Method and system for calculating maximum output power of harmonic generator

Abstract

The invention provides a harmonic generator maximum output power calculation method and system, and belongs to the field of rail transit. The calculation method comprises the following steps: firstly, enabling a runway type superconducting coil to be equivalent to a rectangle, setting a coordinate system at a geometric center, and constructing a magnetic flux density function of the superconducting coil; then, the serial number of 8-shaped coils directly facing the center of the superconducting coil at the t moment is 0, epsilon 8-shaped coils are contained in the space corresponding to one superconducting coil based on a space harmonic method, a magnetic flux density function of the 8-shaped coils is constructed, the maximum harmonic frequency is 2k-1, and the polar distance of the current collection coil is designed according to the maximum harmonic frequency 2k-1; constructing an induced electromotive force function Uc of a single current collection coil, calculating the internal resistance of the harmonic generator, finally constructing a maximum output power function of the harmonic generator, and solving the maximum output power of the harmonic generator. According to the method, the efficiency, accuracy and precision of harmonic generator power solving are improved, and accurate evaluation and optimal design of generator performance are realized.

Description

Technical Field

[0001] The present invention belongs to the field of rail transit, and particularly relates to a method and system for calculating the maximum output power of a harmonic generator of a maglev train. Background Art

[0002] In the field of rail transit, superconducting electromagnetic suspension trains are the fastest passenger transportation vehicles on land, and at the same time have the characteristics of low noise, low maintenance cost and environmental protection, meeting the development requirements of green travel. When a superconducting electromagnetic suspension train exceeds a certain speed, it cannot be powered by the pantograph contact power supply network system of traditional railway transportation, but a non-contact power supply system needs to be adopted. As shown in Figure 1 and Figure 2 A high-speed superconducting electromagnetic suspension train running on a U-shaped ground track is equipped with a battery and a converter on the vehicle body for powering on-vehicle loads; the power and battery energy of the train are supplied by an on-vehicle harmonic generator that generates electricity using the harmonic magnetic field of the "8"-shaped coils that are oppositely connected up and down on the ground in a non-contact power supply manner. The on-vehicle harmonic generator of the superconducting electromagnetic suspension train will generate an induced electromotive force in the "8"-shaped coils during the running of the train, thereby generating the levitation force and guiding force of the train. Since the superconducting coil magnetic field contains harmonic components, the generated air-gap harmonic magnetic field of the "8"-shaped coils will affect the stable operation of the superconducting electromagnetic suspension train, and at the same time reduce the energy utilization rate of the air-gap magnetic field. Therefore, an "8"-shaped current collection coil is arranged on the outer shell of the superconducting coil. On the one hand, it can use the harmonic of the air-gap magnetic field to generate electricity to meet the on-vehicle power consumption requirements, and on the other hand, it can also reduce the negative impact of the air-gap harmonic magnetic field on the vehicle operation and improve the vehicle energy efficiency.

[0003] In the prior art, as the power source of a superconducting electromagnetic suspension train, the parameters and influencing factors of an on-vehicle linear harmonic generator, especially the output power of the harmonic generator, are of great significance for the stable operation of the maglev train. However, the harmonic generator operates in a harmonic environment, and the structure of the current collection coil and the output characteristics of the harmonic generator are closely related to the harmonics of the air-gap magnetic field, and the air-gap magnetic field is a complex function related to the running speed, time, and spatial position of the superconducting coil and the "8"-shaped coils of the superconducting electromagnetic suspension vehicle. Therefore, at present, it is still impossible to accurately calculate the output power of the harmonic generator, which is not conducive to the control of the harmonic generator and the stable operation of the train. Summary of the Invention

[0004] In view of the above defects or deficiencies in the prior art, the present invention aims to provide a method and system for calculating the maximum output power of a harmonic generator. By optimizing the spatial harmonic algorithm, the parameters of the superconducting coil are accurately calculated. According to the magnetic flux density function of the "8" - shaped coil, the maximum harmonic order is determined, and further the optimal power generation pole pitch of the collector coil is determined. By introducing the variable resistance generated by the eddy current in the superconducting coil housing as the internal resistance of the harmonic generator, and considering the influence of the air - gap magnetic field distortion on R o the influence, a method for calculating the maximum output power of the harmonic generator is given, improving the efficiency, accuracy and precision of the power solution of the harmonic generator, and realizing the accurate evaluation and optimal design of the generator performance.

[0005] To achieve the above object, the embodiments of the present invention adopt the following technical solutions:

[0006] In a first aspect, the embodiments of the present invention provide a method for calculating the maximum output power of a harmonic generator, and the method includes the following steps:

[0007] Step S1, set the origin (x, y, z) of the first coordinate system at the geometric center position of the racetrack - type superconducting coil. The actual pole pitches of the superconducting coil are τ sx and τ sz respectively; Equivalent the racetrack - type superconducting coil to a rectangle, with the equivalent length in the x - axis direction being a s and the equivalent height in the z - axis direction being b s ; Assume that there are δ equivalent superconducting coils distributed in the coordinate system. Each single superconducting coil has the same pole pitch τ x =τ z in the x - axis and z - axis, and τ x >>τ sx , τ sz >>τ z ;

[0008] Step S2, construct the magnetic flux density function of the superconducting coil according to the coordinate setting and the equivalent coil. The dependent variables of the magnetic flux density function include the number of coils, structural parameters, electrical parameters, and the spatial position of the sampling points;

[0009] Step S3, assume that at time t, the serial number of the "8" - shaped coil facing the center of the superconducting coil is 0, and the serial numbers of the adjacent "8" - shaped coils in the opposite direction of the superconducting coil movement are 1, 2, 3, ······, and the pole pitch τ ex =τ sx / k (k≠1); Set the origin (xˊ, yˊ, zˊ) of the second coordinate system at the geometric center position of the 0 - th "8" - shaped coil;

[0010] Step S4: Based on the space harmonic method, there are ε “8”-shaped coils in the space corresponding to a superconducting coil; when ε = 3, analyze the magnetic motive force distribution generated by the current of the “8”-shaped coil in the xˊ direction.

[0011] Step S5: Construct the magnetic flux density function of the “8”-shaped coil. The dependent variables of the magnetic flux density function of the “8”-shaped coil include structural parameters, electrical parameters, the relative position between the “8”-shaped coil and the superconducting coil, and the vehicle driving speed; and it can be obtained from the constructed magnetic flux density function that the harmonic components of the air-gap magnetic flux density generated by the current of the “8”-shaped coil do not include harmonics of multiples of k, and its maximum harmonic order is 2k - 1.

[0012] Step S6: According to the magnetic flux density function of the superconducting coil, the magnetic flux density function of the “8”-shaped coil, and the fact that the maximum harmonic order of the air-gap magnetic field of the “8”-shaped coil is 2k - 1, set the position and pole pitch of the current collection coil.

[0013] Step S7: According to the setting of the current collection coil and the magnetic flux density function of the “8”-shaped coil, construct the induced electromotive force function U of a single current collection coil. c ;

[0014] Step S8: Assume that the internal resistance R of the harmonic generator eq includes a fixed resistance R c and a variable resistance R o in two parts, where R c is the inherent property of the harmonic generator, and R o is the resistance formed by the eddy current generated by the air-gap magnetic field on the outer shell of the superconducting coil.

