Dynamic alternating current loss analysis method for high-temperature superconducting rotor magnet

Abstract

The invention discloses a dynamic alternating current loss analysis method for a high-temperature superconducting rotor magnet, which takes a discrete sampling value of an exciting current time sequence as a unique input quantity and takes quasi-static electromagnetic energy dissipation as a definition basis for loss energy. In each sampling period, current increment is calculated, a direction mark is judged, a turning point sampling sequence number set and a turning point current value sequence are updated when the direction is reverse, a hysteresis historical state is constructed, and loop segment state input is formed. Based on the state input of the loop segments, respectively establishing segment-level loss mapping models for the whole straight line segment and the whole arc segment, recursively outputting the whole loss energy of the straight line segment and the whole loss energy of the arc segment in each sampling period, and synthesizing the whole loss energy of the straight line segment and the whole loss energy of the arc segment into single-pole total AC loss energy; and a coupling correction coefficient can be introduced as required to obtain output after coupling correction. The method does not need full-field transient solution of the electromagnetic field, and is suitable for online rapid evaluation and engineering application.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic loss analysis technology of rotor magnets in high-temperature superconducting synchronous condensers, and specifically relates to a method for dynamic AC loss analysis of rotor magnets in high-temperature superconducting condensers. Background Technology

[0002] High-temperature superconducting synchronous condensers achieve high magnetic fields and high energy efficiency by employing high-temperature superconducting excitation windings on the rotor side, while their rotor magnets typically operate in low-temperature environments. To meet the requirements of reactive power regulation, operating state switching, and experimental condition verification, the rotor excitation current inevitably undergoes dynamic changes such as strong excitation, rapid ramps, and step jumps during engineering operation. Rapid changes in the excitation current cause nonlinear evolution of the current distribution and magnetic flux penetration state within the superconducting tape, resulting in AC losses. These AC losses are deposited as heat inside the rotor magnets and are one of the key electromagnetic factors affecting low-temperature stability and system reliability.

[0003] For high-temperature superconducting tapes, AC losses are closely related to the excitation process and exhibit a significant hysteresis history effect. Even under the same current amplitude, different current change paths, rates of change, and prior excitation histories will lead to different loss energy responses. In typical dynamic processes such as strong excitation ramps and steps, the aforementioned hysteresis history effect is usually more pronounced. If only a static correspondence is established between losses and the current current amplitude, it may lead to a deviation in the assessment of dynamic loss energy, thereby affecting the judgment of the load and safety margin of the cryogenic system.

[0004] Among existing AC loss analysis methods, one type relies on high-fidelity electromagnetic field numerical calculations combined with material constitutive relations to obtain loss results. This provides a relatively detailed spatial distribution, but typically requires comprehensive geometric, material, and boundary information, resulting in high computational costs and long time-stepping iterations, making continuous updates within the control system's sampling period difficult. Furthermore, its input quantities are usually far greater than the information readily available in the engineering field, making it difficult to achieve rapid evaluation using the excitation current sequence as the sole input. Another type of method introduces numerous empirical coefficients or additional measurements to reduce computational costs. While this can be used to estimate total losses under specific conditions, its applicability is unclear, and it fails to adequately characterize the hysteresis history effect during strong excitation dynamic processes, making it difficult to stably reproduce loss differences under different excitation histories.

[0005] Furthermore, the electromagnetic environment varies significantly across the rotor pole coil segments. Taking a racetrack-shaped coil as an example, the straight and circular segments differ in terms of applied magnetic field distribution, field angle variation, and magnetic flux penetration paths, resulting in segmented and uneven AC losses within the poles. In engineering, simply providing the total pole loss power or total loss energy is insufficient for quantitative analysis of structural features. Existing methods that can output segmented results typically rely on complex electromagnetic field solutions and detailed geometric modeling, further increasing computational and input complexity burdens and failing to meet engineering requirements for periodic updates.

[0006] Therefore, there is an urgent need to propose a dynamic analysis method that is simple to input, has controllable computational load, can reflect the hysteresis history effect, and outputs the AC energy loss of the straight and circular segments of the magnetic poles. This method should be able to achieve loss assessment updated according to the sampling period under the condition of strong excitation and rapid change, and provide reliable basic data for subsequent related work. Summary of the Invention

[0007] To address the shortcomings of existing AC loss analysis methods, such as heavy reliance on transient solutions of the entire electromagnetic field, difficulty in real-time updates within the control system's sampling period, and difficulty in outputting segmented loss energy for straight and circular pole segments using only the excitation current time series as input, this invention provides a dynamic AC loss analysis method for high-temperature superconducting rotor magnets. This method uses discrete sampled values ​​of the excitation current time series as the sole input, and defines loss energy based on quasi-static electromagnetic energy dissipation. Within each sampling period, the current increment is calculated and the direction marker is determined. When a direction reversal occurs, the set of inflection point sampling numbers and the inflection point current value sequence are updated, constructing a hysteresis history state and forming a loop segment state input. Based on the loop segment state input, segment-level loss mapping models are established for both the overall straight and circular segments, recursively outputting the overall loss energy of the straight and circular segments within each sampling period, and synthesizing it into the total AC loss energy of a single magnetic pole. When necessary, a coupling correction coefficient can be introduced to obtain a coupled-corrected output. This invention eliminates the need for transient solutions of the entire electromagnetic field, making it suitable for online rapid evaluation and engineering applications.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for dynamic AC loss analysis of high-temperature superconducting rotor magnets, which does not use transient solutions of the entire electromagnetic field as a calculation step, but recursively outputs results based on discrete sampled values ​​of excitation current and hysteresis history according to the sampling period, including the following steps:

[0010] Using discrete sampled values ​​of the excitation current time series as the only input, the current increment is calculated and the direction mark is determined in each sampling period. The direction mark is used to characterize the direction of change of the excitation current between adjacent sampling points.

[0011] When the direction of the excitation current change reverses, update the set of inflection point sampling numbers and the sequence of inflection point current values. The inflection point is the sampling point corresponding to the reversal of the excitation current change direction. Construct the hysteresis history state and form the loop segment state input.

[0012] Based on the loop segment state input, segment-level loss mapping models are established for the entire straight segment and the entire circular arc segment respectively; the segment-level loss mapping model is a mapping relationship in which the loop segment state input and current increment are used as independent variables and the loss energy of the corresponding segment within the sampling period is used as the dependent variable.

[0013] The total energy loss of the straight segment and the total energy loss of the circular arc segment within each sampling period are recursively output and combined into the total AC energy loss of a single magnetic pole.

[0014] Furthermore, a coupling correction coefficient is introduced. This makes the corrected total AC loss energy of a single magnetic pole be .

