# Dynamic Wireless Power Transfer for Logistic Robots

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## Abstract

**:**

## 1. Introduction

## 2. Analysis and Characteristic of LCC-S DWPT

_{in}

_{(DC)}). Figure 2 shows that compensator consists of a series resonant inductor (L

_{pr}), a parallel resonant capacitor (C

_{pp}), a series capacitor in the transmitter (C

_{ps}), and a series capacitor in the receiver side (C

_{ss}). This is why it’s named as the LCC-S or LCC-C DWPT. A segmented three lumped coils can be considered as a transmitter inductor (L

_{p}) as expressed in (1). Mutual inductance (M) between the transmitter and receiver is expressed in (2), wherein k is the coupling coefficient. In this section, the analysis of the system is based on the AC analysis by means first harmonic approximation (FHA). We also have presented this analysis for a static WTP system in [19]. In this method, only the fundamental frequency is considered [10]. All of the components are assumed ideal for simplicity.

_{s}) which can be reflected to the transmitter side as Z

_{ref}as shown in (9). By doing so, the circuit can be simplified as illustrated in Figure 3b.

_{inv}) is the total current flow through C

_{pp}(I

_{Cpp}) and transmitter (I

_{p}), (10) can be modified become (11). If the switching frequency is equal to ${\omega}_{o}=1/\sqrt{{L}_{pr}{C}_{pp}}$ then (12) is valid and the impedance of the LC resonant can be eliminated. Thus, the relationship between the primary current and the AC input voltage is written in (13). It shows that the primary coil current (I

_{p}) is independent of load variation and can be maintained constant by maintaining the inverter output voltage and the switching frequency constant [20].

_{o}. The input impedance of DWPT, Z

_{in}, is expressed in (14) and the output to input voltage gain can be derived result in (15). The plots of the gain curve for various loads and mutual inductances in Figure 4 is based on the Table 1 parameters. These parameters can be selected freely depends on the desired design. However, in this paper, the selected parameters are same as the used parameters for hardware implementation. Figure 4 provides the information that the voltage gain of the DWPT system varies with the operation frequency, load, and mutual inductance. In terms of the load variation, this WPT has an independent load voltage gain at the designed frequency for a same mutual inductance. However, the variation of mutual inductance is proportional to the variation of voltage gain. Based on the presented curves, we can also see that the independent load frequency does not change with a different mutual coupling. This characteristic could be used to predict the output voltage if the system works at a fixed frequency. These curves contain information about the capacitive and inductive region which is useful to determine the Zero Voltage Switching (ZVS) and Zero Current Switching (ZCS) region. The ZVS transition frequency range is in the negative slope frequency range and ZCS transition frequency is in the range of positive slope frequency. However, the operation with switching frequency far from the independent load frequency could result in a lower efficiency due to the higher circulating current of the compensation loop.

## 3. Coils and Compensation Design

#### 3.1. Coils Design

_{Lp}) due to the DC resistance of the coil (R

_{Lp}) as expressed in (16). This resistance is related to the material, length and diameter of the wire used to build the coils. Increasing the self-inductance does not always result in the better efficiency because it could increase the DC resistance of the coil. The coils basically carry the high-frequency AC current, therefore, the skin effect is also considered and the Litz wire is used to solve this issue. In this study, the transmitter consists of three identical semi-rectangular coils and a single coil in the receiver. The important values that we have to obtain are the minimum (k

_{min}) and maximum (k

_{max}) coupling coefficients to define the nominal coupling coefficient (k

_{nom}) as expressed in (17). The minimum and maximum coupling coefficients are measured when the receiver coil is in the middle of two transmitter coils and at the center point of a transmitter coil respectively. The parameters in Table 2 are based on the 6 cm distance between transmitter and receiver which is a reasonable distance for logistic robot application.

#### 3.2. Compensation Circuit Design

_{o}), Input and output voltage, and switching frequency (f

_{sw}). In selecting the switching frequency, a designer should aware of the requirement of the industry. In case of logistic robot, a standardized frequency operation has not existed yet. Therefore, converter size, power density, efficiency and cost are the main factors that need to be considered. Once the parameters have been determined, the output current can be determined by ${I}_{o}={P}_{o}/{V}_{o}$ and secondary current calculated by ${I}_{s}={I}_{o}\pi /2\sqrt{2}$.

_{ss}or L

_{s}.

_{pop}) should be determined firstly by (19) and use the obtained value to calculate the C

_{pp}value. It should be noted, this process might need to do the iterative calculation to have a suitable capacitor value that available in the market.

_{ps}). The determined value of both C

_{ps}, and L

_{pr}, must satisfy ${f}_{sw}=1/\left(2\pi \sqrt{{L}_{pr}{C}_{pp}}\right)$. Table 3 shows the compensator that has been used in this study.

