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As a new wireless energy transmission technology, magnetically coupled resonant wireless energy transmission system (MCRETS) is not easily affected by obstacles in the transmission process, and the transmission distance is relatively far. However, how to balance the relationship between transmission efficiency and power to achieve optimal performance is still a huge challenge. In addition, few studies have theoretically investigated the factors affecting the wireless energy transmission system to obtain an optimal solution. Here, through unprecedented theoretical analysis, we find the exact parameters of system optimization and verify them by simulation and experiments. First, the optimal topology of MCRETS is obtained through theoretical analysis and comparison of topologies. Second, to improve the transmission performance of MCRETS, its impact factors, including transmission distance, resonant frequency, relay coil, and relative position of launch and receiving coils, are analyzed in detail to get accurate parameters. Furthermore, based on the analysis, we propose an unprecedented concept for balancing optimal efficiency and power, which is named the power product. Finally, the effectiveness of the proposed method is verified through analysis and experimental results. These findings shed light on the relationship between efficiency and power and provide a comprehensive theoretical basis for subsequent research.

With the increase in the number of traditional receiving terminals of cable power supply, the drawbacks, such as socket exposure, plugs prone to sparks, and other issues, become increasingly evident. To solve these problems, wireless power transfer (WPT) is utilized and it achieves wireless transmission through mutual coupling among physical fields. This technology has improved both equipment safety and functionality and has currently gained attention in the field of electrical research [

Researchers have made numerous breakthroughs in the study on MCRETS [

To address the above issues, a complete modeling and analysis of the wireless energy transmission system based on the transmission efficiency and power is conducted in this study. The basic structure, working principles of the wireless energy transmission system, and topology are analyzed and compared. The four impact factors of transmission performance (i.e., transmission distance, system resonance frequency, relay structure, and relative position of transmitting and receiving coils) are theoretically analyzed to derive the degree of influence of each factor. Although the size and shape of the coil have an impact on the transmission performance, the nature of such effects is the coil’s own parameter settings, such as resistance, which have little effect on practical applications. Therefore, the research factors in this paper set the transmission distance, the resonant frequency, and the relative position of the transmitting and receiving coils. The main reason is that the influence of these factors is more common in practical applications. The validity of the theoretical analysis is experimentally verified. This study also creatively presents the power product parameters, which are theoretically analyzed to obtain a conductive transmission state and optimize the transmission power and transmission efficiency. This analysis can provide theories and solutions for the design and optimization of MCRETSs. The main contributions of this paper are summarized as follows:

We present the complete modeling and analysis of the wireless energy transmission system based on the transmission efficiency and transmission power of two transmission indicators, analysis of its basic structure and working principle, and analysis and comparison for the optimal topology.

The influencing factors of this paper are different from the traditional methods and previous studies. Firstly, we get the exact effect of the four influencing factors from the theoretical deduction and then verify the correctness of the theoretical deduction through experiments. In addition, we get the theoretical value of the turning point, which has a certain significance for optimizing practical problems.

Comparing the factors that affect this system performance listed before, considering the problem that power and efficiency optimization cannot be both concerned in practical applications, this paper presents a novel method of optimal selection, named as power product and elaborates its derivation principle and experimental process in detail.

The theoretical analysis is verified through an experiment, and power product parameters are proposed to reach an optimal transmission power and efficiency of the system, with theoretical analysis.

The remainder of this paper is as follows: Section

In a vibrating system, strong coupling states often exist among several parts with the same intrinsic frequency [

The core structure of MCRETS comprises two or more designed resonant coils: a matching module for supplying high-frequency energy that is equal to the intrinsic frequency of the resonant coil and supporting modules that receive high-frequency energy and change in the form of energy required. Figure

Block diagram of a medium-distance MCRETS.

MCRETS has an external capacitor resonant compensation for each loop. External capacitors can be divided into series and parallel compensations by the capacitive access circuit. The compensation structure is discussed separately for the primary and secondary circuits. Resonant compensation structures can be divided into series-series (SS), series-parallel (SP), parallel-series (PS), and parallel-parallel (PP) [

Four basic resonant compensation structure circuits: (a) SS mode; (b) SP mode; (c) PS mode; (d) PP mode.

