# Research on Load and Mutual Inductance Identification Method of WPT System Based on a LCC-S Type Compensation Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory Analysis of Parameter Identification

#### 2.1. Mathematial Model

_{dc}is the input DC voltage source, which provides power for the whole system. After the high-frequency inverter circuit composed of MOSFET V

_{1}~V

_{4}, it outputs the approximate square wave voltage u

_{in}. Then it passes through the primary LCC resonant topology composed of L

_{0}, C

_{0}, L

_{1}and C

_{1}, and transfers the energy to the secondary LC resonant topology by the coupling between L

_{1}and L

_{2}. Finally, after the rectifier bridge and C, it supplies power to the load R

_{L}. In the system, M is the mutual inductance between the coupling coils L

_{1}and L

_{2}. R

_{1}and R

_{2}are respectively the series equivalent resistances of coils L

_{1}and L

_{2}.

_{in}, the output current i

_{0}(t), the secondary-side circuit impedance Z

_{s}, and the equivalent load R

_{eq}of the rectifier circuit and load R

_{L}are

_{0}of the system is generally made to be similar to the inherent resonant frequency ω of the initial stage side circuit. Therefore, the relationship between t each capacitance and inductance in Figure 1 is

_{11}, A

_{12}, A

_{21}, and A

_{22}are the two-port A-parameters.

_{eq}. It makes it possible to find the value of the other parameter by the formula when one of the parameters is known, which means that the mutual inductance is identified by the mutual inductance identification below, and the load parameters can be identified by substituting the formula.

#### 2.2. Mathematial Model Verification

_{0}is system model and i

_{0′}is identification model). The simulation parameters in the paper are set according to the actual measured values in the experimental system, as shown in Table 1.

## 3. Simulation of Parameter Identification

#### 3.1. Simulation Theory

_{f}and i

_{f}

^{′}of the two models are measured separately, and the errors are obtained after the root mean square operation. When the error between the recognition model and the system model reaches the minimum value, it can be concluded that the two models have reached the best fit, and then the final value of mutual sense recognition can be obtained.

- Set the initial population size to 100, iterate 50 times, and take the value of mutual inductance in the range of [0, 100 μH].
- Collect the actual system primary-side output current i
_{f}. - Calculate the fitness value of each particle, the fitness function in this paper is selected as the error between the output current i
_{f}of the primary side of the system model and the current i_{f}^{′}of the discriminative model.

_{f}(t

_{0}) and i

_{f}(t

_{0}+ T) separated by one cycle as the comparison objects after the system is running stably.

- 4.
- Compare the fitness value e (i) of each particle with the individual extreme value pbest (i). If e (i) < pbest (i), replace e (i) with pbest (i). Similarly obtain the global extreme value gbest for the whole population.
- 5.
- Update the velocity and position of the particles and perform boundary condition processing.

- 6.
- Determine whether the number of iterations is reached. If yes, the algorithm ends and outputs the optimization results; otherwise, it returns to step 3. and continues the optimization search until the identification of mutual inductance parameters is completed. Finally, the load parameters can be calculated by Equation (15) to complete the system mutual inductance and load identification.

#### 3.2. Simulation Results Analysis

## 4. Experimental Verification

_{r}and M

_{i}are respectively the measured and identified values of mutual inductance.

