# Design of LCC-P Constant Current Topology Parameters for AUV Wireless Power Transfer

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Circuit Analysis

_{1}–S

_{4}are four power MOSFETs of the inverter and D

_{1}–D

_{4}are the rectifier diodes, V

_{dc1}and V

_{in}represent the DC input voltage and inverter output voltage, L

_{f}, C

_{f}, are the compensation inductance and capacitance, L

_{p}, L

_{S}, are the self-inductances of the transmitter and the receiver of the magnetic coupler, M is the mutual inductance, C

_{p}and C

_{S}are the compensation capacitance on the transmitting side and the receiving side, respectively. V

_{dc2}represents the DC output voltage on the load.

_{CC}, the reverse-L circuit and the π circuit should satisfy:

_{ref}is the reflected impedance at the receiving side, which can be expressed as:

_{inCC}) = 0, which can be calculated as

_{CC}. Due to the water flow and low positioning accuracy of the underwater WPT system, the transmitter and the receiver of the magnetic coupler are vulnerable to misalignment, resulting in large fluctuations in mutual inductance [19]. It can be found from (1) and (2) that the CC output characteristics of the system are decoupled with the mutual inductance, i.e., the CC output characteristics are not affected by the misalignment of the AUV in the seawater condition, which is conducive to the stable power supply of the AUV wireless charging system.

## 3. Parameter Optimization

#### 3.1. Eddy Current Loss Analysis

_{eddy}can be divided into the sum of the eddy current loss P

_{eddy_p}generated by the transmitting coil and the eddy current loss P

_{eddy_S}generated by the receiving coil.

#### 3.2. Objective Function Construction

**I**

_{in},

**I**

_{p},

**I**

_{S},

**I**

_{eq}are the currents of the corresponding meshes, and the non-source components in the circuit are expressed in impedance form as Z

_{Li}= jωL

_{i}(i = f, p, s); Z

_{Ci}= 1/jωC

_{i}(i = f, p, s), and define Z

_{M}= jωM, the resonant operating frequency of the system ω

_{0}= ω

_{CC}. Based on Kirchhoff’s law, the equations of the equivalent circuit can be obtained:

**I**=

**V**, which the current vector

**I**can be solved, and then the transmission efficiency can be expressed as:

_{eq}in the CC mode is (R

_{min}, R

_{max}), in order to ensure that the system has excellent charging efficiency in the CC mode, an objective function with the optimal efficiency is established to measure the level of charging efficiency throughout the charging phase.

_{sea}of the efficiency corresponding to the R

_{eq}in the load interval (R

_{min}, R

_{max}), and establish the nonlinear programming model with the optimal efficiency as follows:

_{1}, ω

_{2}) is the frequency sweep range, (L

_{f1}, L

_{f2}) is the compensation inductance sweep range. In order to ensure that the output current meets the requirements, the constant current system also needs to constrain the transconductance G

_{V}of the system. Set the lower limit of the transconductance to meet the output requirements is G

_{Vmin}, and integrate the inequality conditions into the objective function is:

#### 3.3. Function Solving

_{W}of the genetic algorithm is to be established and consider the constraints to establish a penalty function W as:

_{i}is the weight coefficient of each constraint, and w

_{i}is the penalty factor, as shown below:

_{W}= F; when an inequality constraint cannot be satisfied, the corresponding penalty amount W>0 will be generated, and the larger the out-of-bounds amount, the greater the value of the penalty amount, at this time, F

_{W}= F/W. The fitness of the individual will be reduced, so that the probability of being selected as the parent for breeding the next generation in the iterative process of the genetic algorithm will be extremely low, which means that the parameters of the non-optimal solution of efficiency will be discarded until the efficiency is optimal. The optimal solution can be obtained by using the rand function of MATLAB to generate the initial population {(ω

_{i}, L

_{fi}) I = 1, 2… 200} and the fmincon function for nonlinear optimization. The process of the genetic algorithm is shown in Figure 6.

#### 3.4. Algorithm Validation

_{p}, L

_{S}and M of the H-shaped magnetic coupler proposed in [17] are fixed. Therefore, it is only necessary to add the coil inductance constraints to the genetic algorithm, which will not affect the correctness of the parameter optimization proposed in this paper.

