Control method of high-temperature superconducting magnet

Abstract

The invention discloses a control method for a high-temperature superconducting magnet, and belongs to the technical field of superconducting energy storage control, and the method comprises the steps: obtaining a measurement voltage, a measurement current and a plan power value sequence of the high-temperature superconducting magnet; based on the measured voltage, the measured current and the electromagnetic dynamic model, internal state variables are obtained, and the internal state variables comprise dynamic resistance capable of reflecting superconducting performance changes; inputting the planned power value sequence and the internal state variable into a magnet state prediction model to generate an internal state variable prediction sequence and a current prediction sequence; judging whether a quench risk or a thermal instability risk exists or not; when the risk exists, adjusting the plan power value sequence to obtain an optimized power value sequence, and taking the optimized power value sequence as a target power value sequence; and if no risk exists, taking the planned power value sequence as a target power value sequence. And controlling according to the target power value sequence. According to the invention, the problem that the control of the high-temperature superconducting magnet is not accurate enough in the prior art is solved.

Description

Technical Field

[0001] This invention relates to the field of superconducting energy storage control technology, specifically to a control method for a high-temperature superconducting magnet. Background Technology

[0002] High-temperature superconducting magnets, as the core energy carriers of superconducting energy storage devices, utilize superconducting coils to store and release electrical energy without loss in a zero-resistance state. With their high power density, millisecond-level response speed, and near-infinite charge-discharge cycle count, they play a crucial role in new power grids, high-energy physics, and rail transportation. However, high-temperature superconducting magnets are complex, highly nonlinear dynamic objects, and their operating state is constantly affected by the coupling effects of multiple physical fields, including current, external magnetic fields, temperature, and mechanical stress. Especially when rapidly processing power to meet grid frequency regulation or pulse load demands, the accumulation of AC losses can easily trigger drastic fluctuations in the magnet's internal state. Therefore, precise control of high-temperature superconducting magnets is not only crucial for energy conversion efficiency but also a prerequisite for preventing quenching or thermal instability and maintaining the safe operation of the device.

[0003] Currently, existing high-temperature superconducting magnet control technologies typically rely on preset empirical values ​​or fixed safety margins to formulate power execution strategies, resulting in relatively rigid control logic. Specifically, existing control methods often only unidirectionally execute power commands issued from above, lacking the ability to predict the potential evolution of the magnet's internal state during future execution. This control approach does not treat power commands as dynamically optimizable variables, failing to proactively adjust the planned power sequence based on the magnet's current actual load-bearing capacity. Therefore, when facing complex and variable operating conditions, this control strategy relying on fixed empirical values ​​often struggles to balance safety and efficiency, leading to inaccurate control of high-temperature superconducting magnets. Summary of the Invention

[0004] This invention provides a control method for high-temperature superconducting magnets, which can solve the problem of insufficient accuracy in the control of high-temperature superconducting magnets in the prior art.

[0005] One embodiment of the present invention provides a method for controlling a high-temperature superconducting magnet, comprising: The system acquires the measured voltage and current of a high-temperature superconducting magnet, as well as a planned power value sequence for the magnet during a future control cycle. Based on the measured voltage, the measured current, and a preset electromagnetic dynamic model, it generates internal state variables of the high-temperature superconducting magnet, including dynamic resistance. The planned power value sequence and the internal state variables are input into a preset magnet state prediction model, which generates a predicted sequence of internal state variables and a predicted current sequence for the magnet during the future control cycle based on the planned power value sequence and the internal state variables. The system then calculates the dynamic resistance based on the predicted internal state variables. The predicted resistance value and the predicted current sequence are used to determine whether the high-temperature superconducting magnet faces a risk of quenching or thermal instability during future control cycles. If such a risk exists, the planned power value sequence is adjusted to generate an optimized power value sequence. This optimized power value sequence is then used as the target power value sequence for the high-temperature superconducting magnet during future control cycles. If no risk of quenching or thermal instability exists, the planned power value sequence is used as the target power value sequence for the high-temperature superconducting magnet during future control cycles. The high-temperature superconducting magnet is then controlled according to the target power value sequence.

