# Capacitive Power Transfer System with Reduced Voltage Stress and Sensitivity

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## Abstract

**:**

## Featured Application

## Abstract

## 1. Introduction

_{L}is 12.3 Ω, the capacitive interface C

_{c}

_{1}= C

_{c}

_{2}= 2C

_{c}= 1 nF and the tuning inductor L is 50.7 μH, which provides the quality factor [22] Q

_{conv}of 8/π

^{2}R

_{L}(sqrt(L/C

_{c})) ≅ 32 and provides the maximum voltage stress across the single pair of the capacitive interface V

_{c_conv}of 320 V for an AC input voltage V

_{in_conv}of just 20 V. Consequently, practically attaining tuning is challenging, and the system is highly sensitive to coupling variation and load change. The high voltage stress across the coupling interface increases the probability of dielectric breakdown and sparks occurrence. In addition, system safety becomes an issue as the related leakage electric field emissions around the plates increase beyond the safety margins as will be detailed in Section 4. These matters result in lower efficiency, decreased ability to deliver power, and increased difficulty in offering commercially accepted systems.

## 2. Proposed System Structure

_{1}–S

_{2}) construct a half-bridge inverter (full bridge can be used) to convert DC input voltage (${V}_{D}$) into an AC signal. Inductor L is placed in series to compensate for the capacitive interface, where ${C}_{c1}$ and ${C}_{c2}$ represent the capacitive coupling interface. Diodes (D

_{1}–D

_{4}) construct the full wave rectifier to obtain DC voltage. The DC–DC buck converter supplies the voltage and current to the load.

## 3. Mathematical Modelling and Analysis

_{in}can be obtained from Equation (1), as shown in Figure 2b.

_{c}as shown in Equation (2). The series compensation inductor L is obtained from Equation (3). The equivalent AC load R [26], assuming the rectifier and the buck converter are ideal, is described in Equation (4).

_{load}is the effective load resistance at the AC side; which is equal to 81% of the actual load resistance R

_{L}at the DC side after the rectifier; and $D$ is the buck converter duty cycle. The values in Table 1 were used as a design example to prove the concept.

_{D}and V

_{in}are the DC input voltage and AC input voltage needed to deliver a specific amount of power to the load, respectively. The DC input voltage and AC input voltage for the conventional system are represented by V

_{D_conv}and V

_{in_conv}, respectively.

#### 3.1. System Sensitivity

^{2}, as shown in Figure 3. By lowering Q, the sensitivity decreases and tuning at resonant frequency will be more obtainable practically. For a less sensitive system, we recommend using $Q\le 6$, which can be easily achieved by choosing $D\le 50\%$ for the chosen values of this design example. The recommended $D$ will change depending on the situation and the system design parameters.

_{conv}denotes the quality factor of the conventional system.

#### 3.2. Voltage Stress Across the Capacitive Interface

_{c}across the one pair of the coupling plates as described in Equations (11) and (12). Figure 8 that shows how V

_{c}varies with the duty cycle of the DC–DC converter. The voltage stress across one pair of the coupling plates (V

_{c}) decreases proportionally with D at the resonant frequency, as given in Equation (14). At low frequencies, the terms ${2C}_{c}{L\omega}^{2}{\mathrm{and}C}_{c}{}^{2}{\omega}^{2}\left({R}^{2}+{L}^{2}{\omega}^{2}\right)$ can be neglected and V

_{c}can be determined, as shown in Equation (15), which explains the high V

_{c}at the low frequencies. According to these results, the probability of having safety issues or the occurrence of sparks and dielectric breakdown is much lower, and can be totally neglected if D is sufficiently low.

_{conv}and V

_{c_conv}are the current flowing through the interface and the voltage across a single pair of the capacitive coupling interface plates for the conventional system, respectively.