_{0}and compensation inductance L

_{f}of the WPT system obtained are 96.15 kHz and 9 μH, respectively. By substituting the optimized results into the CC output conditions of the LCC-P topology, the other parameters of the system can be calculated and values are shown in Table 2.

## 4. Experiments

#### 4.1. Seawater Effects

_{dc1}, I

_{dc1}and P

_{1}represent the system input voltage, current, power, respectively, U

_{dc2}, I

_{dc2}and P

_{2}represent the system output voltage, current, power, respectively, η

_{1}and η

_{2}represent the DC-DC efficiency in air condition and seawater condition, respectively.

#### 4.2. Analysis of System Output Characteristics

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Simulated the eddy current loss caused by different excitation currents. (

**a**) Generated the eddy current loss in seawater by the transmitting coil; (

**b**) Generated the eddy current loss in seawater by the receiving coil.

**Figure 7.**Frequency characteristics of IPT system under different loads. (

**a**) Input impedance angle variation with frequency; (

**b**) G

_{V}variation with frequency.

**Figure 10.**Eddy current loss variation in seawater condition. (

**a**) With V

_{dc1}; (

**b**) With load resistance R

_{L}.

Media | Relative Permittivity | Conductivity (S/m) | Relative Permeability |
---|---|---|---|

air | 1.0006 | 0 | 1.000004 |

freshwater | 81 | 0.01 | 0.999991 |

seawater | 81 | 4 | 0.999991 |

Parameter | Symbol | Value |
---|---|---|

Transconductance | G_{V} | 0.067 |

Resistance range | R_{L} | 10–20 Ω |

Resonant frequency | f_{0} | 96.15 kHz |

Transmitter inductance | L_{p} | 49.84 μH |

Transmitter-side series compensation capacitance | C_{p} | 88.23 nF |

Receiver inductance | L_{S} | 26.28 μH |

Receiver-side parallel compensation capacitance | C_{S} | 104.18 nF |

Compensation inductance | L_{f} | 9 μH |

Transmitter-side parallel compensation capacitance | C_{f} | 304.44 nF |

Note | Symbol | Value (Air) | Value (Seawater) |
---|---|---|---|

Resonant frequency | f_{0} | 96.15 kHz | 96.15 kHz |

DC input voltage | V_{dc1} | 100 V | 100 V |

Transmitter inductance | L_{p} | 49.84 μH | 49.26 μH |

Transmitter resistance | R_{p} | 90 mΩ | 120 mΩ |

Transmitter-side series compensation capacitance | C_{p} | 88.23 nF | 88.23 nF |

Receiver inductance | L_{S} | 26.28 μH | 26.39μH |

Receiver resistance | R_{S} | 35 mΩ | 43 mΩ |

Receiver-side parallel compensation capacitance | C_{S} | 104.18 nF | 104.18 nF |

Compensation inductance | L_{f} | 9 μH | 9μH |

Transmitter-side parallel compensation capacitance | C_{f} | 304.44 nF | 304.44 nF |

Coupling coefficient | k | 0.438 | 0.443 |

Resistance range | R_{L} | 10–20 Ω | 10–20 Ω |

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**MDPI and ACS Style**

Qiao, K.; Rong, E.; Sun, P.; Zhang, X.; Sun, J.
Design of LCC-P Constant Current Topology Parameters for AUV Wireless Power Transfer. *Energies* **2022**, *15*, 5249.
https://doi.org/10.3390/en15145249

**AMA Style**

Qiao K, Rong E, Sun P, Zhang X, Sun J.
Design of LCC-P Constant Current Topology Parameters for AUV Wireless Power Transfer. *Energies*. 2022; 15(14):5249.
https://doi.org/10.3390/en15145249

**Chicago/Turabian Style**

Qiao, Kangheng, Enguo Rong, Pan Sun, Xiaochen Zhang, and Jun Sun.
2022. "Design of LCC-P Constant Current Topology Parameters for AUV Wireless Power Transfer" *Energies* 15, no. 14: 5249.
https://doi.org/10.3390/en15145249