## 5. Conclusions

- Based on the equivalent circuit of WPT system, the identification model is established using two-port theorem and fundamental wave analysis method to obtain the relationship between inverter output current and load and between mutual inductance and load.
- The Simulink platform is used to compare the established state-space equations as the identification model with the actual model, and the accuracy of the proposed model is proved. The particle swarm optimization algorithm is introduced to transform the parameter identification problem of the transmission system into an optimization problem, which completes the identification of parameters and makes the identification results more accurate.
- The corresponding simulation models are built using MATLAB/Simulink. The simulation results show that the maximum error between the identified and actual values of mutual inductance and load is respectively 1.66% and 1.39%. The system experimental platform is also built. The experimental results show that the errors between the identified and actual values of load and mutual inductance do not exceed 5%, which verifies the effectiveness and reliability of the method.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Huang, X.; Wang, W.; Tan, L. Technical Progress and Application Development of Magnetic Coupling Resonant Wireless Power Transfer. Power Syst. Autom.
**2017**, 41, 2–14, 141. [Google Scholar] - Bo, Z.; Xujian, S.; Lihao, W.; Chao, R. Problems and countermeasures of radio energy transmission technology. Autom. Electr. Power Syst.
**2019**, 43, 1–12. [Google Scholar] - Huang, C.; Lu, Y. Frequency Tracking Detuning Control of Magnetic Resonant Wireless Power Transfer System. Electr. Eng. Mag.
**2019**, 34, 3102–3111. [Google Scholar] - Yang, Q.; Zhang, P.; Zhu, L.; Xue, M.; Zhang, X.; Li, Y. Key Fundamental Problems and Technical Bottlenecks of the Wireless Power Transmission Technology. Electr. Eng. Mag.
**2015**, 30, 1–8. [Google Scholar] - Lin, D.; Yin, J.; Hui, S.Y. Parameter identification of wireless power transfer systems using input voltage and current. In Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition, Pittsburgh, PA, USA, 14–18 September 2014. [Google Scholar]
- Dai, X.; Sun, Y.; Tang, C.; Wang, Z.; Su, Y.; Li, Y. Dynamic Parameters Identification Method for Inductively Coupled Power Transfer System. In Proceedings of the 2010 IEEE International Conference on Sustainable Energy Technologies, Kandy, Sri Lanka, 6–9 December 2010. [Google Scholar]
- Zhou, S. Research on Energy Modeling and Application for Wireless Power Transfer System. Ph.D. Thesis, Chongqing University, Chongqing, China, 2012. [Google Scholar]
- Su, Y.; Zhang, H.; Wang, Z. Steady State Load Identification Method of Inductive Power Transfer System Based on Switching Capacitors. IEEE Trans. Power Electron.
**2015**, 30, 6349–6355. [Google Scholar] [CrossRef] - Su, Y.; Chen, L.; Wu, X.; Qing, X. Load and Mutual Inductance Identification Method of SS-Type Magnetically-Coupled WPT System Based om Genetic Algorithm. Electr. Eng. Mag.
**2018**, 33, 4199–4206. [Google Scholar] - Su, Y.-G.; Chen, L.; Wu, X.; Hu, A.P.; Tang, C.-S.; Dai, X.; Hu, P. Load and Mutual Inductance Identification from the Primary Side of Inductive Power Transfer System With Parallel-Tuned Secondary Power Pickup. IEEE Trans. Power Electron.
**2018**, 33, 9952–9962. [Google Scholar] [CrossRef] - Yin, J.; Lin, D.; Thomas, P.; Hui, S.Y. Front-end monitoring of the mutual inductance and load resistance in a series-series compensated wireless power transfer system. IEEE Trans. Power Electron.
**2016**, 31, 7339–7352. [Google Scholar] [CrossRef] - Song, P. Research on Control Strategy for Parameter Identification and Disturbance Rejection Technology of Wireless Power Transfer. Master’s Thesis, Shanghai University of Electric Power, Shanghai, China, 2018. [Google Scholar]
- Xiang, Y. Research on Parameter Identification and Control Simulation of Inductively Coupled Power Transfer System. Master’s Thesis, Hunan University, Changsha, China, 2016. [Google Scholar]
- Chow, J.; Henry, S.; Cheng, C. Use of transmitter-side electrical information to estimate mutual inductance and regulate receiver side power in wireless inductive link. IEEE Trans. Power Electron.
**2016**, 31, 6079–6091. [Google Scholar] [CrossRef] - Zhang, W.; Qin, W.; Song, J.; Lin, L.; Bi, L. Development of constant current and constant voltage wireless charging system with mutual inductance identification function in primary side. Electr. Eng. Mag.
**2021**, 25, 52–60. [Google Scholar] - Liu, J.; Wang, G.; Xu, G.; Peng, J.; Jiang, H. A Parameter Identification Approach with Primary-Side Measurement for DC-DC Wireless-Power-Transfer Converters with Different Resonant Tank Topologies. IEEE Trans. Transp. Electrif.
**2021**, 7, 1219–1235. [Google Scholar] [CrossRef] - Sheng, X.; Shi, L. Mutual Inductance and Load Identification Method for Inductively Coupled Power Transfer System Based on Auxiliary Inverter. IEEE Trans. Veh. Technol.
**2020**, 69, 1533–1541. [Google Scholar] [CrossRef] - Xue, M.; Ma, S. Identification method WPT system load and mutual inductance based on SS-type compensation network. China Sci.
**2020**, 15, 1277–1282. [Google Scholar] - Su, Y.; Yang, J. TensorFlow Neural Network Based Load and Mutual Inductance Identification Method for Magnetic Coupling Resonant Wireless Power Transfer System. Autom. Electr. Power Syst.
**2021**, 45, 162–169. [Google Scholar]