[0015] Step S9: Construct the maximum output power function of the harmonic generator:

[0016]

[0017] In formula (28), η is the efficiency coefficient of the vehicle-mounted rectifier, and R eq is the internal resistance of the harmonic generator.

[0018] Solve the maximum output power of the harmonic generator according to formula (28).

[0019] As a preferred embodiment of the present invention, the structural parameters in Step S2, Step S5, and Step S9 include equivalent length, equivalent height, number of turns, and pole pitch; the electrical parameters in Step S2 and Step S5 at least include the injected current; the electrical parameters in Step S9 include resistivity and inductance.

[0020] As a preferred embodiment of the present invention, Step S2 constructs the magnetic flux density function of the superconducting coil, specifically including:

[0021] Using the space harmonic method, the Fourier expansion coefficients of the magnetomotive force of δ (δ = 0, 1, 2...) superconducting coils in the x direction are as follows:

[0022]

[0023] In formula (1), δ is the number of superconducting coils, and when there is 1 superconducting coil, δ = 0; N s 、I s are the number of turns of the superconducting coil and the injected current respectively; a s is the equivalent length of the superconducting coil in the x-axis direction; τ x is the assumed pole pitch of a single superconducting coil, and there is τ x >> τ sx (actual pole pitch of the superconducting coil).

[0024] The magnetomotive force F s (x) generated by δ superconducting coils in the x-axis direction is expressed as:

[0025]

[0026] The Fourier expansion coefficients of the magnetomotive force of δ superconducting coils in the z direction are as follows:

[0027]

[0028] Substituting formula (2) into formula (3), the expression of the magnetomotive force of δ superconducting coils in the xoz plane is obtained as:

[0029]

[0030] In formula (4), C s = 16N s I s sin(k sx ·a s / 2)sin(k sz ·b s / 2) / nmπ 2 , k sx = nπ / τ x , k sz = mπ / τ sz , and the series numbers n and m are both odd numbers;

[0031] According to the definition of the space scalar magnetic potential and Laplace's equation, it can be known that:

[0032]

[0033] Then the expression of the three-dimensional space scalar magnetic potential of the superconducting coil is:

[0034]

[0035] In Equation (6), λ = (k sx 2 + k sz 2 ) 1 / 2 ;

[0036] The y-axis component B of the magnetic flux density of the superconducting coil sy is represented by the scalar magnetic potential , and the magnetic flux density function of the superconducting coil is obtained as follows:

[0037]

[0038] In Equation (7), G s = 8μ0λN s I s sin(k sx ·a s / 2)sin(k sz ·b s / 2) / τ x τ z k sx k sz .

[0039] As a preferred embodiment of the present invention, in step S5, constructing the magnetic flux density function of the "8"-shaped coil specifically includes:

[0040] Based on the magnetomotive force distribution of the "8"-shaped coil, the Fourier expansion coefficient of the magnetomotive force of the 0th "8"-shaped coil in the x' direction is:

[0041]

[0042] In Equation (8), a e is the length of the "8"-shaped coil in the x' axis direction, and N e is the number of turns of the "8"-shaped coil;

[0043] Respectively, let the pole pitch τ ez = τ sz >> b e ; b e is the height of the "8"-shaped coil in the z' axis direction; then the magnetomotive force generated by the current of the εth upper and lower "8"-shaped coils is expressed as:

[0044]

[0045] In Equations (9) and (10), z U ˊ and z B ˊ are the coordinates of the centers of the upper and lower "8"-shaped coils on the z' axis respectively;

[0046] Adding the magnetomotive forces of ε upper and lower "8" - shaped coils, the magnetomotive force of the "8" - shaped coil corresponding to one superconducting length is obtained as follows:

[0047]

[0048] The current expression of the ε - th "8" - shaped coil at time t is:

[0049]

[0050] In formula (13), Z e = jnωN e / (jnωL e + R e ), F e = G e ·[cos(k sz z′ B ) - cos(k sz z′ U )]·e -λy ′, G e = 4f e G s , f e = sin(k sx ·a e / 2)·sin(k sz ·b e / 2) / k sx k sz ;

[0051] After substituting formula (13) into formulas (11) and (12), we get:

[0052]

[0053] In formulas (14) and (15), I εmax = (-1) δ Z e F e is the effective - value of the current of the ε - th "8" - shaped coil at time t. Using trigonometric - function transformation, we get:

[0054]

[0055] The magnetomotive forces of the upper and lower "8" - shaped coils at time t are obtained as follows:

[0056]

[0057] The scalar magnetic potential of the upper and lower "8" - shaped coils is:

[0058]

[0059]

[0060] Then, the magnetic induction intensities of the upper and lower "8"-shaped coils are expressed by the scalar magnetic potential as follows:

[0061]

[0062] In equations (21) and (22), P e = 4kμ0λN e f e / τ sx τ sz ;

[0063] Transfer the coordinate systems of the current collector coil and the superconducting coil operating synchronously to the maglev train, which coincides with the coordinate system (x, y, z) of the superconducting coil; where x' = x + vt, and the magnetic field of the "8"-shaped coil is the result of the overall excitation of the upper and lower coil currents, and the flux density function of the "8"-shaped coil is obtained as follows:

[0064]

[0065] In equation (23), Δy e is the distance between the midpoint of the superconducting coil and the midpoint of the "8"-shaped coil in the y-axis direction;

[0066] It can be obtained from formula (23) that the harmonic component of the air-gap flux density generated by the current of the "8"-shaped coil does not contain harmonics of multiples of k, and its maximum harmonic order is 2k - 1.

[0067] As a preferred embodiment of the present invention, in step S6, set the position and pole pitch of the current collector coil, and design the pole pitch τ cx of the current collector coil as τ cx = 4τ sx / 3(2k - 1), so as to obtain three-phase sine waves of UVW to cooperate with vehicle power supply.

[0068] As a preferred embodiment of the present invention, in step S7, construct the induced electromotive force function of a single current collector coil, which specifically includes:

[0069] According to formula (23), the fluxes of the upper and lower current collector coils under the induction of the maximum harmonic air-gap magnetic field are obtained as follows:

[0070]

[0071] In equations (24) and (25), f e | 2k-1 = sin(k sx | 2k-1 ·a e / 2)sin(k sz ·be / 2) / k sx | 2k-1 k sz , f cU | 2k-1 = sin(k sx | 2k-1 ·a c / 2)sin(k sz b cU / 2) / k sx | 2k-1 k sz , f cB | 2k-1 =sink sx | 2k-1 ·a c / 2)sin(k sz b cB / 2) / k sx | 2k-1 k sz ,λ| 2k-1 =(k sx | 2k-1 2 +k sz 2 ) 1 / 2 , k sx | 2k-1 =(2k-1)π / τ sx , I εmax | 2k-1 =(-1) δ Z e G e | 2k-1 , G e | 2k-1 =4f e | 2k-1 G s | 2k-1 , G s | 2k-1 =8μ0λ| 2k-1 N s I s sin(k sx | 2k-1 ·a s / 2)sin(k sz b s / 2) / τ x τ z k sx | 2k-1 k sz ;z cU and z cB are the coordinates of the center points of the upper and lower collector coils on the z-axis respectively;

