# Investigation on Induced Energy Extraction from High-Voltage Transmission Lines Based on Three-Coil WPT Systems

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## Abstract

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## 1. Introduction

#### 1.1. Motivation and Incitement

#### 1.2. Literature Review

- Solar power: It collects photovoltaic energy mainly through solar cell arrays, and, at the same time, for online monitoring devices and battery power supplies. However, solar cells are susceptible to weather conditions, and the storage capacity in solar power systems is unlikely to be too large when it is cloudy and rainy for many days; hence, solar power systems may not be able to meet the power needs of online monitoring devices [7].
- Laser power: At the low-voltage side, high-power laser generators are used to send light energy to the high-voltage side, and at the high-voltage side, photocells are used to convert light energy into electricity, which supplies power to high-voltage lines [8]. However, due to the large size of the transmitting and receiving devices and the fact that online detection equipment is usually installed on high-voltage lines, it is difficult to install power supply equipment, and the cost of its operation and maintenance is high.
- Ultrasonic power supply: The utility model relates to an energy supply mode that uses ultrasonic waves as a medium to transmit electric energy. However, its equipment is expensive, and the conversion efficiency is low. Hence, it cannot be used on a large scale.
- Microwave power: It is a means of transmitting energy in a vacuum or in the atmosphere without the aid of any other transmission lines. However, if a microwave power supply is applied to the power supply of online monitoring devices for high-voltage transmission lines, there is also a need to address the design and placement of receiving antennas, determining whether the microwave power supply can interfere with monitoring devices, and the issues surrounding operation and maintenance [9].

#### 1.3. Contribution and Paper Organization

## 2. Theoretical Analysis and Design of Induction Power Extraction

#### 2.1. Analysis of CT Ring Induction Power Extraction

_{m}is the main magnetic flux, φ

_{1m}and φ

_{2m}are the leakage fluxes of the primary and secondary winding, respectively, φ

_{1}and φ

_{2}are the main magnetic fluxes of the primary and secondary winding, respectively, i

_{1}and i

_{2}are the currents of the primary and secondary winding, respectively, N

_{1}and N

_{2}are the turns of the primary and secondary winding, respectively, and e

_{1}and e

_{2}are the potentials of the primary and secondary winding, respectively.

_{r}is the relative permeability of the magnetic core, μ

_{0}is the vacuum permeability, l is the effective magnetic circuit length, S is the cross-sectional area of the iron core, f is the frequency of the transmission line current, and I

_{1}is the effective value of the transmission line current.

#### 2.2. Selection of CT Ring

#### 2.3. Power Extraction of CT Ring

_{max}is the maximum magnetic induction intensity.

#### 2.4. Power Extraction of CT Ring

_{0}= 44 mm; inner diameter R

_{i}= 30 mm; width a = 30 mm; air gap δ = 1 mm; secondary side turns N

_{2}= 200; vacuum permeability μ

_{0}= 4π × 10

^{−7}H/m; system frequency f = 50 Hz.

_{2}. It was shown that, when the current at the transmission terminal was 500 A, it was equivalent to a voltage source with an amplitude of 23.43 V.

## 3. Theoretical Analysis and Design of Magnetic Coupling Resonant WPT System

#### 3.1. Mathematical Model of Magnetic Coupling Resonant Wireless Power Transmission System

#### 3.1.1. Relationships between Output Power, Transmission Efficiency, and Coil Mutual Inductance

#### 3.1.2. Relationships between Output Power, Transmission Efficiency, and Load Resistance

#### 3.2. Theoretical Analysis of Three-Coil Magnetic Coupling Resonant WPT System

_{S}is the high-frequency voltage, R

_{1}, R

_{2}, R

_{3}, R

_{S}, and R

_{L}are the resistance of the transmitting coil, the resistance of the relay coil, the resistance of the receiving coil, the internal resistance of the power supply, and the resistance of the load, respectively; L

_{1}, L

_{2}, and L

_{3}are three equivalent inductance values of the coil, and C

_{1}, C

_{2}, and C

_{3}are the capacitor compensations of the three coils.

#### 3.3. Analysis of Influence Factors of Three-Coil Magnetic Coupling Resonant WPT System

#### 3.3.1. Effect of Coupling Coefficient on Output Power

_{S}= 100 V, R

_{1}= R

_{2}= R

_{3}= R = 0.5 Ω, and L

_{1}= L

_{2}= L

_{3}= L = 297.08 μH. Ignoring the internal resistance of the input power supply R

_{S}and making the load resistance value R

_{L}= 15 Ω, based on these parameters, the relationship between the coupling coefficient and the output power could be obtained, as shown in Figure 9.