[0015] Furthermore, updating the inflection point set includes adding inflection points and removing inflection points corresponding to covered inner loops based on extreme value coverage relationships. An extreme value coverage relationship is determined when the current range formed by the current value of the new inflection point and its adjacent outer boundary inflection points completely covers the current range formed by the removed inflection point pairs. This ensures that the inflection point set always retains outer boundary inflection information that is crucial to the current hysteresis loop. An upper limit is set on the number of inflection points; when the number exceeds this limit, the inflection point with the smallest sampling sequence number is removed in ascending order, retaining only the most recently preset number of inflection points. This ensures that the storage and computational load of the hysteresis history remains limited and controllable.

[0016] Furthermore, the loop segment status input includes the upper boundary current value, lower boundary current value, effective current span, segment progress amount, and segment type marker used to distinguish between the main loop segment and the secondary loop segment. The effective current span is the absolute value of the difference between the upper and lower boundary current values; the segment progress amount is the normalized advance of the current value between the upper and lower boundaries along the current direction of change; and the segment type marker is used to characterize whether it is a main loop segment or a secondary loop segment.

[0017] Furthermore, the type of loop segment is determined by comparing the extreme values ​​of the inflection point current value sequence with the current value. When the upper or lower boundary current value of the loop segment is equal to the maximum or minimum value in the current inflection point current value sequence, it is determined to be a main loop segment; otherwise, it is determined to be a secondary loop segment.

[0018] Furthermore, the segment-level loss mapping model uses the absolute value of the segment-level equivalent dissipation coefficient and the current increment. The energy loss during the sampling period is calculated in the product form, where the segment-level equivalent dissipation coefficient is determined by the effective current span, segment progress, and segment type marking.

[0019] Furthermore, the segment-level equivalent dissipation coefficient is implemented through an analytical function parameterization that includes a baseline term, an amplitude term, and a positional influence term, wherein the amplitude term is described in an exponential saturation form to describe the variation characteristics with the effective current span.

[0020] Furthermore, the model parameters were obtained through offline calibration, which employed representative excitation current time series and their corresponding reference loss data. The reference loss data consisted of experimental measurement data and numerically calculated electromagnetic field data, and the model was fitted to minimize the error between the predicted loss energy and the reference loss energy.

[0021] Furthermore, when the current increment is zero, the energy loss output within this sampling period is zero; and when determining the direction reversal, this sampling period is regarded as continuing the direction of the most recent non-zero current increment.

[0022] Furthermore, the determination of the reverse direction is triggered by the condition that the sign product of the current increment in the current sampling period and the most recent non-zero current increment is less than zero. The most recent non-zero current increment is the most recent non-zero current increment obtained by tracing back from the current sampling period.

[0023] Furthermore, the AC loss refers to the AC electromagnetic dissipation loss generated by the high-temperature superconducting tape body in the rotor magnet pole coil, and does not include the eddy current loss and dielectric loss generated by the metal structural components of the rotor magnet.

[0024] Beneficial effects:

[0025] 1. This invention can update the AC loss energy results in real time according to the sampling period under the condition that only the excitation current time series is used as input. The calculation is stable and easy to implement in engineering.

[0026] 2. This invention can output the segmented loss energy of the entire straight segment and the entire circular arc segment of the magnetic pole, which facilitates quantitative analysis of the structural characteristics of the magnetic pole.

[0027] 3. This invention introduces a hysteresis history effect through a turning point storage update mechanism, which improves the consistency and stability of dynamic loss assessment for rapidly changing processes such as strong excitation ramps and step jumps. Attached Figure Description

[0028] Figure 1 This is a flowchart of a dynamic AC loss analysis method for a high-temperature superconducting rotor magnet according to the present invention.

[0029] Figure 2This is a flowchart illustrating the update process of the inflection point sampling sequence set and inflection point current value sequence of the present invention.

[0030] Figure 3 This diagram illustrates the state input construction of the loop segment and the recursive deduction of segment-level energy loss for the entire straight segment and the entire circular arc segment. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0032] The dynamic AC loss analysis method for high-temperature superconducting rotor magnets described in this invention is applicable to single-pole superconducting windings of high-temperature superconducting synchronous condenser rotor magnets. The pole windings are formed into racetrack-shaped coils by winding high-temperature superconducting tape. In some embodiments, the analysis object is limited to the AC loss generated by the superconducting tape itself, excluding other loss sources such as eddy currents in the metal structure. In engineering implementation, the method can be executed by a control system or a host computer processing unit, performing real-time calculation and updating of the excitation current according to the sampling period, and outputting AC loss energy results for engineering evaluation.

[0033] This invention uses discrete sampled values ​​of the excitation current time series as the sole input. The single-pole superconducting winding is geometrically divided into two types of coil segments: a straight segment and a circular arc segment. A dynamic AC loss energy recursive model is constructed for each segment, outputting the loss energy of the straight segment and the loss energy of the circular arc segment according to the sampling period, and summing them to obtain the total loss energy of the single pole. The loss energy is defined based on quasi-static electromagnetic energy dissipation.

[0034] The dynamic AC loss energy recursive model is based on the hysteresis history state and employs a turning point storage and update mechanism to characterize the excitation current history. Based on the direction of change of the excitation current and the position of the turning points in adjacent sampling periods, a hysteresis history state consisting of a finite number of historical turning points is maintained. When the excitation current undergoes a reverse change, the set of turning points is updated to ensure consistency between the hysteresis history state and the excitation current history. Based on the hysteresis history state, segment-level loss mapping models are established for both the entire straight segment and the entire circular segment. This allows the loss energy in each sampling period to be determined jointly by the current excitation current value and its hysteresis history state, thus achieving recursive calculation of loss energy without performing transient solutions for the entire electromagnetic field. The model parameters for the straight segment and the circular segment are set independently to reflect the differences in the electromagnetic environment of the two types of coil segments.

[0035] To ensure the physical consistency and engineering feasibility of the calculation results, the recursive model satisfies constraints such as non-negative energy loss, hysteresis history state updating with the process without divergence, and energy loss automatically becoming zero when the current remains constant. The model parameters can be obtained through offline high-fidelity electromagnetic simulation calibration, or through calibration using a small amount of representative experimental data, or through a combination of both.

[0036] Furthermore, to take into account both single-pole analysis and the effects of multi-pole coupling, the method can introduce a coupling correction coefficient to correct the total energy loss of a single magnetic pole, thereby characterizing the impact of electromagnetic coupling between adjacent magnetic poles on the loss level, and expanding the applicability of the method without increasing the input.

[0037] Specifically, such as Figure 1 As shown, the method for dynamic AC loss analysis of high-temperature superconducting rotor magnets of the present invention includes reading the discrete sampling sequence of excitation current according to the sampling period, maintaining the hysteresis history state, and recursively outputting the AC loss energy result.