In Figure

If the frequency of the transmission system is

When the resonant compensation circuit is a series structure, impedance ZPS is purely resistant to the resonant frequency, whereas the two coexist in a parallel structure. When the system has a SS compensation structure, the external resonant capacitor is unaffected by the impedance of the secondary loop, the transmission distance, or load characteristics, and the resonant frequency does not affect the choice of the resonant capacitor, so the system design optimization is more convenient. Thus, the topology of the external resonant capacitance has a SS structure.

In traditional methods, most of the previous studies are directly through simulation to get the optimal parameters of each influencing factor, so only the optimal parameters range can be obtained. This paper is different from traditional methods. Firstly, starting with the theoretical model, the exact value of the optimal parameters is deduced by formula, and then the deduced results are verified by simulation and experiment. In this way, we can find the essence of each factor and provide a theoretical basis for future research.

In this chapter, we theoretically analyze the influence factors of transmission performance (transmission distance, system resonance frequency, relay structure, relative position of transmitting, and receiving coils) and get the influence of each factor.

The results and discussion may be presented separately, or in one combined section, and may optionally be divided into headed subsections. The transmission efficiency of MCRETS is defined as the ratio of the power at the load side to the power transmitted by the transmitter. The transmission performance of MCRETS is susceptible to the four factors, namely, transmission distance, resonant frequency, relay coil, and relative position of transmitting and receiving coils. According to the mechanism of magnetic coupling of resonant wireless energy transmission, resonant frequency is proportional to and can directly affect the transmission distance. In principle, the energy efficiency of short-range applications can be quite high, but it will drop rapidly as the transmission distance increases [

Equivalent circuit diagram of the transmitting and receiving circuits.

The equivalent impedance of the transmitting and receiving circuits is

Then,

ZP and ZS are incorporated into (

When

Coil resistance can be equivalent to

Equation (

The output power and transmission efficiency of the load can be expressed as follows:

When resonant frequency

From (

The extreme distance can be derived from (

Then,

Furthermore, when

Similarly, the relationship between mutual inductance and transmission efficiency can be obtained from mutual inductance

The resonant frequency of MCRETS is the driving signal frequency. When the driving signal frequency and the natural frequency of the transmitting and receiving coils are consistent, the system can reach a resonant state. When the output power in (

Based on the above analysis, when

The resonant frequency is derived from the transmission efficiency, that is,

In (

The four-coil structure of MCRETS can achieve energy in a medium-distance transmission. When the distance of wireless energy transmission exceeds the critical coupling distance and into the under-coupled area, the transmission performance of the system will decline. However, adding a relay coil between the transmitting and receiving coils will improve the transmission performance of the system. The diagram of a five-coil wireless energy transmission system is shown in Figure

Schematic of the five-coil wireless energy transmission system.

In this structure, the relay coil is equivalent to the circuit, and the resonant capacitor is serially connected with the circuit. The equivalent circuit of the five-coil wireless energy transmission system is shown in Figure

Equivalent circuit model for a five-coil wireless energy transfer system.

The relay and transmitting coils are near with each other; thus, they can be regarded as a transmitting source with a relay coil. The relay coil itself has a high-quality factor, which can increase the resonant current and enhance the magnetic field effect. This condition allows the relay and receiving coils in the long-distance coupling resonance to increase the transmission distance and enhance the transmission effect.

Nondirectional propagation is a distinguishable feature of magnetically coupled resonance that sets it apart from the electromagnetic induction. In the electromagnetic induction coupling, a slight rotation and translation of the coil significantly induces energy loss in the receiving coil. However, when transmission is performed through MCRETS, the transmission and rotation of the coil within a certain transmission range will have a relatively small transmission loss. When the relative position of the transceiver coil goes beyond the range of the changing position, the rotation of the receiving coil has a considerable effect on the output power.

