A method, device and medium for calculating AC loss of superconducting cable

Abstract

The present invention relates to a method, device, and medium for calculating AC loss in a superconducting cable. The method comprises obtaining superconducting cable operating data and structural parameters; calculating the horizontal and vertical components of the external magnetic field of each layer of strip at a constant critical current density using the operating data and structural parameters based on the Kim extended magnetic field effect; calculating the critical current density of the corresponding layer of strip and updating the zero-field region width parameter of the corresponding layer; obtaining the current density distribution; updating the vertical component of the strip's external magnetic field; and calculating the AC loss of the superconducting cable based on the updated zero-field region width parameter and the vertical component of the strip's external magnetic field. The device and medium are used to implement the above method. Compared with the prior art, the present invention simplifies the calculation of AC loss into a single item, making the calculation more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of power transmission and distribution, and in particular to a method, device and medium for calculating AC loss of a superconducting cable. Background Art

[0002] With the increasing population of large and medium-sized cities and the increasing concentration of electricity loads, the transmission pressure on integrated pipeline systems in cities with high cabling rates is increasing. High-temperature superconducting cables, as a new transmission medium with high transmission capacity, low transmission losses, and a small footprint, are an effective means of optimizing the power grid structure in load-intensive cities. In addition to pipeline heat leakage, heat generated by AC losses in the superconducting cables themselves is the primary contributor to cooling system losses in superconducting cable systems. Therefore, controlling AC losses in superconducting cables can effectively reduce operating costs. However, in traditional analytical calculation methods, self-field transmission loss, a major component of AC loss, is simply calculated by summing the individual strips. However, the helical winding structure and other strip magnetic field effects affect self-field transmission loss, thus affecting the accuracy of the superconducting cable AC loss calculation. While the Chinese patent application "CN103488905A" takes these issues into account, it uses a traditional calculation method that divides the AC loss of superconducting cables into self-field transmission loss and external field magnetization loss. This method deviates from the principle of AC loss generation in actual superconducting cables, making the calculation complex and inaccurate. Therefore, there is a need to provide a method that conforms to the principle of superconducting cable AC loss generation and has accurate calculation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method, device and medium for calculating the AC loss of a superconducting cable in order to overcome the defects of the above-mentioned prior art.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] According to a first aspect of the present invention, a method for calculating AC loss of a superconducting cable is provided, the method comprising:

[0006] Acquiring superconducting cable operation data and structural parameters, wherein the operation data includes transmission current and voltage of the superconducting cable; the structural parameters include the number of layers, winding radius, number of strips, winding direction, and winding angle of the superconducting cable;

[0007] Based on Kim's extended magnetic field effect, the horizontal component and vertical component of the external magnetic field of each layer of strip at a constant critical current density are calculated using operating data and structural parameters.

[0008] Calculating the critical current density of the corresponding layer of strip according to the horizontal component of the external magnetic field and the vertical component of the external magnetic field, and updating the zero field region width parameter of the corresponding layer;

[0009] Obtain current density distribution based on zero field region width parameter and critical current density;

[0010] Update the vertical component of the external magnetic field of the strip based on the current density distribution and critical current density;

[0011] If the error of the updated zero-field region width parameter is less than the preset value, the AC loss of the superconducting cable is calculated based on the updated zero-field region width parameter and the vertical component of the magnetic field outside the strip; if the error of the updated zero-field region width parameter is not less than the preset value, the critical current density of the corresponding layer of strip is recalculated.

[0012] As a preferred technical solution, the method for calculating the horizontal component and the vertical component of the external magnetic field of each layer of strip at a constant critical current density is:

[0013]

[0014] Among them, B ||i represents the horizontal component of the external magnetic field; μ0 represents the vacuum permeability; r i Indicates the strip winding radius; I k represents the transmission current of the kth layer of strip; i, j, k, n all represent the number of layers; B ⊥i Represents the vertical component of the external magnetic field; ε represents the winding direction of the strip, when the winding direction is clockwise, ε = 1, when the winding direction is counterclockwise, ε = -1; θ represents the strip winding angle.

