# SPWM Inverter Control for Wireless Constant Current and Voltage Charging

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Analysis

#### 2.1. Theoretical Model of S-S WPT Circuit

#### 2.2. Analysis of SPWM Single-Phase Inverter Circuit

#### 2.3. Analysis of CC/CV Output

#### 2.4. Adaptive Control Strategy for CC-CV Output of WPT System

- (1)
- Make the WPT circuit operate at the resonant frequency $f={f}_{0}$;
- (2)
- Detect whether ${U}_{L}$ < ${U}_{L,req}$; if ${U}_{L}$ < ${U}_{L,req}$, start the control procedure. Otherwise, close the S-S WPT circuit.
- (3)
- Detect ${U}_{L}$ and ${I}_{L}$, and calculate ${R}_{L}$.
- (4)
- According to Equation (10), adjust the modulation depth m, so that ${I}_{L}$ = ${I}_{L,req}$, and the control system operates in CC mode.
- (5)
- Judge whether ${U}_{L}$ = ${U}_{L,req}$ is true; if it is true, execute step (6); if not true, repeat steps (3)–(4).
- (6)
- Re-detect ${U}_{L}$ and ${I}_{L}$, and calculate ${R}_{L}$.
- (7)
- According to Equation (13), adjust the modulation depth m, so that ${U}_{L}$ = ${U}_{L,req}$, and the control system operates in CV mode.
- (8)
- Repeat steps (6) and (7) until ${I}_{L}\le {I}_{L,end}$.
- (9)
- When ${I}_{L}\le {I}_{L,end}$, the charging is completed, and close the S-S WPT circuit.

#### 2.5. Coupling-Coefficient Estimation

#### 2.6. Control Strategy Based on Coupling-Coefficient Estimation

## 3. Simulation of the Wireless Charging System

## 4. Experimental Verification

#### 4.1. System Experimental Device

#### 4.2. S Verification of the Proposed Control Method

#### 4.2.1. Validation of CC-CV Charging Strategy Based on SPWM Inverter Control

#### 4.2.2. Validation of CC-CV Charging Strategy Based on Coupling Coefficient Estimation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

WPT | Wireless power transfer |

CC | Constant current |

CV | Constant voltage |

SPWM | Sinusoidal pulse width modulation |

$m$ | SPWM inverter circuit modulation depth |

${Q}_{1}\u2013{Q}_{4}$ | Switches of SPWM inverter |

${D}_{1}\u2013{D}_{4}$ | Diodes of full-bridge rectifier |

${L}_{1}$ | Transmitting coil (H) |

${L}_{2}$ | Receiving coil (H) |

${C}_{1}$ | Resonant capacitor of the transmitting coil (F) |

${C}_{2}$ | Resonant capacitor of the receiving coil (F) |

$k$ | Coupling coefficient |

M | Mutual inductance (H) |

$\omega $ | System operating angle frequency (rad/s) |

${\omega}_{0}$ | Resonant angle frequency (rad/s) |

${f}_{0}$ | Resonant frequency (Hz) |

f | Operating frequency (Hz) |

${V}_{DC}$ | DC input voltage of SPWM inverter (V) |

${U}_{1}$ | The rms value of voltage of transmitting coil (V) |

${I}_{1}$ | The rms value of current of transmitting coil (A) |

${U}_{2}$ | The rms value of voltage of receiving coil (V) |

${I}_{2}$ | The rms value of current of receiving coil (A) |

${U}_{L}$ | Load voltage (V) |

${I}_{L}$ | Load current (A) |

${Z}_{1}$ | Impedance of transmitting coil (Ω) |

${Z}_{2}$ | Impedance of receiving coil (Ω) |

${R}_{1}$ | The transmission coil internal resistance is (Ω) |

${R}_{2}$ | Internal resistance of receiving coil (Ω) |

${R}_{r}$ | Equivalent resistance of the rectifier bridge circuit and the load (Ω) |