[0006] Furthermore, based on the measured voltage, the measured current, and a preset electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated, including: determining the operating condition of the high-temperature superconducting magnet based on the measured voltage and the measured current; the operating condition being either a quasi-steady-state condition or a transient condition; when the operating condition of the high-temperature superconducting magnet is a quasi-steady-state condition, generating the internal state variables of the high-temperature superconducting magnet based on the preset quasi-steady-state electromagnetic dynamic model, according to the measured voltage and the measured current; wherein, when the operating condition of the high-temperature superconducting magnet is a quasi-steady-state condition, the internal state variables also include inductance, DC bias voltage, critical current, and power law number; when the operating condition of the high-temperature superconducting magnet is a transient condition, generating the internal state variables of the high-temperature superconducting magnet based on the preset transient electromagnetic dynamic model, according to the measured voltage and the measured current; wherein, when the operating condition of the high-temperature superconducting magnet is a transient condition, the internal state variables also include inductance and DC bias voltage.

[0007] Further, determining the operating conditions of the high-temperature superconducting magnet based on the measured voltage and the measured current includes: extracting the measured voltage values ​​at each sampling time from the measured voltage; extracting the measured current values ​​at each sampling time from the measured current; calculating the operating power of the high-temperature superconducting magnet at the last sampling time based on the measured voltage value and the measured current value at the last sampling time; calculating the operating power of the high-temperature superconducting magnet at the sampling time preceding the last sampling time based on the measured voltage value and the measured current value at the sampling time preceding the last sampling time; and calculating the operating power of the high-temperature superconducting magnet at the sampling time preceding the last sampling time based on the measured voltage value and the measured current value at the sampling time preceding the last sampling time. The measured current value at the previous sampling time is used to calculate the current change rate at the last sampling time. Based on the operating power at the last sampling time and the operating power at the previous sampling time, the power change rate at the last sampling time is calculated. If the current change rate at the last sampling time is less than a preset current change threshold and the power change rate at the last sampling time is less than a preset power change threshold, the operating condition of the high-temperature superconducting magnet is determined to be a quasi-steady-state condition. If the current change rate at the last sampling time is not less than a preset current change threshold, or the power change rate at the last sampling time is not less than a preset power change threshold, the operating condition of the high-temperature superconducting magnet is determined to be a transient condition.

[0008] Furthermore, when the high-temperature superconducting magnet is operating under quasi-steady-state conditions, based on a preset quasi-steady-state electromagnetic dynamic model, and according to the measured voltage and the measured current, the internal state variables of the high-temperature superconducting magnet are generated, including: when the high-temperature superconducting magnet is operating under quasi-steady-state conditions, using the preset quasi-steady-state electromagnetic dynamic model as the first observation equation; repeatedly executing the first state estimation operation until the first state estimation operation has been executed at all sampling times to generate the internal state variables of the high-temperature superconducting magnet; wherein, the first state estimation operation includes: calculating the partial derivative of the preset first state equation based on the first best estimated state vector of the previous round, and generating the first state transition matrix of the current round; In this process, the initial round is the first sampling time; the first best estimated state vector is the best estimated value of the first system state vector; the first system state vector consists of dynamic resistance, inductance, DC bias voltage, critical current, and power law; the best estimated value of the first system state vector of the previous round of the initial round is a preset value; based on the first best estimated state vector of the previous round and the preset first state equation, the first predicted state vector of the current round is calculated and generated; wherein, the first predicted state vector is the predicted value of the first system state vector; based on the first state transition matrix of the current round, the first covariance matrix of the previous round, and the preset process noise matrix, the first predicted state vector of the current round is calculated and generated. The covariance matrix is ​​calculated, where the first covariance matrix of the previous round in the initial round is a preset value. Based on the measured current value of the current round and the measured current value of the previous round, the current change rate of the current round is calculated. Based on the measured current value of the current round and the current change rate of the current round, the first observation equation is linearized to determine the first observation matrix of the current round. Based on the first observation matrix of the current round, the first prediction covariance matrix of the current round, and the preset observation noise matrix, the first Kalman gain matrix of the current round is calculated. Substituting the first predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round into the first observation equation, the current Kalman gain matrix is ​​calculated. The system calculates the predicted voltage value for the current round; based on the predicted voltage value and the measured voltage value for the current round, it generates the voltage deviation value for the current round; based on the first Kalman gain matrix for the current round, and based on the voltage deviation value and the first predicted state vector for the current round, it generates the first best estimated state vector for the current round; it determines whether the current round is the last sampling time. If so, the first best estimated state vector for the current round is used as the internal state variable of the high-temperature superconducting magnet; otherwise, based on the first Kalman gain matrix, the first observation matrix, and the first predicted covariance matrix for the current round, it generates the first updated covariance matrix for the current round.The next sampling time is updated to the next round; the first best estimated state vector of the current round is updated to the first best estimated state vector of the previous round in the next round; and the first updated covariance matrix of the current round is updated to the first covariance matrix of the previous round in the next round.

