Analysis on Transmission Characteristics of Dynamic Magnetic Coupling Mechanism of Racetrack Coil with Deflection Angles

In dynamic magnetically coupled contactless power transmission, the fluctuation of mutual inductance is caused by the relative motion between transmission and receiving coils, which affects the stability of power transmission. In order to reduce the fluctuation characteristics of power transmission, the mutual inductance calculation model of transmission mechanism including a racetrack coil with deflection angle is established by using Neumann formula, and the influence of different deflection angle and layout on mutual inductance fluctuation characteristics is analyse and compare. Then the power transmission system with LCC-S compensation for the transmission mechanism is established. The transmission characteristics of the racetrack coil with deflection angle are studied. The results show that reasonable design of the deflection angle can reduce the fluctuation of the mutual inductance and the power output in dynamic transmission. The fluctuation of power output can also be reduced by changing the distance between transmission coils and the length of straight side of receiving coils.


Introduction
In dynamic power supply technology, lateral and angular offset directly affect the transmission characteristics of magnetic coupling mechanism.At present, many scholars have studied the offset tolerance.Ji et al. [1] studied the influence law of angle deviation and lateral deviation between square coil and circular coil on mutual inductance by Neumann formula, and proved that this method can calculate mutual inductance between regular polygon and circular coil accurately and efficiently through comparison and analysis.Xue Ming et al. [2] [3] analyzed the influence of mutual inductance on transmission power with displacement, different coupling angle and transmission distance, and compared the magnetic field intensity distribution characteristics of different structures by finite element method.Yang et al. [4] analyzed and compared the magnetic field distribution of the square coil, circular coil and racetrack coil at different offset distances by using the finite element method, and proved that the racetrack coil has a higher magnetic coupling coefficient than the rectangular coil.
In order to reduce the fluctuation of dynamic transmission, some control methods for transmission end and receiving end are also applied to the system.Chawalit et al. [5] proposed to realize highefficiency power transmission by using alternating magnetically coupled waveguide for the fluctuation problem of power zero in dynamic radio energy transmission.Faradjiet al. [6] use multi-channel conversion control to drive multiple transmission coils, so as to avoid power zero and ensure transmission stability of receiving coils at different positions.Chen et al. [7] studied the transmission characteristics of the cylindrical radio energy transmission system and proposed to realize stable transmission of the moving receiving coil by changing the input voltage phase of the transmission coil.The validity of the method was verified through the analysis of the transmission performance.
Although there have been many researches on dynamic electric energy transmission, the current dynamic electric energy transmission is mainly in the experimental and research stage [8], and mainly focuses on the flat coil.There is still less research on the dynamic transmission performance of the deflection composite structure coil.In order to improve the transmission stability of the dynamic magnetic coupling mechanism, a racetrack receiving coil with deflection angle is proposed in this paper.The mutual inductance calculation model of the dynamic transmission system is established by Neumann formula.The stable transmission law of the mechanism is obtained by comparing and analyzing the mutual inductance fluctuation characteristics.The LCC-S compensated electric energy transmission system is established for the mechanism to study its efficient transmission mechanism.