[0038] In this embodiment, the only input to the method is a discrete sampling sequence of the excitation current, denoted as ,in The sampling sequence number is denoted as ; the time interval between two adjacent samples is the sampling period, denoted as . This invention does not use rotational speed, external magnetic field measurements, etc., as inputs; all dynamic information is generated by... It reflects the process of change over time.

[0039] To meet the engineering output requirements under the characteristics of the magnetic pole structure, this embodiment equivalently divides the single magnetic pole coil segment into two types of coil segments: a straight line segment and a circular arc segment. The AC loss energy within each sampling period is used as the unified output definition. Accordingly, let the straight line segment be denoted as the [missing information - likely a specific value or term] in the [missing information - likely a specific sampling period]. The AC loss energy within each sampling period is The entire arc segment is in the first The AC loss energy within each sampling period is The total AC energy loss of a single magnetic pole is ,in .

[0040] The aforementioned AC loss energy refers to the cumulative energy generated by electromagnetic dissipation of the superconducting tape within the sampling period. The core of this invention lies in constructing a hysteresis history state based on the excitation current history, and on this basis... and Recursive calculations are performed to update the output of the overall AC energy loss of the single magnetic pole straight segment and the overall circular arc segment according to the sampling period.

[0041] In this embodiment, let the sampling time be... And adjacent sampling times satisfy The discrete sampled values ​​of the excitation current are denoted as... To facilitate the subsequent description of the excitation process, the increment of excitation current at adjacent sampling times is defined as:

[0042] ;

[0043] in, The sign of the slash is used to characterize the direction of current change within adjacent sampling intervals, and its amplitude... Used to characterize the intensity of change; when Time can Set to 0 or process according to the actual initial conditions.

[0044] The output of this invention is uniformly defined as the AC loss energy within each sampling period. Specifically, the first... The time interval corresponding to each sampling period is Let the AC loss energy of the entire straight segment during this time interval be denoted as . The overall AC energy loss of the circular arc segment is The total AC energy loss of a single magnetic pole during that sampling period is... for:

[0045] ;

[0046] in, and All are non-negative quantities, representing the entirety of the line segment, the entirety of the arc segment, and their sum, respectively. The result of energy accumulation within. To clarify the physical meaning of the output, the above energy can be expressed in relation to the instantaneous AC power loss as follows:

[0047] ;

[0048] In the formula, and They are respectively the entire straight line segment and the entire circular arc segment at time [time]. The AC power loss. It should be noted that this invention does not require direct solution during online calculations. and The full-field expression for the electromagnetic field is given. The above integral relationship is used to define the output and its physical meaning. Further analysis will be conducted using the excitation current history and hysteresis history. and Perform recursive calculations, where t represents time.

[0049] In the online calculation of this invention, the direct calculation is performed on... and Perform recursive output.

[0050] To characterize the direction of change of the excitation current within adjacent sampling periods, a direction marker is defined. for:

[0051] ;

[0052] in, Indicates the excitation current at The internal process is in an upward trend. This indicates that it is in a downward trend. This indicates that it remains unchanged.

[0053] Furthermore, to facilitate the establishment of loss mapping models for the entire straight segment and the entire circular arc segment respectively, the parameter sets for the two types of coil segment models are denoted as follows: and Its specific composition and acquisition method will be given in a later section; in the optional extension considering the influence of multi-pole coupling, the coupling correction coefficient is denoted as... Used to measure the total energy loss of a single magnetic pole Corrections will be made. The symbols mentioned above retain only one meaning in this specification and will not be redefined thereafter.

[0054] To ensure that the output of this invention matches the characteristics of the magnetic pole structure and to provide a clear spatial bearing object for the subsequent segment-level loss mapping model, this embodiment makes the following stipulations regarding the segmentation method of the single-pole superconducting winding. The single-pole superconducting winding is formed into a racetrack-shaped coil by winding high-temperature superconducting tape, which can be divided into straight segment regions and circular arc segment regions along the circumference of the magnetic pole.

[0055] During rapid changes in excitation, such as strong excitation ramps and step jumps, the AC losses of high-temperature superconducting tapes are related not only to the current excitation current value but also to the evolution of the excitation current. This is to address the issue of discrete sampling sequences based solely on the excitation current. To reflect the above-mentioned process correlation under the input conditions, this embodiment introduces a hysteresis history state to compress and characterize the key transition features in the excitation current process, thereby reducing energy loss in subsequent stages. and The calculation can rely on both the current and historical information simultaneously, without the need for a full-field transient solution of the electromagnetic field.

[0056] In this embodiment, the turning point refers to the extreme point of the excitation current when its direction of change with time changes from rising to falling, or from falling to rising. Based on the aforementioned direction marker... A turning point can be determined when the direction of excitation current change reverses within adjacent sampling periods, and both changes are non-zero. Specifically, if the following conditions are met:

[0057] ;

[0058] Then at the sampling time The point where the upward trend turns into a downward trend is denoted by the sampling number of the inflection point. The corresponding inflection point current value is denoted as:

[0059] ;

[0060] The sampling sequence number is the inflection point. This represents the corresponding inflection point current value.

[0061] If the following conditions are met:

[0062] ;

[0063] Then at the sampling time The turning point from decline to rise is also taken at this point. ,and .when This indicates that the excitation current remains constant during the sampling period. This situation does not produce a new turning point and can be regarded as a continuation of the process of maintaining the previous non-zero change direction.

[0064] To facilitate online recursive calculations and maintain sign consistency, this embodiment uses a set of inflection points to represent the hysteresis history. Let the inflection point be denoted as... The set of inflection point sampling indices maintained at each sampling time is: The elements are ordered chronologically; correspondingly, the sequence of inflection point current values ​​is denoted as:

[0065] ;

[0066] in, express The first in Each inflection point sampling sequence number, and This is the current value at the turning point. Therefore, the hysteresis history state is recorded as:

[0067] ;

[0068] Regression to historical status Within each sampling period The evolution is updated, and the update rule ensures that the number of turning points is finite and consistent with the excitation current history, thus providing a unified historical state input for the subsequent establishment of segment-level loss mapping models for the entire straight segment and the entire circular arc segment.

[0069] When the excitation current is continuously rising, continuously falling, or experiences a short-term constant plateau without reversing direction, the excitation history does not form new current extreme points, and therefore should not generate new inflection point information. This embodiment employs a hold-behind rule to handle such situations, ensuring simple updates to the hysteresis history and achieving stability.