[0072] The induced electromotive force of a single collector coil is as follows:

[0073]

[0074] In Equation (26), G c | 2k-1 = 128k 2 μ0N c N e ωI εmax | 2k-1 f e | 2k-1 (f cU | 2k-1 - f cB | 2k-1 )λ| 2k-1 / τ sx τ sz 。

[0075] As a preferred embodiment of the present invention, the variable resistor R in step S8 o The solution process is as follows:

[0076] The existence of Δz makes the eddy current heights in the upper and lower parts of the superconducting coil housing corresponding to the "8" - shaped coil position of the air - gap magnetic field different. The upper - part eddy current height b oU = b o / 2 - Δz, and the lower - part eddy current height b oB = b o / 2 + Δz, where b o is the height of the superconducting coil housing;

[0077] The magnetic field of the "8" - shaped coil will cause distortion at the edge of the superconducting coil housing. The corresponding air - gap correction coefficient ζ caused by the edge effect of the harmonic generator is as follows:

[0078]

[0079] In Equation (27), B eymax and Bey av are respectively the maximum value and the average value of the air - gap magnetic field of the "8" - shaped coil;

[0080] The variable resistor R o is expressed as:

[0081]

[0082] In Equation (28), μ r and ρ are respectively the relative magnetic permeability and resistivity of the superconducting coil housing, and v is the vehicle running speed.

[0083] As a preferred embodiment of the present invention, when constructing the maximum power output function of the harmonic generator in step S8, the corresponding load obtains the maximum power;

[0084] When U c ≠ 0, the condition for the load to obtain the maximum power is:

[0085]

[0086] In formula (29), X and R are the reactance and resistance of the load respectively, and X c is the reactance of the harmonic generator.

[0087] Second, the embodiment of the present invention also provides a system for calculating the maximum output power of a harmonic generator. The system includes: a superconducting coil equivalent module, a superconducting coil magnetic density function construction module, an "8" - shaped coil setting module, an "8" - shaped coil magnetomotive force analysis module, an "8" - shaped coil magnetic density function construction module, a collector coil setting module, an electromotive force function construction module for a single collector coil, an internal resistance calculation module of the harmonic generator, and a maximum output power function construction module; among them,

[0088] The superconducting coil equivalent module is used to set the origin (x, y, z) of the first coordinate system at the geometric center position of the racetrack - type superconducting coil. The actual pole pitches of the superconducting coil are τ sx and τ sz respectively; the racetrack - type superconducting coil is equivalent to a rectangle, and its length and height are a s and b s respectively; it is assumed that there are δ equivalent superconducting coils distributed in the coordinate system, and the superconducting coils with the same pole pitch τ x = τ z on the x - axis and z - axis, and τ x >> τ sx , τ sz >> τ z ;

[0089] The superconducting coil magnetic density function construction module is used to construct the magnetic flux density function of the superconducting coil according to the coordinate setting and equivalent coils. The dependent variables of the magnetic flux density function include the number of coils, structural parameters, electrical parameters, and the spatial position of the sampling points;

[0090] The "8" - shaped coil setting module is used to set the serial number of the "8" - shaped coil facing the center of the superconducting coil as 0 at time t, and the serial numbers of the adjacent "8" - shaped coils in the opposite direction to the traveling direction of the superconducting coil are 1, 2, 3, ······, and the pole pitch τ ex = τ sx / k, and k ≠ 1; the origin (x′, y′, z′) of the second coordinate system is set at the geometric center position of the 0 - th "8" - shaped coil;

[0091] The "8"-shaped coil magnetomotive force analysis module is used to analyze the magnetomotive force distribution generated by the current of the "8"-shaped coil in the x' direction in the space corresponding to a superconducting coil based on the space harmonic method. When ε = 3, there are ε "8"-shaped coils in the space corresponding to a superconducting coil.

[0092] The "8"-shaped coil magnetic flux density function construction module is used to construct the magnetic flux density function of the "8"-shaped coil. The dependent variables of the magnetic flux density function of the "8"-shaped coil include structural parameters, electrical parameters, the relative position between the "8"-shaped coil and the superconducting coil, and the vehicle driving speed. And it can be obtained from the constructed magnetic flux density function that the harmonic components of the air-gap magnetic flux density generated by the current of the "8"-shaped coil do not include harmonics of multiples of k, and its maximum harmonic order is 2k - 1.

[0093] The collector coil setting module is used to set the position and pole pitch of the collector coil according to the magnetic flux density function of the superconducting coil, the magnetic flux density function of the "8"-shaped coil, and the fact that the maximum harmonic order of the air-gap magnetic field of the "8"-shaped coil is 2k - 1.

[0094] The single collector coil electromotive force function construction module is used to construct the single collector coil induced electromotive force function U according to the setting of the collector coil and the magnetic flux density function of the "8"-shaped coil. c ;

[0095] The harmonic generator internal resistance calculation module is used to calculate the internal resistance R of the harmonic generator, which includes two parts: a fixed resistance R c and a variable resistance R o . The internal resistance R of the harmonic generator is the sum of these two parts. Among them, R eq is the inherent property of the harmonic generator, and R c is the resistance formed by the eddy current generated by the air-gap magnetic field on the outer shell of the superconducting coil. o ;

[0096] The maximum output power function construction module is used to construct the maximum output power function of the harmonic generator:

[0097]

[0098] In Equation (30), η is the efficiency coefficient of the vehicle-mounted rectifier, and R eq is the internal resistance of the harmonic generator. It is also used to solve the maximum output power of the harmonic generator according to Equation (30).

[0099] The technical solution provided by the embodiment of the present invention has the following beneficial effects:

[0100] The method and system for calculating the maximum output power of a harmonic generator provided by the embodiments of the present invention solve the calculation bottleneck of inaccurate calculation of harmonic magnetic field parameters of traditional superconducting coils by using an optimized spatial harmonic algorithm. The maximum harmonic order is determined to be 2k - 1 according to the magnetic flux density function of the "8" - shaped coil, and the optimal power generation pole pitch of the UVW three - phase collector coil is further determined to be 4τ sx / 3(2k - 1). By introducing a variable resistance R o generated by the eddy current in the superconducting coil housing as the internal resistance of the harmonic generator, and considering the influence of the air - gap magnetic field distortion on R o , a method for calculating the maximum output power of the harmonic generator is given. The present invention is applicable to a variety of superconducting electromagnetic levitation structures, including multiple superconducting coils, various "8" - shaped coil pole pitch configurations, and the calculation of the output power of the harmonic generator at different speeds. It improves the efficiency, accuracy, and precision of solving the power of the harmonic generator, can quickly and accurately verify the output characteristics of the superconducting electromagnetic levitation harmonic generator in the initial design stage, and realizes the accurate evaluation and optimal design of the generator performance, thus laying a solid foundation for promoting the innovative development and practical application process of electromagnetic levitation technology.

