CN104917302B - Embedded Energy Transmitting Coil, Design Method and Coil System for Electric Vehicle Wireless Power Supply System - Google Patents

Abstract

The present invention propose a kind of electric automobile wireless power supply system to embedded energy transmitting coil, method for designing and coil system, along automobilism direction, embedded energy transmitting coil is included with operation area and is located at forward and backward Zone switched in operation area；In the direction perpendicular to automobilism, the Zone switched size being smaller in size than operation area；Operation area coil turn and Zone switched coil ratio are ζ, and 0<ζ<1.Using the present invention to embedded energy transmitting coil, IPT wireless power electric motor car is able to maintain that mutual inductance is relatively stable in handoff procedure between energy transmitting coil.

Description

Embedded energy transmitting coils, design methods and methods of electric vehicle wireless power supply system coil system

technical field

The invention relates to the technical field of wireless energy transmission, in particular to an embedded energy transmitting coil of an electric vehicle wireless power supply system, a parameter design method thereof, and a formed coil system.

Background technique

With the continuous improvement of people's living standards, the number of automobiles has increased sharply, and environmental and energy problems have continued to intensify. Electric vehicles have broad prospects for solving the environmental and energy problems brought about by traditional vehicles, and have received extensive attention from the government, related companies, and related research institutions. However, the development of electric vehicles is relatively slow, and batteries are one of the key factors restricting its development.

The production cost of vehicle batteries is high and its production will harm the environment, the charging time is long and there are safety problems. Due to the existence of vulcanization, the service life of the battery pack will continue to decrease. In addition, the bulky battery pack not only increases the weight of the electric vehicle body, but also increases the energy consumption of the locomotive.

The above-mentioned problems that batteries exist have seriously restricted the development of electric vehicles. If the electric vehicle has no battery pack, the above problems can be fundamentally eliminated. The trolley bus replaces the on-board battery pack by contact power supply, so there is no problem caused by the battery pack, but it faces other problems, such as the safety of operation, the flexibility of driving, and the aesthetics of the road. The wireless powered electric vehicle based on IPT (Inductive Power Transfer) technology transmits energy without contact and the energy transmitting coil is buried under the ground, so not only there is no problem caused by the battery pack, but also there is no problem faced by the trolleybus. question. The wireless power supply method based on IPT technology has brought new hope for the development of electric vehicles.

The energy transmitting coil is a crucial part of the IPT wireless power supply electric vehicle system, so the design of the energy transmitting coil is very critical. In order to reduce energy loss, improve energy utilization, and reduce EMF, the energy transmitting coil of a wireless power supply electric vehicle based on IPT technology should not use a single-segment energy transmitting coil, but should be cascaded in segments. Segmented cascaded energy transmitting coils are generally adopted by relevant research institutions at home and abroad.

There are two power supply control methods for segmented cascaded energy transmitting coils: multi-coil simultaneous power supply and single coil power supply. Simultaneous power supply of multiple coils can effectively ensure that the mutual inductance between the energy transmitting coil and the on-board pickup mechanism meets the requirements of the mutual inductance value required for the pickup voltage. However, this power supply control method will greatly increase energy loss, electromagnetic radiation range and radiation time. A single coil power supply is beneficial to reduce energy loss and reduce EMF. However, when the electric vehicle switches from the front-stage coil to the rear-stage coil, the mutual inductance between the energy transmitting coil and the on-board energy pickup mechanism will drop sharply. It is beneficial to the acquisition of the pickup voltage, and will affect the stable operation of the system. In addition, if the electric vehicle stops at the junction of the two energy transmitting coils, the mutual inductance will not be able to reach the mutual inductance value required for picking up the voltage, and the electric vehicle will not be able to run because the required picking up voltage cannot be obtained.

In the case that the energy transmitting coils are cascaded in segments and powered by a single coil, how to effectively solve or improve the sharp fluctuations in mutual inductance of the IPT wireless power supply electric vehicle during the switching process between energy transmitting coils is a technical problem that needs to be solved urgently.

Contents of the invention

In order to overcome the above-mentioned defects in the prior art, the purpose of the present invention is to provide an embedded energy transmitting coil for a wireless power supply system of an electric vehicle and its parameter design method, as well as an energy transmitting coil system formed by cascading them.