${R}_{L}$ | Load resistance (Ω) |

$\eta $ | Transmission efficiency |

${U}_{L,req}$ | Charging voltage required for CV mode (V) |

${I}_{L,req}$ | Charging current required for CC mode (A) |

${I}_{L,end}$ | End of charge current (A) |

## References

- Zhang, Y.; Chen, S.; Li, X.; Tang, Y. Design Methodology of Free-Positioning Nonoverlapping Wireless Charging for Consumer Electronics Based on Antiparallel Windings. IEEE Trans. Ind. Electron.
**2022**, 69, 825–834. [Google Scholar] [CrossRef] - Shi, K.; Tang, C.; Long, H.; Lv, X.; Wang, Z.; Li, X. Power Fluctuation Suppression Method for EV Dynamic Wireless Charging System Based on Integrated Magnetic Coupler. IEEE Trans. Power Electron.
**2022**, 37, 1118–1131. [Google Scholar] [CrossRef] - Kim, J.; Ryu, J.; Kim, G.; Lee, J.; Chang, S.; Lee, C.; Kim, J.; Oh, Y.; Lee, H.; Kim, J. A Proposed Fast Charging and High-Power System for Wireless Railway Trains Adopting the Input Voltage Sharing Topology and the Balancing Control Scheme. IEEE Trans. Ind. Electron.
**2020**, 67, 6407–6417. [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] - Lopes, P.; Costa, P.; Pinto, S. Wireless Power Transfer System For Electric Vehicle Charging. In Proceedings of the 2021 International Young Engineers Forum (YEF-ECE), Caparica, Portugal, 9 July 2021; pp. 132–137. [Google Scholar]
- Corti, F.; Reatti, A.; Nepote, A.; Pugi, L.; Pierini, M.; Paolucci, L.; Grasso, F.; Grasso, E.; Nienhause, M. A Secondary-Side Controlled Electric Vehicle Wireless Charger. Energies
**2020**, 13, 6527. [Google Scholar] [CrossRef] - Du, J.; Sun, Y. The influence of high power charging on the lithium battery based on constant and pulse current charging strategies. In Proceedings of the 17th IEEE Vehicle Power and Propulsion Conference, VPPC 2020, Gijon, Spain, 18 November–16 December 2020. [Google Scholar]
- Fang, H.Z.; Depcik, C.; Lvovich, V. Optimal pulse-modulated Lithium-ion battery charging: Algorithms and simulation. J. Energy Storage
**2018**, 15, 359–367. [Google Scholar] [CrossRef] - Majid, N.; Hafiz, S.; Arianto, S.; Yuono, R.Y.; Astuti, E.T.; Prihandoko, B. Analysis of effective pulse current charging method for lithium ion battery. J. Phys. Conf. Ser.
**2017**, 817, 012008. [Google Scholar] [CrossRef] - Zhang, B.; Carlson, R.B.; Smart, J.G.; Dufek, E.J.; Liaw, B. Challenges of future high power wireless power transfer for light-duty electric vehicles: Technology and risk management. eTransportation
**2019**, 2, 100012. [Google Scholar] [CrossRef] - Tran, D.H.; Vu, V.B.; Choi, W. Design of a High-Efficiency Wireless Power Transfer System With Intermediate Coils for the On-Board Chargers of Electric Vehicles. IEEE Trans. Power Electron.
**2018**, 33, 175–187. [Google Scholar] [CrossRef] - Gati, E.; Kampitsis, G.; Manias, S. Variable Frequency Controller for Inductive Power Transfer in Dynamic Conditions. IEEE Trans. Power Electron.
**2017**, 32, 1684–1696. [Google Scholar] [CrossRef] - Tritschler, J.; Reichert, S.; Goeldi, B. A practical investigation of a high power, bidirectional charging system for electric vehicles. In Proceedings of the 2014 16th European Conference on Power Electronics and Applications, Lappeenranta, Finland, 26–28 August 2014; pp. 1–7. [Google Scholar]
- Gyu Bum, J.; Cho, B.H. An energy transmission system for an artificial heart using leakage inductance compensation of transcutaneous transformer. IEEE Trans. Power Electron.
**1998**, 13, 1013–1022. [Google Scholar] [CrossRef] - Si, P.; Hu, A.P.; Malpas, S.; Budgett, D. A Frequency Control Method for Regulating Wireless Power to Implantable Devices. IEEE Trans. Biomed. Circuits Syst.
**2008**, 2, 22–29. [Google Scholar] [CrossRef] [PubMed] - Keeling, N.A.; Covic, G.A.; Boys, J.T. A Unity-Power-Factor IPT Pickup for High-Power Applications. IEEE Trans. Ind. Electron.
**2010**, 57, 744–751. [Google Scholar] [CrossRef] - Li, Z.; Zhu, C.; Jiang, J.; Song, K.; Wei, G. A 3-kW Wireless Power Transfer System for Sightseeing Car Supercapacitor Charge. IEEE Trans. Power Electron.
**2017**, 32, 3301–3316. [Google Scholar] [CrossRef] - Cai, H.; Shi, L.; Li, Y. Harmonic-Based Phase-Shifted Control of Inductively Coupled Power Transfer. IEEE Trans. Power Electron.
**2014**, 29, 594–602. [Google Scholar] [CrossRef] - Berger, A.; Agostinelli, M.; Vesti, S.; Oliver, J.A.; Cobos, J.A.; Huemer, M. A Wireless Charging System Applying Phase-Shift and Amplitude Control to Maximize Efficiency and Extractable Power. IEEE Trans. Power Electron.
**2015**, 30, 6338–6348. [Google Scholar] [CrossRef] - Qianhong, C.; Siu Chung, W.; Chi, K.T.; Xinbo, R. Analysis, design and control of a transcutaneous power regulator for artificial heart. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008; pp. 1833–1838. [Google Scholar]
- Huang, Z.; Wong, S.C.; Tse, C.K. Design methodology of a series-series inductive power transfer system for electric vehicle battery charger application. In Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, USA, 14–18 September 2014; pp. 1778–1782. [Google Scholar]
