Method and device for calculating alternating current loss of superconducting cable and medium

Abstract

The invention relates to a superconducting cable alternating current loss calculation method and device and a medium. The method comprises the steps that operation data and structure parameters of a superconducting cable are acquired; calculating an external magnetic field horizontal component and an external magnetic field vertical component of each layer of strip under the constant critical current density by using the operation data and the structure parameters based on a Kim extended magnetic field effect; calculating the critical current density of the strip of the corresponding layer, and updating the zero field region width parameter of the corresponding layer; acquiring current density distribution; updating the vertical component of the external magnetic field of the strip; calculating the AC loss of the superconducting cable based on the updated zero field region width parameter and the vertical component of the external magnetic field of the strip; the device and the medium are used for realizing the method. Compared with the prior art, the calculation of the alternating current loss is simplified into a single item, so that the calculation is 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 gradual increase in the population of large and medium-sized cities, the electricity load is gradually concentrated, and the power transmission pressure of the integrated pipeline system in cities with high cable rates is increasing. As a new type of transmission medium with large transmission capacity, low transmission loss and small space occupation, high-temperature superconducting cable is an effective way to optimize the structure of load-intensive urban power grids. In the superconducting cable system, in addition to pipeline heat leakage, the heat generated by the AC loss of the superconducting cable body is the main factor in the loss of the cooling system. Therefore, controlling the AC loss of the superconducting cable can effectively reduce its operating cost. However, in the traditional analytical calculation method, the self-field transmission loss is the main component of the AC loss, and its calculation is only a simple summation of each single strip. The spiral winding structure and other strip magnetic field effects will affect the self-field transmission loss, thereby affecting the calculation accuracy of the superconducting cable AC loss. Although the Chinese patent application "CN103488905A" takes the above problems into consideration, the calculation method it adopts is the traditional calculation method, that is, the AC loss of the superconducting cable is divided into the self-field transmission loss and the external field magnetization loss, which is inconsistent with the principle of AC loss generated by the actual superconducting cable. Not only is the calculation complicated, but the calculation accuracy cannot be guaranteed. Therefore, there is a need to provide a method that conforms to the principle of AC loss generation in superconducting cables and has accurate calculations. Summary of the invention

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

[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 of the external magnetic field and the 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 material 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 according to zero field region width parameter and critical current density;

[0010] Update the vertical component of the magnetic field outside the strip based on the current density distribution and the 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 external magnetic field of 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 of the external magnetic field and the vertical component of the external magnetic field of each layer of strip under 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 current transmitted by the k-th strip; i, j, k, n all represent the number of layers; B ⊥i It 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 winding angle of the strip.

[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 strip; J c represents the constant critical current density; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th 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 represents the current density distribution of the i-th 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 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 external magnetic field of the strip is to update the vertical component of the external magnetic field of the strip using the current density distribution according to Ampere's theorem, 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 vertical component of the updated 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, and 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 strip; B' ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; Ji(u) represents the current density distribution; x and u represent the strip width parameters; z represents the strip axial parameter; 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 the superconducting cable; N i Indicates the number of strips in the i-th layer.

[0035] According to a second aspect of the present invention, there is provided a superconducting cable AC loss calculation device, 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, there is provided a computer-readable storage medium having a computer program stored thereon, wherein the program implements the method described above when executed by a processor.

[0037] Compared with the prior art, 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, simplifies the calculation of AC loss into a single phase, is more in line with the generation principle of AC loss of superconducting cables, simplifies the calculation process, and improves the 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 is a comparison of the results of various AC loss calculation methods of the present invention. DETAILED DESCRIPTION

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

[0041] In this embodiment, starting from the AC loss calculation principle, the traditional analytical calculation process is improved based on the Kim extended magnetic field effect model, and 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 a superconducting cable considering the magnetic field effect is proposed. This method is based on the calculation principle of the AC loss of a superconducting cable, and has the advantages of simple and easy-to-understand principle, high calculation accuracy, and fast calculation speed.

