# Analysis of Losses in Two Different Control Approaches for S-S Wireless Power Transfer Systems for Electric Vehicle

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## Abstract

**:**

## 1. Introduction

## 2. Methods of Operation of SAHFWPT and DAHFWPT

#### 2.1. Circuit Schematic

#### 2.2. Operation and Analysis

## 3. Methods of Loss Analysis of SAHFWPT and DAHFWPT

#### 3.1. S-S Coil Loss

#### 3.2. Loss of HFSR, HFSC and HFPC

#### 3.2.1. Conduction Loss of MOSFET and Diodes

#### 3.2.2. Hard Turn on and off Loss

#### 3.2.3. Other Switching Losses in the MOSFET

## 4. Efficiency of SAHFWPT and DAHFWPT

## 5. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

SAHFWPT | Single Active High-Frequency wireless power transfer |

DAHFWPT | Dual Active High-Frequency wireless power transfer |

SPS | Single Phase Shift |

EPS | Extended Phase Shift |

DPS | Dual Phase Shift |

TPS | Triple Phase shift |

EV | Electrical Vehicle |

RE | Renewable Energy |

ESS | Energy Storage System |

SAB | Single Active Bridge |

DAB | Dual Active Bridge |

PSFB | Phase Shift Full Bridge |

DC | Direct Current |

${V}_{S}$ | Source Voltage |

${R}_{B}$ | Battery Equivalent Resistance |

${C}_{O}$ | Output low pass filter capacitor |

${L}_{O}$ | Output low pass filter inductor |

$\mathrm{ZVS}$ | Zero Voltage Switching |

$\mathrm{ZCS}$ | Zero Current Switching |

HFPC | High-frequency Primary Converter |

HFSC | High-frequency Secondary Converter |

HFSR | High-frequency Secondary Rectifier |

${V}_{DCP\_S}$$,{V}_{DCP\_D}$ | DC voltage source of SAHFWPT and DAHFWPT |

${v}_{HFPC\_S}$$,{v}_{HFPC\_D}$ | Output voltage of HFPC of SAHFWPT and DAHFWPT |

${i}_{P\_S}$$,{i}_{P\_D}$ | Output current of HFPC of SAHFWPT and DAHFWPT |

${v}_{HFSR\_S}$$,{v}_{HFSC\_S}$ | Input voltage of HFSR and HFSC of SAHFWPT and DAHFWPT |

${i}_{S\_S}$$,{i}_{S\_D}$ | Input current of HFSR and HFSC of SAHFWPT and DAHFWPT |

${V}_{O\_S},$${V}_{O\_D}$ | Output voltage of HFSR and HFSC of SAHFWPT and DAHFWPT |

${\omega}_{r}$ | Resonant Frequency |

Φ | External Phase shift angle |

α | Internal phase shift angle of HFPC |

β | Internal phase shift angle of HFSC |

${v}_{HFPC\_M}$$,{v}_{HFSC\_M}$ | Peak amplitude of output and input voltage of HFPC and HFSC of DAHFWPT |

${v}_{HFSR\_M}$ | Peak amplitude of input voltage of HFSR of SAHFWPT |

C_{P}, C_{S} | Primary and secondary resonant capacitor |

L_{P}, L_{S} | Primary and secondary coil self-inductance |

R_{P}, R_{S} | Primary and secondary coil resistance |

${Z}_{P}$,${Z}_{S}$ | Impedance of primary and secondary coil |

M | Coils mutual inductance |

${v}_{P},$${v}_{S}$ | Primary and secondary coil induce voltage |

${i}_{P},{i}_{S}$ | Primary and secondary coil circulating current |

${P}_{PS}$ | Average power flow from primary to secondary |

${v}_{HFPC\_1},{v}_{HFSC\_1}$ | Fundamental Output and Input voltage of HFPC and HFSC of DAHFWPT |

