Sensorless current control method of non-insulated high temperature superconducting coil

Abstract

The present invention relates to a sensorless current control method of a non-insulated high temperature superconducting coil, the method comprising the steps of: outputting, by a command output unit, a magnetic field command to a coil; detecting, by a voltage detection unit, a voltage of the coil if a current is supplied to the coil according to the magnetic field command; calculating, by a magnetic field calculation unit, a magnetic field of the coil using a Kalman filter on the basis of the voltage of the coil and the current output according to the magnetic field command; and controlling, by a magnetic field control unit, the magnetic field of the coil on the basis of a magnetic field calculation value.

Description

Sensorless current control method for uninsulated high-temperature superconducting coils

[0001] The present invention relates to a sensorless current control method for an insulated high-temperature superconducting coil, and more specifically, to a sensorless current control method for an insulated high-temperature superconducting coil that excludes existing expensive magnetic field sensors, calculates an estimated value of the winding direction current using a state estimator utilizing a Kalman filter, and enables feedback control of the insulated high-temperature superconducting coil using the calculated estimated value.

[0002] Generally, a superconducting coil is manufactured by winding a superconducting wire into an electric coil, and because it has no electrical resistance, it can carry a large current, thereby enabling the creation of a strong magnetic field.

[0003] Among the candidates for superconducting conductors that can be used to manufacture such superconducting coils, second-generation high-temperature superconducting wires have a copper plating layer formed on the outermost surface of the conductor to improve the mechanical and electrical stability of the conductor.

[0004] The conventional method of fabricating superconducting coils using these second-generation high-temperature superconducting wires allows for the current flow to be induced in the winding direction by attaching an insulating film between turns during coil winding. This is called an "insulated superconducting coil."

[0005] However, if problems such as quenching occur in a part of the coil due to electrical, thermal, or mechanical factors, high resistance is generated, hindering the smooth flow of current. As a result of the continuous flow of current, the temperature of the resistive part rises, leading to the problem of the coil burning out due to the high temperature.

[0006] Non-insulating winding technology can increase the energy density of application systems by enhancing the miniaturization and lightness of superconducting coils through the removal of insulators used for electrical insulation between winding turns when fabricating second-generation high-temperature superconducting coils. However, since the coil's self-stabilization function operates within a limited range when the phenomenon of superconductivity occurs, separate protection methods and devices are required to protect the coil.

[0007] In addition, due to direct physical contact between the second-generation high-temperature superconducting wires, the contact resistance between the winding turns is very low, causing some of the current flowing in the winding direction to leak into adjacent turns, which reduces the current flowing in the winding direction that generates a magnetic field, and consequently, there is a problem that a time difference occurs between the current flowing and the target magnetic field generated.

[0008] To address this, a technology has been proposed to ensure fast responsiveness by reducing the charging time delay to the target center magnetic field through feedback control of the center magnetic field of an existing uninsulated high-temperature superconducting coil.

[0009] However, it becomes necessary to have an expensive magnetic field sensor that can operate in a cryogenic environment while simultaneously accurately measuring high magnetic fields.

[0010] In addition, it has the problem that a separate power supply is required to operate the magnetic field sensor, and additional devices and supporting structures are needed to measure the magnetic field.

[0011] The present invention aims to solve the aforementioned problems by providing a sensorless current control method for an insulated high-temperature superconducting coil, which eliminates existing expensive magnetic field sensors and calculates an estimated value of the winding direction current using a state estimator utilizing a Kalman filter, and enables the feedback of the insulated high-temperature superconducting coil to be controlled using the calculated estimated value.

[0012] A sensorless current control method for an insulated high-temperature superconducting coil according to one embodiment of the present invention may include: a step of outputting a magnetic field command to a coil in a command output unit; a step of detecting the voltage of the coil in a voltage detection unit when current is supplied to the coil according to the magnetic field command; a step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command in a magnetic field calculation unit; and a step of controlling the magnetic field of the coil based on the previously calculated magnetic field value in a magnetic field control unit.