[0009] Furthermore, when the high-temperature superconducting magnet is operating under transient conditions, based on a preset transient electromagnetic dynamic model, and according to the measured voltage and the measured current, the internal state variables of the high-temperature superconducting magnet are generated. This includes: when the high-temperature superconducting magnet is operating under transient conditions, using the preset transient electromagnetic dynamic model as the second observation equation; repeatedly executing the second state estimation operation until the second state estimation operation has been executed at all sampling times to generate the internal state variables of the high-temperature superconducting magnet; wherein, the second state estimation operation includes: calculating the partial derivative of the preset second state equation based on the second best estimated state vector of the previous round, and generating the second state transition matrix of the current round; wherein, the initial round is the... A sampling time; the second best estimated state vector is the best estimated value of the second system state vector; the second system state vector consists of a resistance auxiliary variable, an inductance, and a DC bias voltage; the best estimated value of the second system state vector of the previous round in the initial round is a preset value; the resistance auxiliary variable is the square root of the dynamic resistance; based on the second best estimated state vector of the previous round and the preset second state equation, the second predicted state vector of the current round is calculated and generated; wherein, the second predicted state vector is the predicted value of the second system state vector; based on the second state transition matrix of the current round, the second covariance matrix of the previous round, and the preset process noise matrix, the second predicted state vector of the current round is calculated and generated. The covariance matrix is ​​calculated, where the second covariance matrix of the previous round in the initial round is a preset value. Based on the measured current value of the current round and the measured current value of the previous round, the current change rate of the current round is calculated. Based on the measured current value of the current round, the resistance auxiliary variable in the second predicted state vector of the current round, and the current change rate of the current round, the second observation equation is linearized to determine the second observation matrix of the current round. Based on the second observation matrix of the current round, the second predicted covariance matrix of the current round, and the preset observation noise matrix, the second Kalman gain matrix of the current round is calculated. The second predicted state vector of the current round, the measured current value of the current round, and the current change rate of the previous round are used to calculate the current change rate of the current round. The rate of change of current is substituted into the second observation equation to calculate the predicted voltage value for the current round; based on the predicted voltage value and the measured voltage value for the current round, the voltage deviation value for the current round is calculated; based on the second Kalman gain matrix for the current round, the voltage deviation value and the second predicted state vector for the current round are used to calculate the second best estimated state vector for the current round; it is determined whether the current round is the last sampling time. If so, the dynamic resistance is calculated based on the resistance auxiliary variable in the second best estimated state vector for the current round, and the dynamic resistance, the inductance and the DC bias voltage in the second best estimated state vector for the current round are determined as the internal state variables of the high-temperature superconducting magnet.If not, then based on the second Kalman gain matrix, the second observation matrix, and the second prediction covariance matrix of the current round, calculate and generate the second updated covariance matrix of the current round; update the next sampling time to the next round, update the second best estimated state vector of the current round to the second best estimated state vector of the previous round in the next round, and update the second updated covariance matrix of the current round to the second covariance matrix of the previous round in the next round.

[0010] Furthermore, the preset quasi-steady-state electromagnetic dynamic model is specifically as follows: In the formula, For the first quasi-steady-state condition The predicted voltage value at the nth sampling time, i.e., the voltage value at the quasi-steady-state condition. The predicted voltage values ​​for each round; For the first Dynamic resistance at each sampling time; For the first The measured current value at each sampling time; For the first Inductance at each sampling time; The sampling time interval; For the first DC bias voltage at each sampling time; For the first The rate of change of current at each sampling time; The preset transient electromagnetic dynamic model is specifically as follows: In the formula, For the first transient condition The predicted voltage value at the nth sampling time, i.e., the voltage value at the nth sampling time under transient conditions. The predicted voltage values ​​for each round; For the first The resistance auxiliary variable at each sampling time. Used to characterize the Dynamic resistance at each sampling time; For the first The measured current value at each sampling time; For the first Inductance at each sampling time; The sampling time interval; For the first DC bias voltage at each sampling time; For the first The rate of change of current at each sampling time.