In this paper, the launch coil and receiving coil are simulated by ANSYS 10.0 software. Because of the different analysis objects and different analysis methods, the nodal method of SOLID97 unit type is adopted in the analysis of the ray coil, which has the characteristics of simplicity, rapidity, and effectiveness. The simulation calculation of adding iron core between the launch coil and the receiving coil by using the edge method of the SOLID117 unit type can be simpler and more accurate.

Taking SOLID97 as an example, we set the degrees of freedom as AX, AY, and AZ. Then, the three-dimensional model of the cylindrical coil and the air can be built. Because the magnetic induction intensity produced by the coil model is relatively symmetrical, in order to save calculation time, the copper wire is chosen as the current-carrying winding coil, whose resistivity is

Cylindrical coil model.

For the following simulation, the following assumptions and conventions are made: approximate material isotropy; the influence of temperature change is not considered for the time being; the air region is considered as infinite; when iron core is added to the simulation, the B-H curve of iron core is approximately considered linear; when iron core is added to the simulation, the effect of eddy current demagnetization is not considered for the time being.

For the ANSYS analysis model, network partitioning is particularly important. The accuracy and speed of solution are greatly affected by the density of network partitioning. In this paper, the coil and air dimensions of the model are quite different, so it cannot be divided in one time. The size of coil/iron core and air setting unit need to be separately divided freely. Considering the requirement of solving accuracy and solving time, the coil region needs to be partitioned in detail, while the air region follows the partitioning rule from inner to outer meshes to dense to sparse meshes. Figure

Grid of coils.

Overall grid with air.

The coil in simulation is a planar spiral coil. In order to effectively limit the number of subdivision units in FEM simulation, it is necessary to simplify the coil shape in modeling. Simplifying the coil shape will not affect the magnetic field distribution in the transmission channel too much. In the simulation software, the model is shown in Figure

Coil 3D model drawn in Maxwell.

During the simulation, Maxwell and Simplorer are used to simulate the magnetic field distribution. The result of magnetic field distribution is shown in Figure

The maximum value of the magnetic field of the transmitting coil in transient field simulation.

Transient field simulation receiver coil maximum magnetic field.

Because of the similarity of the design simulation experiment process, this paper takes the above process as an example. By resetting the parameters of the simulation process, including transmission distance, system resonance frequency, relay structure, and relative position of transmitting and receiving coils, we can get multiple sets of simulation data through repeated simulation. In the next chapter, these simulated data will be used to compare and discuss with experimental data.

The corresponding experimental physical device is built based on the working principle of MCRETS. The theoretical analysis results of the transmission performance of the wireless energy transmission system can be verified experimentally through this device, which is shown in Figure

Physical diagram of MCRETS.

Experimental equipment-related parameter.

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

Device input voltage | 220 V AC/50 Hz |

Maximum device input | 1600 W, 220 V AC/8 A |

Maximum output power of the device | 400 W, 24 V DC/5 A |

Transmitting and receiving coil radius | 3 mm |

Transceiver turns | 20 |

Coil winding radius | 100 mm |

The minimum distance between transmitting and receiving coils | 10 mm |

Receiving coil and launch coil of the practical MCRETS system.

Experimental setup of the proposed MCRETS system.

The results of the transmission distance are experimentally verified. In the experiment, the position of the transmitting coil is kept constant, the receiving coil is moved to the right, and the transmission distance of the system is gradually increased. The relevant experimental data are collected by the transmitting and receiving devices. Data can be obtained from the theoretical analysis and experiment. The graph of the relationship between transmission distance and transmission power is shown in Figure

Transmission distance-output power and transmission distance-transmission efficiency curves.

From Figure

The resonant compensation capacitor of the wireless energy transmission system can be matched. The change in the resonant frequency of the system can be achieved by a change in the resonant compensation capacitor. In the experiment, the transmission distance is fixed at 2.5, 3.0, and 3.5 cm. Experimental data are collected from the changes in the resonant frequency of the system and then graphed with simulated data to show the relationships between the resonant frequency and output power and between the resonant frequency and transmission efficiency. The graph of the relationship between the output power and the resonant frequency is shown in Figure

(a) Resonant frequency-output power efficiency relationships; (b) resonant frequency-transmission efficiency relationships.