[0013] The step of calculating the magnetic field of the coil using the Kalman filter according to one embodiment of the present invention may include the step of calculating in real time the covariance of the magnetic field estimation error and the magnetic field prediction value of the coil based on the voltage of the coil and the current output according to the magnetic field command in the magnetic field calculation unit; the step of updating the Kalman gain in real time based on the covariance and the magnetic field prediction value calculated in the magnetic field calculation unit; and the step of calculating the magnetic field of the coil based on the Kalman gain updated in the magnetic field calculation unit.

[0014] The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command according to one embodiment of the present invention may further include the step of calculating the error covariance, the predicted value for the error covariance, the Kalman gain, and the estimated value of the coil's state corresponding to the steady state, respectively, using a state estimation formula derived through the following mathematical formulas 1 to 6 in the magnetic field calculation unit.

[0015] [Mathematical Formula 1]

[0016]

[0017] [Mathematical Formula 2]

[0018]

[0019] [Mathematical Formula 3]

[0020]

[0021] [Mathematical Formula 4]

[0022]

[0023] [Mathematical Formula 5]

[0024]

[0025] [Mathematical Formula 6]

[0026]

[0027] (Here, k is the time step, x is the state variable to be estimated, u is the system input variable, y is the output variable and a measurable value, x is the current in the winding direction, u is the supply current of the coil, y is the voltage across the coil, parameter Q is the process noise generated in the uninsulated high-temperature superconducting coil, and parameter R is the measurement noise.)

[0028]

[0029] The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command according to one embodiment of the present invention may further include the step of detecting the estimated state value of the coil using the state-space equation derived through the following mathematical formulas 7 and 8 in the magnetic field calculation unit.

[0030] [Mathematical Formula 7]

[0031]

[0032] [Mathematical Formula 8]

[0033]

[0034] (here, i φ is the component of current flowing in the direction of the coil's winding, i is the current supplied to the coil, v is the voltage across the coil, and R cis the characteristic resistance of the coil, and L is the inductance of the coil)

[0035] The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command according to one embodiment of the present invention may further include the step of converting the state-space equation into a discretized state-space equation through the following mathematical formulas 9 to 11 in the magnetic field calculation unit.

[0036] [Mathematical Formula 9]

[0037]

[0038] [Mathematical Formula 10]

[0039]

[0040] [Mathematical Formula 11]

[0041]

[0042] (here, i φ is the component of current flowing in the direction of the coil's winding, i is the current supplied to the coil, v is the voltage across the coil, and R c is the characteristic resistance of the coil, and L is the inductance of the coil)

[0043]

[0044] The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command according to one embodiment of the present invention may further include the step of deriving each variable of the state equation and the output equation for the one-dimensional Kalman filter into the following mathematical equations 12 to 15 using the discretized state-space equation through the magnetic field calculation unit.

[0045] [Mathematical Formula 12]

[0046]

[0047] [Mathematical Formula 13]

[0048]

[0049] [Mathematical Formula 14]

[0050]

[0051] [Mathematical Formula 15]

[0052]

[0053] According to the present invention, there is an advantage in that an estimated value of the winding direction current is calculated using a state estimator utilizing a Kalman filter, excluding existing expensive magnetic field sensors, and the feedback of an uninsulated high-temperature superconducting coil can be controlled using the calculated estimated value.

[0054] In particular, according to the present invention, the use of expensive magnetic field sensors is excluded, which has the advantage of significantly reducing the cost of building a control system.

[0055] In addition, according to the present invention, there is an advantage of being able to improve the magnetic field charging speed of an insulated high-temperature superconducting coil without the need for an expensive magnetic field sensor capable of accurately measuring high magnetic fields while operating in a low-temperature environment.

[0056] In addition, according to the present invention, there is an advantage of being able to stably control the magnetic field by excluding magnetic field sensors that cause errors or malfunctions.