[0070] Specifically, when the direction of excitation current change remains consistent within adjacent sampling periods, the set of inflection points remains unchanged; when the excitation current remains constant within a certain sampling period, i.e. At this time, the constant interval is considered a continuation of the most recent non-zero change direction, and is not considered a new turning point feature. Based on the above convention, the hysteresis history state is not updated until a reversal occurs, and the set of turning point sampling numbers and corresponding current value sequences maintained at the previous sampling time are still used, that is:

[0071] ;

[0072] When the excitation current reverses direction after several sampling cycles on a constant platform, the current extreme value usually falls on that constant platform. To ensure consistency in extreme value location, this embodiment uniformly uses the sampling point before the end of the platform as the turning point and writes it into the turning point set when the direction reverses. The relevant triggering conditions and the rules for adding, overwriting, and erasing the turning point set will be explained in detail in subsequent sections.

[0073] To ensure that the hysteresis historical state can operate online for a long time and that the computational load remains controllable, this embodiment introduces a finiteness mechanism for the inflection point set, so that the inflection point set remains a set of finite key historical points during repeated excitation adjustments, thereby avoiding the unbounded growth of computational load caused by continuous accumulation over time.

[0074] Let the first The set of inflection point sampling indices maintained at each sampling time is: ,in , The number of inflection points; the corresponding sequence of inflection point current values ​​is as follows: Once a new inflection point is detected and written into the set, the latest inflection point current value is recorded. This embodiment uses a hysteresis compression rule based on extreme value coverage to prune the set: if the turning point corresponds to an extreme point where the rise turns into a fall, then it is a local maximum; when the following conditions are met... When the newly formed local maximum value is not less than the current value corresponding to the previous extreme point of the same type, the pair of inflection points located between the two only correspond to the covered inner loop segment, and their contribution to the hysteresis history of subsequent processes can be effectively eliminated. Therefore, they are removed from the set at the same time. and And its corresponding current value. After one removal, continue to repeat the above criteria with the updated end inflection point and its previous extreme point of the same type until the covering relationship is no longer satisfied. If the inflection point corresponds to an extreme point where the value changes from decreasing to increasing, then it is a local minimum; when the condition is satisfied... Similarly, remove the inflection point pairs corresponding to the covered inner loops in the same manner, and iterate until the covering relationship is no longer valid. Through the above-mentioned coverage erasure rules, the inflection point set always retains the outer boundary inflection information that has a decisive effect on the current hysteresis loop, avoiding the repeated accumulation of invalid inner loops.

[0075] In engineering implementation, to further limit the storage size under the worst-case scenario, an upper limit can be set on the number of inflection points. ,make The condition remains true even after cropping. In such a case, then and Several turning points from the earliest time in the middle are removed in chronological order, and only the most recent ones are retained. The sequence of inflection points and their current values ​​is used for subsequent calculations, thereby ensuring that the storage and online computation of hysteresis historical states remain within a limited and controllable range.

[0076] When the excitation current changes from an upward process to a downward process, or from a downward process to an upward process, a new current extreme point will be formed and a turning point will be triggered and written into the turning point set. In order to ensure that the triggering criterion remains consistent in the presence of a constant current plateau, this embodiment adopts a reverse determination method based on the sign of the current increment, and regards the constant plateau as a continuation of the previous non-zero change direction.

[0077] For any The excitation current increment corresponding to the current sampling period is defined as... Furthermore, the definition and the first The previous non-zero increment sampling sequence number corresponding to each sampling period is:

[0078] ;

[0079] When the above set is empty, it means that the first set is empty. If the excitation current does not change to non-zero before a sampling period, no direction reversal determination is performed, and no inflection point is written.

[0080] when It exists and satisfies:

[0081] ;

[0082] Then determine the excitation current in the first... A reversal in direction occurs during the sampling period, triggering a turning point write operation. The meaning of this criterion is: the first... The direction of the excitation current change in each sampling period is opposite to the direction of the most recent non-zero change; when there are several [sampling cycles] between two non-zero changes... When the sampling period is constant, the above criterion is equivalent to identifying the reverse direction at the end of the constant platform, thereby avoiding ambiguity in the identification of the turning point caused by the constant platform.

[0083] After triggering a reversal of direction, this embodiment positions the turning point at the sampling moment before the reversal of direction occurs. And take the inflection point sampling sequence number as:

[0084] ;

[0085] The corresponding inflection point current value is:

[0086] ;

[0087] When the reversal of direction occurs after the constant plateau, since the excitation current value within the plateau remains constant, take... The current value at the inflection point is consistent with the current extreme value.

[0088] After completing the location of the turning point, A set of inflection points is written, and an adjustment process for the inflection point set is initiated to maintain the consistency of the hysteresis loop and ensure that the inflection point set is a finite set. The writing and adjustment process includes update and overwrite / erase rules for the inflection point set, the specific execution method of which will be further explained in subsequent sections. The update process for the inflection point sampling sequence set and the inflection point current value sequence is as follows: Figure 2 As shown.

[0089] When the excitation current reverses direction and forms a turning point, in order to ensure that the hysteresis loop represented by the set of turning points remains consistent and to avoid retaining inner loop information that has been covered by subsequent processes in the hysteresis history, this embodiment performs an overwrite erasure rule on the set of turning points after the turning point is written. The goal of the overwrite erasure rule is to retain only the outer loop boundary turning information that has a decisive effect on the current and subsequent processes, so that the set of turning points always corresponds to a self-consistent hysteresis loop as time progresses.

[0090] Let the first Each sampling cycle triggers the direction in reverse and locates the inflection point sampling sequence number. The inflection point current value is After writing the turning point into the turning point set, the sampling numbers of the turning points are sorted according to time sequence to obtain the updated sequence form:

[0091] ;

[0092] And the corresponding sequence of inflection point current values ​​is obtained:

[0093] ;

[0094] in, , , This represents the number of turning points after the write operation. To distinguish the types of turning points,

[0095] When a certain reversal is an upward trend Decrease (the new turning point is a local maximum) and satisfy Then remove it from the set of turning points. and When a certain reversal is downward... The value increases (the new turning point is a local minimum) and satisfies the following conditions: Then remove it from the set of turning points. and .

[0096] The overwrite rule is executed based on extreme overwrite relationships. When At that time, examine the three most recent inflection points at the end of the sequence. .like ,express For a newly formed local maximum; when:

[0097] ;

[0098] This indicates that the newly formed outer layer maximum value is not less than the previous maximum value of the same type, marking a turning point. and The defined inner loop segment has been covered by the current outer loop, and its constraint on subsequent hysteresis processes can be effectively eliminated. At this point, it is simultaneously removed from the sequence. and and their corresponding current values, retained As the current outer boundary inflection point. If ,express This is the newly formed local minimum.

[0099] When the following conditions are met: ;

[0100] Similarly, if an inner loop segment is covered by the current outer loop, it must be removed from the sequence simultaneously. and .