[0101] Of course, when implementing any product or method of the present invention, it is not necessarily required to achieve all the above - mentioned advantages simultaneously. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0103] Figure 1 is a schematic diagram of the overall power structure of a superconducting electromagnetic levitation train in the prior art;

[0104] Figure 2 is a schematic cross - sectional view of the power structure of a superconducting electromagnetic levitation train in the prior art;

[0105] Figure 3 is a flowchart of the method for calculating the maximum output power of the harmonic generator in the embodiments of the present invention;

[0106] Figure 4 is a schematic diagram of the rectangular equivalence of a superconducting coil in the embodiments of the present invention;

[0107] Figure 5 is Figure 3 the distribution diagram of the magnetomotive force in the x - direction of the superconducting coil equivalent to a rectangle;

[0108] Figure 6It is the distribution diagram of the magnetomotive force in the x' direction of the "8" - shaped coil in the embodiment of the present invention;

[0109] Figure 7 It is the schematic diagram of the collector coil structure in the embodiment of the present invention;

[0110] Figure 8 It is the schematic diagram of the eddy current of the "8" - shaped coil in the embodiment of the present invention;

[0111] Figure 9 It is the schematic diagram of the eddy current of the superconducting coil housing in the embodiment of the present invention;

[0112] Figure 10 It is the equivalent circuit diagram of the linear generator in the embodiment of the present invention. Specific embodiments

[0113] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and illustrated here can be arranged and designed in various different configurations. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can also be combined with each other.

[0114] It should be noted that: similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present invention, the terms "first", "second", "third", "fourth", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0115] Regarding the power calculation problem of harmonic generators in the prior art, the embodiments of the present invention propose a method and system for calculating the maximum output power of a harmonic generator. As Figure 3 shown, the method includes the following steps:

[0116] Step S1, as Figure 4 shown, set the origin (x, y, z) of the first coordinate system at the geometric center position of the racetrack - shaped superconducting coil. The actual pole pitches of the superconducting coil are τ sx and τ sz respectively; Equivalent the racetrack - shaped superconducting coil to a rectangle. The equivalent length in the x - axis direction is a s , and the equivalent height in the z - axis direction is b s ; Assume that there are δ equivalent superconducting coils distributed in the coordinate system. Each single superconducting coil has the same pole pitch τ x = τ z on the x - axis and the z - axis, and τ x >> τ sx , τsz >>τ z 。

[0117] In this step, the racetrack-shaped superconducting coil is equivalently processed to facilitate the analysis of the magnetic field of the superconducting coil. In the traditional space harmonic method, when equivalent the pole pitch of the superconducting coil, the actual pole pitch is used for calculation. Such a result will make the magnetic flux density of the superconducting coil an infinite loop without boundaries when calculating. In this step, a hypothetical superconducting coil is introduced to optimize the space harmonic method. The pole pitch of the hypothetical superconducting coil is much larger than the actual pole pitch. In this way, when calculating, the magnetic flux density of each superconducting coil can be calculated individually, and then according to the actual number of coils, the magnetic flux densities of multiple coils are added together. Such a calculation result can accurately express the magnitude of the magnetic flux density of the two-sided coils, thereby improving the accuracy of the subsequent harmonic calculation.

[0118] Step S2, according to the coordinate setting and the equivalent coil, construct the magnetic flux density function of the superconducting coil. The dependent variables of the magnetic flux density function include the number of coils, structural parameters (equivalent length, equivalent height, number of turns, pole pitch), electrical parameters (injected current), and the spatial position of the sampling point.

[0119] In this step, the optimized space harmonic algorithm is used to solve the calculation bottleneck of inaccurate calculation of the harmonic magnetic field parameters of the traditional superconducting coil. The construction process of the magnetic flux density function of the superconducting coil is as follows:

[0120] As Figure 5 shown, using the space harmonic method, the Fourier expansion coefficients of the magnetomotive force of δ (δ = 0, 1, 2...) superconducting coils in the x direction are:

[0121]

[0122] In formula (1), δ is the number of superconducting coils. When there is 1 superconducting coil, δ = 0; N s , I s are the number of turns and the injected current of the superconducting coil respectively; a s is the equivalent length of the superconducting coil in the x-axis direction; τ x is the pole pitch of a single hypothetical superconducting coil, and there is τ x >>τ sx (actual pole pitch of the superconducting coil).

[0123] Since the superconducting magnetic field distribution is symmetric about the y-axis, the magnetomotive force F s (x) generated by δ superconducting coils in the x-axis direction is expressed as:

[0124]

[0125] When calculating the magnetomotive force in the z-axis direction, F should be includeds (x) component, then the Fourier expansion coefficient of the magnetomotive force of δ superconducting coils in the z direction is:

[0126]

[0127] After substituting formula (2) into formula (3), the expression of the magnetomotive force of δ superconducting coils in the xoz plane can be obtained as:

[0128]

[0129] In formula (4), C s = 16N s I s sin(k sx ·a s / 2)sin(k sz ·b s / 2) / nmπ 2 , k sx = nπ / τ x , k sz = mπ / τ sz , and both the series numbers n and m are odd numbers.

[0130] According to the definition of the space scalar magnetic potential and Laplace's equation, it can be known that:

[0131]

[0132] Then the expression of the superconducting coil three-dimensional space scalar magnetic potential is:

[0133]

[0134] In formula (6), λ = (k sx 2 + k sz 2 ) 1 / 2 .

[0135] The y-axis component B sy of the superconducting coil magnetic flux density can be expressed by the scalar magnetic potential , that is:

[0136]

[0137] In formula (7), G s = 8μ0λN s I s sin(k sx ·a s / 2)sin(k sz ·b s / 2) / τ x τz k sx k sz 。

[0138] Step S3: At time t, let the serial number of the figure-eight coil facing the center of the superconducting coil be 0, and the serial numbers of the adjacent figure-eight coils in the direction opposite to the traveling direction of the superconducting coil be 1, 2, 3, ······, and the pole pitch τ of the figure-eight coil ex = τ sx / k (k≠1); Set the origin (x′, y′, z′) of the second coordinate system at the geometric center position of the 0th figure-eight coil.

[0139] In this step, by comparing with the superconducting coil, the air-gap magnetic field of the figure-eight coil is analyzed.

[0140] Step S4: Based on the space harmonic method, there are ε figure-eight coils in the space corresponding to one superconducting coil; when ε = 3, the magnetomotive force distribution generated by the figure-eight coil current in the x′ direction is as Figure 6 shown.

[0141] Step S5: Construct a figure-eight coil magnetic flux density function. The dependent variables of the figure-eight coil magnetic flux density function include structural parameters (equivalent length, equivalent height, number of turns, pole pitch), electrical parameters (resistivity, inductance), the relative position between the figure-eight coil and the superconducting coil, and the vehicle traveling speed; and it can be obtained from the constructed magnetic flux density function that the harmonic components of the air-gap magnetic flux density generated by the figure-eight coil current do not include harmonics of multiples of k, and its maximum harmonic order is 2k - 1.