[0057]

[0058] Figure 1 is a diagram showing the magnetic field control structure of an insulated high-temperature superconducting coil using a conventional magnetic field sensor.

[0059] FIG. 2 is a conceptual diagram showing a sensorless current control structure of an insulated high-temperature superconducting coil according to one embodiment of the present invention.

[0060] FIG. 3 is a flowchart showing a sensorless current control method of an insulated high-temperature superconducting coil according to one embodiment of the present invention in a series of sequences.

[0061] Figure 4 is a flowchart schematically illustrating the state estimation process using a Kalman filter.

[0062] FIG. 5 is a graph showing the magnetic field control results of an insulated high-temperature superconducting coil through a sensorless current control structure of an insulated high-temperature superconducting coil according to one embodiment of the present invention.

[0063]

[0064] In a sensorless current control structure of an insulated high-temperature superconducting coil according to one embodiment of the present invention, a magnetic field command of the insulated high-temperature superconducting coil is applied, an estimated value of the winding direction current is calculated through a state estimator using a Kalman filter, the estimated value of the winding direction current is fed back to a controller of the winding direction current, a supply current command is sent out based on the fed-back estimated value of the winding direction current, and the supply current command value is corrected to within a limited range and sent out.

[0065]

[0066] Hereinafter, specific details for implementing the present invention will be described in detail with reference to the attached drawings. However, in the following description, specific descriptions regarding widely known functions or configurations will be omitted if there is a risk that the gist of the present invention may be unnecessarily obscured.

[0067] In the attached drawings, identical or corresponding components are given the same reference numerals. Additionally, in the description of the following embodiments, the description of identical or corresponding components may be omitted. However, even if a description of a component is omitted, it is not intended that such component is not included in any embodiment.

[0068] The advantages and features of the disclosed embodiments and the methods for achieving them will become clear by referring to the embodiments described below in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below but can be implemented in various different forms, and these embodiments are provided merely to make the present invention complete and to fully inform those skilled in the art of the scope of the invention.

[0069] The terms used in this specification will be briefly explained, and the disclosed embodiments will be described in detail. The terms used in this specification have been selected to be as generally used as possible, taking into account their functions in the present invention; however, these terms may vary depending on the intent of those skilled in the relevant field, case law, the emergence of new technologies, etc. Additionally, in specific cases, terms may be arbitrarily selected by the applicant, and in such cases, their meanings will be described in detail in the relevant description of the invention. Therefore, the terms used in this invention should be defined not merely by their names, but based on their meanings and the overall content of the present invention.

[0070] In this specification, singular expressions include plural expressions unless the context clearly specifies them as singular. Additionally, plural expressions include singular expressions unless the context clearly specifies them as plural. Throughout the specification, when a part is described as including a certain component, this means that, unless specifically stated otherwise, it does not exclude other components but may include additional components.

[0071] Additionally, the terms 'module' or 'part' as used in the specification refer to software or hardware components, and the 'module' or 'part' performs certain roles. However, the meaning of 'module' or 'part' is not limited to software or hardware. The 'module' or 'part' may be configured to reside in an addressable storage medium or configured to run on one or more processors. Thus, as an example, the 'module' or 'part' may include components such as software components, object-oriented software components, class components, and task components, and at least one of processes, functions, attributes, procedures, subroutines, segments of program code, drivers, firmware, microcode, circuits, data, databases, data structures, tables, arrays, or variables. The components and the functions provided within the 'module' or 'part' may be combined into a smaller number of components and 'modules' or 'parts', or further separated into additional components and 'modules' or 'parts'.