Mutual Inductance Calculation F Composite Coil
As shown in figure 1, the magnetically coupled electric energy transmission mechanism consists of a plurality of circular transmission coils (TR) with radius of r p arranged between phases Hs0 and a composite structure receiving coil (RE), where Hs0 ≥ 2rp, xO0y-z is the overall coordinate system of the system, x'O0y '-z' is the local coordinate system of RE, O1 and O2 are the centers of semicircles with radius of rs at both ends of RE, respectively, θs,1 and θs,2 is the acute angle between the two semicircles and the horizontal plane, Ls0 is the length of the straight side of the receiving coil, the z-direction distance between TR and RE is d0, and the x-direction distance between their centers is Δ.For the micro-elements dls, j and dls,0 in the illustrated receiving coil, the coordinates of j can be expressed as: s j x j g s j r g r r g 。The radius of the i turn coil of the m transmission coil and the j turn semicircle coil of the receiving coil are respectively: = 1 Where rpo,m is the outer diameter of the m transmission coil, rso is the outer diameter of the receiving coil, w and s are the diameter of the conductor and the spacing between adjacent conductors, Thus, the vector product of each micro-element between the i turn coil of the m transmission coil and the j turn semicircle coil of the receiving coil can be expressed as: = sin sin cos + cos cos , , 0 , sin The distance between the i turn transmission coil Trm micro-element dlp,m,i and the j turn semicircle receiving coil micro-element dls,j is: sin sin cos sin Similarly, the distance between the i turn transmission coil Trm micro-element dlp,m,i and the straight micro-element dls0,j in the j turn receiving coil is: The mutual inductance between the parts can be obtained according to Newman's formula [1]: , , , _ 0, 0 2 , , _ 0, sin 4 Where, Mp,m,i_s,j represents the mutual inductance between the i turn coil of the m transmission coil and the j turn semicircle coil of the receiving coil, is the mutual inductance between the i turn coil of the m transmission coil and the j turn straight side coil of the receiving coil, then the mutual inductance between the single-turn transmission coil and the receiving coil is: Where np is the number of transmitting coil turns and ns is the number of receiving coil turns.

Influence of Each Parameter on Mutual Inductance
For the magnetically coupled electric energy transmission mechanism shown in figure 1, 6 transmission coils are preliminarily selected, and the lateral offset distance of the receiving coil is 4Hs0.In order to simplify the analysis θs,1=θs,2 The initial position is shown in figure 1, and the initial parameters are given in table 1.If no description is given in the subsequent analysis, the parameters are consistent with the initial parameters.  2 (a), it can be seen that for a single transmitting coil θs, the maximum mutual inductance gradually decreases, and θs has little influence on the minimum mutual inductance, so the mutual inductance change rate between single transmission coil and receiving coil varies with θs increases and decreases; In figure 2 (b), when θs increases, the maximum value of total mutual inductance decreases continuously, while the minimum mutual inductance increases first and then decreases, and the difference between the maximum and minimum mutual inductances decreases gradually.Therefore, increasing the deflection angle can reduce mutual inductance fluctuation, but larger deflection angle can reduce mutual inductance more.

Impact of Distance between Transmission Coils Hs0 on Mutual Inductance
It can be seen from figure 3 (a) that when the distance between transmission coils Hs0 increases, the relative reduction rate of mutual inductance of a single coil increases; Figure 3 (b) shows that, with the increase of Hs0, the total mutual inductance decreases continuously, and larger Hs0 will make the difference between the maximum and minimum values of the total mutual inductance bigger, making the transmission stability worse.However, reasonable arrangement of the transmission coil spacing, for example, when Hs0=30mm, the mutual inductance fluctuation is the smallest, which can improve the transmission performance of the wireless electric energy.