#### 3.3.2. Influence of Coupling Coefficient on Transmission Efficiency

_{12}and k

_{23}. Moreover, the influence of the coupling coefficient of the transmitting coil and the relay coil on the transmission efficiency of the system was slightly larger than that of the coupling coefficient of the relay coil and the receiving coil. Since the coupling coefficients k

_{12}and k

_{23}of the system had a certain negative correlation, it was difficult to make the transmission efficiency reach the maximum value. However, the transmission efficiency of the system would be improved with the increase in k

_{12}.

#### 3.3.3. Determination of Three-Coil Parameters

#### 3.3.4. Influence of Load Resistance on Transmission Performance

_{1}= L

_{2}= L

_{3}= L = 297.08 μH and M

_{12}= M

_{23}= 10.315 μH, respectively. The coil resistance was R

_{1}= R

_{2}= R

_{3}= R = 0.5 Ω, the input voltage U

_{S}was =100 V, and the resonant frequency f was =100 kHz. Based on the above parameters, the load, output power, and transmission efficiency curves are shown in Figure 12 and Figure 13.

## 4. Simulation

## 5. The Innovation of the Paper

- This paper discussed a new power supply mode of online detecting equipment for high-voltage transmission lines, which included CT induction power extraction technology and three-coil WPT.
- The designed method of the CT induction power extraction devices was presented, related parameters, such as the material structure of the iron core, were given, and the optimization was verified.
- The three-coil system with a relay coil was analyzed theoretically and the energy efficiency effect of related parameters of the three-coil system was analyzed. Based on this, a three-coil WPT system was designed.

## 6. Comparative Analysis

## 7. Conclusions

## 8. Patents

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Notations

Symbol | Description | Unit |

φ_{m} | the main magnetic flux | Wb |

φ_{1m} | the leakage fluxes of the primary winding | Wb |

φ_{2m} | the leakage fluxes of the secondary winding | Wb |

φ_{1} | the main fluxes of the primary winding | Wb |

φ_{2} | the main fluxes of the secondary winding | Wb |

i_{1} | the current of the primary winding | mA |

i_{2} | the current of the secondary winding | mA |

N_{1} | the turns of the primary winding | - |

N_{2} | the turns of the secondary winding | - |

e_{1} | the potentials of the primary winding | V |

e_{2} | the potentials of the secondary winding | V |

E_{2} | the voltage effective value of the CT secondary side under no-load conditions | V |

μ_{r} | the relative permeability of the magnetic core | H/m |

μ_{0} | the vacuum permeability | H/m |

l | the effective magnetic circuit length | m |

S | the cross-sectional area of the iron core | m^{2} |

f | the frequency of the transmission line current | Hz |

I_{1} | the effective value of the transmission line current | mA |

μ_{Fe} | the ferrum permeability | H/m |

ω | the resonant angular frequency | r/s |

M | the mutual inductance factor | H |

R_{1} | the primary impedance | Ω |

R_{2} | the secondary impedance | Ω |

R_{L} | the load resistance | Ω |

P_{max} | the expression of the maximum power | W |

B_{max} | the maximum magnetic induction intensity | Wb/m^{2} |

η | the transmission efficiency | - |

P_{out} | the output power | W |

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**Figure 3.**Equivalent circuit of topological structure: (

**a**) SS topology structure; (

**b**) SP topology structure; (

**c**) PS topology structure; (

**d**) PP topology structure.

**Figure 10.**Relationship between transmission efficiency and coupling coefficients k

_{12}and k

_{23}.