## 4. Simulation and Experimental Verifications

#### 4.1. Simulation

_{ps}). The output voltage variation for the same coupling coefficient (k) occurs because of the voltage drop due to the presence of parasitic resistance.

#### 4.2. Hardware Implementation

#### 4.3. Performance at the Maximum Coupling Coefficient

#### 4.4. Dynamic Performance

#### 4.5. Zero-Voltage Switching Transition

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The system architecture of the Dynamic Wireless Power Transfer (DWPT) (

**a**) with a single track; (

**b**) with segmented lumped coils.

**Figure 3.**AC Modeling of LCC-S WPT (

**a**) with the induced voltage and (

**b**) with the reflected impedance.

**Figure 4.**Gain curve characteristic of LCC-S compensated DWPT for various load and mutual inductance conditions.

**Figure 8.**Key-waveforms of LCC-S compensation dynamic WPT at maximum coupling coefficient with various loads. (

**a**) P

_{o}= 150 W (

**b**) P

_{o}= 1.5 kW.

**Figure 9.**The measurement of transferred power of LCC-S DWPT under the various x-axis position and y-axis misalignment.

**Figure 10.**The measurement of efficiency of LCC-S DWPT under the various x-axis position and y-axis misalignment.

Components | Units | Values |
---|---|---|

Transmitter inductance (Lp) | µH | 410.4 |

Receiver inductance (Ls) | µH | 143.9 |

Mutual inductance (M) | µH | 24.93 |

Series resonant inductor (Lpr) | µH | 60 |

Parallel primary resonant capacitor (Cpp) | nF | 29.4 |

Series primary resonant capacitor (Cps) | nF | 5 |

Series primary resonant capacitor (Css) | nF | 12.2 |

AC equivalent output resistance (RL(AC)) | Ω | 48.634 |

Parameters | Units | Values |
---|---|---|

Self-inductance of transmitter coil 1 L_{p}_{1} | µH | 137.3 |

Self-inductance of transmitter coil 2 L_{p}_{2} | µH | 143.3 |

Self-inductance of transmitter coil 3 L_{p}_{3} | µH | 141.4 |

Self-inductance of receiver coil 4 L_{s} | µH | 143.9 |

Total transmitter inductance L_{p} | µH | 410.4 |

Minimum coupling coefficient (k_{min}) | - | 0.102 |

Maximum coupling coefficient (k_{max}) | - | 0.228 |

Nominal coupling coefficient (k_{nom}) | - | 0.153 |

DC resistance/coil | mΩ | 50 |

Number of turn/coil | - | 22 |

Ferrite bar size | mm | 14 × 5 × 120 |

Component | Unit | Value | ESR |
---|---|---|---|

Primary Series Resonant Inductor (L_{p}) | µH | 60 | 6 mΩ |

Primary Series Resonant Capacitor (C_{ps}) | nF | 5 | 15 mΩ |

Primary Parallel Resonant Capacitor (C_{pp}) | nF | 29.4 | 19 mΩ |

Secondary Series Resonant Capacitor (C_{ss}) | nF | 12.2 | 9.7 mΩ |

Designed Switching Frequency (f_{sw}) | kHz | 120 |

k | Power (W) | V_{o} (V) | V_{C}_{2,max} (kV) | I_{p,}_{rms} (A) | η (%) |
---|---|---|---|---|---|

0.1026 | 150 | 165.5 | 2.99 | 8.08 | 59.7 |

1500 | 151.15 | 2.98 | 8.1 | 87.29 | |

0.153 | 150 | 251.8 | 2.99 | 8.1 | 56.4 |

1500 | 243.2 | 2.98 | 8 | 92.2 | |

0.228 | 150 | 393 | 2.99 | 8.05 | 48.1 |

1500 | 367.2 | 2.99 | 8.06 | 92.6 |

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## Share and Cite

**MDPI and ACS Style**

Tampubolon, M.; Pamungkas, L.; Chiu, H.-J.; Liu, Y.-C.; Hsieh, Y.-C.
Dynamic Wireless Power Transfer for Logistic Robots. *Energies* **2018**, *11*, 527.
https://doi.org/10.3390/en11030527

**AMA Style**

Tampubolon M, Pamungkas L, Chiu H-J, Liu Y-C, Hsieh Y-C.
Dynamic Wireless Power Transfer for Logistic Robots. *Energies*. 2018; 11(3):527.
https://doi.org/10.3390/en11030527

**Chicago/Turabian Style**

Tampubolon, Marojahan, Laskar Pamungkas, Huang-Jen Chiu, Yu-Chen Liu, and Yao-Ching Hsieh.
2018. "Dynamic Wireless Power Transfer for Logistic Robots" *Energies* 11, no. 3: 527.
https://doi.org/10.3390/en11030527