In order to achieve the above object of the present invention, according to one aspect of the present invention, the present invention provides an embedded energy transmitting coil of a wireless power supply system for an electric vehicle. Along the running direction of the vehicle, the embedded energy transmitting coil includes a running area And the switching area positioned at the front and rear of the operating area; in the direction perpendicular to the running of the automobile, the size of the switching area is smaller than the size of the operating area, and the ratio of the coil turns in the operating area to the switching area coil turns is ζ, and 0<ζ<1.

Using the embedded energy transmitting coils of the electric vehicle wireless power supply system of the present invention, the mutual inductance of the IPT wireless power supply electric vehicle during the switching process between the energy transmitting coils will not fluctuate greatly, and the mutual inductance can be kept relatively stable.

In a preferred embodiment of the present invention, the size and the number of coil turns of the switching regions before and after the operating region are the same. It is ensured that the mutual inductance in the process of switching between energy transmitting coils can be relatively stable, and the design is simple and easy to realize.

In another preferred embodiment of the present invention, the switching area is distributed axisymmetrically or centrally symmetrically with respect to the operating area. Diverse designs improve the applicability of the energy transmitting coil.

In a preferred embodiment of the present invention, the length l of the switching region is not less than the length L _p of the vehicle-mounted energy pickup coil, ie: l≧L _p . Therefore, it is ensured that the mutual inductance will not fluctuate violently during the switching process between the energy transmitting coils.

In a preferred embodiment of the present invention, the width D of the operating area is not greater than the wheel spacing D _m of the electric vehicle, and is not smaller than the width D _p of the on-board energy pickup coil, ie: D _p ≤ D ≤ D _m . This ensures efficient energy harvesting.

In a preferred embodiment of the present invention, the width d of the switching region is half of the width D of the operating region.

In a preferred embodiment of the present invention,

Among them, f(L,D,L _p ,h) is a function of the length and width of the operating domain, the length of the pickup coil and the coupling distance:

in, where x=L _p ,D in in

g(l,d,L _p ,h) is a function of the length and width of the switching domain, the length of the pickup coil and the coupling distance:

in,

Where: x = L _P ,2d,3d;

in:

Therefore, it is ensured that the mutual inductance of the on-board energy pickup mechanism of the IPT wireless power supply electric vehicle relative to the different state domain positions of the embedded energy transmitting coil is basically equal.

In order to achieve the above object of the present invention, according to one aspect of the present invention, the present invention provides a parameter design method for an embedded energy transmitting coil of a wireless power supply system for an electric vehicle, comprising the following steps:

S1, obtain the length L _p and width D _p of the vehicle-mounted energy pickup coil, and set the coupling distance h between the energy transmitting coil and the vehicle-mounted energy pickup coil;

S2, the length L of the design operation area and the length l of the switching area, the length l of the switching area is not less than the length L _p of the vehicle-mounted energy pickup coil, that is: l≥L _p ;

S3, design the width D of the operating area and the width d of the switching area, the width D of the operating area is not greater than the wheel spacing D _m of the electric vehicle, and is not smaller than the width D _p of the on-board energy pickup coil, that is: D _p ≤ D ≤D _m ; the width d of the switching area is half of the width D of the operating area;

S4, designing the optimal turns ratio ζ _o .

The energy transmission coil designed by using the parameter design method of the present invention enables the mutual inductance of the IPT wireless power supply electric vehicle to be relatively stable during the switching process between the energy transmission coils.

In order to achieve the above object of the present invention, according to one aspect of the present invention, the present invention provides an embedded energy transmitting coil system of an electric vehicle wireless power supply system, which consists of m blocks of embedded energy transmitting coil systems of the electric vehicle wireless power supply system of the present invention The energy transmitting coils are connected, and the m is a positive integer greater than 1. Along the running direction of the vehicle, the switching area of the previous energy transmitting coil and the switching area of the following energy transmitting coil are sequentially smoothly and closely fitted, and the vertical direction of the running direction of the vehicle is direction, the sum of the switching area of the previous energy transmitting coil and the switching area of the following energy transmitting coil is equal to the size of the operating area.

The embedded energy transmission coil system of the electric vehicle wireless power supply system of the present invention enables the mutual inductance of the IPT wireless power supply electric vehicle to be relatively stable during the switching process between energy transmission coils.

Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Description of drawings

The above and/or additional aspects and advantages of the present invention will become apparent and comprehensible from the description of the embodiments in conjunction with the following drawings, wherein:

Fig. 1 is a schematic structural view of the embedded energy transmitting coil of the electric vehicle wireless power supply system of the present invention;

Fig. 2 is a schematic structural diagram of the embedded energy transmitting coil system of the electric vehicle wireless power supply system of the present invention.

detailed description

Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

The present invention provides an embedded energy transmitting coil of a wireless power supply system for an electric vehicle. As shown in FIG. The lines are wound in the same direction. Among the three areas shown in Figure 1, I and III are the areas where the switching operation occurs, that is, the switching area; II is the area where the electric vehicle operates normally and does not perform switching operations, that is, the operating area.

