# A Uniform Voltage Gain Control for Alignment Robustness in Wireless EV Charging

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## Abstract

**:**

## 1. Introduction

## 2. Overview of the WPT System

Specification | Primary | Secondary |
---|---|---|

Inductance (µH) | 65.3 | 65.1 |

Tuning capacitor (µF) | 1.0 | 1.0 |

Turns | 12 | 12 |

Coil inside diameter (cm) | 11 | 11 |

Coil outside diameter (cm) | 56 | 56 |

Copper tube outside diameter (inch) | 3/8 | 3/8 |

Copper tube inside diameter (inch) | 1/4 | 1/4 |

## 3. Phase Angle Measurement

_{sense}) and current (I

_{sense}) signals from the power inverter (modeled as an AC source in Figure 2) are transformed into two square waveforms by comparators. An exclusive-OR gate (XOR) combines the two square waveforms to one pulse waveform whose width is equal to the phase delay between V

_{sense}and I

_{sense}. A low-pass filter converts the pulse into a DC signal V

_{phs}, which can be acquired by the analog-to-digital converter (ADC) in the DSP controller. The DC output of the filter is proportional to the phase angle between V

_{sense}and I

_{sense}. Since the high power in the WPT system can destroy the comparators and control circuit, four relays were used to isolate the power and control sides, as shown in Figure 2.

## 4. Analysis and Simulation of WPT

_{p}is the series tuning capacitance of the primary side and C

_{s}is the tuning capacitance of the secondary side. C

_{p}must equal C

_{s}to achieve resonance. L

_{pl}and L

_{sl}are the leakage inductances of each coil. Since both coils are the same, L

_{pl}equals L

_{sl}. L

_{m}is the mutual inductance. The leakage and mutual inductance can be experimentally measured. The battery is equivalent to a resistive load, R

_{L}, which can be calculated using the delivered power and voltage across the battery. For a desired 1.4 kW/120 V battery charging condition, R

_{L}is 20 Ω. j is the imaginary unit.

_{2}over input voltage V

_{1}as shown in Figure 3c and is determined by

**Figure 3.**Circuit diagram of proposed WPT system: (

**a**) SP topology for WPT; (

**b**) Simplified SP topology; (

**c**) Equivalent circuit of SP topology.

_{0}. The phase angle is fixed at f

_{0}no matter how the coupling varies, but the voltage gain G and impedance magnitude are the most unstable at f

_{0}, so the WPT system cannot operate at f

_{0}. On the left side of f

_{0}, uniform gain theoretically exists, but the corresponding phase angle is much lower than on the right side of f

_{0}, showing that the overall efficiency will be low if the WPT system operates on the left side of f

_{0}. Therefore, the frequency range marked in Figure 4c, on the right side of f

_{0}, is seen as the uniform gain control area. In Figure 4c, the frequency range for uniform gain control decreases from 24.4 kHz to 20.2 kHz when the coupling becomes weaker, and the corresponding phase angle is 18° at 24.4 kHz and 90° at 20.2 kHz. The total impedance is inductive in this frequency domain where the input voltage leads the input current, which realizes zero-voltage switching (ZVS) operation of the inverter.

**Figure 4.**Impedance and voltage gain G in frequency domain. (

**a**) Impedance magnitude; (

**b**) Impedance phase characteristics; (

**c**) Voltage gain in frequency domain. The simulation conditions were L

_{p}= 65 μH, L

_{s}= 65 μH, C

_{p}= 1 μF, C

_{s}= 1 μF, R = 20 Ω, and L

_{m}= 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, and 25 μH.

## 5. Control Loop Design

_{current}and θ

_{previous}). As the polarity of the phase angle cannot be detected by the measurement circuit, a direction flag p is utilized in the firmware to determine whether to shift the frequency to larger or smaller frequencies. The phase-angle which corresponds to the resonant frequency is zero, but the phase angle read by the DSP at the resonant frequency is not exactly zero due to the measurement error of digital devices. Therefore, the resonant frequency is set when the current phase angle (θ

_{current}) is lower than t, where t is a value within the range of acceptable measurement accuracy. Secondly, the WPT system determines the uniform gain frequency once the resonant frequency is known. The tuning program increases the frequency step by step (∆f) while measuring the load phase angle. The resonant frequency acquired in the first step determines the phase angle curve (Figure 4b) and the mutual inductance between the two coils can be calculated according to Equation (1). Once the mutual inductance is known, the phase angle (θ

_{uniform}) for the uniform gain can be obtained using Equations (1) and (5). Then the DSP program increases the switching frequency step by step (∆f) while measuring the load phase angle until the phase angle is equal to θ

_{uniform}. Finally, the WPT sets the switching frequency to the uniform gain frequency and raises the input DC voltage to begin charging the EV.