[0101] After the above removal operation is completed, the length of the inflection point sequence is reduced by 2. The same type of judgment is then repeated using the updated last three inflection points until the coverage condition is no longer met or the sequence length is less than 3. The result after erasure... and It only includes inflection points that have a decisive effect on the current hysteresis loop, which not only maintains the alternating characteristics of the inflection point sequence between the maximum and minimum values, but also makes the inflection point current value sequence reflect the coverage relationship of the outer loop to the inner loop, thereby providing a consistent hysteresis history state input for the subsequent segment-level loss mapping model.

[0102] Furthermore, for situations involving multiple consecutive reversals within a short period, such as a reversal occurring again within adjacent or very short sampling periods after an initial reversal (e.g., rising to falling then falling to rising, or falling to rising then rising to falling), the frequency of inflection point writes may increase, but the overwrite and erase rules should still maintain consistent loops. To address this, this embodiment requires that after each reverse write to an inflection point and completion of the erase, the inflection point sequence maintains basic consistency in alternating inflection point types; that is, adjacent inflection points should correspond to alternating local maximum and local minimum values. If the difference between the written inflection point current value and the adjacent inflection point current value is negligible due to sampling noise or extremely small amplitude reversals, this reversal can be considered a correction to the previous inflection point rather than a new loop segment, ensuring the inflection point set maintains an alternating structure and preventing noise-triggered non-real loop segments from entering a hysteresis history state.

[0103] To facilitate the use of hysteresis history information as input for segment-level loss energy calculation and to avoid directly using variable-length inflection point sequences in subsequent models, this embodiment maintains an inflection point set. With the inflection point current value sequence Based on this, a hysteresis history state quantity corresponding to the current excitation process is constructed to characterize the boundary information and evolution direction information of the current loop segment.

[0104] Let the first After the inflection point writing, finite clipping, and erasure processes are completed at each sampling time point, the set of inflection point sampling sequence numbers is represented chronologically as follows:

[0105] ;

[0106] in, The number of inflection points currently retained, and the corresponding inflection point current value. .when At that time, take the two most recent turning points. The corresponding current value is used as the boundary current value of the current loop segment, and the upper boundary current value is defined. With lower boundary current value for:

[0107] ;

[0108] The above definition reflects the effective range of the current loop segment on the current axis. .when At this point, if there is only one identified inflection point, the current value at that inflection point and the current value are used together as the basis for boundary determination, defined as follows:

[0109] ;

[0110] when This indicates that a turnaround point sequence has not yet been formed. To ensure the completeness of the definition, the initial excitation current can be used. With current Used together for boundary determination, defined as follows:

[0111] ;

[0112] This allows the hysteresis historical state quantity to also have a clear interval meaning in the initial stage of the excitation process.

[0113] To characterize the evolution direction within the current loop segment, this embodiment uses a direction marker. Characterizing the first The direction of change of excitation current within each sampling period, among which Indicates an upward process. Indicates the descent process. This indicates that it remains unchanged. (By) , and Together they constitute the hysteresis historical state quantity, denoted as:

[0114] ;

[0115] in, This is used to characterize the loop segment boundary and its evolution direction in subsequent segment-level loss mapping models, so that the loss energy can depend on both the current excitation current value and historical process boundary information.

[0116] Furthermore, to ensure that the positional quantities within the loop segment have uniform dimensions and are easy to represent in the model, normalized positional quantities can be defined. for:

[0117] ;

[0118] in, This indicates the relative position of the current current within the effective range. When... When the current remains constant or degenerates within a certain range, take Used to maintain consistency in expression. The above. and The definition provides a unified and implementable state input definition for the subsequent segment-level loss energy recursion model of the entire straight line segment and the entire circular arc segment.

[0119] During the rolling change of the excitation current according to the sampling period, there is a monotonically evolving excitation process between any two adjacent inflection points. In order to enable the subsequent segment-level loss mapping model to use consistent independent variables to describe this monotonically evolving process in each sampling period, this embodiment defines the excitation process at the current sampling moment as a loop segment, and gives the judgment rules of the loop segment and its state driving relationship.

[0120] In the At each sampling point, the hysteresis historical state quantity has changed from Characterization, in which and These are the upper and lower boundaries of the current loop segment on the current axis, respectively. For the excitation current in The direction of change within. Define the effective current span of the current loop segment. for:

[0121] ;

[0122] when At that time, the current value of the loop segment is limited by the interval. And before a new direction reversal occurs, the excitation current moves along this interval. The indicated direction advances monotonously; when When the current is constant or the interval degrades, the loop segment does not advance effectively.

[0123] In order to not change Given a unified segment advance amount under the given definition, this embodiment introduces a segment progress amount. This causes it to increase monotonically within the loop segment as the excitation current advances along the current direction, defined as:

[0124] ;

[0125] in, For normalized position quantities, satisfying .when hour, This indicates the relative progress of the excitation current advancing from the lower boundary to the upper boundary; when hour, This indicates the relative progress of the excitation current advancing from the upper boundary to the lower boundary. This ensures that within any loop segment, The range of values ​​is Furthermore, it aligns with the direction of segment progression, thus facilitating the subsequent representation of segment-level energy loss as... Functions for segment boundaries.

[0126] Regarding the loop segment hierarchy, to distinguish between main loop segments and secondary loop segments, this embodiment uses the extreme values ​​of the inflection point current value sequence to determine the current segment boundary. Let the first segment be... The sequence of inflection point current values ​​retained at each sampling time is as follows The upper envelope current and lower envelope current of this sequence are defined as follows:

[0127] ;

[0128] ;

[0129] Among them, the current current Included in the extreme value set to cover cases with a small number of inflection points or the initial stage of excitation. If the current lap segment satisfies:

[0130] ;

[0131] If the current segment is located at the outer boundary, it is considered a primary loop segment; otherwise, it is considered to be located inside the outer boundary, corresponding to a secondary loop segment. To facilitate subsequent model calls, a loop segment type marker is defined. for:

[0132] ;

[0133] in, Indicates the main loop segment. This indicates a secondary loop segment. This determination method relies solely on the maintained inflection point storage information and the current current value, without introducing additional measurements, and is compatible with the finite pruning and overwrite rules of the inflection point set.

[0134] In summary, this embodiment uniformly represents the loop segment state input used for segment-level loss energy calculation as:

[0135] ;

[0136] in, In each sampling period The system updates continuously and serves as the state driver for subsequent segment-level loss mapping models of the entire straight segment and the entire circular arc segment. This allows the segment-level loss energy to simultaneously reflect the current current position, segment boundary constraints, and hysteresis history hierarchy information. The diagram illustrates the construction of the loop segment state input and the recursive derivation of the segment-level loss energy for the entire straight segment and the entire circular arc segment as follows: Figure 3 As shown.