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

[0043] S1. Obtaining the operation data and structural parameters of the superconducting cable, wherein the operation 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 Strip number 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 Kim's extended magnetic field effect, the horizontal component of the external magnetic field and the vertical component of the external magnetic field of each layer of strip under 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 current transmitted by the k-th strip; i, j, k, n all represent the number of layers; B ⊥i It 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 winding angle of the strip.

[0049] S3. Calculate 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 update the zero field region width parameter of the corresponding layer. The specific process is as follows:

[0050] S31, obtaining the transmission current of the superconducting cable, integrating the critical current density according to the transmission current of the superconducting cable, and the expression thereof 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 strip; J c represents the constant critical current density; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th strip;

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

[0054] S4. Obtain the current density distribution according to 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 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 represents the current density distribution of the i-th 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 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 magnetic field outside the strip based on the current density distribution and the critical current density. Specifically, update the vertical component of the magnetic field outside 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 external magnetic field of 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 vertical component of the updated strip external magnetic field 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 strip center within the unit length. Repeat the calculation of the vertical magnetic flux of each layer of strip, and 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 strip; B' ⊥i (x) represents the updated vertical component of the external magnetic field of the strip; Ji(u) represents the current density distribution; x and u represent the strip width parameters; z represents the strip axial parameter; w represents half of the strip width.

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

[0067]

[0068] Where P represents the AC loss per unit length of the 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 method are used to study the magnetic field distribution characteristics under multi-dimensional parameters, taking 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 on calculation accuracy:

[0071] exist Figure 2 It can be seen that the AC loss data measured in the actual operation of the superconducting cable project is greater than the results obtained by all measurement methods due to the loss caused by other wear. The AC loss at rated current is about 2.2W / m. The red dotted line is the calculation result of the traditional analytical calculation method. It can be seen that due to the failure to consider the influence of the external magnetic field effect and the spiral winding structure, the result is about 1.67W / m lower than the numerical calculation method. Compared with the AC loss calculation result obtained by this method, the accuracy of this method is nearly 14.4%, and the calculation accuracy of the actual measured loss of the cable is improved by about 11.4%. Although the calculation result of this method differs from the three-dimensional model numerical calculation method by about 5.5%, the calculation result curve of this method is closer to the result curve obtained by actual operation measurement.

[0072] b) Analysis of computational efficiency:

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

[0074] Table 2 Time loss calculation table 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] Combination 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 calculation 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 conciseness 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 device 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] Multiple components in the device are connected to the I / O interface, including: input units, such as keyboards, mice, etc.; output units, such as various types of displays, speakers, etc.; storage units, such as disks, optical disks, etc.; and communication units, such as network cards, modems, wireless communication transceivers, etc. The communication unit allows the device to exchange information / data with other devices through 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, which 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 on 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 in any other appropriate manner (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, 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 chips (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. These program codes 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 the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code can be executed entirely on the machine, partially on the machine, partially on the machine as a stand-alone software package and partially on a remote machine, or entirely on a remote machine or server.

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

[0084] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope 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 of the external magnetic field and the 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 material 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 according to zero field region width parameter and critical current density; Update the vertical component of the magnetic field outside the strip based on the current density distribution and the 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 external magnetic field of 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.

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 of the external magnetic field and the vertical component of the external magnetic field of each layer of strip under 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 i Indicates the strip winding radius; I k represents the current transmitted by the k-th strip; i, j, k, n all represent the number of layers; B ⊥i It 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 winding angle of the strip.

3. A method for calculating AC loss of a superconducting cable according to claim 1, characterized in that: 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 strip; J c represents the constant critical current density; J c (B ⊥i ,B ||i ) represents the critical current density of the i-th strip; 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 1, characterized in that: The method for obtaining the current density distribution is: Among them, J i represents the current density distribution of the i-th 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 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 1, characterized in that: The method for updating the vertical component of the external magnetic field of the strip is to update the vertical component of the external magnetic field of the strip using the current density distribution according to Ampere's theorem, 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 1, characterized in that: The method for calculating the AC loss of a superconducting cable is: The vertical component of the updated 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, and 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.

7. A method for calculating AC loss of a superconducting cable according to claim 6, 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 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.

8. 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 the superconducting cable; N i Indicates the number of strips in the i-th layer.

9. 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 8 is implemented.

10. 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 8 is implemented.

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