_{uniform}for a known coupling can be derived from Equations (1)–(5). However, a floating calculation could consume the computational resources of a 16-bit DSP dramatically and might influence the tuning speed as well. In addition, the theoretical value might have an error due to parasitic resistance and stray inductance in the electronic elements. Hence, the phase angle θ

_{uniform}is calibrated for each increase (set 2 cm in our test) in misalignment and the coupling between two calibration points will linearly map the phase angle θ

_{uniform}.

## 6. Experimental Validation

#### 6.1. 3-Axis Platform for Alignment Study

#### 6.2. Experimental Results with Misalignment under a Constant Air Gap

**Figure 7.**Experimental comparison in three control modes at a fixed air gap of 100 mm and different misaligned coil conditions. (

**a**) Efficiency at a fixed frequency; (

**b**) Voltage at a fixed frequency; (

**c**) Efficiency at resonant frequencies (phase angle θ = 0); (

**d**) Voltage at resonant frequencies (phase angle θ = 0); (

**e**) Efficiency at uniform gain frequencies; (

**f**) Voltage at uniform gain frequencies.

_{in}is the DC input voltage of the inverter) was maintained at about 3.04 across the misalignment range up to 200 mm, which coincides well with the simulation result in Figure 4c. The DC output voltage V

_{b}after the rectifier and the smoothing capacitor (Figure 3a) is the rectifier input RMS voltage V

_{2}multiplied by a constant value, specifically: V

_{2}= $\frac{\sqrt{3}}{2}$V

_{b}[12]. The theoretical peak-peak voltage gain is 4.0 (Figure 4c); hence the theoretical DC output voltage over DC input is 3.27, which is quite close to the measured gain.

#### 6.3. Experimental Results with Air Gap Variations under Zero Misalignment

**Figure 8.**Experimental comparison in three control modes with different air gaps and no coil misalignment. (

**a**) Efficiency at a fixed frequency; (

**b**) Voltage at a fixed frequency; (

**c**) Efficiency at resonant frequencies (phase angle θ = 0); (

**d**) Voltage at resonant frequencies (phase angle θ = 0); (

**e**) Efficiency at uniform gain frequencies; and (

**f**) Voltage at uniform gain frequencies.

#### 6.4. Accuracy of Frequency Tracking

**Figure 9.**The theoretical and acquired switching frequencies for uniform voltage gain control with various couplings (misalignment at an air gap of 100 mm).

#### 6.5. Frequency Control at a Large Misalignment

**Figure 10.**Switching signals and the inverter circulating current under two extreme conditions (misalignment = 200 mm, air gap = 100 mm) (

**a**) Fixed frequency control (20.2 kHz); Sinusoidal current waveform: Max = 32 A, RMS = 22.7 A; (

**b**) Uniform gain operation (19.5 kHz). Sinusoidal current waveform: Max = 37 A, RMS = 26.2 A. The voltage-current ratio of the current sensor is 0.2 V/A.