${v}_{HFSR\_1}$ | Fundamental of Input voltage of HFSR of SAHFWPT |

${i}_{P\_D\_1},{i}_{P\_S\_1}$ | Fundamental primary coil current of DAHFWPT and SAHFWPT |

${i}_{s\_1}$ | Fundamental secondary coil current of DAHFWPT and SAHFWPT |

${P}_{DAHFWPT\_S},{P}_{SAHFWPT\_S}$ | Secondary Power of DAHFWPT and SAHFWPT |

${P}_{S-S\_coil\_DAHFWPT\_loss},{P}_{S-S\_coil\_SAHFWPT\_loss}$ | Coil Loss of DAHFWPT and SAHFWPT |

${\eta}_{S-S\_coil\_DAHFWPT},{\eta}_{S-S\_coil\_SAHFWPT}$ | Efficiency of coil of DAHFWPT and SAHFWPT |

${P}_{HFPC\_Cond\_S\_loss},{P}_{HFSR\_Cond\_loss}$ | Conduction loss of HFPC and HFSR of SAHFWPT |

${P}_{HFPC\_Cond\_D\_loss},{P}_{HFSC\_Cond\_loss}$ | Conduction loss of HFPC and HFSC of DAHFWPT |

${P}_{HFSC\_on\_\_off\_loss}$ | Switching loss of switches for HFSC |

${P}_{HFPC\_on\_\_off\_D\_loss},{P}_{HFPC\_on\_\_off\_S\_loss}$ | Switching loss of switches for HFPC of DAHFWPT and SAHFWPT |

${P}_{Coss\_loss}$ | Output capacitor loss of MOSFET |

${P}_{body\_loss}$ | Body diode reverse recovery loss |

η | Efficiency |

P_{O} | Output Power |

${P}_{in}$ | Input Power |

${P}_{loss}$ | Power Loss |

${P}_{B}$ | Power of Battery |

${P}_{SAHFWPT\_loss}$ | Overall loss Power of SAHFWPT |

${P}_{DAHFWPT\_loss}$ | Overall loss Power of DAHFWPT |

${\eta}_{SAHFWPT}$ | Efficiency of SAHFWPT |

${\eta}_{DAHFWPT}$ | Efficiency of DAHFWPT |

WPT | Wireless Power Transfer |

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**Figure 5.**Secondary of the S-S coupling coil power relation of SAHFWPT and DAHFWPT w.r.t. $\alpha $.

**Figure 7.**Current (red) and voltage (blue) wave input of primary coil and output of the secondary coil of (

**a**) SAHFWPT (

**b**) and DAHFWPT.

Feature | SAHFWPT | DAHFWPT | |||||
---|---|---|---|---|---|---|---|

Reference | [3] | [5] | [6,7,8,9] | [3] | [5] | [6,7,8,9] | |

Switching control | SPS | × | √ | √ | × | √ | √ |

EPS | √ | √ | √ | × | √ | √ | |

DPS | × | × | × | √ | √ | √ | |

TPS | × | × | × | × | √ | √ | |

Additional chopper | √ | √ | √ | × | × | × | |

Hard switching of MOSFET | × | × | √ | × | × | √ | |

Circulating current | × | × | × | × | √ | √ | |

S-S coil loss | √ | √ | √ | √ | √ | √ | |

Overall loss analysis | × | × | √ | × | × | √ |

${v}_{HFPC\_1}\left(t\right)={v}_{HFPC\_1\_M}\mathit{sin}\left(\frac{\alpha}{2}\right)\mathit{sin}\left({\omega}_{r}t\right)$ | (8) | ${v}_{HFSC\_1}\left(t\right)={v}_{HFSC\_1\_M}\mathit{sin}\left(\frac{\beta}{2}\right)\mathit{sin}\left({\omega}_{r}t+\Phi \right)$ | (9) |

