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The range of the power transmission region can be effectively enlarged by a multiple-transmitter (TXs) and single-receiver (RX) magnetic wireless power transfer (WPT) system. However, the power transfer efficiency (PTE) of the WPT system with two TXs and a single RX has been intensively studied in the past few years. Therefore, a deep analysis of multiple-TX WPT systems needs to be implemented urgently to achieve the highest PTE in a wider range of power transmission. This paper analyzes a general multiple-TX single-RX system in detail based on the circuit model. Two optimal conditions, in which the feeding amplitude ratios need be equal to the mutual inductance ratios and the optimal load should be connected to RX, are derived to obtain the highest PTE. In the experiment part, the feeding amplitude ratios for multiple TXs are implemented by a proposed lumped transformer for the first time. The use of the lumped transformer reduces the complexity compared with the use of multiple inverters to achieve predetermined feeding amplitude ratios. Multiple-TX systems are designed and measured to validate the theoretical analysis. Experimental results agree very well with theoretical calculations.

The research of magnetic-resonance coupling is particularly prized in the areas of wireless power transfer (WPT) since this research was published in the US journal Science in 2007 [

In [

In this paper, the PTE of a multiple-TX WPT system is investigated. The analytical expression of PTE is derived. We observe that the relationship between the amplitude in each TX and the mutual inductance between the RX and any TX crucially determines the highest PTE. Based on the analysis, two experimental schemes of efficiencies versus the number of TXs and power transfer distance are implemented later in this paper.

The operating wavelengths are considerably larger than the sizes of power coils and the transmission distance. Thus, circuit theory can be used to analyze the model of the WPT system. Figure

Circuit model of a multiple-TX single-RX WPT system.

Based on Kirchhoff’s voltage law (KVL), at operating frequency

Mesh currents

Solving (

Substituting (

Solving simultaneous equations of (

The PTE for the system is

It can be found from (

Under condition of (

From (

We set

Forms of expression in (

In order to illustrate the analyses in part II, we use MATLAB software to perform the numerical calculations. An important target of using such multiple-TX WPT techniques is to improve the energy efficiency of the system. Thus, in the designed system, multiple small TXs with the same size and a large RX are considered, which is used for decreasing the coupling between TXs to satisfy the theoretical presuppositions. To facilitate comparison discussion for the multiple-TX WPT system, coils of TXs are placed side to side with a coil of RX in this part for numerical calculations and experiments. The center of the study area,

The RX moving within the circle of the study area for optimal PTE investigation.

The radii of RX and the study area are

Spatial layout for a multiple-TX single-RX system: (a) two TX, (b) three TX, and (c) four TX.

Dimensions of system structure.

Dimension | Value |
---|---|

1 m | |

5.5 cm | |

15.75 cm | |

29 cm | |

36.9 cm | |

49.5 cm | |

Turn number of |
25 |

Turn number of |
11 |

High of |
3.4 cm |

High of |
1.5 cm |

The general calculation method of mutual inductance between each TX and RX has been presented in the former works of our team [

Figure

Calculated values of a two-TX system when RX is moving in the study area. Efficiency distribution in the study area (a) without optimization, (b) under conditions of

Loading with

Calculated values of a three-TX system when RX is moving in the study area. Efficiency distribution in the study area (a) without optimization, (b) under conditions of

Calculated values of a four-TX system when RX is moving in the study area. Efficiency distribution in the study area (a) without optimization, (b) under conditions of

In the condition of

From the investigations of the optimal PTE in Figures

The maximum values of optimal PTE in the three kinds of multiple-TX systems are the same result of 0.791 and always appear at the closest position to the TXs. Similarly, the optimal load values for the maximum PTE are also the same. These are due to the distance between TXs

Two parameters of PTE and power delivered to the load (PDL) are the main criterions to evaluate the performance of a WPT system. The high PTE means a low system loss; however, if feeding power is largely limited under optimal PTE conditions, the PDL of this system would be very low. Here, we present the PDL of a multiple-TX system under the optimal PTE conditions. The specific values of PDL can be calculated with specific values of feeding voltage. Therefore, setting up reference values of

The voltage values of

The values of PDL under conditions of maximizing PTE: (a) two-, (b) three-, and (c) four-TX systems.

According to the theoretical analysis presenting in Section

Experimental investigation of

Figure

To further confirm the conclusion obtained from analysis, two TXs and one RX are arranged face to face to construct a complete system, and the distance between the two TXs is fixed at 0.6 m. Using the dual channel function generator shown in Figure

Efficiencies versus transfer distance when two TXs and a single RX are arranged face to face to construct a complete system: (a) mutual inductance ratio and optimal load for the highest efficiency; (b) calculated and measured efficiency values under different conditions.

In this section, we also present the PTE characteristics of a one-TX and one-RX system. The values of PTE of a one-TX system with an optimal load and a fixed load of

In this paper, the procedures of efficiencies for a multiple-TX WPT system are analyzed in details based on the circuit model. There are two steps to obtain the highest efficiency via the theoretical analysis. Firstly, the feeding voltage ratio should be set to the mutual inductance ratio to achieve a higher PTE. Then the optimal load needs be attached to the RX to obtain the highest efficiency. The expressions for the highest efficiency and optimal loads for any multiple-TX system can be unified to the same form. Numerical results of two-, three-, and four-TX systems are further illustrated to compare the optimal and nonoptimized efficiencies. Experiments for a two-TX system are carried out to verify the numerical analysis when transmission distance is changed. Theoretical and experimental results indicate that the optimal efficiency increases along with the number of TXs mounting up.

In terms of two optimal conditions for the highest efficiency, the expressions of the conditions are simple but universal, which provide a guideline for the optimal design of a multiple-TX WPT system.

The proposed multiple-TX system is easy to fit on the surrounding environment (such as four TXs embedded in the four corners of a table and one RX positioned on any point of the table) to achieve a large effective charging area.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research work was supported in part by the Scientific Research Foundation for the High-Level Talents of Jinling Institute of Technology (jit-b-201719), the National Natural Science Foundation of China (61601245), and the Nanjing University of Posts and Telecommunications Foundation of China (Grant no. NY 214050).