[0011] Furthermore, the preset first state equation is specifically as follows: in, For the first The first system state vector of each round; A nonlinear function characterizing the power-law properties of superconducting materials, used according to the first... Critical current of each cycle Power Law and measuring current Calculate and generate the first Dynamic resistance of each round ; For the first Inductance in each round; For the first DC bias voltage for each round; For the first Critical current for each cycle; For the first The power law number of each round; The first noise driving matrix is ​​preset; This is the preset first process noise vector; The preset second state equation is specifically as follows: in, For the first The second system state vector for each round; For the first Resistance auxiliary variables for each round; For the first Inductance at each sampling time; For the first DC bias voltage for each round; This is a preset second noise driving matrix; This is the preset second process noise vector.

[0012] Furthermore, the preset magnet state prediction model is trained in the following manner: A magnet state prediction dataset is acquired; wherein the magnet state prediction dataset includes several historical planned power value sequences, historical initial internal state variables, and corresponding magnet state prediction labels; the magnet state prediction labels are historical internal state variable sequences and historical current sequences; the magnet state prediction dataset is randomly divided into several batches of training samples according to a preset number; each batch of training samples is sequentially input into the magnet state prediction model to train the magnet state prediction model until a preset number of training iterations is reached; wherein, when the magnet state prediction model receives each batch of training samples, it outputs the corresponding internal state variable prediction sequence and current prediction sequence; based on the internal state variable prediction sequence, current prediction sequence, and corresponding magnet state prediction labels, a loss function value is calculated using a loss function; the magnet state prediction model is updated based on the loss function value.

[0013] Furthermore, based on the predicted dynamic resistance values ​​in the internal state variable prediction sequence and the current prediction sequence, it is determined whether the high-temperature superconducting magnet faces quenching or thermal instability risks during future control cycles, including: From the predicted sequence of internal state variables, a predicted sequence of dynamic resistance values ​​for future control cycles is extracted; it is determined whether there is a predicted dynamic resistance value in the predicted sequence that is greater than a preset quench resistance threshold; if so, it is determined that the high-temperature superconducting magnet has a quench risk in the future control cycle; if not, it is determined that the high-temperature superconducting magnet does not have a quench risk in the future control cycle; based on the predicted dynamic resistance value sequence and the predicted current sequence, an AC loss power sequence for the high-temperature superconducting magnet in the future control cycle is calculated and generated; the AC loss power sequence is input into a preset magnet thermal model to calculate and generate a temperature rise prediction sequence for the high-temperature superconducting magnet in the future control cycle; it is determined whether there is a predicted temperature value in the temperature rise prediction sequence that is greater than a preset thermal instability temperature threshold; if so, it is determined that the high-temperature superconducting magnet has a thermal instability risk in the future control cycle; if not, it is determined that the high-temperature superconducting magnet does not have a thermal instability risk in the future control cycle.