From Figure

The experimental data of the relay and nonrelay coils are collected by the experimental devices. The relevant experimental data, which are fluctuations in the receiving terminal voltage as transmission distance changes, are collected, and the curves of the voltage and transmission distance of the relay and the nonrelay are drawn. The comparison chart is shown in Figure

Receipt of voltage change of the experimental device, with distance changing with or without relay coil.

The variation curve in Figure

Findings from the theoretical analysis in this study are verified through an experiment. Before the start of the experiment, the angle between the receiving coils is set at −40° and the receiving coil is then rotated slowly in the direction vertical to the coil diameter until it rotates to an angle of 35°. The value of the output power during rotation is recorded. The output power varies with the rotation angle of the receiving coil. The experimental data are graphed in Figure

Output voltage-direction curve.

The above theoretical analysis and experiments reveal that when the system output power is at maximum, the transmission efficiency is often extremely low. A wireless energy transmission system is a relatively easily affected system, and its transmission performance is easily affected by many factors. At present, many scholars are analyzing the power and efficiency of the wireless energy transmission system, but this cannot guarantee the optimal transmission performance of the system. This paper combines the power and efficiency problems of wireless energy system transmission, that is, taking into account the power and efficiency of transmission and optimizing the system transmission performance. This kind of research is still rare.

The literature [

For the above problem, this study proposes the power product. The optimal parameters for the wireless energy transmission system are analyzed to allow higher transmission efficiency in the system even when the output power is high. The power product is the product of the output power and the transmission efficiency, and it can be expressed by

For simplicity, the wireless energy transmission system is assumed to be in the ideal state and that the remaining items are constant; thus, the amount of change is only one-unit resonance frequency. It is necessary to set a series of parameters according to the idealized situation. According to the parameters set, the related formulas can be analyzed more effectively and conveniently. The analysis is simpler and clearer. System parameters are listed in Table

System parameters.

DC input voltage | LS (Ld) |
_{0} |
---|---|---|

15 V | 14.25 |
0.27 Ω |

F | RW | R |

500 kHz | 5 Ω | 2.5 Ω |

Relationship between the power product and resonant frequency.

In Figure

The solvable output power

From the above analysis, it shows that when

Similarly, if other conditions are not changed, only the change in transmission distance is controlled. When the transmission distance satisfies

In summary, the use of power product parameters for optimization ensures that the output and transmission powers will be relatively high, which optimizes the transmission performance.

This study introduced the MCRETS model, obtaining an optimal topology through modeling and analysis of its four topological structures. Theoretical analysis and experimental verification of the factors, which affect the transmission performance of the MCRETS (i.e., transmission distance, resonant frequency, relay coil, and relative position of transmitting and receiving coils) were conducted and discussed. The theoretical analysis and experimental results show that these factors greatly influence the transmission performance of the wireless energy transmission system, such that the factors can further improve the transmission performance once optimized. Based on the above analysis, this study proposed the parameters of the power product to ensure a relatively high transmission power with the maximized performance. This concept is of great significance in practical application. For example, the problem of choosing the highest power or higher charging efficiency has always existed. With the concept of power product, the maximum efficiency product can be preferentially selected, which is more conducive to the optimization of charging performance.

However, the research on the transmission structure of MCRETS is limited because it is based on a two-coil structure. Further research will study the effect of single or multiple power supply charging using a one-to-one structure or a network of structures. Based on the analysis, further research on the design for a more efficient, more powerful, and more stable MCRETS is also desirable.

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

The authors declare that they have no conflicts of interest.

The authors would like to acknowledge the support from the National Key R&D Program of China (grant no. 2018YFB1304600), CAS Interdisciplinary Innovation Team (grant no. JCTD-2018-11), DREAM project of EU FP7-ICT (grant no. 611391), and National Natural Science Foundation of China (grant nos. 51575412, 51575338, and 5157540).