## 4. Electric Field Simulation

## 5. Experimental Results

_{c}

_{1}). A differential probe was used to eliminate the common ground effect. The voltage stress is proportionally decreasing with the duty cycle which follows Equation (14) from the mathematical analysis. The maximum voltage stress across the capacitive interface (C

_{c}

_{1}) is reduced to about 65 V at D = 30% and 44 V at D = 20%, corresponding to an output power of 10 W, while 211 V is measured for the no buck converter used case. The values of the experimental results of V

_{c}is higher than the calculated ones due to the non-ideal components in the system and the switching losses which decrease the efficiency, so a higher input voltage is needed to deliver 10 W resulting in higher voltage stress across the interface. By using 64 V DC input voltage (V

_{D}), the system could deliver 10 W of power at the duty cycle of 30% and operating frequency 1 MHz, while the end-to-end system efficiency reached 80%. Figure 17 shows the measured V

_{in}, V

_{c}, and V

_{out}.

## 6. Conclusions

^{2}. Accordingly, the system tolerance to the change in the system parameters has improved. While transferring the same amount of power, the voltage stress is reduced proportionally to D and the related leakage electric field around the plates is drastically shrunk so the system becomes safer and the probability of dielectric breakdown or spark occurrence becomes much less. The experimental results from a 10 W CPT prototype demonstrated that by adding the buck converter, Q and voltage stress could effectively be reduced by changing the duty cycle. The maximum voltage stress across one pair of the coupling plates has been reduced to 65 V and 44 V at duty cycles of 30% and 20%, respectively, compared to 211 V for the conventional system without using a DC–DC converter. By applying 64 V input DC voltage and 30% buck converter duty cycle the system has achieved a system input to output (end-to-end) power efficiency of 80% at an output power of 10 W.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Tesla, N. Electrical Transformer or Induction Device. U.S. Patent No. 433,702, 5 August 1890. [Google Scholar]
- Hu, A.P. Wireless/Contactless Power Supply—Inductively Coupled Resonant Converter Solutions; VDM Verlag Dr Mueller: Saarbrücken, Germany, 2009; ISBN 978-3-639-11673-1. [Google Scholar]
- Green, A.W.; Boys, J.T. 10 kHz Inductively Coupled Power Transfer-Concept and Control. In Proceedings of the 1994 Fifth International Conference on Power Electronics and Variable-Speed Drives, London, UK, 26–28 October 1994; pp. 694–699. [Google Scholar]
- Hui, S.Y.R.; Ho, W.W.C. A new generation of universal contactless Battery Charging platform for portable Consumer Electronic equipment. IEEE Trans. Power Electron.
**2005**, 20, 620–627. [Google Scholar] [CrossRef] - Covic, G.A.; Boys, J.T.; Kissin, M.L.G.; Lu, H.G. A three-phase inductive power transfer system for roadway-powered vehicles. IEEE Trans. Ind. Electron.
**2007**, 54, 3370–3378. [Google Scholar] [CrossRef] - Thrimawithana, D.J.; Madawala, U.K. A Three-Phase Bi-Directional IPT System for Contactless Charging of Electric Vehicles. In Proceedings of the 2011 IEEE International Symposium on Industrial Electronics, Gdansk, Poland, 27–30 June 2011. [Google Scholar]
- Hu, A.P.; You, Y.W.; Chen, F.Y.B.; McCormick, D.; Budgett, D.M. Wireless Power Supply for ICP Devices with Hybrid Supercapacitor and Battery Storage. IEEE J. Emerg. Sel. Top. Power Electron.
**2016**, 4, 273–279. [Google Scholar] [CrossRef] - Kurs, A.; Karalis, A.; Moffatt, R.; Joannopoulos, J.D.; Fisher, P.; Soljačić, M. Wireless power transfer via strongly coupled magnetic resonances. Science
**2007**, 317, 83–86. [Google Scholar] [CrossRef] [PubMed] - Karalis, A.; Joannopoulos, J.D.; Soljačić, M. Efficient wireless non-radiative mid-range energy transfer. Ann. Phys.
**2008**, 323, 34–48. [Google Scholar] [CrossRef] [Green Version] - Chao, L.; Hu, A.P.; Wang, B.; Nair, N.C. A Capacitively Coupled Contactless Matrix Charging Platform with Soft Switched Transformer Control. IEEE Trans. Ind. Electron.
**2013**, 60, 249–260. [Google Scholar] [CrossRef] - Liu, C.; Hu, A.P. Wireless/Contactless Power Transfer-Capacitevely Coupled Solutions; LAP Lambert Academic Publishing: Saarbrucken, Germany, 2012. [Google Scholar]
- Mostafa, T.M.; Muharam, A.; Hattori, R. Wireless Battery Charging System for Drones via Capacitive Power Transfer. In Proceedings of the 2017 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Chongqing, China, 20–22 May 2017; pp. 1–6. [Google Scholar]