[0015] As a preferred technical solution, the method for updating the zero field region width parameter is:

[0016] The transmission current of the superconducting cable is obtained, and the critical current density is integrated according to the transmission current of the superconducting cable. The expression is:

[0017]

[0018] Where, I represents the transmission current of the superconducting cable; w ci ' represents half the width of the zero field region of the i-th layer of strip; J c represents the constant critical current density; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th layer of strip;

[0019] Calculate the zero-field region width parameter based on the integral expression.

[0020] As a preferred technical solution, the method for obtaining the current density distribution is:

[0021]

[0022] Among them, J i (x) represents the current density distribution of the i-th layer of strip; J c represents the constant critical current density; w represents half of the strip width; w ci ' represents half the width of the zero field region of the i-th layer of strip; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th layer of strip; B ||i Represents the horizontal component of the external magnetic field; B ⊥i represents the vertical component of the external magnetic field.

[0023] As a preferred technical solution, the method for updating the vertical component of the strip's external magnetic field is to update the vertical component of the strip's external magnetic field using the current density distribution according to Ampere's law, and its expression is:

[0024]

[0025] Among them, B′ ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; J i (u) represents the current density distribution; u and x both represent the strip width parameters; w represents half of the strip width.

[0026] As a preferred technical solution, the method for calculating the AC loss of a superconducting cable is:

[0027] The updated vertical component of the external magnetic field of the strip is integrated along the width direction, and then integrated along the axial direction per unit length to obtain the vertical magnetic flux symmetrically distributed about the center of the strip within the unit length. The vertical magnetic flux of each layer of the strip is repeatedly calculated.

[0028] The AC loss per unit length of the superconducting cable is calculated based on the perpendicular magnetic flux of all layers of tape.

[0029] As a preferred technical solution, the expression for calculating the vertical magnetic flux is:

[0030]

[0031] Among them, Φ i (x) represents the vertical flux of the i-th layer, w ci ' represents half the width of the zero field region of the i-th layer of strip; B' ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; J i (u) represents the current density distribution; x and u represent the strip width parameters; z represents the strip axial parameter; and w represents half of the strip width.

[0032] As a preferred technical solution, the expression for calculating the AC loss per unit length of the superconducting cable is:

[0033]

[0034] Where P represents the AC loss per unit length of superconducting cable; N i Indicates the number of strips in the i-th layer.

[0035] According to a second aspect of the present invention, a superconducting cable AC loss calculation device is provided, comprising a memory and a processor, wherein a computer program is stored in the memory, and the method described above is implemented when the processor executes the program.

[0036] According to a third aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the method described above is implemented.

[0037] Compared with the existing technology, the present invention converts the calculation of alternating external field loss into the influence of external magnetic field effect on the calculation of self-field transmission loss, and simplifies the calculation of AC loss into a single phase, which is more in line with the generation principle of AC loss of superconducting cables, simplifies the calculation process, and improves calculation efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flow chart of the method of the present invention;

[0039] Figure 2 The figure compares the results of various AC loss calculation methods of the present invention. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0041] In this embodiment, the traditional analytical calculation process is improved based on the Kim extended magnetic field effect model from the AC loss calculation principle. The influence of the spiral winding structure and the external magnetic field is taken into account in the solution of the self-field transmission loss. An improved analytical calculation method for the AC loss of superconducting cables considering the magnetic field effect is proposed. This method is based on the calculation principle of the AC loss of superconducting cables and has the advantages of simple and easy-to-understand principles, high calculation accuracy, and fast calculation speed.

[0042] Specifically, the flowchart of this method is as follows Figure 1 As shown, the detailed steps include:

[0043] S1. Obtain the operating data and structural parameters of the superconducting cable, wherein the operating data includes the transmission current and voltage of the superconducting cable; the structural parameters include the number of layers, winding radius, number of tapes, winding direction, and winding angle of the superconducting cable, as shown in Table 1.