[0137] Input the status of the loop segment Then, hysteresis history information can be incorporated into the segment-level loss energy calculation. This embodiment uses the entire straight segment as an example to give the overall form of the segment-level loss mapping model, which is used in the first... Each sampling period Internal calculation of overall AC energy loss of straight segment To ensure that the output definition is consistent with the aforementioned definition and to satisfy the requirement that the energy is zero when the current is constant, it is first agreed that when... Time to take:

[0138] ;

[0139] when In this case, the energy loss of the entire straight segment during the sampling period is expressed as the product of the magnitude of the change in excitation current and the segment-level equivalent dissipation coefficient:

[0140] ;

[0141] In the formula, For the entire line segment in the th... The segment-level equivalent dissipation coefficient for each sampling period is physically defined as the equivalent energy loss corresponding to a unit change in excitation current. Its value is determined by the boundary of the current loop segment, the position of the current within the segment, and the type of loop segment.

[0142] To enable the model to distinguish the impact of primary loop segments and secondary loop segments on the loss level, a loop segment type label is used. As the switching quantity, Indicates the main loop segment. This represents the second loop segment. Therefore... It can be written as:

[0143] ;

[0144] In the formula, The effective current span of the loop segment. This is the segment progress quantity, used to characterize the extent to which the current current advances along the current direction within the segment; and These are the segment-level dissipation coefficient functions corresponding to the primary loop segment and the secondary loop segment, respectively.

[0145] Without introducing a full-field electromagnetic field solution, and to ensure the simplicity of the function form and ease of calibration, this embodiment uses a few-parameter analytical function. Perform parameterization. For example, the following can be taken:

[0146] ;

[0147] In the formula, , , and For the model parameters of the entire line segment, where It is a scale parameter for the current span, used to characterize the rate of change of the dissipation coefficient under different effective current spans; This is a symmetrical representation of the segment progress, used to characterize the effect of position within a segment on the dissipation coefficient. `exp()` represents an exponential function. The above parameters are summarized as follows: The values ​​of these parameters are obtained through offline simulation or experimental calibration. The parameter constraints that allow the model to satisfy requirements such as non-negative energy, non-divergent numerical values, and constant zero current will be further explained in subsequent sections in conjunction with the overall model of the straight line segment.

[0148] During the online calculation process with rolling updates of the sampling period, the overall AC energy loss of the straight segment is... The calculation should be consistent with the update of the hysteresis history state. That is, the hysteresis history state corresponding to the excitation process of this cycle should be maintained first, and then the energy loss calculation of this cycle should be completed under the constraints of this state to ensure that the time interval corresponding to the output is always consistent. And avoid the hysteresis boundary from being disconnected from energy calculation.

[0149] In the Each sampling time Read the excitation current sampling value Calculate the current increment Then, based on the direction-reverse trigger criterion, it is determined whether it is in A turning point is formed at this point; if a turning point is formed, the sampling sequence number of the turning point is recorded. and its current value Write the inflection point set and apply overwrite pruning and overwrite erasure rules to the inflection point set to ensure that the inflection point set remains finite and consistent with the current hysteresis loop; if no inflection point is formed, the inflection point set remains unchanged. After completing the above processing, the inflection point set and the current current are compared. Calculate the state input of the loop segment. This includes the boundary information of the loop segment, the segment span, the segment progress amount, and the segment type marker amount.

[0150] In obtaining Then, the overall energy loss of the straight segment is calculated according to the following recursive relationship. If Then take:

[0151] ;

[0152] like Then take:

[0153] ;

[0154] Among them, the segment-level equivalent dissipation coefficient Input from loop segment status Decision. (Note) The effective current span in is The segment progress is The number of fragment type tags is ,but:

[0155] ;

[0156] and by parameter set right Perform analytical parameterization to directly obtain the parameters within each sampling period. And thus obtain Therefore, the online calculation of the overall energy loss of the straight segment depends only on the current excitation current sampling value in each sampling period. Previous sample value And the hysteresis historical state maintained by the set of turning points.

[0157] In engineering applications, if a periodic equivalent AC loss power consistent with the energy output is required, the following can be taken:

[0158] ;

[0159] in, For the first Periodic equivalent power within each sampling period.

[0160] To ensure consistency between the physical meaning and numerical calculation of the overall segment-level loss mapping model for straight segments, this embodiment... and The range of values ​​and parameter set The constraints are specified as follows to ensure that the model meets the requirements of non-negative energy loss, zero energy loss when the current is constant, and non-divergence of long-term online recursion.

[0161] when At that time, it was stipulated This ensures, from the output definition, that no energy loss accumulates when the excitation current remains constant within the sampling period. In this case, the model adopts Therefore, it only needs to guarantee the segment-level equivalent dissipation coefficient. If it is non-negative and bounded, then it can be made It satisfies nonnegativity and boundedness within any sampling period.

[0162] Depend on It can be known This is a weighted sum of the dissipation coefficients of the two types of loop segments, where... Therefore, as long as... All Then there must be ,and then .

[0163] This embodiment imposes the following parameter constraints on the following formula:

[0164] ;

[0165] Pick To ensure that the exponent term is calculated effectively and follows the trend. Increasing monotonicity tends towards saturation; taking , To ensure that the baseline and amplitude terms do not introduce negative dissipation; take To ensure that for any All of the following are available:

[0166] ;

[0167] Thus It is non-negative across the entire domain. The above constraints do not limit the specific parameter values, but only the signs and value ranges, which helps to ensure the physical consistency of the model without narrowing the scope of protection.

[0168] Furthermore, in engineering implementation, if there are quantization errors or noise in the excitation current sampling, the extremely small current increment can be treated as zero change and set... This is to avoid the accumulation of non-physical energy triggered by noise; this processing does not change the input-output definition and core calculation relationship of the present invention, but is only used to improve the stability and noise resistance of the online implementation.

[0169] Input the status of the loop segment Afterwards, the overall AC energy loss of the circular arc segment The calculation can employ the same recursive framework as the entire straight line segment, but the model parameter set is set independently to characterize the differences in dissipation levels caused by the differences between the entire circular arc segment and the entire straight line segment in terms of electromagnetic environment and magnetic flux penetration process. To ensure consistent output definition and meet the requirement of zero energy when the current is constant, it is first agreed that when... Time to take:

[0170] ;

[0171] when At that time, the entire arc segment is placed on the first... The energy loss within each sampling period is expressed as:

[0172] ;

[0173] In the formula, For the entire arc segment in the first... The segment-level equivalent dissipation coefficient for each sampling period, its physical meaning is... Both represent the equivalent energy loss corresponding to a unit change in excitation current, but their values ​​are determined by the overall parameter set of the circular arc segment.

