Coil Position Control Technology in Magnetic Coupled Wireless Power Transmission

This article mainly studies the issue of power and efficiency fluctuations at the receiving end caused by changes in the relative positions of the transmitting coil and the receiving coil in a magnetic coupled radio energy transmission system. A circuit model was built to analyze the logical relationship of energy transmission in a wireless energy transmission system, and the optimal transmission position of the two-coil system was calculated. Simulation analysis and experimental measurements were conducted to obtain the transmission power of the coil at different distances. Based on the microcontroller, a closed-loop automatic control algorithm is designed for the laser rangefinder and the stepping motor. When the position of the receiving coil changes, the transmitting coil can move with the position of the receiving coil so that the system can quickly stabilize at the optimal power transmission point. The method used in this article can achieve stable transmission power of over 7 W when the receiving coil moves 0-100 cm along the axis.


Introduction
Wireless power transmission technology is an energy transmission method that utilizes energy carriers in physical space (such as microwaves, electric fields, magnetic fields, lasers, ultrasound, etc.) to transfer electrical energy from the power side to the load side without using metal wire connections.At present, there are three main forms of wireless power transmission technology: inductive wireless power transmission (I-WPT), magnetic coupling resonant wireless power transmission (MCR-WPT), and microwave wireless power transmission (M-WPT), each suitable for different fields [1] [2].Among them, MCR-WPT has high transmission power and efficiency, and the transmission is not affected by non-metallic obstacles on the path, making it a highly promising wireless transmission method [3] [4].
MCR-WPT uses electromagnetic fields between coils for energy transmission, and the most serious problem it faces is the change in system output power caused by changes in coil spacing.Some researchers have analyzed this problem by changing the coil structure.In [5] and [6], the most common planar coil structure was used, while in [7] and [8], it was found that solenoid-shaped coils can achieve far axial offset.In [9], a scheme was designed to replace a single coil resonator by forming an array of multiple small resonators, which not only increases the effective transmission area but also improves the transmission efficiency of the system in under-coupled and over-coupled states.However, when the offset distance between coils is greater than the coil diameter, it is difficult to achieve good transmission performance solely by changing the coil structure.Some scholars use the method of adjusting electrical parameters to deal with coil offset.In [10], the method of adjusting the system frequency was used for tuning, achieving a transmission efficiency of 70% at any position with coil spacing ranging from 0 to 70 cm.In [11], the detuning problem generated by radio energy transmission systems with different coil spacing was dynamically adjusted through the use of switch capacitors, and the value of the resonant capacitor was adjusted by detecting input and output impedance and scattering parameters.The advantage of this type of method is that it can detect system changes more sensitively, while the disadvantage is that the electrical parameters of the system are affected by load changes.
By changing the spacing between coils through spatial positioning, better transmission power can be achieved.In [12], the voltage values of the four auxiliary coils on the receiving side were measured to perform spatial positioning on the receiving side coil.The probability of positioning accuracy below 2 cm exceeds 92%, but it has a relatively complex measurement system.In [13], the lateral movement of the coil in radio energy transmission was studied, and theoretical expressions were derived; a simulated analysis of the change in transmission efficiency was studied when the coil in a four-coil WPT system experienced lateral misalignment.In [14], a closed-loop three-level position correction algorithm was designed, which achieved automatic tracking of the transmitting end to the receiving end installed at the rear of the electric vehicle.It solved the problem of coil offset by using magnetic attraction to attract the transmitting coil installed on the guide rail.But when the coil moves, the friction force it receives on the guide rail will gradually increase, resulting in inaccurate positioning.
To address the impact of coil offset on magnetically coupled radio energy transmission, this paper proposes a new analysis method that calculates the functional relationship between coil spacing and output power to obtain the optimal power transmission position of the system.The coil spacing is measured by the laser rangefinder and compared with the optimal transmission position of the system measured by the experiment.According to the comparison results, the transmission coil installed on the guide rail is moved so as to achieve constant coil spacing and stable power transmission of the system.
This article mainly consists of the following parts.Chapter 2 provides a theoretical analysis of the relationship between coil spacing and transmission power.Chapter 3 measures the relationship between coil spacing and transmission power through simulation experiments.Chapter 4 is about the construction of the experimental platform and the measured results.Chapter 5 is a summary.