[0014] Furthermore, if the high-temperature superconducting magnet faces a risk of quenching or thermal instability during future control cycles, the planned power value sequence is adjusted to generate an optimized power value sequence. This includes: repeatedly performing a power value correction operation until the high-temperature superconducting magnet is free from quenching and thermal instability risks during future control cycles, thereby generating an optimized power value sequence. The power value correction operation includes: adjusting the current power value sequence to be adjusted based on a preset adjustment strategy to obtain a current candidate power value sequence. The initial power value sequence to be adjusted is the planned power value sequence. The preset adjustment strategy includes reducing the power change rate, limiting peak power values, or inserting low power values. The current candidate power value sequence is then adjusted. The sequence of candidate power values ​​and the internal state variables are input into a preset magnet state prediction model, so that the magnet state prediction model generates a current internal state variable prediction sequence and a current current prediction sequence for the high-temperature superconducting magnet in the future control cycle based on the current candidate power value sequence and the internal state variables. Based on the dynamic resistance prediction value in the current internal state variable prediction sequence and the current current prediction sequence, it is determined whether the high-temperature superconducting magnet has a risk of quenching or thermal instability in the future control cycle. If the high-temperature superconducting magnet does not have a risk of quenching or thermal instability in the future control cycle, the current candidate power value sequence is used as the optimized power value sequence. If the high-temperature superconducting magnet has a risk of quenching or thermal instability in the future control cycle, the current candidate power value sequence is updated to the current power value sequence to be adjusted.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a control method for high-temperature superconducting magnets. By acquiring real-time measured electrical quantities of the high-temperature superconducting magnet and combining them with an electromagnetic dynamic model, the internal state variables, including dynamic resistance, are accurately calculated. This overcomes the shortcomings of existing technologies that rely solely on empirical values ​​and cannot accurately perceive the actual operating conditions of the magnet. Simultaneously, a magnet state prediction model is used to predict future internal state variables and currents, effectively solving the problem that traditional control logic lacks the ability to predict the consequences of power command execution. Based on the prediction results, this invention can optimize the planned power value sequence when quench or thermal instability risks are identified, generating a target power value sequence that balances safety. This control method breaks away from the traditional approach of passively executing power commands issued from the upper layer, ensuring precise control while eliminating risks, thus solving the problem of inaccurate control of high-temperature superconducting magnets in existing technologies. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a control method for a high-temperature superconducting magnet according to an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] like Figure 1 As shown, to address the problem of insufficient accuracy in controlling high-temperature superconducting magnets in existing technologies, an embodiment of the present invention provides a method for controlling high-temperature superconducting magnets, comprising at least the following steps: Step S1: Obtain the measurement voltage of the high-temperature superconducting magnet, the measurement current of the high-temperature superconducting magnet, and the planned power value sequence of the high-temperature superconducting magnet in the future control cycle.

[0019] Specifically, the measured voltage and current of the high-temperature superconducting magnet obtained in step S1 are acquired in real time by high-precision voltage sensors arranged at both ends of the high-temperature superconducting magnet and current sensors in the circuit. Given that the high-temperature superconducting magnet has the operating characteristics of large current and low voltage, the relative error of its current measurement is usually much smaller than that of its voltage measurement. Therefore, in this embodiment, the measurement error of the current sensor is ignored, and the acquired measured current is directly regarded as the actual current of the high-temperature superconducting magnet, while the measured voltage is regarded as a comprehensive observation value including the dynamic resistance voltage drop of the magnet, the inductance voltage, the DC bias voltage, and the high-frequency electromagnetic interference noise.

[0020] The planned power value sequence of the high-temperature superconducting magnet in the future control cycle refers to the set of power commands issued by the upper-level dispatching system based on the grid or load demand, which are expected to be tracked by the high-temperature superconducting magnet in the next N control cycles. The future control cycle refers to a preset time window that is extrapolated from the current moment.

[0021] It should be noted that, considering the physical response delay of the power converter and power controller when executing the planned power value sequence, the values ​​in the planned power value sequence serve as reference instructions and have the following transfer function relationship with the actual power followed by the high-temperature superconducting magnet: In the formula, This is the Laplace transform of the actual power following a high-temperature superconducting magnet. This is the Laplace transform of the power command corresponding to the planned power value sequence; The response time delay constant of the power converter and controller; For the Laplace operator.

[0022] By acquiring the aforementioned precise real-time measurement data and clear future power control targets, a reliable data foundation is laid for accurately identifying the complex nonlinear states inside the magnet and predicting future evolution trends.

[0023] Step S2: Based on the measured voltage, the measured current, and the preset electromagnetic dynamic model, generate the internal state variables of the high-temperature superconducting magnet; the internal state variables include dynamic resistance.

