapacitors for electrical train traction. In Proceedings of the 2010 IEEE International Symposium on Industrial Electronics, Bari, Italy, 4–7 July 2010; pp. 2163–5145. [Google Scholar]
- Cheng, L.; Acuna, P.; Wei, S.; Fletcher, J.; Wang, W.; Jiang, J. Fast-Swap Charging: An Improved Operation Mode For Catenary-Free Light Rail Networks. IEEE Trans. Veh. Technol.
**2018**, 67, 2912–2920. [Google Scholar] [CrossRef] - Covic, G.A.; Boys, J.T. Modern trends in inductive power transfer for transportation applications. IEEE J. Emerg. Sel. Top. Power Electron.
**2013**, 1, 28–41. [Google Scholar] [CrossRef] - Huh, J.; Lee, S.W.; Lee, W.Y.; Cho, G.H. Narrow-width inductive power transfer system for online electrical vehicles. IEEE Trans. Power Electron.
**2011**, 26, 3666–3679. [Google Scholar] [CrossRef] - Shin, J.; Shin, S.; Kim, Y.; Ahn, S.; Lee, S.; Jung, G.; Jeon, S.; Cho, D. Design and implementation of shaped magnetic-resonance-based wireless power transfer system for roadway-powered moving electric vehicles. IEEE Trans. Power Electron.
**2014**, 61, 1179–1192. [Google Scholar] [CrossRef] - Wang, Y.; Zhang, L.; Hou, H.; Xu, W.; Duan, G.; He, S.; Liu, K.; Jiang, S. Recent progress in carbon-based materials for supercapacitor electrodes: A review. J. Mater. Sci.
**2021**, 56, 173–200. [Google Scholar] [CrossRef] - Yin, J.; Zhang, W.; Alhebshi, N.A.; Salah, N.; Alshareef, H.N. Synthesis strategies of porous carbon for supercapacitor applications. Small Methods
**2020**, 4, 1900853. [Google Scholar] [CrossRef] - Cheng, F.; Yang, X.; Zhang, S.; Lu, W. Boosting the supercapacitor performances of activated carbon with carbon nanomaterials. J. Power Sources
**2020**, 450, 227678. [Google Scholar] [CrossRef] - Saikia, B.K.; Benoy, S.M.; Bora, M.; Tamuly, J.; Pandey, M.; Bhattacharya, D. A brief review on supercapacitor energy storage devices and utilization of natural carbon resources as their electrode materials. Fuel
**2020**, 282, 118–196. [Google Scholar] [CrossRef] - Kandasamy, M.; Sahoo, S.; Nayak, S.K.; Chakraborty, B.; Rout, C.S. Recent advances in engineered metal oxide nanostructures for supercapacitor applications: Experimental and theoretical aspects. J. Mater. Chem. A
**2021**, 9, 17643–17700. [Google Scholar] [CrossRef] - Yassine, M.; Fabris, D. Performance of Commercially Available Supercapacitors. Energies
**2017**, 10, 1340. [Google Scholar] [CrossRef] [Green Version] - Münchgesang, W.; Meisner, P.; Yushin, G. Supercapacitors specialities-Technology review. AIP Conf. Proc.
**2014**, 1597, 196–203. [Google Scholar] - Zhu, F.; Yang, Z.; Zhao, Z.; Lin, F. Two-Stage Synthetic Optimization of Supercapacitor-Based Energy Storage Systems, Traction Power Parameters and Train Operation in Urban Rail Transit. IEEE Trans. Veh. Technol.
**2021**, 70, 8590–8605. [Google Scholar] [CrossRef] - Fedele, E.; Pasquale, A.D.; Iannuzzi, D.; Pagano, M. Integration of Onboard Batteries and Supercapacitors Based on the Multi-Source Inverter for Light Rail Vehicle. In Proceedings of the 2022 International Power Electronics Conference (IPEC-Himeji 2022—ECCE Asia), Himeji, Japan, 15–19 May 2022; pp. 698–704. [Google Scholar]
- Yıldırım, D.; Akşit, M.H.; Yolaçan, C.; Pul, T.; Ermiş, C.; Aghdam, B.H.; Çadırcı, I.; Ermiş, M. Full-Scale Physical Simulator of All SiC Traction Motor Drive With Onboard Supercapacitor ESS for Light-Rail Public Transportation. IEEE Trans. Ind. Electron.
**2020**, 67, 6290–6630. [Google Scholar] [CrossRef] - Li, J.; Xin, D.; Wang, H.; Liu, C. Application of Energy Storage System in Rail Transit: A Review. In Proceedings of the 2022 International Conference on Power Energy Systems and Applications (ICoPESA), Virtual Conference, 25–27 February 2022; pp. 539–552. [Google Scholar]
- Chu, A.; Braatz, P. Comparison of commercial supercapacitors and high-power lithium-ion batteries for power-assist applications in hybrid electric vehicles: I. Initial characterization. J. Power Sources
**2002**, 112, 236–246. [Google Scholar] [CrossRef] - Yasha, P.; Vahidi, A.; Fayazi, S.A. Heuristic versus optimal charging of supercapacitors, lithium-ion, and lead-acid batteries: An efficiency point of view. IEEE Trans. Control Syst. Technol.
**2018**, 26, 167–180. [Google Scholar] - Yang, H. Analysis of supercapacitor charge redistribution through constant power experiments. In Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA, 16–20 July 2017; pp. 1–5. [Google Scholar]
- Şahİn, M.E.; Blaabjerg, F.; Sangwongwanİch, A. Modelling of supercapacitors based on simplified equivalent circuit. CPSS TPEA
**2021**, 6, 31–39. [Google Scholar] [CrossRef] - Guo, W.; Yu, C.; Li, S.; Qiu, J. Toward commercial-level mass-loading electrodes for supercapacitors: Opportunities, challenges and perspectives. Energy Environ. Sci.
**2021**, 14, 576–601. [Google Scholar] [CrossRef] - Zhang, S.; Pan, N. Supercapacitors Performance Evaluation. Adv. Energy Mater.
**2015**, 5, 1401401. [Google Scholar] [CrossRef] - Zhu, Q.; Zhao, D.; Cheng, M.; Zhou, J.; Owusu, K.A.; Mai, L.; Yu, Y. A new view of supercapacitors: Integrated supercapacitors. Adv. Energy Mater.
**2019**, 9, 1901081. [Google Scholar] [CrossRef] - Geng, Y.; Yang, Z.; Lin, F. Design and Control for Catenary Charged Light Rail Vehicle Based on Wireless Power Transfer and Hybrid Energy Storage System. IEEE Trans. Power Electron.
**2020**, 35, 7894–7903. [Google Scholar] [CrossRef] - Li, Y.; Mai, R.; Lin, T.; Liu, Y.; Li, Y.; He, Z.; Yu, J. Design and implementation of a novel WPT system for railway applications. In Proceedings of the 2017 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Chongqing, China, 20–22 May 2017; pp. 213–221. [Google Scholar]
- Song, K.; Zhu, C.; Koh, K.E.; Imura, T.; Hori, Y. Wireless power transfer for running EV powering using multi-parallel segmented rails. In Proceedings of the 2015 IEEE PELS Workshop on Emerging Technologies: Wireless Power (2015 WoW), Daejeon, Korea, 5–6 June 2015; pp. 1–6. [Google Scholar]
- Pang, J.; Li, Z.; Xu, C. Design of Automatic Switch of Charging Rail for Electric Vehicle Dynamic Charging System Based on Wireless Power Transmission. In Proceedings of the 2021 IEEE International Conference on Advances in Electrical Engineering and Computer Applications (AEECA), Dalian, China, 27–28 August 2021; pp. 731–737. [Google Scholar]