In the direction perpendicular to the running of the vehicle, the size of the switching area is smaller than that of the running area, and the ratio of the number of coil turns in the running area to the number of turns in the switching area is ζ, and 0<ζ<1.

In a preferred embodiment of the present invention, the size and the number of turns of the coils are the same for both the switching areas before and after the operating area. That is, the size and number of turns of the switching domains I and III are equal,

d ₁ =d ₃ =d, l ₁ =l ₃ =l; N ₁ =N ₂ =N _s (1)

Among them, l ₁ , l ₃ and d ₁ , d ₃ are the length and width of switching regions I and III respectively, l and d are respectively defined as the length and width of switching regions; N ₁ and N ₃ are switching regions I and III respectively The number of turns, N _s is defined as the number of turns in the switching domain; the positions of the two switching domains relative to the operating domain II are shown in Figure 1.

The length, width, and number of turns of the operating domain II are defined as L, D, and N _r , respectively, and have the following relationship with the corresponding parameters of the switching domain:

D=2d, L>l; N _r =ζ×N _s ,ζ∈(0,1) (2)

In formula (2), ζ is defined as the ratio of the coil turns in the operating domain to the coil turns in the switching domain, that is, the turns ratio, which takes a value between 0 and 1. The turns ratio ζ is the most critical parameter of this new type of energy transmitting coil, and the value of ζ is of great significance for the switching of wireless powered electric vehicles controlled by a single coil power supply.

Maintaining the relative stability of mutual inductance is the basic requirement for smooth switching of IPT wireless power electric vehicles. Therefore, the principle of optimizing the value of the turns ratio ζ in the present invention is to keep the mutual inductance of the vehicle-mounted energy pickup mechanism of the IPT wireless power supply electric vehicle relative to the different state domain positions of the embedded energy transmitting coil to be basically equal. In this embodiment, the parameter selection method for the embedded energy transmitting coil is:

Let the vehicle-mounted energy pick-up coil be a typical rectangular coil, the length and width of which are L _p and D _p respectively, and D _p =D; the number of turns is N _p . And the coupling distance between the energy transmitting coil and the vehicle-mounted energy pickup coil is h.

Principles for selecting the size of each area of the guide rail:

L——can take the length of the general operating area in this field;

l——l is not less than the length of the on-board energy pick-up coil along the running direction of the vehicle, that is: l≥L _p ;

D——not greater than the wheel spacing D _m of the electric vehicle, and should not be smaller than the width D _p of the on-board energy pickup coil, that is: D _p ≤ D ≤ D _m , in a preferred embodiment of the present invention, D=D _p ;

d——d=D/2.

In order to achieve the relative smoothness of the switching process, the mutual induction of the coupling mechanism in the operating domain part and the switching domain part remains constant, and the optimal turns ratio ζ _o is set as:

Among them, under certain conditions such as the number of turns and other non-dimensional parameters, the value of f(L,D,L _p ,h) will affect the change of mutual inductance in the operating domain, so define f(L,D,L _p ,h ) is the size parameter influence function of the mutual inductance value in the operating domain. Since the calculation expression of f(L,D,L _p ,h) is too complicated, it is divided into four algebraic expressions without physical meaning. As shown in formula (4):

Among them, L and D are the length and width of the energy transmitting coil in the running domain, respectively; L _p is the length of the vehicle energy pickup coil along the running direction of the vehicle; h is the coupling distance between the energy transmitting coil and the vehicle energy pickup coil. Each composition expression of formula (4) is shown in formula (5):

where x=L _p ,D in in

Similarly, define g(l,d,L _p ,h) as the size parameter influence function of the mutual inductance value of the switching domain. To facilitate calculation in parts, g(l,d,L _p ,h) is also divided into four algebraic expressions without physical meaning. Specifically, it is shown in formula (6):

Among them, l and d are the length and width of the energy transmitting coil in the switching domain respectively; L _p is the length of the vehicle energy pickup coil along the running direction of the vehicle; h is the coupling distance between the energy transmitting coil and the vehicle energy pickup coil. Each composition expression of formula (6) is shown in formula (7):

Where: x = L _P ,2d,3d;

in:

Using the parameters designed above, the mutual inductance calculation formula of the vehicle-mounted energy pickup coil located in different state domains of the embedded energy transmission coil is as follows.