[0072] According to one embodiment of the present invention, a 'module' or 'part' may be implemented as a processor and memory. The term 'processor' should be broadly interpreted to include a general-purpose processor, a central processing unit (CPU), a microprocessor, a digital signal processor (DSP), a controller, a microcontroller, a state machine, etc. In some environments, the term 'processor' may refer to an application-specific integrated circuit (ASIC), a programmable logic device (PLD), a field programmable gate array (FPGA), etc. The term 'processor' may also refer to a combination of processing devices, such as, for example, a combination of a DSP and a microprocessor, a combination of multiple microprocessors, a combination of one or more microprocessors combined with a DSP core, or a combination of any other configurations. Additionally, the term 'memory' should be broadly interpreted to include any electronic component capable of storing electronic information. 'Memory' may refer to various types of processor-readable media, such as Random Access Memory (RAM), Read-Only Memory (ROM), Non-Volatile Random Access Memory (NVRAM), Programmable Read-Only Memory (PROM), Erasable-Programmable Read-Only Memory (EPROM), Electrically Erasable PROM (EEPROM), Flash Memory, Magnetic or Optical Data Storage Devices, Registers, etc. If a processor can read information from memory and / or write information to memory, memory is considered to be in an electronic communication state with the processor. Additionally, memory integrated into a processor is considered to be in an electronic communication state with the processor.

[0073] In the present invention, the 'system' may include at least one device among a computing device including a device management device, a server device, and a cloud device, but is not limited thereto. For example, the system may be composed of one or more computing devices or server devices. As another example, the system may be composed of one or more cloud devices. As yet another example, the system may be configured to operate together with a computing device or server device and a cloud device.

[0074]

[0075] Figure 1 is a diagram showing the magnetic field control structure of an insulated high-temperature superconducting coil using a conventional magnetic field sensor.

[0076] Looking at Fig. 1, in the case of a magnetic field control structure of an insulated high-temperature superconducting coil using a conventional magnetic field sensor, a magnetic field command from a user is input, and a process of detecting the magnetic field using an expensive magnetic field sensor is performed.

[0077] In this process, conventional magnetic field control structures require expensive magnetic field sensors capable of operating in cryogenic environments while simultaneously accurately measuring high magnetic fields. Furthermore, there are issues in that a separate power supply is required to operate the magnetic field sensor, and additional devices and supporting structures are needed to measure the magnetic field.

[0078]

[0079] FIG. 2 is a conceptual diagram showing a sensorless current control structure of an insulated high-temperature superconducting coil according to one embodiment of the present invention.

[0080] In a sensorless current control structure of an insulated high-temperature superconducting coil according to one embodiment of the present invention, a magnetic field command of the insulated high-temperature superconducting coil is applied, an estimated value of the winding direction current is calculated through a state estimator using a Kalman filter, the estimated value of the winding direction current is fed back to a controller of the winding direction current, a supply current command is sent out based on the fed-back estimated value of the winding direction current, and the supply current command value is corrected to within a limited range and sent out.

[0081]

[0082] FIG. 3 is a flowchart showing a sensorless current control method of an insulated high-temperature superconducting coil according to one embodiment of the present invention in a series of sequences.

[0083] Referring to FIG. 3, first, the command output unit outputs a magnetic field command to the uninsulated high-temperature superconducting coil (S301). In addition, the voltage detection unit detects the supply current and voltage supplied at the current time (S302), calculates an estimated magnetic field value of the uninsulated high-temperature superconducting coil using a state estimator with a Kalman filter based on the detected supply current and the voltage value of the coil (S303), and the magnetic field control unit controls the magnetic field of the coil based on the calculated magnetic field value (S304).

[0084] The process of calculating the magnetic field of a coil using a Kalman filter in the state estimator is as follows.

[0085] Figure 4 is a flowchart schematically illustrating the state estimation process of a state estimator using a Kalman filter.

[0086] Referring to FIG. 4, the state estimator first sets an initial value to estimate the magnetic field state of an uninsulated high-temperature superconducting coil (S401), predicts the covariance of the error between the magnetic field estimate (S402), updates the Kalman gain (S403), calculates the magnetic field estimate based on this (S404), and corrects the error covariance (S405).