[0174] To reflect the difference in dissipation levels between primary and secondary loop segments, a loop segment type label is used. Switching results in:

[0175] ;

[0176] in, For the effective current span of the loop segment, For segment progress, and These are the overall segment-level dissipation coefficient functions for the arc segments corresponding to the primary loop segment and the secondary loop segment, respectively.

[0177] Without introducing a full-field transient solution for the electromagnetic field, and to ensure the simplicity of the function form and ease of calibration, this embodiment also employs a few-parameter analytical function. Perform parameterization. For example, the following can be taken:

[0178] ;

[0179] In the formula, and For the overall model parameters of the arc segment, where This is a current span scale parameter used to characterize the saturation characteristics of the dissipation coefficient as a function of the segment span; This is used to characterize the effect of location within a fragment on the dissipation coefficient. The above parameters are summarized as follows:

[0180] ;

[0181] Its value can be obtained through offline simulation or experimental calibration. To ensure the non-negativity of energy loss and the stability of online recursion, the following can be used: Apply the same sign and value range constraints as the entire line segment, such that for any and All Thus ensuring And it does not experience unbounded growth.

[0182] Obtain the total AC loss energy of the straight segment Energy loss due to overall AC interaction with the arc segment After that, the single magnetic pole in the first Each sampling period The total AC loss energy within the pole is synthesized according to the piecewise summation rule under the law of energy conservation. Based on the aforementioned output definition, the total AC loss energy of a single magnetic pole is denoted as... And satisfy:

[0183] ;

[0184] in, and These correspond to two non-overlapping high-temperature superconducting tape regions: the straight segment region and the circular arc segment region. Therefore, the above summation will not result in duplicate measurement and is consistent with the energy definition of the single-pole high-temperature superconducting tape region.

[0185] To ensure the consistency of each output quantity on the time axis during the online calculation process, this embodiment executes the following sequence in each sampling period: (1) complete the sampling of excitation current and the calculation of current increment; (2) complete the direction reversal determination and the update of the set of turning points; (3) complete the calculation of the state quantity of the loop segment; (4) calculate the AC loss energy of the entire straight segment and the entire circular arc segment respectively, and synthesize it into the total AC loss energy output of a single magnetic pole.

[0186] Regarding the maintenance of hysteresis history, the inflection point set is implemented through overwrite pruning, overwrite erasure rules, and an upper limit on the number of inflection points. The constraint ensures that the set remains finite, thus guaranteeing that the storage and computational costs of hysteresis historical states are finite and controllable. The boundary current values ​​of the loop segments formed by the set of inflection points... Always satisfied Therefore, the effective current span of the loop segment Non-negative quantity; segment progress quantity Constructed from normalized position quantities and its range of values ​​is limited. Therefore, the key independent variables of the loop segment state input are naturally bounded in their domain, avoiding state drift caused by the infinite accumulation of historical information.

[0187] In the segment-level loss mapping calculation, the loss energy per sampling period is defined as a unified output quantity: when Time to take:

[0188] ;

[0189] when When:

[0190] ;

[0191] in, The dissipation coefficient function of the two types of segments is switched by the segment type marker, and satisfies the parameter constraints. .because ,therefore:

[0192] ;

[0193] This ensures that the non-negativity requirement of energy loss is met within any sampling period.

[0194] Furthermore, since the dissipation coefficient function adopts an exponentially saturated form, and The range of values ​​for is finite, which shows that... and All are bounded quantities under parameter constraints, therefore , , The upper bound is determined by Together with the upper bound of the parameter, it determines that there will be no unbounded accumulation due to the increase of online running time.

[0195] To ensure the feasibility of this invention and to prevent it from relying on transient solutions across the entire electromagnetic field, this embodiment addresses the overall parameter set of the line segment. With the overall parameter set of the arc segment The method for obtaining the calibration rules is described. The calibration is completed in the offline stage, and in the online stage, only the calibrated parameters are called for recursive calculation, thereby realizing dynamic AC loss output updated according to the sampling period.

[0196] The input excitation data required for calibration consists of several representative excitation current time series, which are in the same format as the online input, both consisting of discrete sampled values. With sampling period Composition. To ensure the model can cover rapidly changing operating conditions such as strong excitation ramps and steps, the representative current sequence includes at least: a monotonically rising ramp sequence, a monotonically falling ramp sequence, a rising step sequence, a falling step sequence, and a reciprocating sequence containing at least one reversal. The amplitude range and rate of change of the above sequences can be selected according to the typical excitation regulation requirements of the target device, but are not limited to specific values ​​to avoid narrowing the protection range.

[0197] The required output reference data for calibration is the segment-level AC loss energy or equivalent loss power result corresponding to the above representative current sequence. This reference data can be obtained in the following ways: First, by calculating using an offline high-fidelity electromagnetic numerical analysis model. This numerical analysis model can be established based on the constitutive relation of superconducting materials and electromagnetic field numerical methods, with the output within the same sampling period interval. The overall energy loss of the straight segment within. Overall energy loss of the arc segment Secondly, equivalent loss reference values ​​are obtained through experimental methods. For example, the loss energy reference results for a single magnetic pole or coil segment are obtained through thermal balance or equivalent heat load measurement of a cryogenic system, and then aggregated according to the statistical methods of the entire straight segment and the entire circular segment. Thirdly, a joint calibration is adopted using the above two methods, where electromagnetic numerical analysis is used to provide the distribution trend of segment-level losses, and experimental results are used to correct the total level. Regardless of the method used, the reference data is consistent with the output definition of this invention, using the loss energy per sampling cycle as the basic calibration value, and the energy can be converted from equivalent power when necessary.

[0198] During the calibration process, a representative current sequence will be used. By inputting the hysteresis history state maintenance module of this invention, the hysteresis segment state input for each sampling period is obtained. And based on this, the model is constructed to predict the overall energy loss of the straight segment. Overall energy loss of the arc segment Then, using the error between the model's predicted values ​​and the reference values ​​as the objective function, the model is... and We perform fitting and solving separately. Taking the entire line segment as an example, the objective function can be:

[0199] ;

[0200] in, This is the set of sampling period numbers included in the calibration data. The circular arc segment is constructed similarly. During the fitting process, the aforementioned nonnegativity and bounded constraints are applied to the parameters to ensure that the calibration results meet physical consistency requirements. After calibration, the obtained... and Solidification is used for online recursive calculations.