[0024] In a preferred embodiment, the internal state variables of the high-temperature superconducting magnet are generated based on the measured voltage, the measured current, and a preset electromagnetic dynamic model, including: The operating conditions of the high-temperature superconducting magnet are determined based on the measured voltage and the measured current; the operating conditions are either quasi-steady-state or transient. When the high-temperature superconducting magnet is operating under quasi-steady-state conditions, based on a preset quasi-steady-state electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated according to the measured voltage and the measured current; wherein, when the high-temperature superconducting magnet is operating under quasi-steady-state conditions, the internal state variables also include inductance, DC bias voltage, critical current, and power law number. When the high-temperature superconducting magnet is operating under transient conditions, based on a preset transient electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated according to the measured voltage and the measured current; wherein, when the high-temperature superconducting magnet is operating under transient conditions, the internal state variables also include inductance and DC bias voltage.

[0025] Specifically, the step of generating the internal state variables of the high-temperature superconducting magnet based on the measured voltage, the measured current, and the preset electromagnetic dynamic model is achieved through in-depth modeling of the physical properties of the high-temperature superconducting magnet. First, the preset electromagnetic dynamic model in this embodiment is based on the general continuous-time voltage equation of the high-temperature superconducting magnet, which treats the magnet as a time-varying, non-autonomous object composed of a nonlinear dynamic resistor and an inductor connected in series. Considering the unavoidable DC component drift and high-frequency electromagnetic interference in the measurement system, the time-domain relationship between the terminal voltage and current of the high-temperature superconducting magnet can be expressed as: In the formula, These are the observed terminal voltage values ​​of the high-temperature superconducting magnet; The nonlinear dynamic resistance of a magnet is a key parameter characterizing the loss characteristics of the magnet. The current flowing through the magnet; This is the equivalent inductance of the magnet. The value of this inductance is not constant, but fluctuates within a small range depending on the current density distribution and operating conditions. To measure the DC bias voltage of the system; This represents the background noise voltage. It is a continuous-time variable.

[0026] Based on the above general model, the operating conditions of the high-temperature superconducting magnet are further determined according to the dynamic characteristics of the measured voltage and the measured current. The operating conditions are divided into quasi-steady-state operating conditions with relatively smooth changes in current and power, and transient operating conditions with high-frequency fluctuations or rapid charging and discharging, so as to apply more suitable physical constraints for different operating conditions, thereby improving the accuracy of state estimation.

[0027] Under quasi-steady-state operating conditions, the magnetic flux motion inside the high-temperature superconducting magnet is mainly dominated by thermally activated flux creep. In this case, the change in nonlinear dynamic resistance follows a voltage-current power law relationship unique to superconducting materials. Therefore, based on a pre-defined quasi-steady-state electromagnetic dynamic model, when generating the internal state variables of the high-temperature superconducting magnet according to the measured voltage and current, in addition to the basic dynamic resistance, inductance, and DC bias voltage, the critical current and power law number characterizing this power law characteristic are also incorporated into the internal state variables for synchronous identification. At this point, the constraint relationship between the dynamic resistance and each state variable satisfies the following power law equation: In the formula, The preset superconducting critical voltage criterion constant (usually taken as...) (Multiplied by the coil length) The critical current state variable varies with time and magnetic field. These are power-law state variables characterizing the properties of superconducting materials. By introducing these two physical parameters as state variables, the state estimation process can be constrained using physical mechanisms, giving it extremely high physical interpretability and accuracy in steady state.

[0028] When the high-temperature superconducting magnet operates under transient conditions, due to the high rate of current change and the complex AC loss mechanism within the magnet, the traditional DC power-law relationship is no longer applicable, and forcibly fitting the power-law parameters may lead to algorithm divergence. Therefore, in this case, when generating the internal state variables of the high-temperature superconducting magnet based on the preset transient electromagnetic dynamic model and the measured voltage and current, the critical current and power-law number are no longer estimated. To ensure that the dynamic resistance always maintains its non-negative physical characteristics in the numerical calculation, this embodiment introduces a resistance auxiliary variable to parametrically model the dynamic resistance, and its numerical relationship is as follows: In the formula, The resistance is used as an auxiliary variable. Under this operating condition, the internal state variables specifically include dynamic resistance, inductance, and DC bias voltage, which are indirectly characterized by auxiliary variables. By adopting a hierarchical modeling strategy for quasi-steady state and transient state, both the physical accuracy under steady state and the algorithm robustness under transient state are preserved, thereby achieving accurate perception of the internal state of the high-temperature superconducting magnet under all operating conditions.