[0142] In this step, when constructing the figure-eight coil magnetic flux density function, various figure-eight coil pole pitch structures are considered. Specifically, the process of constructing the figure-eight coil magnetic flux density function is as follows:

[0143] Based on the magnetomotive force distribution as Figure 6 shown, the Fourier expansion coefficient of the magnetomotive force of the 0th figure-eight coil in the x′ direction is:

[0144]

[0145] In Equation (8), a e is the length of the figure-eight coil in the x′ axis direction, and N e is the number of turns of the figure-eight coil. Since the current directions of the upper and lower figure-eight coils are opposite, it is necessary to analyze their space magnetomotive force distributions separately. Let the pole pitches τ of the upper and lower figure-eight coils in the zˊ axis direction be ez = τ sz >> b e(Height of the figure-eight coil in the z' axis direction), the magnetomotive force generated by the ε-th upper and lower figure-eight coil currents can be expressed as:

[0146]

[0147] In equations (9) and (10), z U ˊ and z B ˊ are the coordinates of the centers of the upper and lower figure-eight coils on the z' axis respectively. Summing up the magnetomotive forces of the ε upper and lower figure-eight coils, the magnetomotive force of the figure-eight coil corresponding to a superconducting length can be obtained as:

[0148]

[0149] Because the currents of adjacent figure-eight coils differ by π / k but have the same amplitude, the current expression of the ε-th figure-eight coil at time t is:

[0150]

[0151] In equation (13), Z e =jnωN e / (jnωL e +R e ), F e =G e ·[cos(k sz z′ B )-cos(k sz z′ U )]·e -λy ′, G e =4f e G s , f e =sin(k sx ·a e / 2)·sin(k sz ·b e / 2) / k sx k sz ;

[0152] Substituting formula (13) into formulas (11) and (12), we get:

[0153]

[0154] In equations (14) and (15), I εmax =(-1) δ Z e F e is the effective value of the current of the ε-th figure-eight coil at time t. Using trigonometric function transformation, we get:

[0155]

[0156] Finally, the magnetomotive force of the upper and lower "8" - shaped coils at time t can be obtained as follows:

[0157]

[0158] Furthermore, from formula (5), it can be known that the scalar magnetic potential of the upper and lower "8" - shaped coils is:

[0159]

[0160]

[0161] Then, the magnetic induction intensity of the upper and lower "8" - shaped coils can be expressed by the scalar magnetic potential, that is:

[0162]

[0163] In formulas (21) and (22), P e = 4kμ0λN e f e / τ sx τ sz , since the current - collecting coil runs synchronously with the superconducting coil, for the convenience of calculation, the coordinate system is transferred to the maglev train and coincides with the coordinate system (x, y, z) of the superconducting coil. Among them, x′ = x + vt, and the magnetic field of the "8" - shaped coil is the result of the overall excitation of the upper and lower coil currents. Therefore, the expression of the magnetic flux density of the "8" - shaped coil is:

[0164]

[0165] In formula (23), Δy e is the distance between the mid - point of the superconducting coil and the mid - point of the "8" - shaped coil in the y - axis direction.

[0166] It can be seen from the result of formula (23) that the harmonic components of the air - gap magnetic flux density generated by the current of the "8" - shaped coil do not contain harmonics of multiples of k, and its maximum harmonic order is 2k - 1. In addition, the structure of the 8 - shaped coil includes physical structure (length and height) and electrical structure (pole pitch, current, magnetic flux density). The above calculation of the expression of the magnetic flux density of the 8 - shaped coil can be applied to various physical structures and electrical structures, and a unified calculation formula can be given according to different pole pitches of the 8 - shaped coil, and the maximum harmonic order related to the pole pitch can be obtained.

[0167] Step S6: Set the position and pole pitch of the current - collecting coil according to the magnetic flux density function of the superconducting coil, the magnetic flux density function of the "8" - shaped coil, and the maximum harmonic order of the air - gap magnetic field of the "8" - shaped coil being 2k - 1.

[0168] In this step, since the collector coil and the superconducting coil operate synchronously, it is impossible to generate electricity using the air-gap fundamental magnetic field. In order to obtain three-phase sine waves of UVW to cooperate with vehicle power supply, the pole pitch of the collector coil is designed based on the air-gap magnetic field of the "8"-shaped coil.

[0169] As Figure 7 shown, the magnetic flux density of the "8"-shaped coil contains three directions of x, y, and z. However, for the collector coil, only the magnetic flux density in the y direction is effective. Therefore, only B ey , that is, formula (23), needs to be calculated. In addition, the selection of y e and y c should match the actual track distance and the on-vehicle power consumption requirements. Since the maximum harmonic order of the "8"-shaped coil is 2k - 1, the period distance corresponding to a complete 2k - 1 harmonic represented by the superconducting coil pole pitch is 2τ sx / (2k - 1). Placing the three-phase collector coils within this distance, the pole pitch of the collector coil is 2τ sx / 3(2k - 1). However, such a setting will make the collector coils too dense, wasting resources, and there may not be enough space for the three-phase collector coils due to the too large maximum harmonic order. Therefore, the pole pitch of the collector coil needs to be doubled, and finally, the pole pitch of the collector coil is determined to be 4τ sx / 3(2k - 1).

[0170] Step S7: Construct the induced electromotive force function of a single collector coil according to the setting of the collector coil and the magnetic flux density function of the "8"-shaped coil.

[0171] In this step, according to formula (23), the magnetic fluxes of the upper and lower collector coils under the induction of the maximum harmonic air-gap magnetic field can be obtained as follows:

[0172]

[0173]

[0174] In equations (24) and (25), f e | 2k-1 =sin(k sx | 2k-1 ·a e / 2)sin(k sz ·b e / 2) / k sx | 2k-1 k sz ,f cU | 2k-1 =sin(k sx | 2k-1 ·a c / 2)sin(k sz ·bcU / 2) / k sx | 2k-1 k sz ,f cB | 2k-1 =sink sx | 2k-1 ·a c / 2)sin(k sz ·b cB / 2) / k sx | 2k-1 k sz ,λ| 2k-1 =(k sx | 2k-1 2 +k sz 2 ) 1 / 2 ,k sx | 2k-1 =(2k - 1)π / τ sx ,I εmax | 2k-1 =(-1) δ Z e G e | 2k-1 ,G e | 2k-1 =4f e | 2k-1 G s | 2k-1 ,G s | 2k-1 =8μ0λ| 2k-1 N s I s sin(k sx | 2k-1 ·a s / 2)sin(k sz ·b s / 2) / τ x τ z k sx | 2k-1 k sz 。z cU and z cB are the coordinates of the centers of the upper and lower current - collecting coils on the z - axis, respectively. Since the magnetic field directions induced by the "8" - shaped coil in the upper and lower current - collecting coils are opposite, and the current - collecting coil is also in the "8" - shaped structure, the induced electromotive force of a single current - collecting coil is:

[0175]

[0176] In Equation (26), G c | 2k-1 =128k 2μ0N c N e ωI εmax | 2k-1 f e | 2k-1 (f cU | 2k-1 -f cB | 2k-1 )λ| 2k-1 / τ sx τ sz 。

[0177] Step S8, set the internal resistance R of the harmonic generator eq including a fixed resistor R c and a variable resistor R o in two parts, where R c is the inherent property of the harmonic generator, and R o is the resistance formed by the eddy current generated by the air-gap magnetic field on the outer shell of the superconducting coil.