[0087] In step S402, the state estimator can calculate the error covariance, the predicted value for the error covariance, the Kalman gain, and the estimated state value of the coil, respectively, using the state estimation formula derived through the following mathematical formulas 1 to 6.

[0088]

[0089] [Mathematical Formula 1]

[0090]

[0091] [Mathematical Formula 2]

[0092]

[0093] [Mathematical Formula 3]

[0094]

[0095] [Mathematical Formula 4]

[0096]

[0097] [Mathematical Formula 5]

[0098]

[0099] [Mathematical Formula 6]

[0100]

[0101]

[0102] Here, k is a time step, x is a state variable to be estimated, u is a system input variable, y is a measurable value as an output variable, x is a current in the winding direction, u is the supply current of the coil, y is the voltage across the coil, parameter Q is process noise generated in an uninsulated high-temperature superconducting coil, and parameter R is measurement noise.

[0103] In this case, parameter Q can be determined by the performance of the designed coil and the coil's power supply system. Additionally, parameter R can be determined by the performance of the sensor and measuring equipment that use the noise generated by the measuring system as a designed value.

[0104] In addition, in one embodiment, the state estimator detects the state estimate of the coil using the state-space equation derived through the following mathematical formulas 7 and 8.

[0105]

[0106] [Mathematical Formula 7]

[0107]

[0108] [Mathematical Formula 8]

[0109]

[0110]

[0111] Here, i φ is the component of current flowing in the direction of the coil's winding, i is the current supplied to the coil, v is the voltage across the coil, and R c is the characteristic resistance of the coil, and L is the inductance of the coil.

[0112] In this case, the state-space equation can consist of a state equation and an output equation.

[0113] In addition, in one embodiment, the state estimator can convert the previously calculated state-space equation into a discretized state-space equation through the following mathematical equations 9 to 11 in order to calculate the real-time state estimate of the coil.

[0114]

[0115] [Mathematical Formula 9]

[0116]

[0117] [Mathematical Formula 10]

[0118]

[0119] [Mathematical Formula 11]

[0120]

[0121]

[0122] Here, i φε is the component current flowing in the direction of the coil's winding, i is the current supplied to the coil, v is the voltage across the coil, Rc is the characteristic resistance of the coil, and L is the inductance of the coil.

[0123] In addition, in one embodiment, the state estimator can derive each variable of the state equation and output equation for a one-dimensional Kalman filter using discretized state-space equations as shown in the following mathematical equations 12 to 15.

[0124] [Mathematical Formula 12]

[0125]

[0126] [Mathematical Formula 13]

[0127]

[0128] [Mathematical Formula 14]

[0129]

[0130] [Mathematical Formula 15]

[0131]

[0132]

[0133] FIG. 5 is a graph showing the magnetic field control results of an insulated high-temperature superconducting coil through a sensorless current control method of an insulated high-temperature superconducting coil according to one embodiment of the present invention.

[0134] Looking at Fig. 5, the uninsulated high-temperature superconducting coil receives a magnetic field command value from the command output unit, and the voltage detection unit detects the supply current and voltage for the current time of the coil when current is supplied to the coil according to the magnetic field command.

[0135] The state estimator calculates the magnetic field estimate for the current time from a state estimator using a Kalman filter, based on the detected supply current and the coil voltage.

[0136] In addition, the state estimator calculates the error between the magnetic field command value and the magnetic field estimate value from the summer. At this time, the magnetic field control unit controls the supply current to follow the magnetic field command value when the estimated value of the magnetic field is smaller than the magnetic field command value, and controls the supply current to decrease the supply current when it is smaller.

[0137] Through this, the sensorless current control method of an insulated high-temperature superconducting coil according to the present invention enables active control of the feedback of the insulated high-temperature superconducting coil without excluding conventional expensive magnetic field sensors.