Running domain status:

Toggle domain state:

Among them, μ ₀ is the air permeability, and μ ₀ = 4π×10 ^-7 H/m; N _p is the number of turns of the on-board energy pickup coil, N _r and N _s are the operating domain and switching domain of the embedded coil respectively The number of turns; M _r and M _s are the calculated values of mutual inductance in different operating states of the electric vehicle.

By taking the optimal coil ratio, there is M _r =M _s , so as to ensure the stability of the energy picking process.

The invention provides a parameter design method for an embedded energy transmitting coil of a wireless power supply system for an electric vehicle, comprising the following steps:

S1, obtain the length L _p and width D _p of the vehicle-mounted energy pickup coil, and set the coupling distance h between the energy transmitting coil and the vehicle-mounted energy pickup coil;

S2, the length L of the design operation area and the length l of the switching area, the length l of the switching area is not less than the length L _p of the vehicle-mounted energy pickup coil, that is: l≥L _p ;

S3, design the width D of the operating area and the width d of the switching area, the width D of the operating area is not greater than the wheel spacing D _m of the electric vehicle, and is not smaller than the width D _p of the on-board energy pickup coil, that is: D _p ≤ D ≤D _m ; the width d of the switching area is half of the width D of the operating area;

S4, designing the optimal turns ratio ζ _o .

The present invention also provides an embedded energy transmitting coil system of an electric vehicle wireless power supply system. In a preferred embodiment of the present invention, as shown in FIG. 2, it is composed of m blocks as shown in FIG. The electric vehicle wireless power supply system is composed of connected embedded energy transmitting coils, m is a positive integer greater than 1, and along the running direction of the vehicle, the switching area of the previous energy transmitting coil and the switching area of the latter energy transmitting coil are smoothly and closely embedded in turn. Therefore, in the direction perpendicular to the running of the vehicle, the sum of the switching area of the previous energy transmitting coil and the switching area of the latter energy transmitting coil is equal to the size of the operating area, thereby ensuring that the mutual inductance remains relatively stable.

In a preferred embodiment of the present invention, based on the accurate finite element software Ansoft Maxwell, the corresponding embedded energy transmitting coil simulation model and the classic and widely used rectangular energy transmitting coil simulation model are established, further to the embedded energy transmitting coil Toggle performance for analysis. The energy pick-up coil used in the simulation model is the rectangular coil used in the previous analysis.

The simulation parameters are set as shown in Table I:

Table I Anosft Maxwell simulation parameter table for embedded guide rails, rectangular guide rails and pickup coils

According to the optimization analysis of the turns ratio ζ in the previous section, D, L, d, l, L _p are as in the above table, and if the coupling distance h=20cm, the optimal turns ratio ζ _o =0.353 can be obtained, and N _r =6, then N _s =17; also take the number of turns of the pick-up coil N _p =20, and the coil of the rectangular energy transmitting coil N _r =6.

The IPT wireless power supply electric vehicle switches from the operation domain of the front-stage energy transmission coil to the operation domain of the rear-stage energy transmission coil, that is, a switch between energy transmission coils is completed. Similarly, take the optimal turns ratio _ζo and its nearby values to conduct a complete switching operation simulation. According to the simulation results, when the turns ratio ζ of the embedded energy transmitting coil is the optimal turns ratio _ζo , During the switching process, the mutual inductance of the magnetic coupling mechanism fluctuates more smoothly than that of other turns ratios; and the mutual inductance at the position where the switching operation occurs is almost equal to the mutual inductance in the operating domain. In order to verify the effectiveness of the embedded energy transmitting coil in the switching experiment, relevant experimental verification is carried out based on the related wireless power supply electric vehicle system experimental platform. Due to the limitation of the actual laying size, the optimal turns ratio ζ _o = 0.368, that is, N _r = 7, then N _s = 19; the corresponding experimental parameter settings are shown in Table II.

Table Ⅱ Experiments on embedded rails, rectangular rails and pickup coils

After the ICPT wireless power supply electric vehicle switching experiment, it is found that when the wireless power supply electric vehicle performs guide rail switching, the mutual inductance can remain relatively stable, and the pickup voltage can meet the value required for the normal operation of the electric vehicle throughout the process.

In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.