[0178] In this step, as Figure 8 shown, due to the existence of Δz, the eddy current heights in the upper and lower parts of the air-gap magnetic field corresponding to the "8"-shaped coil position on the outer shell of the superconducting coil are different, that is, the upper part eddy current height b oU = b o / 2 - Δz, and the lower part eddy current height b oB = b o / 2 + Δz, where b o is the height of the outer shell of the superconducting coil. In addition, as Figure 9 shown, the magnetic field of the "8"-shaped coil will cause distortion at the edge of the outer shell of the superconducting coil. Therefore, in order to determine the variable resistor R o , the corresponding air-gap correction coefficient ζ caused by the edge effect of the harmonic generator also needs to be considered.

[0179]

[0180] In Equation (27), B eymax and Bey av are respectively the maximum value and the average value of the air-gap magnetic field of the "8"-shaped coil.

[0181] Then the variable resistor R o can be expressed as:

[0182]

[0183] In Equation (28), μ r and ρ are respectively the relative magnetic permeability and resistivity of the outer shell of the superconducting coil, and v is the vehicle running speed.

[0184] Step S9: Construct the maximum output power function of the harmonic generator. The dependent variables of the maximum output power function include the structural parameters of the current collection coil (equivalent length, equivalent height, number of turns, pole pitch), electrical parameters (resistivity, inductance), the relative position between the current collection coil and the figure-eight coil, and the vehicle traveling speed.

[0185] In this step, as Figure 10 shown, when U c ≠ 0, the condition for the load to obtain the maximum power is:

[0186]

[0187] In formula (29), X and R are the reactance and resistance of the load respectively, and X c and R eq are the reactance and internal resistance of the harmonic generator. For the load to obtain the maximum power, two conditions need to be met simultaneously. First, when the harmonic generator is inductive, a capacitive power device needs to be connected in series at the load end to offset the influence of the inductive part on the phase of the load current, so that the same phase of voltage and current can be obtained. In addition, since the internal resistance R eq of the harmonic generator contains the variable resistance R o , from formula (28), it can be seen that the value of R eq depends on the speed V, the pole pitch τ ex of the figure-eight coil, as well as the size of the superconducting outer shell and the figure-eight coil. Therefore, the load resistance also needs to be adjusted to satisfy R = R eq . In this way, the load can obtain the maximum output power of the harmonic generator.

[0188] Then the maximum output power of the harmonic generator can be expressed as:

[0189]

[0190] In formula (30), η is the efficiency coefficient of the vehicle-mounted rectifier, and R eq is the internal resistance of the harmonic generator.

[0191] As can be seen from the above technical solutions, the method for calculating the maximum output power of the harmonic generator based on the maglev train provided by the embodiment of the present invention uses the optimized spatial harmonic algorithm to solve the calculation bottleneck of inaccurate calculation of the harmonic magnetic field parameters of the traditional superconducting coil. According to the magnetic flux density function of the figure-eight coil, the maximum harmonic order is determined to be 2k - 1 times, and the optimal power generation pole pitch of the UVW three-phase current collection coil is further determined to be 4τ sx / 3(2k - 1). By introducing the variable resistance R o generated by the eddy current of the superconducting coil outer shell as the internal resistance of the harmonic generator, and considering the influence of the air-gap magnetic field distortion on R oThe influence is given, and a calculation method for the maximum output power of a harmonic generator is provided. The present invention is applicable to various superconducting electromagnetic levitation structures, including multiple superconducting coils, various "8"-shaped coil pole pitch configurations, calculation of the output power of a harmonic generator at different speeds, improving the efficiency, accuracy, and precision of solving the power of a harmonic generator, enabling rapid and accurate verification of the output characteristics of a superconducting electromagnetic levitation harmonic generator in the initial design stage, realizing accurate evaluation and optimal design of the generator performance, and thus laying a solid foundation for promoting the innovative development and practical application process of electromagnetic levitation technology.

[0192] Based on the same idea, an embodiment of the present invention also provides a system for calculating the maximum output power of a harmonic generator, the system includes: a superconducting coil equivalent module, a superconducting coil magnetic density function construction module, an "8"-shaped coil setting module, an "8"-shaped coil magnetomotive force analysis module, an "8"-shaped coil magnetic density function construction module, a collector coil setting module, a single collector coil electromotive force function construction module, a harmonic generator internal resistance calculation module, a maximum output power function construction module; wherein,

[0193] The superconducting coil equivalent module is used to set the origin (x, y, z) of the first coordinate system at the geometric center position of the runway-shaped superconducting coil, and the actual pole pitches of the superconducting coils are τ sx and τ sz respectively; the runway-shaped superconducting coil is equivalent to a rectangle, the equivalent length in the x-axis direction is a s , and the equivalent height in the z-axis direction is b s ; assuming that there are δ superconducting coils distributed in the coordinate system, and a single superconducting coil has the same pole pitch τ x =τ z on the x-axis and z-axis, and τ x >>τ sx , τ sz >>τ z ;

[0194] The superconducting coil magnetic density function construction module is used to construct the magnetic flux density function of the superconducting coil according to the coordinate setting and the equivalent coil, and the dependent variables of the magnetic flux density function include the number of coils, structural parameters, electrical parameters, and sampling point spatial positions;

[0195] The "8"-shaped coil setting module is used to set the serial number of the "8"-shaped coil facing the center of the superconducting coil at t time to 0, and the serial numbers of the adjacent "8"-shaped coils in the opposite direction to the traveling direction of the superconducting coil are 1, 2, 3, ······, and the pole pitch τ ex =τ sx / k (k≠1); set the origin (xˊ, yˊ, zˊ) of the second coordinate system at the geometric center position of the 0th "8"-shaped coil;

[0196] The "8"-shaped coil magnetomotive force analysis module is used to analyze the magnetomotive force distribution generated by the current of the "8"-shaped coil in the x'-direction in the space corresponding to a superconducting coil based on the space harmonic method. When ε = 3, there are ε "8"-shaped coils in the space corresponding to a superconducting coil.

[0197] The "8"-shaped coil magnetic flux density function construction module is used to construct the magnetic flux density function of the "8"-shaped coil. The dependent variables of the magnetic flux density function of the "8"-shaped coil include structural parameters, electrical parameters, the relative position between the "8"-shaped coil and the superconducting coil, and the vehicle driving speed. And it can be obtained from the constructed magnetic flux density function that the harmonic components of the air-gap magnetic flux density generated by the current of the "8"-shaped coil do not include harmonics of multiples of k, and its maximum harmonic order is 2k - 1.

[0198] The collector coil setting module is used to set the position and pole pitch of the collector coil according to the magnetic flux density function of the superconducting coil, the magnetic flux density function of the "8"-shaped coil, and the maximum harmonic order of the air-gap magnetic field of the "8"-shaped coil being 2k - 1.

[0199] The single collector coil electromotive force function construction module is used to construct the single collector coil induced electromotive force function U according to the setting of the collector coil and the magnetic flux density function of the "8"-shaped coil. c ;

[0200] The harmonic generator internal resistance calculation module is used to set the internal resistance R of the harmonic generator. eq It includes a fixed resistance R. c and a variable resistance R. o Two parts, where R. c is the inherent property of the harmonic generator, and R. o is the resistance formed by the eddy current generated by the air-gap magnetic field on the outer shell of the superconducting coil.