Dynamic Magnetic-coupled Power Transmission System with LCC Compensation
The equivalent circuit model of the dynamic transmission system as shown in figure 4, uin is the power voltage of the transmitting terminal, ic is the power output current, ip is the current of the primary transmitting coil, and is the current of the secondary receiving line.In the system circuit, Lc is the compensation inductance of the primary coil, Cc is the parallel compensation capacitance of the primary coil, and Rc is the parasitic resistance of the compensation inductance; Lp refers to self-induction of primary coil, Cp refers to series compensation capacitance of primary coil, and Rp refers to parasitic resistance of primary coil; Ls is self-inductance of receiving coil, Cs is series compensation capacitance of receiving coil, Rs is parasitic resistance of receiving coil, RL is load resistance; The subscript i=1,...,n denotes the i transmission coil, where Mi is the mutual inductance between the i transmission coil and the receiving coil, and Mjk is the mutual inductance between the receiving coils j and k (j ≠ k).Based on Kirchhoff's voltage law and Ohm's law, the KVL circuit equation in figure 6 is: , Since the cross-coupling between the receiving coils has little impact on the energy of the system, Mjk can be ignored in the parameter design stage to simplify the analysis.And make in the transmitting terminal loop Lc,i =Lc，Cc,i =Cc，Lpi=Lp，Cp,i=Cp，Rp,i=Rp。When the system is in resonance working state, meet the following requirements: , among ω=2πf is the system angular frequency (rad/s), f is the system operating frequency.According to SAEJ2954 international standard, the system resonance frequency is set as f0=85kHz.The mutual inductance between each primary coil and secondary coil is: , k is the coupling coefficient.The input and output current can be obtained from equation (11), then the input active power Pin, output power Po and efficiency η are: From figure 5 (a) above, when θs increases, the maximum power of the dynamic wireless transmission system increases, but when θs=20°, the difference between the maximum and minimum power values is 5.9W at least, so the reasonable design θs can reduce power fluctuation in dynamic transmission.From figure 5(b), it can be seen that the efficiency variation of the offset coil transmission system compensated by LCC-S is complex, but when selecting a specific θs will make the efficiency fluctuation smaller, such as θs=20°, the maximum and minimum difference of efficiency is only 0.055, while that of flat coil is 0.101; However, it is also noted that, θs too much leads to greater efficiency fluctuations.
, , , , In the influence curve of different transmission coil spacing on transmission characteristics, figure 6(a) shows that the larger the transmission coil spacing Hs0 is, the smaller the transmission power is.Reasonable selection of Hs0 can reduce the power fluctuation, but larger spacing will increase the power fluctuation amplitude.It can be seen from figure 6(b) that the maximum transmission efficiency increases with increasing spacing, but the fluctuation amplitude of efficiency also increases.However, the larger the spacing, in dynamic transmission, the number of transmission coils will be effectively reduced under a specific laying length, and the dynamic transmission cost can be reduced.Under different load resistances, it can be seen from figure 7(a) that with the increase of load resistance RL, the output power decreases continuously, but the decrease amplitude also decreases gradually, and the power fluctuation amplitude also decreases with the increase of RL; In figure 7(b), the larger the RL, the higher the transmission efficiency, and the smaller the efficiency fluctuation, but the efficiency increase gradually decreases.

Conclusion
The following main conclusions can be drawn through the mutual inductance and efficiency analysis of the deflection track coil mechanism and the LCC-S compensated dynamic transmission system: 1) The deflection receiving coil can enhance the magnetic field coupling strength with the transmission coils on both sides and reduce the mutual inductance fluctuation amplitude in dynamic transmission, but it will make the coupling of the coil facing worse, so as to reduce the maximum mutual inductance; 2) In the dynamic power transmission of LCC-S compensation type, the specific deflection angle can realize large power transmission under the condition of reducing power and efficiency fluctuation, so as to enhance the stability of dynamic transmission; 3) Reasonable design of track coil straight side length and transmission coil spacing can reduce mutual inductance fluctuation in dynamic transmission and increase stability of power and efficiency of electric energy transmission of LCC-S compensation system.4) For the power transmission system compensated by LCC-S, the bigger the external load resistance is, the smaller the transmission rate is, and the bigger the transmission efficiency is, the better the transmission stability of the system is.

Figure 1 .
Figure 1.Magnetically coupled mechanism of racetrack coil with deflection angle.
the micro-element dlp,m,i of the i turn coil of the m transmission coil, the coordinates are: 0

Figure 2 .
Figure 2. Influence of different θs on mutual inductance.

Figure 3 .
Figure 3. Influence of different Hs0 on mutual inductance.

Figure 4 .
Figure 4. Equivalent circuit of dynamic transmission system.

Figure 5 .
Figure 5. Transmission power and efficiency at different θs.

Figure 6 .
Figure 6.Transmission power and efficiency at different Hs0.

Figure 7 .
Figure 7. Transmission power and efficiency at different RL

Table 1 .
Initial parameters of magnetic coupling mechanism.