The relationship between coil spacing and coil mutual inductance
Mutual inductance is a common electromagnetic induction phenomenon.Its principle is that when the current in one coil changes, an induced electromotive force will be generated in the adjacent coil.In a magnetic coupled resonant radio energy transmission system, the variation of mutual inductance between coils can significantly affect the transmission power and efficiency.According to the principle of electromagnetic field, for the coaxial two-group single coil system shown in Figure 1, The mutual inductance value can be obtained from the Neumann formula.
in the formula, 0  is the permeability, 1 N and 2 N are the number of coil turns, 1 l and 2 l are the perimeter of two coils, 1 dl  and 2 dl  are the two vector on the coil loop, h is the coil spacing, 1 r and 2 r is the coil radius, r is the distance between two vectors. is set to be the angle between two vectors in the same plane, it can be calculated that: By substituting Formulas ( 2) and (3) to Formula (1), the formula becomes: After a series of variable substitutions, the relationship between mutual inductance and coil parameters can be obtained as the following formula.
is the second kind of complete elliptic integral.
The elliptic integral function in Matlab is used to calculate the formula, where μ 0 =4π×10 -7 H/m, N 1 =N 2 =5, r 1 =r 2 =0.125 m, the variation range of coil spacing h is 0~0.2 m, the functional relationship between coil spacing and mutual inductance is shown in Figure 2.
Figure 2 The relationship between coil mutual inductance and coil spacing From Figure 2, it can be seen that the mutual inductance of the coil decreases monotonically with the increase of coil spacing and decreases rapidly at close range.As the coil spacing gradually increases, the decrease rate also decreases.

The relationship between coil spacing and output power
The two-coil magnetic resonance system has four forms according to the different connection methods of the resonance circuit: Series-Series resonance (SS), Series-Parallel resonance (SP), Parallel-Series resonance (PS), and Parallel-Parallel resonance (PP).Figure 3 shows the circuit model of a SS connected resonant system.
The impedance of the transmitting circuit is set to Z 1, and the impedance of the receiving circuit is set to Z 2 .The formula of Z 1 and Z 2 is : in the formula, R 1 , L 1 , and C 1 are the transmitting side coil resistance, inductance, and resonant capacitance; R 2 .L 2 , and C 2 are the receiving side coil resistance, inductance, and resonant capacitance; R L is the load; ω is the resonant frequency.According to Kirchhoff's voltage law, the sum of the voltages at both ends of all components along a closed circuit is 0. The circuit current of the transmitting side is set as I 1 , the circuit current of the receiving end is set as I 2 , the AC power source is set as U in , M is set as the mutual inductance between the coils, and the circuit formula can be written as: I 1 and I 2 can be calculated as: The output power P OUT can be calculated as: According to Formula (10), the smaller the module of Z 1 and Z 2 is, the higher the output power will be.When the circuit is purely resistive, the maximum output power can be achieved.The output power in the resonant state can be obtained as: For a certain system, the values of its working voltage, working frequency, impedance, coil inductance, resonant capacitance, and load are generally constant.At this time, the parameter that affects the transmission power is the mutual inductance M between the coils.To explore the relationship between transmission power and mutual inductance M, Formula (11) can be derived from M and then zero to find the trend of output power changing with mutual inductance.To simplify the calculation, we have the following: At this point, the output power After taking the derivative of M can obtain the following formula: Finding the zero point of this formula reveals the existence of two zero points.0 M  and

( )
Based on the functional relationship between coil spacing and mutual inductance calculated in the previous text, it can be concluded that in a magnetically coupled energy transmission system, coil spacing directly affects the transmission power.The specific relationship is that the transmission power shows a trend of first increasing and then decreasing with the increase of coil spacing, and there is a maximum value.

Simulation analysis of the MCR-WPT system
To verify the conclusion of theoretical derivation, this article uses Matlab Simulink software to model the MCR-WPT system, as shown in Figure 4.

Figure 4 Simulink model of MCR-WPT
The model consists of five parts: DC power supply, high-frequency inverter circuit, LC resonant circuit, rectification and filtering circuit, and load.According to the previous theoretical derivation, changes in coil spacing can lead to changes in output power.The relationship is that the output power will first increase and then decrease with the increase of coil spacing.In the simulation model, by modifying the mutual inductance value of the coil, the output power of the system can be detected instead of the change in coil distance.The coil distance is gradually increased from 20 mm to 200 mm, and the variation data of output power with coil distance is shown in Table 1.The fitting curve of output power with coil spacing is shown in Figure 5.