- Liu, C.; Hu, A.P. Power Flow Control of a Capacitively Coupled Contactless Power Transfer System. In Proceedings of the 2009 35th Annual Conference of IEEE Industrial Electronics, Porto, Portugal, 3–5 November 2009; pp. 743–747. [Google Scholar]
- Huang, L.; Hu, A.P. Defining the mutual coupling of capacitive power transfer for wireless power transfer. Electron. Lett.
**2015**, 51, 1806–1807. [Google Scholar] [CrossRef] - Culurciello, E.; Andreou, A.G. Capacitive Inter-Chip Data and Power Transfer for 3-D VLSI. IEEE Trans. Circuits Syst. II Expr. Briefs
**2006**, 53, 1348–1352. [Google Scholar] [CrossRef] - Salzman, D.; Knight, T., Jr.; Franzon, P. Application of Capacitive Coupling to Switch Fabrics. In Proceedings of the 1995 IEEE Multi-Chip Module Conference (MCMC-95), Santa Cruz, CA, USA, 31 January–2 February 1995; pp. 195–199. [Google Scholar]
- Wang, K.; Sanders, S. Contactless USB—A Capacitive Power and Bidirectional Data Transfer System. In Proceedings of the 2014 IEEE Applied Power Electronics Conference and Exposition—APEC 2014, Fort Worth, TX, USA, 16–20 March 2014; pp. 1342–1347. [Google Scholar]
- Muharam, A.; Mostafa, T.M.; Hattori, R. Design of Power Receiving Side in Wireless Charging System for UAV Application. In Proceedings of the 2017 International Conference on Sustainable Energy Engineering and Application (ICSEEA), Jakarta, Indonesia, 23–24 October 2017; pp. 133–139. [Google Scholar]
- Hu, A.P.; Liu, C.; Li, H.L. A Novel Contactless Battery Charging System for Soccer Playing Robot. In Proceedings of the 2008 15th International Conference on Mechatronics and Machine Vision in Practice, Auckland, New Zealand, 2–4 December 2008; pp. 646–650. [Google Scholar]
- Kim, J.; Bien, F. Electric Field Coupling Technique of Wireless Power Transfer for Electric Vehicles. In Proceedings of the IEEE 2013 Tencon-Spring, Sydney, NSW, Australia, 17–19 April 2013; pp. 267–271. [Google Scholar]
- Lu, F.; Zhang, H.; Hofmann, H.; Mi, C. A Double-Sided LCLC-Compensated Capacitive Power Transfer System for Electric Vehicle Charging. IEEE Trans. Power Electron.
**2015**, 30, 6011–6014. [Google Scholar] [CrossRef] - Bowick, C. Resonant Circuits. In RF Circuit Design, 2nd ed.; Elsevier/Newnes: New York, NY, USA, 2008; Chapter 2; pp. 26–28. ISBN 9780750685184. [Google Scholar]
- Theodoridis, M.P. Effective Capacitive Power Transfer. IEEE Trans. Power Electron.
**2012**, 27, 4906–4913. [Google Scholar] [CrossRef] - Funato, H.; Kobayashi, H.; Kitabayashi, T. Analysis of Transfer Power of Capacitive Power Transfer System. In Proceedings of the 2013 IEEE 10th International Conference on Power Electronics and Drive Systems (PEDS), Kitakyushu, Japan, 22–25 April 2013; pp. 1015–1020. [Google Scholar]
- Kline, M.; Izyumin, I.; Boser, B.; Sanders, S. Capacitive Power Transfer for Contactless Charging. In Proceedings of the 2011 Twenty-Sixth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Fort Worth, TX, USA, 6–11 March 2011; pp. 1398–1404. [Google Scholar]
- Erickson, R.W.; Maksimovic, D. Resonant Conversion. In Fundamentals of Power Electronics, 2nd ed.; Kluwer Academic: New York, NY, USA, 2001; Chapter 19; pp. 711–713. [Google Scholar]
- Zhang, H.; Lu, F.; Hofmann, H.; Liu, W.; Mi, C. A Large Air-Gap Capacitive Power Transfer System with a 4-Plate Capacitive Coupler Structure for Electric Vehicle Charging Applications. In Proceedings of the 2016 IEEE Applied Power Electronics Conference and Exposition (APEC), Long Beach, CA, USA, 20–24 March 2016; pp. 1726–1730. [Google Scholar] [CrossRef]
- IEEE Standards Association. IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz; IEEE Standard C95.1; IEEE: Piscataway, NJ, USA, 2005. [Google Scholar]
- Taranovich, S. Si vs. GaN vs. SiC: Which Process and Supplier Are Best for My Power Design? EDN NETWORK. 15 March 2013 [Online]. Available online: https://www.edn.com/design/power-management/4409627/Si-vs--GaN-vs--SiC--Which-process-and-supplier-are-best-for-my-power-design- (accessed on 14 April 2018).