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Deng, J.; Li, W.; Nguyen, T.-D.; Li, S.; Mi, C. Compact and efficient bipolar pads for wireless power chargers: Design and analysis. IEEE Trans. Power Electron.
**2015**, 30, 6130–6140. [Google Scholar] [CrossRef] - Covic, G.A.; Boys, J.T. Modern trends in inductive power transfer for transportation applications. Emerg. Sel. Top Power Electron.
**2013**, 1, 28–41. [Google Scholar] [CrossRef] - Fisher, T.M.; Farley, K.B.; Gao, Y.; Bai, H.; Tse, Z.T.H. Electric vehicle wireless charging technology: A state-of-the-art review of magnetic coupling systems. Wirel. Power Transf.
**2014**, 1, 87–96. [Google Scholar] [CrossRef] - Duan, C.; Jiang, C.; Taylor, A.; Bai, K. Design of a zero-voltage-switching large-air-gap wireless charger with low electrical stress for plugin hybrid electric vehicles. In Proceeding of Transportation Electrification Conference and Expo (ITEC 2013), Detroit, MI, USA, 16–19 June 2013; pp. 1–5.
- RamRakhyani, A.K.; Mirabbasi, S.; Chiao, M. Design and optimization of resonance-based efficient wireless power delivery systems for biomedical implants. IEEE Trans. Biomed. Circuits Syst.
**2011**, 5, 48–63. [Google Scholar] [CrossRef] [PubMed] - Park, C.; Lee, S.; Cho, G.-H.; Choi, S.-Y.; Rim, C.T. Two-dimensional inductive power transfer system for mobile robots using evenly displaced multiple pickups. IEEE Trans. Ind. Appl.
**2014**, 50, 558–565. [Google Scholar] [CrossRef] - Gao, Y.; Farley, K.B.; Tse, Z.T.H. Investigating safety issues related to electric vehicle wireless charging technology. In Proceeding of Transportation Electrification Conference and Expo (ITEC 2014), Dearborn, MI, USA, 15–18 June 2014; pp. 1–4.
- Sample, A.P.; Meyer, D.A.; Smith, J.R. Analysis, experimental results, and range adaptation of magnetically coupled resonators for wireless power transfer. IEEE Trans. Ind. Electron.
**2011**, 58, 544–554. [Google Scholar] [CrossRef] - Zheng, C.; Chen, R.; Faraci, E.; Zahid, Z.U.; Senesky, M.; Anderson, D.; Lai, J.-S.; Yu, W.; Lin, C.-Y. High efficiency contactless power transfer system for electric vehicle battery charging. In Proceeding of Energy Conversion Congress and Exposition (ECCE 2013), Denver, CO, USA, 15–19 September 2013; pp. 3243–3249.
- Duan, C.; Jiang, C.; Taylor, A.; Bai, K.H. Design of a zero-voltage-switching large-air-gap wireless charger with low electric stress for electric vehicles. IET Power Electron.
**2013**, 6, 1742–1750. [Google Scholar] [CrossRef] - Liu, N.; Habetler, T.G. Design of a universal inductive charger for multiple electric vehicle models. IEEE Trans. Power Electron.
**2015**, 30, 6378–6390. [Google Scholar] [CrossRef] - Miller, J.; Daga, A. Elements of wireless power transfer essential to high power charging of heavy duty vehicles. IEEE Trans.Transp. Electrification
**2015**, 1, 26–39. [Google Scholar] [CrossRef] - Aldhaher, S.; Luk, P.-K.; Whidborne, J.F. Electronic tuning of misaligned coils in wireless power transfer systems. IEEE Trans.Power Electron.
**2014**, 29, 5975–5982. [Google Scholar] [CrossRef] - Han, J.; Kim, Y.; Myung, N.-H. Efficient performance optimisation of wireless power transmission using genetic algorithm. Electron. Lett.
**2014**, 50, 462–464. [Google Scholar] [CrossRef] - Kar, D.; Nayak, P.; Bhuyan, S.; Panda, S. Automatic frequency tuning wireless charging system for enhancement of efficiency. Electron. Lett.
**2014**, 50, 1868–1870. [Google Scholar] [CrossRef] - Nam, I.; Dougal, R.; Santi, E. Novel unity gain frequency tracking control of series-series resonant converter to improve efficiency and receiver positioning flexibility in wireless charging of portable electronics. IEEE Trans. Ind. Appl.
**2015**, 51, 385–397. [Google Scholar] [CrossRef] - Schneider, J. SAE j2954 Overview and Path forward. 2013. Available online: http://www.sae.org/smartgrid/sae-j2954-status_1-2012.pdf (accessed on 3 July 2015).
- Carlson, R.W.; Normann, B. Test results of the plugless™ inductive charging system from evatran group, inc. SAE Int. J. Altern. Powertrains
**2014**, 3, 64–71. [Google Scholar] [CrossRef]

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## Share and Cite

**MDPI and ACS Style**

Gao, Y.; Farley, K.B.; Tse, Z.T.H.
A Uniform Voltage Gain Control for Alignment Robustness in Wireless EV Charging. *Energies* **2015**, *8*, 8355-8370.
https://doi.org/10.3390/en8088355

**AMA Style**

Gao Y, Farley KB, Tse ZTH.
A Uniform Voltage Gain Control for Alignment Robustness in Wireless EV Charging. *Energies*. 2015; 8(8):8355-8370.
https://doi.org/10.3390/en8088355

**Chicago/Turabian Style**

Gao, Yabiao, Kathleen Blair Farley, and Zion Tsz Ho Tse.
2015. "A Uniform Voltage Gain Control for Alignment Robustness in Wireless EV Charging" *Energies* 8, no. 8: 8355-8370.
https://doi.org/10.3390/en8088355