[0201] The maximum output power function construction module is used to construct the maximum output power function of the harmonic generator:

[0202]

[0203] In formula (30), η is the efficiency coefficient of the vehicle-mounted rectifier, and R. eq is the internal resistance of the harmonic generator; it is also used to solve the maximum output power of the harmonic generator according to formula (30).

[0204] In this embodiment, each module is implemented by a processor, and a memory is appropriately added when storage is required. Among them, the processor may be, but is not limited to, a microprocessor MPU, a central processing unit (CPU), a network processor (NP), a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), other programmable logic devices, discrete gate, transistor logic devices, discrete hardware components, etc. The memory may include a random access memory (RAM), and may also include a non-volatile memory (NVM), such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the aforementioned processor.

[0205] In the above embodiment, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present invention are generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.).

[0206] In addition, it should be noted that the harmonic generator output power calculation system of the maglev train in this embodiment corresponds to the harmonic generator output power calculation method of the maglev train. The description and limitation of the method also apply to the system, and will not be repeated here.

[0207] The above description is only a preferred embodiment of the present invention and an explanation of the applied technical principles, and is not intended to limit the scope of the claimed invention, but merely represents a preferred embodiment of the present invention. Those skilled in the art should understand that the scope of the invention involved in the present invention is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present invention.

Claims

1. A method for calculating the maximum output power of a harmonic generator, characterized in that: The method comprises the following steps: Step S1, setting the origin of the first coordinate system (x, y, z) at the geometric center of the racetrack-shaped superconducting coil, and the actual pole pitches of the superconducting coil are τ sx and τ sz ; The racetrack superconducting coil is equivalent to a rectangle, and the equivalent length in the x-axis direction is a s , the equivalent height in the z-axis direction is b s ; Assume that there are δ equivalent superconducting coils distributed in the coordinate system, and a single superconducting coil has the same pole distance τ on the x-axis and z-axis x =τ z , and τ x >>τ sx , τ sz >>τ z ; Step S2, constructing a magnetic flux density function of the superconducting coil according to the coordinate setting and the equivalent coil, wherein the dependent variables of the magnetic flux density function include the number of coils, structural parameters, electrical parameters and spatial positions of sampling points; Step S3, assuming that at time t, the number of the "8" coil facing the center of the superconducting coil is 0, the numbers of the adjacent "8" coils in the opposite direction of the superconducting coil are 1, 2, 3, ..., and the "8" coil pole pitch τ ex =τ sx / k, and k≠1; set the origin of the second coordinate system (x′, y′, z′) at the geometric center of the No. 0 "8" coil; Step S4, based on the space harmonic method, a space corresponding to a superconducting coil contains ε "8" coils; when ε=3, the magnetomotive force distribution generated by the current of the "8" coil in the x' direction is analyzed; Step S5, constructing a magnetic flux density function of the "8"-shaped coil, the dependent variables of which include structural parameters, electrical parameters, the relative position of the "8"-shaped coil and the superconducting coil, and the vehicle speed; and from the constructed magnetic flux density function, it can be obtained that the harmonic component of the air gap magnetic flux density generated by the "8"-shaped coil current does not contain multiple harmonics of k, and its maximum harmonic order is 2k-1 times; Step S6, setting the position and pole pitch of the collector coil according to the magnetic flux density function of the superconducting coil and the magnetic flux density function of the "8" coil and the maximum harmonic order of the air gap magnetic field of the "8" coil is 2k-1 times; Step S7, constructing the induced electromotive force function U of a single collector coil according to the setting of the collector coil and the magnetic flux density function of the "8" coil c ; Step S8, set the internal resistance R of the harmonic generator eq Including fixed resistor R c and variable resistor R o Two parts, R c is the inherent property of the harmonic generator, R o The resistance formed by the eddy current generated by the air gap magnetic field in the superconducting coil shell; Step S9, constructing the maximum output power function of the harmonic generator: In formula (30), η is the efficiency coefficient of the on-board rectifier, R eq is the internal resistance of the harmonic generator; The maximum output power of the harmonic generator is solved according to formula (30).

2. The method according to claim 1, characterized in that: The structural parameters in step S2, step S5 and step S9 include equivalent length, equivalent height, number of turns, and pole pitch; the electrical parameters in step S2 and step S5 include at least injected current; and the electrical parameters in step S9 include resistivity and inductance.

3. The method according to claim 2, characterized in that Step S2 constructs the magnetic flux density function of the superconducting coil, specifically including: Using the spatial harmonic method, the Fourier expansion coefficient of the magnetomotive force of δ (δ=0,1,2...) superconducting coils in the x direction is: In formula (1), δ is the number of superconducting coils. When there is one superconducting coil, δ = 0; N s ,I s are the number of superconducting coil turns and the injected current respectively; The magnetomotive force F generated by the δ superconducting coils in the x-axis direction s (x) is expressed as: The Fourier expansion coefficient of the magnetomotive force of δ superconducting coils in the z direction is: Substituting formula (2) into formula (3), we get the expression of the magnetomotive force of δ superconducting coils in the xoz plane: In formula (4), C s =16N s I s sin(k sx ·a s / 2)sin(k sz b s / 2) / nmπ 2 , k sx =nπ / τ x , k sz =mπ / τ sz , the set numbers n and m are both cardinal numbers; According to the spatial scalar magnetic potential From the definition of and Laplace equation, we know that: Then the expression of the scalar magnetic potential of the superconducting coil in three-dimensional space is: In formula (6), λ=(k sx 2 +k sz 2 ) 1 / 2 ; Superconducting coil magnetic flux density y-axis component B sy Scalar magnetic potential The magnetic flux density function of the superconducting coil is shown as follows: In Equation (7), G s = 8μ0λN s I s sin(k sx ·a s / 2)sin(k sz ·b s / 2) / τ x τ z k sx k sz .

4. The method according to claim 3, characterized in that In step S5, the "8" coil magnetic flux density function is constructed, which specifically includes: Based on the magnetomotive force distribution of the "8" coil, the Fourier expansion coefficient of the magnetomotive force of the "8" coil No. 0 in the x' direction is: In formula (8), a e N is the length of the "8" coil in the x' axis direction, e The number of turns of the "8" coil; Let the pole distance τ of the upper and lower "8" coils in the zˊ axis direction be ez =τ sz >>b e ; b e is the height of the "8" coil in the zˊ axis direction; then the magnetomotive force generated by the current of the εth upper and lower "8" coils is expressed as: In formulas (9) and (10), z U ˊ and z B ˊ are the coordinates of the center points of the upper and lower "8" coils on the zˊ axis; Add the magnetomotive force of the ε upper and lower "8" coils to obtain the magnetomotive force of the "8" coil corresponding to one superconducting length: At time t, the current expression of the εth "8" coil is: In Equation (13), Z e = jnωN e / (jnωL e + R e ), F e = G e ·[cos(k sz z′ B ) - cos(k sz z′ U )]·e -λy ′, G e = 4f e G s , f e = sin(k sx ·a e / 2)·sin(k sz ·b e / 2) / k sx k sz ; Substituting formula (13) into formula (11) and (12), we get: In formulas (14) and (15), I εmax =(-1) δ Z e F e is the effective value of the current of the εth "8" coil at time t, which can be transformed by trigonometric functions: The magnetomotive force of the upper and lower "8" coils at time t is obtained as follows: The scalar magnetic potential of the upper and lower "8" coils is: Then the magnetic induction intensity of the upper and lower "8" coils is expressed by the scalar magnetic potential as: In formulas (21) and (22), P e =4kμ0λN e f e / τ sx τ sz ; The coordinate system of the synchronously running collector coil and superconducting coil is transferred to the maglev train, and coincides with the superconducting coil coordinate system (x, y, z); where x′=x+vt, and the "8" coil magnetic field is the result of the overall excitation of the upper and lower coil currents, and the "8" coil magnetic flux density function is obtained as follows: In formula (23), Δy e is the distance between the midpoint of the superconducting coil and the midpoint of the "8" coil in the y-axis direction; It can be concluded from formula (23) that the harmonic component of the air gap flux density generated by the "8" coil current does not contain harmonics of multiples of k, and its maximum harmonic order is 2k-1.