**Figure 3.**Waveforms of i0 and i0′ at each conduction angle of the input voltage. (

**a**) Voltage conduction angle 90°; (

**b**) Voltage conduction angle 120°; (

**c**) Voltage conduction angle 180°.

**Figure 9.**Waveforms of u1 and u2 under different offset distances. (

**a**) s = 0 cm; (

**b**) s = 5 cm; (

**c**) s = 10 cm; (

**d**) s = 15 cm.

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

Primary/secondary-side coil internal resistance R_{1,2} | 0.13/0.13 Ω |

Primary-side coil inductance L_{1} | 108.47 µH |

Secondary-side coil inductance L_{2} | 108 µH |

Primaryside compensation capacitor C_{1} | 114 nF |

Secondary-side compensation capacitor C_{2} | 93.8 nF |

Resonance frequency f | 50 kHz |

Operating frequency f_{0} | 50 kHz |

Compensation of resonant coil inductance L_{0} | 20 µH |

Primary-side shunt compensation capacitor C_{0} | 507 nF |

Compensation of resonant coil internal resistance R_{0} | 0.1 Ω |

Load Resistance (Ω) | Mutual Inductance M (μH) | Relative Error (%) |
---|---|---|

15 | 30.12 | 0.99 |

20 | 30.42 | 0.23 |

25 | 30.66 | 0.78 |

30 | 30.97 | 1.8 |

35 | 31.06 | 2.1 |

Lateral offset Distance s (cm) | Mutual Inductance M (μH) | Load Resistance R_{L} (Ω) |
---|---|---|

10 | 19.13 | 15 |

5 | 26.76 | 15 |

15 | 11.36 | 20 |

10 | 19.13 | 20 |

5 | 26.76 | 25 |

0 | 30.49 | 25 |

10 | 19.13 | 30 |

15 | 26.76 | 30 |

Lateral Offset Distance s (cm) | Real Measurement of Mutual Inductance M_{r} (µH) | Identify Mutual Inductance M_{i} (µH) | Identify Load R_{L} (Ω) |
---|---|---|---|

0 | 30.4951 | 29.3668 | 29.93 |

5 | 26.7625 | 25.6652 | 28.85 |

10 | 19.1275 | 18.4007 | 28.99 |

15 | 11.2875 | 10.7457 | 29.36 |

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**MDPI and ACS Style**

Xue, M.; Lu, K.; Zhu, L.
Research on Load and Mutual Inductance Identification Method of WPT System Based on a LCC-S Type Compensation Network. *World Electr. Veh. J.* **2021**, *12*, 197.
https://doi.org/10.3390/wevj12040197

**AMA Style**

Xue M, Lu K, Zhu L.
Research on Load and Mutual Inductance Identification Method of WPT System Based on a LCC-S Type Compensation Network. *World Electric Vehicle Journal*. 2021; 12(4):197.
https://doi.org/10.3390/wevj12040197

**Chicago/Turabian Style**

Xue, Ming, Keyan Lu, and Lihua Zhu.
2021. "Research on Load and Mutual Inductance Identification Method of WPT System Based on a LCC-S Type Compensation Network" *World Electric Vehicle Journal* 12, no. 4: 197.
https://doi.org/10.3390/wevj12040197