[0029] In a preferred embodiment, determining the operating conditions of the high-temperature superconducting magnet based on the measured voltage and the measured current includes: Extract the measured voltage values ​​at each sampling time from the measured voltage; Extract the measured current values ​​at each sampling time from the measured current; Based on the measured voltage value and the measured current value at the last sampling moment, the operating power of the high-temperature superconducting magnet at the last sampling moment is calculated and generated. Based on the measured voltage value at the previous sampling time and the measured current value at the previous sampling time, the operating power of the high-temperature superconducting magnet at the previous sampling time is calculated. The rate of change of current at the last sampling moment is calculated based on the measured current value at the last sampling moment and the measured current value at the previous sampling moment. The power change rate at the last sampling time is calculated based on the operating power at the last sampling time and the operating power at the sampling time before the last sampling time. If the rate of change of current at the last sampling moment is less than the preset current change threshold and the rate of change of power at the last sampling moment is less than the preset power change threshold, the operating condition of the high-temperature superconducting magnet is determined to be the quasi-steady-state operating condition. If the rate of change of current at the last sampling moment is not less than the preset current change threshold, or the rate of change of power at the last sampling moment is not less than the preset power change threshold, the operating condition of the high-temperature superconducting magnet is determined to be the transient operating condition.

[0030] In one specific embodiment, the operating condition of the high-temperature superconducting magnet is determined based on the measured voltage and the measured current. This process is essentially a real-time digital determination of the operating state of the high-temperature superconducting magnet. First, data is discretized and extracted from the continuous analog signal through an analog-to-digital conversion interface. The measured voltage value at each sampling moment is extracted from the measured voltage, and the measured current value at each sampling moment is extracted from the measured current. The latest sampling moment is defined as the last sampling moment. Its previous sampling time was The data from these two moments are used to capture the instantaneous energy flow state of the magnet.

[0031] Specifically, based on the measured voltage value at the last sampling time and the measured current value at the last sampling time. The operating power of the high-temperature superconducting magnet at the last sampling moment is calculated through product operations. Similarly, based on the measured voltage value of the previous sampling time from the last sampling time... And the measured current value at the previous sampling time before the last sampling time. Calculate the operating power of the high-temperature superconducting magnet at the time preceding the last sampling time. The formula for calculating operating power is as follows: In the formula, For the first Operating power at each sampling time; For the first The measured voltage value at each sampling time; For the first The measured current value at each sampling time.

[0032] Based on this, to quantify the severity of system state changes, it is necessary to calculate the rate of change index. The current rate of change at the last sampling moment is calculated using the first-order backward difference method, based on the measured current value at the last sampling moment and the measured current value at the previous sampling moment. Simultaneously, the power rate of change at the last sampling moment is calculated based on the operating power at the last sampling moment and the operating power at the previous sampling moment. The specific calculation logic is shown in the following formula: In the formula, The rate of change of current at the last sampling time (the absolute value is used to characterize the magnitude of the change). The power change rate at the last sampling time (the absolute value is used to characterize the magnitude of the change). This represents the sampling time interval.

[0033] Finally, the calculated rates of change of physical quantities are compared with preset stability thresholds. If the rate of change of current at the last sampling moment is less than the preset current rate of change, and the rate of change of power at the last sampling moment is less than the preset power rate of change, it indicates that the electromagnetic state inside the magnet is stable, and the magnetic flux motion is in the thermally activated flux creep range. Therefore, the operating condition of the high-temperature superconducting magnet is determined to be a quasi-steady-state condition. Conversely, if the rate of change of current at the last sampling moment is not less than the preset current rate of change, or the rate of change of power at the last sampling moment is not less than the preset power rate of change, it indicates that the magnet is in a state of rapid charging and discharging or being disturbed, and there is violent magnetic flux flow and eddy current loss inside. Therefore, the operating condition of the high-temperature superconducting magnet is determined to be a transient condition. Through this dual-criteria operating condition identification mechanism, it can be ensured that the subsequent state estimation stage calls the most suitable electromagnetic model for different physical processes, thereby maximizing the physical reality of the state assessment while ensuring the convergence of the algorithm.