5. The method according to claim 4, characterized in that In step S6, the position and polar distance of the current collecting coil are set, and the polar distance τ of the current collecting coil is set. cx Designed as τ cx =4τ sx / 3(2k-1), thereby obtaining UVW three-phase sinusoidal waves to match the vehicle power supply.

6. The method according to claim 5, characterized in that In step S7, the induced electromotive force function of a single collector coil is constructed, which specifically includes: According to formula (23), the magnetic flux of the upper and lower collector coils under the maximum harmonic air gap magnetic field induction is: In Equations (24) and (25), f e | 2k-1 = sin(k sx | 2k-1 ·a e / 2)sin(k sz ·b e / 2) / k sx | 2k-1 k sz ,f cU | 2k-1 = sin(k sx | 2k-1 ·a c / 2)sin(k sz ·b cU / 2) / k sx | 2k-1 k sz ,f cB | 2k-1 = sink sx | 2k-1 ·a c / 2)sin(k sz ·b cB / 2) / k sx | 2k-1 k sz ,λ| 2k-1 = (k sx | 2k-1 2 + k sz 2 ) 1 / 2 ,k sx | 2k-1 = (2k - 1)π / τ sx ,I εmax | 2k-1 = (-1) δ Z e G e | 2k-1 ,G e | 2k-1 = 4f e | 2k-1 G s | 2k-1 ,G s | 2k-1 = 8μ0λ| 2k-1 N s I s sin(k sx | 2k-1 ·a s / 2)sin(k sz ·b s / 2) / τ x τ z k sx | 2k- 1k sz ; z cU and z cB are the coordinates of the center points of the upper and lower collector coils on the z-axis respectively; The induced electromotive force of a single collector coil is: In Equation (26), G c | 2k-1 = 128k 2 μ0N c N e ωI εmax | 2k-1 f e | 2k-1 (f cU | 2k-1 -f cB | 2k-1 )λ| 2k-1 / τ sx τ sz 。 7. The method according to claim 6, characterized in that In step S8, the variable resistor R o The solution process is as follows: The existence of Δz makes the eddy current heights of the upper and lower parts of the air gap magnetic field at the position of the "8" coil corresponding to the superconducting coil shell different. The eddy current height b oU =b o / 2-Δz, height of the lower vortex b oB =b o / 2+Δz, where b o is the height of the superconducting coil housing; The magnetic field of the "8" coil will be distorted at the edge of the superconducting coil shell. The corresponding air gap correction coefficient ζ caused by the edge effect of the harmonic generator is as follows: In formula (27), B eymax and Bey av They are respectively the maximum value and average value of the air gap magnetic field of the "8" coil; Variable resistor R o It is expressed as: In formula (28), μ r and ρ are the relative magnetic permeability and resistivity of the superconducting coil housing, respectively, and v is the vehicle running speed.

8. The method according to claim 7, characterized in that When the maximum output rate function of the harmonic generator is constructed in step S8, the corresponding load obtains the maximum power; When U c ≠0, the condition for the load to obtain maximum power is: In formula (29), X and R are the reactance and resistance of the load respectively. c is the reactance of the harmonic generator.

9. A system for calculating the maximum output power of a harmonic generator, characterized in that: The system includes: a superconducting coil equivalent module, a superconducting coil magnetic density function construction module, an "8" coil setting module, an "8" coil magnetomotive force analysis module, an "8" coil magnetic density function construction module, a collector coil setting module, a single collector coil electromotive force function construction module, a harmonic generator internal resistance calculation module, and a maximum output power function construction module; wherein, The superconducting coil equivalent module is used to set the origin of the first coordinate system (x, y, z) at the geometric center of the racetrack-type superconducting coil. The actual pole pitches of the superconducting coil are τ sx and τ sz ; The racetrack superconducting coil is equivalent to a rectangle, and the equivalent length in the x-axis direction is a s , the equivalent height in the z-axis direction is b s ; Assume that there are δ equivalent superconducting coils distributed in the coordinate system, and a single superconducting coil has the same pole distance τ on the x-axis and z-axis x =τ z , and τ x >>τ sx , τ sz >>τ z ; The superconducting coil magnetic flux density function construction module is used to construct the magnetic flux density function of the superconducting coil according to the coordinate setting and the equivalent coil, and the dependent variables of the magnetic flux density function include the number of coils, structural parameters, electrical parameters and the spatial position of the sampling point; The "8" coil setting module is used to set the "8" coil numbered 0 at the time t facing the center of the superconducting coil, and the adjacent "8" coil numbers in the opposite direction of the superconducting coil are 1, 2, 3, ..., and the "8" coil pole pitch τ ex =τ sx / k (k≠1); set the origin of the second coordinate system (x′, y′, z′) at the geometric center of the No. 0 "8" coil; The "8" coil magnetomotive force analysis module is used to include ε "8" coils in the space corresponding to a superconducting coil based on the space harmonic method; when ε=3, the magnetomotive force distribution generated by the "8" coil current in the x' direction is analyzed; The "8" coil magnetic flux density function construction module is used to construct the "8" coil magnetic flux density function, and the dependent variables of the "8" coil magnetic flux density function include structural parameters, electrical parameters, the relative position of the "8" coil and the superconducting coil, and the vehicle driving speed; and from the constructed magnetic flux density function, it can be obtained that the air gap magnetic flux density harmonic component generated by the "8" coil current does not contain multiple harmonics of k, and its maximum harmonic order is 2k-1 times; The collector coil setting module is used to set the position and pole pitch of the collector coil according to the magnetic flux density function of the superconducting coil and the magnetic flux density function of the "8" coil and the maximum harmonic order of the air gap magnetic field of the "8" coil is 2k-1 times; The single collector coil electromotive force function construction module is used to construct a single collector coil induced electromotive force function U according to the setting of the collector coil and the magnetic flux density function of the "8" coil. c ; The harmonic generator internal resistance calculation module is used to calculate the fixed resistance R c and variable resistor R o Two-part harmonic generator internal resistance R eq , where R c is the inherent property of the harmonic generator, R o The resistance formed by the eddy current generated by the air gap magnetic field in the superconducting coil shell; The maximum output power function construction module is used to construct the maximum output power function of the harmonic generator: In formula (30), η is the efficiency coefficient of the on-board rectifier, R eq is the internal resistance of the harmonic generator; it is also used to solve the maximum output power of the harmonic generator according to formula (30).

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