Claims (10)

1. The pair of embedded energy transmitting coils of the wireless power supply system of the electric automobile is characterized in that the pair of embedded energy transmitting coils comprises an operation area and switching areas positioned in front of and behind the operation area along the running direction of the automobile; in the direction perpendicular to the running direction of the automobile, the size of the switching area is smaller than that of the running area; the ratio of the number of turns of the operating area coil to the number of turns of the switching area coil is zeta, and 0< zeta < 1.

2. The opposed-embedded energy transmitting coil of the wireless power supply system of the electric automobile according to claim 1, wherein the size and the number of coil turns of both the switching regions before and after the operation region are the same.

3. The opposed-embedded energy transmitting coil of the wireless power supply system of the electric automobile according to claim 2, wherein the switching regions are distributed in axial symmetry or central symmetry with respect to the operation region.

4. The opposed-embedded energy transmitting coil of the wireless power supply system of the electric automobile according to claim 1, wherein the length L of the switching region is not less than the length L of the on-board energy pickup coil_pNamely: l is not less than L_p。

5. The opposed-embedded energy transmitting coil of the wireless power supply system of the electric vehicle as claimed in claim 1, wherein the width D of the operating region is not greater than the wheel spacing D of the electric vehicle_mAnd not less than the width D of the on-board energy pickup coil_pNamely: d_p≤D≤D_m。

6. The opposed-embedded energy transmitting coil of the wireless power supply system of the electric vehicle as claimed in claim 1, wherein the width D of the switching region is half of the width D of the operating region.

7. The embedded energy transmitting coil of the wireless power supply system of the electric vehicle as claimed in claim 1, wherein the optimal turns ratio is:

${\mathrm{\&zeta;}}_o=\frac{N_r}{N_s}=\frac{g(l,d,L_p,h)}{f(L,D,L_p,h)},$

wherein N is_rNumber of turns in the operating region, N_sFor the number of turns of the switching region, L is the length of the switching region, d is the width of the switching region, L_pLength of the on-board energy pick-up coil, D is the width of the operating field, f (L, D, L)_pH) is a function of the length and width dimensions of the operating field, the length of the pick-up coil, and the coupling distance:

wherein,

wherein, L is the length of the operation area, and h is the coupling distance between the energy transmitting coil and the vehicle-mounted energy pickup coil;

g(l,d,L_ph) is a function of the switching domain length-width dimension, the pick-up coil length, and the coupling distance:

$g(l,d,L_p,h)=\mathrm{\&chi;}\left(L_p\right)+\mathrm{\&chi;}\left(2d\right)-\mathrm{\&chi;}\left(3d\right)+\mathrm{\&lambda;}\&lsqb;\frac{1}{2}(l-L_p)\&rsqb;-\mathrm{\&lambda;}\&lsqb;-\frac{1}{2}(l+L_p)\&rsqb;+\mathrm{\&rho;}\left(h\right),$

$\mathrm{\&chi;}\left(x\right)=x\ln \left(\frac{-x+\sqrt{\frac{4h^2+{(l+L_P)}^2}{4}+x^2}}{-x+\sqrt{\frac{4h^2+{(l-L_P)}^2}{4}+x^2}}\right)-x\ln \left(\frac{-x+\sqrt{\frac{4h^2+{(l-L_P)}^2}{4}+x^2}}{-x+\sqrt{\frac{4h^2+{(l+L_P)}^2}{4}+x^2}}\right),$

wherein: x ═ L_P,2d,3d；

$\begin{array}{c}\mathrm{\&lambda;}\left(y\right)=y\ln \left(\frac{y+\sqrt{h^2+y^2}}{y+\sqrt{h^2+{L_P}^2+y^2}}\right)+y\ln \left(\frac{-y+\sqrt{h^2+{L_P}^2+y^2}}{-y+\sqrt{h^2+y^2}}\right)\\ -y\ln \left(\frac{y+\sqrt{h^2+4d^2+y^2}}{y+\sqrt{h^2+9d^2+y^2}}\right)-y\ln \left(\frac{-y+\sqrt{h^2+9d^2+y^2}}{-y+\sqrt{h^2+4d^2+y^2}}\right),\end{array}$

Wherein:

$\mathrm{\&rho;}\left(h\right)=hln\left(\frac{\sqrt{4h^2+{(l+L_P)}^2}}{\sqrt{4h^2+{(l-L_P)}^2}}\right)$

wherein l is the length of the switching region, and h is the coupling distance between the energy emitting coil and the vehicle-mounted energy pickup coil.