[0044] Table 1 Structural parameters

[0045] Number of layers Winding radius Number of strips Winding direction Winding angle 1 12.15 15 Clockwise 9.628 2 12.75 15 Counterclockwise 15.7 3 19.4 24 Clockwise 15.827 4 20.15 24 Counterclockwise 12.963

[0046] S2. Based on the Kim extended magnetic field effect, the horizontal component and vertical component of the external magnetic field of each layer of strip at a constant critical current density are calculated using the operating data and structural parameters. The expressions are:

[0047]

[0048] Among them, B ||i represents the horizontal component of the external magnetic field; μ0 represents the vacuum permeability; r i Indicates the strip winding radius; I k represents the transmission current of the kth layer of strip; i, j, k, n all represent the number of layers; B ⊥i Represents the vertical component of the external magnetic field; ε represents the winding direction of the strip, when the winding direction is clockwise, ε = 1, when the winding direction is counterclockwise, ε = -1; θ represents the strip winding angle.

[0049] S3. Calculate the critical current density of the corresponding layer of strip according to the horizontal component and the vertical component of the external magnetic field, and update the zero-field region width parameter of the corresponding layer. The specific process is as follows:

[0050] S31. Obtain the transmission current of the superconducting cable, and integrate the critical current density according to the transmission current of the superconducting cable. The expression is:

[0051]

[0052] Where, I represents the transmission current of the superconducting cable; w ci ' represents half the width of the zero field region of the i-th layer of strip; J c represents the constant critical current density; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th layer of strip;

[0053] S32. Calculate the zero-field region width parameter according to the integral expression.

[0054] S4. Obtain the current density distribution based on the zero-field region width parameter and the critical current density:

[0055] In this embodiment, the Norris formula is used to solve the AC loss of a single superconducting tape. Under the constant critical current density model, the current density of the zero-field part of the superconducting tape is taken as a constant value J c According to the conformal mapping and mirror method, the current density distribution expression of the strip along the width direction is obtained as follows:

[0056]

[0057] Among them, J i (x) represents the current density distribution of the i-th layer of strip; J c represents the constant critical current density; w represents half of the strip width; w ci ' represents half the width of the zero field region of the i-th layer of strip; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th layer of strip; B ||i Represents the horizontal component of the external magnetic field; B ⊥i represents the vertical component of the external magnetic field.

[0058] S5. Update the vertical component of the external magnetic field of the strip based on the current density distribution and the critical current density. Specifically, update the vertical component of the external magnetic field of the strip using the current density distribution according to Ampere's theorem. The expression is:

[0059]

[0060] Among them, B′ ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; J i (u) represents the current density distribution; u and x both represent the strip width parameters; w represents half of the strip width.

[0061] S6. If the error of the updated zero-field region width parameter is less than the preset value, the AC loss of the superconducting cable is calculated based on the updated zero-field region width parameter and the vertical component of the magnetic field outside the strip; if the error of the updated zero-field region width parameter is not less than the preset value, the critical current density of the corresponding layer of strip is recalculated.

[0062] The detailed steps for calculating the AC loss of superconducting cables are:

[0063] S61. Integrate the updated vertical component of the external magnetic field of the strip along the width direction, and then integrate it along the axial direction per unit length to obtain the vertical magnetic flux symmetrically distributed about the center of the strip within the unit length. Repeat the calculation of the vertical magnetic flux of each layer of the strip. The expression is:

[0064]

[0065] Among them, Φ i(x) represents the vertical flux of the i-th layer, w ci ' represents half the width of the zero field region of the i-th layer of strip; B' ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; J i (u) represents the current density distribution; x and u represent the strip width parameters; z represents the strip axial parameter; and w represents half of the strip width.

[0066] S62. Calculate the AC loss per unit length of the superconducting cable based on the perpendicular magnetic flux of all layers of strips. The expression is:

[0067]

[0068] Where P represents the AC loss per unit length of superconducting cable; N i Indicates the number of strips in the i-th layer.