[0138]

[0139] The method described above may be provided as a computer program stored on a computer-readable recording medium for execution on a computer. The medium may continuously store a computer-executable program, or temporarily store it for execution or download. Additionally, the medium may be various recording or storage means in the form of a combination of single or multiple hardware, and may not be limited to a medium directly connected to a computer system but may exist distributed over a network. Examples of media may include magnetic media such as hard disks, floppy disks, and magnetic tapes; optical recording media such as CD-ROMs and DVDs; magneto-optical media such as floptical disks; and media configured to store program instructions, including ROM, RAM, and flash memory. Furthermore, other examples of media may include recording or storage media managed by app stores that distribute applications or sites and servers that supply or distribute various other software.

[0140] The methods, operations, or techniques of the present invention may be implemented by various means. For example, these techniques may be implemented in hardware, firmware, software, or a combination thereof. Those skilled in the art will understand that the various exemplary logical blocks, modules, circuits, and algorithmic steps described in connection with the disclosure of the present invention may be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate such interchangeability between hardware and software, various exemplary components, blocks, modules, circuits, and steps have been generally described above in terms of their functional aspects. Whether such functions are implemented as hardware or as software depends on the design requirements imposed on the specific application and the overall system. Those skilled in the art may implement the described functions in various ways for each specific application, but such implementations should not be construed as departing from the scope of the present invention.

[0141] In a hardware implementation, the processing units used to perform the techniques may be implemented in one or more ASICs, DSPs, digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, electronic devices, other electronic units designed to perform the functions described in the present invention, computers, or a combination thereof.

[0142] Accordingly, the various exemplary logic blocks, modules, and circuits described in connection with the present invention may be implemented or performed by any combination of general-purpose processors, DSPs, ASICs, FPGAs or other programmable logic devices, discrete gate or transistor logic, discrete hardware components, or those designed to perform the functions described in the present invention. A general-purpose processor may be a microprocessor, but alternatively, the processor may be any conventional processor, controller, microcontroller, or state machine. The processor may also be implemented as a combination of computing devices, for example, a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other combination of configurations.

[0143] In firmware and / or software implementations, techniques may be implemented as instructions stored on a computer-readable medium such as random access memory (RAM), read-only memory (ROM), non-volatile random access memory (NVRAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable PROM (EEPROM), flash memory, compact disc (CD), magnetic or optical data storage devices, etc. The instructions may be executable by one or more processors, and the processor may be enabled to perform specific aspects of the functions described in the present invention.

[0144] Where implemented in software, the techniques may be stored on a computer-readable medium as one or more instructions or code, or transmitted through a computer-readable medium. Computer-readable media include both computer storage media and communication media, including any medium that facilitates the transfer of a computer program from one place to another. Storage media may be any available medium accessible by a computer. As a non-limiting example, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, and any other medium accessible by a computer that can be used to transfer or store program code in the form of instructions or data structures. Additionally, any connection is appropriately referred to as a computer-readable medium.

[0145] For example, if software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair cable, digital subscriber line (DSL), or wireless technologies such as infrared or microwave, coaxial cable, fiber optic cable, twisted pair cable, digital subscriber line, or wireless technologies such as infrared or microwave are included within the definition of a medium. The disks used in the present invention include CDs, laser disks, optical disks, DVDs (digital versatile discs), floppy disks, and Blu-ray disks, wherein disks typically play data magnetically, whereas discs play data optically using a laser. The above combinations must also be included within the scope of computer-readable media.

[0146] Software modules may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disks, removable disks, CD-ROMs, or any other known form of storage media. An exemplary storage medium may be connected to a processor so that the processor can read information from the storage medium or write information to the storage medium. Alternatively, the storage medium may be integrated into the processor. The processor and the storage medium may exist within an ASIC. The ASIC may exist within a user terminal. Alternatively, the processor and the storage medium may exist as separate components within the user terminal.