${i}_{P\_D\_1}\left(t\right)=\frac{{v}_{HFSC\_1\_M}}{M{\omega}_{r}}\mathit{sin}\left(\frac{\beta}{2}\right)\mathit{cos}\left({\omega}_{r}t+\Phi \right)$ | (10) | ${i}_{s\_1}\left(t\right)=\frac{-{v}_{HFPC\_1\_M}}{M{\omega}_{r}}\mathit{sin}\left(\frac{\alpha}{2}\right)\mathit{cos}\left({\omega}_{r}t\right)$ | (11) |

${v}_{HFPC\_1}\left(t\right)={v}_{HFPC\_1\_M}\mathit{sin}\left(\frac{\alpha}{2}\right)\mathit{sin}\left({\omega}_{r}t\right)$ | (12) | ${v}_{HFSR\_1}\left(t\right)={v}_{HFSR\_1\_M}\mathit{sin}\left({\omega}_{r}t+\Phi \right)$ | (13) |

${i}_{P\_S\_1}\left(t\right)=\frac{{v}_{HFSR\_1\_M}}{M{\omega}_{r}}\mathit{cos}\left({\omega}_{r}t+\Phi \right)$ | (14) | ${i}_{s\_1}\left(t\right)=\frac{-{v}_{HFPC\_1\_M}}{M{\omega}_{r}}\mathit{sin}\left(\frac{\alpha}{2}\right)\mathit{cos}\left({\omega}_{r}t\right)$ | (15) |

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

Source Rated Voltage | ${V}_{DCP\_S},{V}_{DCP\_D}$ | 384 V |

Battery Rated voltage | ${V}_{O\_S}$, ${V}_{O\_D}$ | 120 V |

Resonating frequency | ${f}_{r}$ | 85 kHz |

MOSFETs | ${T}_{5}-{T}_{12}$ | SiHG33N60EF |

Self-Inductance | ${L}_{P}{L}_{S}$ | 220 µH |

Compensation Capacitors | ${C}_{P}{C}_{S}$ | 15.9 nF |

S-S coil Resistance | ${R}_{P}{R}_{S}$ | 0.5 $\mathsf{\Omega}$ |

Mutual-Inductance | M | 22.5 µH |

α | Input Power | Loss into the System | % Loss into the System | |||
---|---|---|---|---|---|---|

SAHFWPT | DAHFWPT | SAHFWPT | DAHFWPT | SAHFWPT | DAHFWPT | |

3.12 | 3605 | 3605 | 586 | 586 | 16.25 | 16.25 |

2.16 | 3146 | 2807 | 469 | 453 | 14.97 | 16.15 |

1.82 | 2795 | 2252 | 388 | 361 | 13.87 | 16.05 |

1.44 | 2312 | 1574 | 290 | 250 | 12.54 | 15.88 |

1.14 | 1881 | 1057 | 217 | 165 | 11.51 | 15.65 |

0.73 | 1245 | 467 | 136 | 71 | 10.94 | 15.23 |

0.33 | 605 | 102 | 99 | 23 | 16.34 | 22.43 |

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## Share and Cite

**MDPI and ACS Style**

Kumar, A.; Bertoluzzo, M.; Jha, R.K.; Sagar, A.
Analysis of Losses in Two Different Control Approaches for S-S Wireless Power Transfer Systems for Electric Vehicle. *Energies* **2023**, *16*, 1795.
https://doi.org/10.3390/en16041795

**AMA Style**

Kumar A, Bertoluzzo M, Jha RK, Sagar A.
Analysis of Losses in Two Different Control Approaches for S-S Wireless Power Transfer Systems for Electric Vehicle. *Energies*. 2023; 16(4):1795.
https://doi.org/10.3390/en16041795

**Chicago/Turabian Style**

Kumar, Abhay, Manuele Bertoluzzo, Rupesh Kumar Jha, and Amritansh Sagar.
2023. "Analysis of Losses in Two Different Control Approaches for S-S Wireless Power Transfer Systems for Electric Vehicle" *Energies* 16, no. 4: 1795.
https://doi.org/10.3390/en16041795