- Niu, W.; Liu, J.; Chen, Z.; Gu, W. Misalignment and range adaptive wireless charging system with constant current/constant voltage output based on coupling coefficient estimation. Int. J. Circuits Syst. Signal Process.
**2021**, 15, 334–348. [Google Scholar] [CrossRef] - Su, Y.G.; Zhang, H.Y.; Wang, Z.H.; Hu, A.P.; Chen, L.; Sun, Y. Steady-State Load Identification Method of Inductive Power Transfer System Based on Switching Capacitors. IEEE Trans. Power Electron.
**2015**, 30, 6349–6355. [Google Scholar] [CrossRef] - Kobayashi, D.; Imura, T.; Hori, Y. Real-time coupling coefficient estimation and maximum efficiency control on dynamic wireless power transfer for electric vehicles. In Proceedings of the 1st IEEE PELS Workshop on Emerging Technologies: Wireless Power, IEEE WoW 2015, Daejeon, Republic of Korea, 5–6 June 2015. [Google Scholar]
- Dai, X.; Li, X.F.; Li, Y.L.; Hu, A.G.P. Maximum Efficiency Tracking for Wireless Power Transfer Systems with Dynamic Coupling Coefficient Estimation. IEEE Trans. Power Electron.
**2018**, 33, 5005–5015. [Google Scholar] [CrossRef] - Liu, Y.Y.; Feng, H.W. Maximum Efficiency Tracking Control Method for WPT System Based on Dynamic Coupling Coefficient Identification and Impedance Matching Network. IEEE J. Emerg. Sel. Top. Power Electron.
**2020**, 8, 3633–3643. [Google Scholar] [CrossRef] - Stielau, O.H.; Covic, G.A. Design of loosely coupled inductive power transfer systems. In Proceedings of the PowerCon 2000. 2000 International Conference on Power System Technology. Proceedings (Cat. No.00EX409), Perth, Australia, 4–7 December 2000; Volume 81, pp. 85–90. [Google Scholar]
- Chwei-Sen, W.; Stielau, O.H.; Covic, G.A. Design considerations for a contactless electric vehicle battery charger. IEEE Trans. Ind. Electron.
**2005**, 52, 1308–1314. [Google Scholar] [CrossRef] - Chopra, S.; Bauer, P. Analysis and design considerations for a contactless power transfer system. In Proceedings of the 2011 IEEE 33rd International Telecommunications Energy Conference (INTELEC), Amsterdam, The Netherlands, 9–13 October 2011; pp. 1–6. [Google Scholar]
- Bosshard, R.; Kolar, J.W.; Mühlethaler, J.; Stevanović, I.; Wunsch, B.; Canales, F. Modeling and η-α-pareto Optimization of Inductive Power Transfer Coils for Electric Vehicles. IEEE J. Emerg. Sel. Top. Power Electron.
**2015**, 3, 50–64. [Google Scholar] [CrossRef] - Zheng, C.; Lai, J.S.; Chen, R.; Faraci, W.E.; Zahid, Z.U.; Gu, B.; Zhang, L.; Lisi, G.; Anderson, D. High-Efficiency Contactless Power Transfer System for Electric Vehicle Battery Charging Application. IEEE J. Emerg. Sel. Top. Power Electron.
**2015**, 3, 65–74. [Google Scholar] [CrossRef] - Qu, X.; Han, H.; Wong, S.C.; Tse, C.K.; Chen, W. Hybrid IPT Topologies With Constant Current or Constant Voltage Output for Battery Charging Applications. IEEE Trans. Power Electron.
**2015**, 30, 6329–6337. [Google Scholar] [CrossRef] - Mai, R.; Chen, Y.; Li, Y.; Zhang, Y.; Cao, G.; He, Z. Inductive Power Transfer for Massive Electric Bicycles Charging Based on Hybrid Topology Switching With a Single Inverter. IEEE Trans. Power Electron.
**2017**, 32, 5897–5906. [Google Scholar] [CrossRef] - Song, K.; Li, Z.; Jiang, J.; Zhu, C. Constant Current/Voltage Charging Operation for Series–Series and Series–Parallel Compensated Wireless Power Transfer Systems Employing Primary-Side Controller. IEEE Trans. Power Electron.
**2018**, 33, 8065–8080. [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] - Li, H.; Li, J.; Wang, K.; Chen, W.; Yang, X. A Maximum Efficiency Point Tracking Control Scheme for Wireless Power Transfer Systems Using Magnetic Resonant Coupling. IEEE Trans. Power Electron.
**2015**, 30, 3998–4008. [Google Scholar] [CrossRef] - Niu, W.Q.; Chu, J.X.; Gu, W.; Shen, A.D. Exact Analysis of Frequency Splitting Phenomena of Contactless Power Transfer Systems. IEEE Trans. Circuits Syst. I Regul. Pap.
**2013**, 60, 1670–1677. [Google Scholar] [CrossRef] - Shi, J.; Tian, M.; Han, S.; Wu, T.-Y.; Tang, Y. Electric vehicle battery remaining charging time estimation considering charging accuracy and charging profile prediction. J. Energy Storage
**2022**, 49, 104132. [Google Scholar] [CrossRef] - Zhu, Q.; Wang, L.; Guo, Y.; Liao, C.; Li, F. Applying LCC Compensation Network to Dynamic Wireless EV Charging System. IEEE Trans. Ind. Electron.
**2016**, 63, 6557–6567. [Google Scholar] [CrossRef] - Wang, Z.H.; Xiao, L.; Sun, Y.; Dai, X.; Li, Y. A simple approach for load identification in current-fed inductive power transfer system. In Proceedings of the 2012 IEEE International Conference on Power System Technology (POWERCON), Auckland, New Zealand, 30 October–2 November 2012; pp. 1–5. [Google Scholar]