**Figure 2.**The proposed system: (

**a**) CPT system with a DC–DC buck converter; (

**b**) circuit simplification by the sinusoidal approximation, and (

**c**) equivalent circuit used for analysis.

**Figure 3.**Input voltage needed to deliver 10 W to the load and the change in the quality factor of the circuit Q with different duty cycles D.

**Figure 5.**The tolerance of the output power with the change in the capacitive interface value using different duty cycles D.

**Figure 8.**The frequency response of the voltage V

_{c}across one pair of the coupling plates at different duty cycles D.

**Figure 12.**Simulated electric field at measurement points C, D, and E above the center of Tx1 and Rx1.

**Figure 15.**The tolerance of the output power with the change in the capacitive interface equivalent series value.

**Figure 16.**Frequency response of the voltage across the single pair of the capacitive interface C

_{c}

_{1}(amplitude).

**Figure 17.**Waveforms of the input AC voltage, voltage across the coupling capacitor, and the DC output voltage.

Parameter | Unit | Value |
---|---|---|

${P}_{\mathit{load}}$ | Watt | 10 |

$f$ | MHz | 1 |

${C}_{c1}{=C}_{c2}$ = 2C_{c} | nF | 2 |

$L$ | µH | 25 |

${R}_{\mathit{load}}$ | Ω | 10 |

Point | Distance to the Plates (cm) X, Y, Z |
---|---|

A | In the center between Tx1 and Rx1 |

B | 2, 0, 0 (in front of Tx1 and Rx1) |

C | 0, 0, 1 (above the center of Tx1 and Rx1) |

D | 0, 0, 3 (above the center of Tx1 and Rx1) |

E | 0, 0, 4 (above the center of Tx1 and Rx1) |

Parameter | Unit | Value |
---|---|---|

${P}_{\mathit{load}}$ | Watt | 10 |

$\mathit{freq}.$ | MHz | 1 |

${C}_{c1}$ | nF | ~2.1 |

${C}_{c2}$ | nF | ~1.9 |

Duty Cycle | % | 20, 30, 100 |

$L$ | µH | 25 |

${R}_{\mathit{load}}$ | Ω | 10 |

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**MDPI and ACS Style**

Mostafa, T.M.; Bui, D.; Muharam, A.; Hattori, R.; Hu, A.P.
Capacitive Power Transfer System with Reduced Voltage Stress and Sensitivity. *Appl. Sci.* **2018**, *8*, 1131.
https://doi.org/10.3390/app8071131

**AMA Style**

Mostafa TM, Bui D, Muharam A, Hattori R, Hu AP.
Capacitive Power Transfer System with Reduced Voltage Stress and Sensitivity. *Applied Sciences*. 2018; 8(7):1131.
https://doi.org/10.3390/app8071131

**Chicago/Turabian Style**

Mostafa, Tarek M., Dai Bui, Aam Muharam, Reiji Hattori, and Aiguo Patrick Hu.
2018. "Capacitive Power Transfer System with Reduced Voltage Stress and Sensitivity" *Applied Sciences* 8, no. 7: 1131.
https://doi.org/10.3390/app8071131