Figure 5 Relationship between coil distance and P OUT
From Table 1 and Figure 5, it can be seen that the output power increases first and then decreases with the variation of coil distance, and the optimal transmission power is obtained at 60 mm-80 mm.At a distance of 20 mm to 60 mm, the coil is in an over-coupled state, and the transmission power increases as the distance between the transmitting coil and the receiving coil increases.Within the range of 60 mm to 80 mm, the coil is in a critical coupling state, at which point higher transmission power can be obtained.When the coil spacing is greater than 80 mm, the transmission power rapidly decreases.

MCR-WPT experimental platform with coil position control function
Based on the basic principle of MCR-WPT and the theoretical and simulation experiments mentioned earlier, an MCR-WPT experimental platform with variable coil spacing was established.The structural diagram of the experimental platform is shown in Figure 6.The system consists of two parts, namely the coil position automatic control system and the energy transmission system.The coil position automatic control system consists of four parts: the main control chip, laser ranging sensor, stepper motor driver, and motor guide rail transmission module.The software flowchart is shown in Figure 7.After powering on, the various modules in the control system are initialized first, and then the main control chip will output distance measurement instructions to the distance measurement module.Depending on whether the measurement results are successful or not, the display module will display different results.If the measurement is successful, the main control chip will compare the measured distance data with the distance data set internally in the system based on simulation and measurement results and control the motor's steering based on the comparison results.When the motor rotates, it will drive the ranging module to measure a new coil spacing.After cyclic judgment, the coil spacing reaches the range of the optimal transmission position.At this point, the motor stops rotating and returns to the main program waiting for further measurement results from the ranging module.
The energy transmission system consists of six parts: a high-frequency signal generator, a power amplifier, a resonant capacitor, an energy transmission coil, a rectification and filtering circuit, and a load.The experimental setup is shown in Figure 8.The electrical parameters of the system are shown in Table 2. Table 2


Using the above experimental platform and electrical parameters, without activating the coil position automatic control system, the coil spacing is gradually increased from 50 mm to 200 mm.The power of the load is measured, and the curve is obtained, as shown in Figure 9.
Figure 9 The relationship between coil distance and output power without an automatic control system It can be seen that the output power increases first and then decreases with the increase of coil distance.The transmission system achieved a maximum transmission power of approximately 7 W at a distance of approximately 92 mm~94 mm.When the maximum power point is near the coil distance, the change in transmission power is more pronounced with the change in coil distance and has a faster downward trend.
After turning on the automatic control system for coil position, the load coil is set to its initial position as the distance zero point and moved along the axis for a certain distance each time.After the movement is completed, the following status of the transmitting coil is observed, and the output power after positioning is detected.The axial movement distance ranges from -100 mm to 100 mm, with each movement increasing in steps of 10 mm.The measured load power variation curve is shown in Figure 10.It can be clearly seen from the figure that after adjusting the coil spacing using the automatic control system, the stability of the transmission power has significantly increased, and it is basically stable at the optimal transmission power position.It has been proven that this method can still enable the system to have sufficient transmission power even when the load coil moves axially.

Conclusion
In response to the issue of output power changes caused by changes in axial coil spacing in magnetically coupled radio energy transmission, this article analyzes the relationship between coil spacing, coil mutual inductance, and output power in magnetically coupled radio energy transmission.It is concluded that the output power first increases and then decreases as the coil spacing increases.On the basis of theory and simulation experiments, a coil position automatic control system has been designed, which can automatically control the distance between the transmitting coil and the receiving coil when the receiving coil undergoes axial displacement so as to achieve maximum power for the load.After experiments, it has been verified that this system can effectively ensure a maximum output power of 7 W at the load end when the receiving coil undergoes a displacement of -100-100 mm along the axial direction.

Figure 1
Figure 1 Mutual inductance analysis of coaxial two-coil system P  .It means that the output power will first increase and then decrease with the increase of mutual inductance.It can obtain the maximum transmission power at the M

FinishFigure 7
Figure 7 Overall software flowchart of the system

Figure 10
Figure 10  The relationship between coil distance and output power after opening the automatic control system

Table 1
Relationship between M, coil spacing, and output power