Basic Parameter | Silicon Steel | Permalloy | Nanocrystal |
---|---|---|---|

Saturation induction (B/H) | 2.03 | 0.75 | 1.25 |

Initial permeability (μH/m) | 10^{2}~10^{3} | (5~8) × 10^{4} | (5~10) × 10^{4} |

Maximum permeability (μH/m) | 4 × 10^{4} | 60 × 10^{4} | 60 × 10^{4} |

Density (g/cm^{3}) | 7.65 | 8.75 | 7.25 |

Packing fraction | 0.95 | 0.9 | 0.7 |

Thickness (mm) | 0.3 | 0.15 | 0.3 |

Topological Structure | Output Power | Transmission Efficiency |
---|---|---|

SS | $\frac{{\left(\omega M{U}_{S}\right)}^{2}{R}_{L}}{{\left({Z}_{11}{Z}_{21}+{\omega}^{2}{M}^{2}\right)}^{2}}$ | $\frac{{\omega}^{2}{M}^{2}{R}_{L}}{\left({Z}_{11}{Z}_{21}+{\omega}^{2}{M}^{2}\right){Z}_{21}}$ |

SP | $\frac{{\left(\omega M{U}_{S}\right)}^{2}{R}_{L}}{{\left({Z}_{11}{Z}_{22}+{\omega}^{2}{M}^{2}\right)}^{2}\left(1+j\omega {C}_{2}\right)}$ | $\frac{{\omega}^{2}{M}^{2}{R}_{L}}{\left({Z}_{11}{Z}_{22}+{\omega}^{2}{M}^{2}\right)\left(1+j\omega {C}_{2}{R}_{L}\right)}$ |

PS | $\frac{{\left(\omega M{U}_{S}\right)}^{2}{R}_{L}}{{\left({Z}_{12}{Z}_{21}+{\omega}^{2}{M}^{2}\right)}^{2}}$ | $\frac{{\omega}^{2}{M}^{2}{R}_{L}}{\left({Z}_{12}{Z}_{21}+{\omega}^{2}{M}^{2}\right){Z}_{21}}$ |

PP | $\frac{{\left(\omega M{U}_{S}\right)}^{2}{R}_{L}}{{\left({Z}_{12}{Z}_{22}+{\omega}^{2}{M}^{2}\right)}^{2}\left(1+j\omega {C}_{2}\right)}$ | $\frac{{\omega}^{2}{M}^{2}{R}_{L}}{\left({Z}_{12}{Z}_{22}+{\omega}^{2}{M}^{2}\right)\left(1+j\omega {C}_{2}{R}_{L}\right)}$ |

Topological Structure | Compensation Capacitor C_{1} | Compensation Capacitor C_{2} |
---|---|---|

SS | $\frac{1}{{\omega}^{2}{L}_{1}}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

SP | $\frac{{L}_{2}}{{\omega}^{2}\left({L}_{1}{L}_{2}-{M}^{2}\right)}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

PS | $\frac{{L}_{1}{R}_{L}^{2}}{{\omega}^{2}{L}_{1}^{2}{R}_{L}^{2}+{\omega}^{4}{M}^{4}}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

PP | $\frac{{L}_{1}{L}_{2}-{M}^{2}{L}_{2}^{2}}{{\omega}^{2}{\left({L}_{1}{L}_{2}-{M}^{2}\right)}^{2}+\frac{{M}^{4}{R}_{L}^{2}}{{L}_{2}^{2}}}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

Voltage Level (kV) | 110 | 220 | 330 | 500 |
---|---|---|---|---|

Single Insulator Thickness (mm) | 146 | 146 | 146 | 155 |

Number of Insulator | 7 | 13 | 17 | 25 |

Insulation Distance (m) | 1.022 | 1.898 | 2.482 | 3.878 |

Diameter of Wire (cm) | Coil Diameter (cm) | Outer Diameter of Coil (cm) | Number of Coils |
---|---|---|---|

0.2 | 20 | 32 | 20 |

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## Share and Cite

**MDPI and ACS Style**

Li, W.; Chen, Y.; Peng, Z.; Wang, X.; Xia, C. Investigation on Induced Energy Extraction from High-Voltage Transmission Lines Based on Three-Coil WPT Systems. *Energies* **2023**, *16*, 3079.
https://doi.org/10.3390/en16073079

**AMA Style**

Li W, Chen Y, Peng Z, Wang X, Xia C. Investigation on Induced Energy Extraction from High-Voltage Transmission Lines Based on Three-Coil WPT Systems. *Energies*. 2023; 16(7):3079.
https://doi.org/10.3390/en16073079

**Chicago/Turabian Style**

Li, Weilong, Yuhang Chen, Zhou Peng, Xirui Wang, and Chenyang Xia. 2023. "Investigation on Induced Energy Extraction from High-Voltage Transmission Lines Based on Three-Coil WPT Systems" *Energies* 16, no. 7: 3079.
https://doi.org/10.3390/en16073079