[0069] In order to verify that the calculation method provided in this embodiment has excellent calculation performance, the traditional analytical calculation method, the three-dimensional model numerical calculation method and the present method are used to study the magnetic field distribution characteristics under multi-dimensional parameters using the world's first 35kV / 2.2kA three-phase turnkey superconducting cable demonstration project put into operation in Shanghai at the end of 2021 as an example. The calculation results are as follows: Figure 2 shown.

[0070] a) Analysis of calculation accuracy:

[0071] exist Figure 2 As can be seen in the figure, the AC loss data measured in actual operation of superconducting cable projects is greater than the results obtained by all other measurement methods due to the influence of losses caused by other wear and tear. The AC loss at rated current is approximately 2.2 W / m. The red dashed line shows the results of the traditional analytical calculation method. As can be seen, due to the lack of consideration of external magnetic field effects and the influence of the spiral winding structure, the results are lower than the numerical calculation method by approximately 1.67 W / m. Compared with the AC loss calculation results obtained by this method, the accuracy of this method is nearly 14.4% higher, and the accuracy of the loss calculation is improved by approximately 11.4% compared to the actual measurement of the cable. Although the results of this method differ by approximately 5.5% compared to the three-dimensional model numerical calculation method, the calculated results curve of this method is closer to the results obtained from actual operation measurements.

[0072] b) Computational efficiency analysis:

[0073] The calculation time of the three methods is statistically analyzed, and the data shown in Table 2 is obtained.

[0074] Table 2 Calculation time loss of each method

[0075] Method Type Traditional analytical calculation method Numerical calculation method of three-dimensional model This method Calculation time 0.5s 5h26min57s 1.3s

[0076] Combine Figure 2 It can be concluded that although the computational efficiency of this method is slightly lower than that of the traditional analytical calculation method, the computational accuracy of this method is much higher than that of the traditional analytical calculation method; although the computational accuracy of the three-dimensional model numerical calculation method is high, the computational time it takes is too long. In summary, the method provided in this embodiment has both high computational accuracy and computational efficiency.

[0077] This embodiment also provides a superconducting cable AC loss calculation device, which is used to implement the above method. Technical personnel in the relevant field can clearly understand that for the convenience and brevity of description, the specific working process described can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here.

[0078] The apparatus of the present invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for the operation of the device can also be stored. The CPU, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0079] Many components in a device are connected to the I / O interface, including: input units, such as a keyboard and mouse; output units, such as various types of displays and speakers; storage units, such as magnetic disks and optical disks; and communication units, such as network cards, modems, and wireless communication transceivers. The communication unit allows the device to exchange information / data with other devices via computer networks such as the Internet and / or various telecommunication networks.

[0080] The processing unit performs the various methods and processes described above, such as methods S1 to S6. For example, in some embodiments, methods S1 to S6 may be implemented as a computer software program that is tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed onto the device via a ROM and / or a communication unit. When the computer program is loaded into the RAM and executed by the CPU, one or more steps of methods S1 to S6 described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute methods S1 to S6 by any other appropriate means (e.g., by means of firmware).

[0081] The functions described above herein may be performed, at least in part, by one or more hardware logic components. For example, and without limitation, exemplary types of hardware logic components that may be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chip (SOCs), complex programmable logic devices (CPLDs), and the like.