**Figure 7.**Flow chart of modulation depth adjustment based on coupling-coefficient estimation in CC mode.

**Figure 8.**Flow chart of modulation depth adjustment based on coupling-coefficient estimation in CV mode.

**Figure 10.**Comparison between simulation results and theoretical values of CC-CV output of the WPT system based on Simulink.

**Figure 13.**The current ${I}_{1}$ of the transmitting coil and the current ${I}_{2}$ of the receiving coil.

**Figure 16.**Comparison between the estimated value of coupling coefficient k and Inca value at different transmission distances.

**Figure 17.**Comparison between experimental results and theoretical values of CC-CV output based on coupling-coefficient estimation.

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

${V}_{DC}$ | 12 V | ${C}_{2}$ | 0.2 μF |

${L}_{1}$ | 67.89 μH | ${R}_{2}$ | 0.5 Ω |

${C}_{1}$ | 0.2 μF | ${f}_{2}$ | 43.2 kHz |

${R}_{1}$ | 0.5 Ω | ${R}_{L}$ | 10–25 Ω |

${f}_{1}$ | 43.2 kHz | ${U}_{L,req}$ | 12 V |

${L}_{2}$ | 66.15 μH | ${I}_{L,req}$ | 0.75 A |

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**MDPI and ACS Style**

Sun, K.; Niu, W.
SPWM Inverter Control for Wireless Constant Current and Voltage Charging. *World Electr. Veh. J.* **2023**, *14*, 111.
https://doi.org/10.3390/wevj14040111

**AMA Style**

Sun K, Niu W.
SPWM Inverter Control for Wireless Constant Current and Voltage Charging. *World Electric Vehicle Journal*. 2023; 14(4):111.
https://doi.org/10.3390/wevj14040111

**Chicago/Turabian Style**

Sun, Kang, and Wangqiang Niu.
2023. "SPWM Inverter Control for Wireless Constant Current and Voltage Charging" *World Electric Vehicle Journal* 14, no. 4: 111.
https://doi.org/10.3390/wevj14040111