[0147] Although the embodiments described above have been described as utilizing aspects of the subject matter disclosed herein in one or more standalone computer systems, the present invention is not limited thereto and may be implemented in conjunction with any computing environment, such as a network or a distributed computing environment. Furthermore, aspects of the subject matter in the present invention may be implemented in a plurality of processing chips or devices, and storage may be similarly affected across a plurality of devices. Such devices may include PCs, network servers, and portable devices.

[0148] Although the present invention has been described in relation to some embodiments, various modifications and changes may be made without departing from the scope of the invention as understood by a person skilled in the art to which the invention pertains. Furthermore, such modifications and changes should be considered to fall within the scope of the claims appended to this specification.

[0149]

Claims

1. A step of outputting a magnetic field command to a coil in a command output unit; When current is supplied to the coil according to the above magnetic field command, a step of detecting the voltage of the coil in a voltage detection unit; In a magnetic field calculation unit, a step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command; and A step comprising controlling the magnetic field of the coil based on the previously calculated magnetic field value in the magnetic field control unit; Sensorless current control method for uninsulated high-temperature superconducting coils.

2. In Paragraph 1, The step of calculating the magnetic field of the coil using the Kalman filter above is, A step of calculating in real time the covariance of the magnetic field estimation error of the coil and the magnetic field prediction value based on the voltage of the coil and the current output according to the magnetic field command in the above magnetic field calculation unit; In the magnetic field calculation unit above, a step of updating the Kalman gain in real time based on the calculated covariance and the magnetic field prediction value; and The above magnetic field calculation unit comprises the step of calculating the magnetic field of the coil based on the updated Kalman gain. Sensorless current control method for uninsulated high-temperature superconducting coils.

3. In Paragraph 2, The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command is: The above magnetic field calculation unit further comprises the step of calculating the error covariance, the predicted value for the error covariance, the Kalman gain, and the estimated state value of the coil, respectively, using a state estimation formula derived through the following mathematical formulas 1 to 6. Sensorless current control method for uninsulated high-temperature superconducting coils. [Mathematical Formula 1] [Mathematical Formula 2] [Mathematical Formula 3] [Mathematical Formula 4] [Mathematical Formula 5] [Mathematical Formula 6] (Here, k is the time step, x is the state variable to be estimated, u is the system input variable, y is a measurable value as the output variable, x is the current in the winding direction, u is the supply current of the coil, y is the voltage across the coil, parameter Q is the process noise generated in the uninsulated high-temperature superconducting coil, and parameter R is the measurement noise.) 4. In Paragraph 2, The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command is: The above magnetic field calculation unit further comprises the step of detecting an estimated state value of the coil using a state-space equation derived through the following mathematical formulas 7 and 8. Sensorless current control method for uninsulated high-temperature superconducting coils. [Mathematical Formula 7] [Mathematical Formula 8] (here, i φ is the component of current flowing in the direction of the coil's winding, i is the current supplied to the coil, v is the voltage across the coil, and R c is the characteristic resistance of the coil, and L is the inductance of the coil.

5. In Paragraph 2, The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command is: The above magnetic field calculation unit further comprises the step of converting the state-space equation into a discretized state-space equation through the following mathematical formulas 9 to 11. Sensorless current control method for uninsulated high-temperature superconducting coils. [Mathematical Formula 9] [Mathematical Formula 10] [Mathematical Formula 11] (here, i φ is the component of current flowing in the direction of the coil's winding, i is the current supplied to the coil, v is the voltage across the coil, and R c ε is the characteristic resistance of the coil, and L is the inductance of the coil.

6. In Paragraph 5, The step of calculating the magnetic field of the coil using a Kalman filter based on the voltage of the coil and the current output according to the magnetic field command is: The method further comprises the step of deriving each variable of the state equation and the output equation for a one-dimensional Kalman filter into the following mathematical equations 12 to 15 using the discretized state-space equation through the magnetic field calculation unit. Sensorless current control method for uninsulated high-temperature superconducting coils. [Mathematical Formula 12] [Mathematical Formula 13] [Mathematical Formula 14] [Mathematical Formula 15]

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