[0201] It should be noted that, in order to reduce the calibration workload, priority should be given to ensuring that the parameters of the main loop segment and the secondary loop segment are consistent in trend, and a small number of representative reciprocating sequences are allowed to be used to correct the parameters of the secondary loop segment. At the same time, if only the reference data of the total loss energy of a single magnetic pole can be obtained, additional allocation constraints or empirical ratios can be introduced to equivalently decompose the segment-level reference quantities while keeping the parameters of the two segments independently set, so as to complete the parameter calibration and ensure that the method is feasible.

[0202] Furthermore, to characterize the impact of electromagnetic coupling between adjacent magnetic poles on the AC loss level without increasing the input, this embodiment introduces a coupling correction coefficient. This is used to equivalently correct the total AC loss energy of a single magnetic pole. The coupling correction coefficient is a constant parameter obtained from offline calibration and is not used as an online input. is a dimensionless coefficient, taking a non-negative value, whose magnitude can be determined by offline analysis of the overall electromagnetic environment or by a small number of experimental results. The total AC loss energy of a single magnetic pole considering coupling effects is defined as... Then we have:

[0203] ;

[0204] in, When coupling effects are not considered, we can take... ,at this time The above modifications only apply to the output and do not change the form of the hysteresis history maintenance and segment-level loss mapping model, which facilitates a moderate extension of the multi-pole coupling effect within the single-pole analysis framework.

[0205] To illustrate the online organization method of the present invention, the following embodiment is given. A discrete sequence of a single magnetic pole excitation current is selected. As input, the sampling period is The excitation current history includes a monotonic ramp-up section, a constant plateau section, a step change section, and at least one reversal section. The current amplitude can cover the typical excitation level of the prototype, for example, rising to near the typical excitation current level of the prototype and then adjusting it. During online operation, data is read in each sampling cycle. And calculate ,when Time output , ;when At that time, the inflection point set is updated according to the reverse trigger criterion of the excitation current direction, and the overlay clipping and erasure processing are completed to obtain the loop segment state input. And then from the parameter set and Calculate the equivalent dissipation coefficient at the segment level respectively. , ,get:

[0206] ;

[0207] and synthesize ;

[0208] This outputs the total AC loss energy for the entire straight segment, the entire circular segment, and the single magnetic pole in each sampling period. The periodic equivalent power can be further obtained from the energy output. or It serves as an interface for subsequent engineering evaluation or thermal analysis.

[0209] The above embodiments are only used to illustrate the technical solutions and implementation methods of the present invention, and are not intended to limit the scope of protection of the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the equivalent expression of the hysteresis history state, the parameterized form of the segment-level dissipation coefficient function, and the determination method of the coupling correction coefficient without departing from the core idea of ​​the present invention should fall within the scope of protection of the present invention.

Claims

1. A method for analyzing the dynamic AC loss of a high-temperature superconducting rotor magnet, characterized in that: The output result is recursively calculated based on the discrete sampled values ​​of the excitation current and the historical hysteresis state according to the sampling period, including the following steps: Using discrete sampled values ​​of the excitation current time series as the only input, the current increment is calculated and the direction mark is determined in each sampling period. The direction mark is used to characterize the direction of change of the excitation current between adjacent sampling points. When the direction of the excitation current change reverses, update the set of inflection point sampling numbers and the sequence of inflection point current values. The inflection point is the sampling point corresponding to the inflection point when the direction of the excitation current change reverses. Construct the hysteresis history state and form the loop segment state input. Based on the loop segment state input, segment-level loss mapping models are established for the entire straight segment and the entire circular arc segment respectively; the segment-level loss mapping model is a mapping relationship in which the loop segment state input and current increment are used as independent variables and the loss energy of the corresponding segment within the sampling period is used as the dependent variable. The total energy loss of the straight segment and the total energy loss of the circular arc segment within each sampling period are recursively output and combined into the total AC energy loss of a single magnetic pole.

2. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: Introducing coupling correction coefficient This makes the corrected total AC loss energy of a single magnetic pole be .

3. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: The update of the inflection point set includes adding inflection points and removing inflection points corresponding to covered inner loops based on extreme value coverage relationships. When the current range formed by the current value of the new inflection point and its adjacent outer boundary inflection points completely covers the current range formed by the removed inflection point pairs, an extreme value coverage relationship is determined. This ensures that the inflection point set always retains the outer boundary inflection information that plays a decisive role in the current hysteresis loop. An upper limit is set for the number of inflection points. When the number of inflection points exceeds the upper limit, the inflection point with the smallest sampling sequence number is removed in ascending order, and only the most recently preset number of inflection points are retained to ensure that the storage and computational load of the hysteresis history state remains limited and controllable.

4. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: The loop segment status input includes the upper boundary current value, lower boundary current value, effective current span, segment progress amount, and segment type marker amount used to distinguish between the main loop segment and the secondary loop segment; wherein the effective current span is the absolute value of the difference between the upper boundary current value and the lower boundary current value; the segment progress amount is the normalized advance amount of the current value between the upper and lower boundaries along the current change direction; and the segment type marker amount is used to characterize the main loop segment or the secondary loop segment.

5. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 4, characterized in that: The type of loop segment is determined by comparing the extreme value of the inflection point current value sequence with the current value. When the upper or lower boundary current value of the loop segment is equal to the maximum or minimum value in the current inflection point current value sequence, it is determined to be a main loop segment; otherwise, it is determined to be a secondary loop segment.

6. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: The segment-level loss mapping model uses the absolute value of the segment-level equivalent dissipation coefficient and the current increment. The energy loss during the sampling period is calculated in the product form, where the segment-level equivalent dissipation coefficient is determined by the effective current span, segment progress, and segment type marking.

7. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 6, characterized in that: The segment-level equivalent dissipation coefficient is implemented by an analytical function parameterization that includes a baseline term, an amplitude term, and a location influence term. The amplitude term is described in an exponential saturation form to describe its variation with the effective current span.

8. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: The model parameters were obtained through offline calibration. The calibration process used representative excitation current time series and their corresponding reference loss data. The reference loss data included experimental measurement data and electromagnetic field numerical calculation data. The model was fitted and solved with the goal of minimizing the error between the model's predicted loss energy and the reference loss energy.

9. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: When the current increment is zero, the energy loss output during this sampling period is zero; and when determining the direction reversal, this sampling period is regarded as continuing the direction of the most recent non-zero current increment.

10. The method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to claim 1, characterized in that: The determination of reverse direction is triggered by the condition that the sign product of the current increment in the current sampling period and the most recent non-zero current increment is less than zero. The most recent non-zero current increment is the most recent non-zero current increment obtained by tracing back from the current sampling period.

11. A method for dynamic AC loss analysis of a high-temperature superconducting rotor magnet according to any one of claims 1-10, characterized in that: AC loss refers to the AC electromagnetic dissipation loss generated by the high-temperature superconducting tape body in the rotor magnet pole coil.

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