8. A method for designing parameters of an embedded energy transmitting coil of the wireless power supply system of the electric automobile according to claim 1, which is characterized by comprising the following steps:

s1, acquiring the length L of the vehicle-mounted energy pickup coil_pAnd width D_pAcquiring a coupling distance h between the energy transmitting coil and the vehicle-mounted energy pickup coil;

s2, designing the length L of the operation area and the length L of the switching area, wherein the length L of the switching area is not less than the length L of the vehicle-mounted energy pickup coil_pNamely: l is not less than L_p；

S3, designing the width D of the operation area and the width D of the switching area, wherein the width D of the operation area is not more than the wheel spacing D of the electric vehicle_mAnd not less than the width D of the on-board energy pickup coil_pNamely: d_p≤D≤D_m(ii) a The width D of the switching area is half of the width D of the operation area;

s4, designing the optimal turn ratio Zeta_o。

9. The method for designing the parameters of the embedded energy transmitting coil of the wireless power supply system of the electric automobile according to claim 8, wherein the optimal turn ratio is as follows:

${\mathrm{\&zeta;}}_o=\frac{N_r}{N_s}=\frac{g(l,d,L_p,h)}{f(L,D,L_p,h)},$

wherein N is_rNumber of turns in the operating region, N_sFor the number of turns of the switching region, L is the length of the switching region, d is the width of the switching region, L_pLength of the on-board energy pick-up coil, D is the width of the operating field, f (L, D, L)_pH) is a function of the length and width dimensions of the operating field, the length of the pick-up coil, and the coupling distance:

$f(L,D,L_p,h)=m\left(L_p\right)-m\left(D\right)+n\left(\frac{L-L_p}{2}\right)-n(-\frac{L+L_p}{2})+v\left(\frac{L+L_p}{2}\right)-v(-\frac{L-L_p}{2})+q$

wherein,

g(l,d,L_ph) is a function of the switching domain length-width dimension, the pick-up coil length, and the coupling distance:

$g(l,d,L_p,h)=\mathrm{\&chi;}\left(L_p\right)+\mathrm{\&chi;}\left(2d\right)-\mathrm{\&chi;}\left(3d\right)+\mathrm{\&lambda;}\&lsqb;\frac{1}{2}(l-L_p)\&rsqb;-\mathrm{\&lambda;}\&lsqb;-\frac{1}{2}(l+L_p)\&rsqb;+\mathrm{\&rho;}\left(h\right)$

wherein,

$\mathrm{\&chi;}\left(x\right)=x\ln \left(\frac{-x+\sqrt{\frac{4h^2+{(l+L_P)}^2}{4}+x^2}}{-x+\sqrt{\frac{4h^2+{(l-L_P)}^2}{4}+x^2}}\right)-x\ln \left(\frac{-x+\sqrt{\frac{4h^2+{(l-L_P)}^2}{4}+x^2}}{-x+\sqrt{\frac{4h^2+{(l+L_P)}^2}{4}+x^2}}\right),$

wherein: x ═ L_P,2d,3d；

$\begin{array}{c}\mathrm{\&lambda;}\left(y\right)=y\ln \left(\frac{y+\sqrt{h^2+y^2}}{y+\sqrt{h^2+{L_P}^2+y^2}}\right)+y\ln \left(\frac{-y+\sqrt{h^2+{L_P}^2+y^2}}{-y+\sqrt{h^2+y^2}}\right)\\ -y\ln \left(\frac{y+\sqrt{h^2+4d^2+y^2}}{y+\sqrt{h^2+9d^2+y^2}}\right)-y\ln \left(\frac{-y+\sqrt{h^2+9d^2+y^2}}{-y+\sqrt{h^2+4d^2+y^2}}\right),\end{array}$

Wherein:

$\mathrm{\&rho;}\left(h\right)=hln\left(\frac{\sqrt{4h^2+{(l+L_P)}^2}}{\sqrt{4h^2+{(l-L_P)}^2}}\right).$

10. a coil system formed by utilizing the embedded energy transmitting coils of the wireless power supply system of the electric automobile according to claim 1, characterized in that the coil system is formed by connecting m embedded energy transmitting coils of the wireless power supply system of the electric automobile according to claim 1, wherein m is a positive integer larger than 1, along the running direction of the automobile, the switching region of the previous energy transmitting coil and the switching region of the next energy transmitting coil are smoothly and tightly embedded in sequence, and in the direction perpendicular to the running direction of the automobile, the sum of the switching regions of the previous energy transmitting coil and the next energy transmitting coil is equal to the size of the running region.