[0082] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. Such program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device so that when the program code is executed by the processor or controller, the functions / operations specified in the flow chart and / or block diagram are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0083] In the context of the present invention, machine-readable medium can be a tangible medium that can contain or store a program for use with an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. Machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. More specific examples of machine-readable storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0084] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for calculating AC loss of a superconducting cable, characterized in that: The method includes: Acquiring superconducting cable operation data and structural parameters, wherein the operation data includes transmission current and voltage of the superconducting cable; the structural parameters include the number of layers, winding radius, number of strips, winding direction, and winding angle of the superconducting cable; Based on Kim's extended magnetic field effect, the horizontal component and vertical component of the external magnetic field of each layer of strip at a constant critical current density are calculated using operating data and structural parameters. Calculating the critical current density of the corresponding layer of strip according to the horizontal component of the external magnetic field and the vertical component of the external magnetic field, and updating the zero field region width parameter of the corresponding layer; Obtain current density distribution based on zero field region width parameter and critical current density; Update the vertical component of the external magnetic field of the strip based on the current density distribution and critical current density; If the error of the updated zero-field region width parameter is less than the preset value, the AC loss of the superconducting cable is calculated based on the updated zero-field region width parameter and the vertical component of the magnetic field outside the strip; if the error of the updated zero-field region width parameter is not less than the preset value, the critical current density of the corresponding layer of strip is recalculated; The method for calculating the AC loss of superconducting cables is: The updated vertical component of the external magnetic field of the strip is integrated along the width direction, and then integrated along the axial direction per unit length to obtain the vertical magnetic flux symmetrically distributed about the center of the strip within the unit length. The vertical magnetic flux of each layer of the strip is repeatedly calculated. The AC loss per unit length of the superconducting cable is calculated based on the perpendicular magnetic flux of all layers of tape.

2. A method for calculating AC loss of a superconducting cable according to claim 1, characterized in that: The method for calculating the horizontal component and vertical component of the external magnetic field of each layer of strip at a constant critical current density is: Among them, B ||i represents the horizontal component of the external magnetic field; μ0 represents the vacuum permeability; r represents the strip winding radius; I i , I j and I k Represents the transmission current of the i, j and k layers of strip respectively; i, j, k, n all represent the number of layers; B ⊥i Represents the vertical component of the external magnetic field; ε represents the winding direction of the strip, when the winding direction is clockwise, ε = 1, when the winding direction is counterclockwise, ε = -1; θ represents the strip winding angle.

3. The method for calculating AC loss of a superconducting cable according to claim 2, wherein: The method for updating the zero field region width parameter is: The transmission current of the superconducting cable is obtained, and the critical current density is integrated according to the transmission current of the superconducting cable. The expression is: Where, I represents the transmission current of the superconducting cable; w ci ' represents half the width of the zero field region of the i-th layer of strip; J c represents the constant critical current density; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th layer of strip; x represents the strip width parameter; w represents half of the strip width; Calculate the zero-field region width parameter based on the integral expression.

4. A method for calculating AC loss of a superconducting cable according to claim 3, characterized in that: The method for obtaining the current density distribution is: Among them, J i (x) represents the current density distribution of the i-th layer of strip; J c represents the constant critical current density; w represents half of the strip width; w ci ' represents half the width of the zero field region of the i-th layer of strip; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th layer of strip; B ||i Represents the horizontal component of the external magnetic field; B ⊥i represents the vertical component of the external magnetic field.

5. A method for calculating AC loss of a superconducting cable according to claim 4, characterized in that: The method for updating the vertical component of the magnetic field outside the strip is to update the vertical component of the magnetic field outside the strip using the current density distribution according to Ampere's law, and the expression is: Among them, B′ ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; J i (u) represents the current density distribution; u and x both represent the strip width parameters; w represents half of the strip width.

6. A method for calculating AC loss of a superconducting cable according to claim 5, characterized in that: The expression for calculating the vertical magnetic flux is: Among them, Φ i (x) represents the vertical flux of the i-th layer, w ci ' represents half the width of the zero field region of the i-th layer of strip; B' ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; J i (u) represents the current density distribution; x and u represent the strip width parameters; z represents the strip axial parameter; and w represents half of the strip width.

7. A method for calculating AC loss of a superconducting cable according to claim 6, characterized in that: The expression for calculating the AC loss per unit length of the superconducting cable is: Where P represents the AC loss per unit length of superconducting cable; N i Indicates the number of strips in the i-th layer.

8. A superconducting cable AC loss calculation device, comprising a memory and a processor, wherein a computer program is stored in the memory, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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