Parameters | Value |
---|---|

Input supply voltage V_{in} | 72 V |

Inverter switching frequency f_{s} | 85 kHz |

Load matching converter switching frequency f_{dc} | 40 kHz |

Inductance L | 220 μH |

Primary resonant inductance L_{p} | 500 μH |

Primary capacitor C_{p} | 32 nF |

Secondary inductance L_{s} | 100 μH |

Secondary capacitor C_{s} | 4 μF |

Resonant frequency f_{r} | 85 kHz |

Components | Pattern/Parameter |
---|---|

Digital controller | dsPIC33FJ64GS606 |

Driving power supplier | KA7805, FSL336 |

Current sensor | 56200C, CHCS-GB5-50A |

Primary inductance L_{p} | 500 μH |

Primary capacitor C_{p} | 7 nF |

Secondary inductance L_{s} | 43.6 μH |

Resonant frequency f_{r} | 85.07 kHz |

Secondary capacitor C_{s} | 0.1 μF |

Supercapacitor | 25 V/15 F |

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**MDPI and ACS Style**

Xu, S.; Wang, Z.; Chen, J.; Jiang, W.
Research and Design of LC Series Resonant Wireless Power Transfer System with Modulation Control Method for Supercapacitor Charging in Linear Motion Systems. *Energies* **2022**, *15*, 6739.
https://doi.org/10.3390/en15186739

**AMA Style**

Xu S, Wang Z, Chen J, Jiang W.
Research and Design of LC Series Resonant Wireless Power Transfer System with Modulation Control Method for Supercapacitor Charging in Linear Motion Systems. *Energies*. 2022; 15(18):6739.
https://doi.org/10.3390/en15186739

**Chicago/Turabian Style**

Xu, Song, Zhenlin Wang, Jingfei Chen, and Wei Jiang.
2022. "Research and Design of LC Series Resonant Wireless Power Transfer System with Modulation Control Method for Supercapacitor Charging in Linear Motion Systems" *Energies* 15, no. 18: 6739.
https://doi.org/10.3390/en15186739