[0034] In a preferred embodiment, when the high-temperature superconducting magnet is operating under quasi-steady-state conditions, based on a preset quasi-steady-state electromagnetic dynamic model, and according to the measured voltage and the measured current, the internal state variables of the high-temperature superconducting magnet are generated, including: Under the condition that the high-temperature superconducting magnet is in a quasi-steady-state condition, the preset quasi-steady-state electromagnetic dynamic model is used as the first observation equation; Repeat the first state estimation operation until the first state estimation operation has been performed at all sampling times to generate the internal state variables of the high-temperature superconducting magnet; The first state estimation operation includes: Based on the first best estimated state vector from the previous round, the partial derivatives of the preset first state equation are calculated to generate the first state transition matrix for the current round; wherein, the initial round is the first sampling time; the first best estimated state vector is the best estimated value of the first system state vector; the first system state vector consists of dynamic resistance, inductance, DC bias voltage, critical current, and power law; the best estimated value of the first system state vector from the previous round of the initial round is the preset value; Based on the first best estimated state vector from the previous round and the preset first state equation, the first predicted state vector for the current round is calculated and generated; wherein, the first predicted state vector is the predicted value of the first system state vector; The first prediction covariance matrix for the current round is calculated and generated based on the first state transition matrix of the current round, the first covariance matrix of the previous round, and the preset process noise matrix; wherein, the first covariance matrix of the previous round of the initial round is a preset value. The current change rate for the current round is calculated based on the measured current value of the current round and the measured current value of the previous round. Based on the measured current value and the current change rate of the current cycle, the first observation equation is linearized to determine the first observation matrix of the current cycle. The first Kalman gain matrix for the current round is calculated and generated based on the first observation matrix of the current round, the first prediction covariance matrix of the current round, and the preset observation noise matrix. Substitute the first predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round into the first observation equation to calculate the predicted voltage value of the current round. Based on the predicted voltage value of the current cycle and the measured voltage value of the current cycle, the voltage deviation value of the current cycle is calculated and generated; Based on the first Kalman gain matrix of the current round, the first best estimated state vector of the current round is calculated and generated according to the voltage deviation value of the current round and the first predicted state vector of the current round. Determine whether the current round is the last sampling time. If so, use the first best estimated state vector of the current round as the internal state variable of the high-temperature superconducting magnet. If not, calculate and generate the first updated covariance matrix of the current round based on the first Kalman gain matrix, the first observation matrix, and the first prediction covariance matrix of the current round. Update the next sampling time to the next round, update the first best estimated state vector of the current round to the first best estimated state vector of the previous round in the next round, and update the first updated covariance matrix of the current round to the first covariance matrix of the previous round in the next round.

[0035] Specifically, firstly, under the condition that the high-temperature superconducting magnet is in a quasi-steady-state condition, the preset quasi-steady-state electromagnetic dynamic model is used as the first observation equation, which establishes a mathematical mapping between the internal state and the external observed physical quantities.

[0036] The preset quasi-steady-state electromagnetic dynamic model is specifically as follows: In the formula, For the first quasi-steady-state condition The predicted voltage value at the nth sampling time, i.e., the voltage value at the quasi-steady-state condition. The predicted voltage values ​​for each round; For the first Dynamic resistance at each sampling time; For the first The measured current value at each sampling time; For the first Inductance at each sampling time; The sampling time interval; For the first DC bias voltage at each sampling time; For the first The rate of change of current at each sampling time.

[0037] Subsequently, a recursive loop is entered, and the first state estimation operation is repeatedly executed until the first state estimation operation has been executed at all sampling times, thereby generating the internal state variables of the high-temperature superconducting magnet containing the dynamic resistance evolution trajectory throughout the entire time period.

[0038] The specific execution logic of the first state estimation operation is as follows: First, based on the first best estimated state vector from the previous round, the partial derivatives of the preset first state equation are calculated to generate the first state transition matrix for the current round. Since the first state equation contains a nonlinear EJ power-law function, covariance cannot be directly transferred using a linear matrix. Therefore, it is necessary to calculate the partial derivatives of the nonlinear function (i.e., calculate the Jacobian moment) for linearization approximation. This calculated Jacobian matrix... This is precisely the first state transition matrix. This step aims to obtain the gradient information of the system state evolution under quasi-steady-state conditions.

[0039] Specifically, the preset first state equation is expressed as follows: in, For the first The first system state vector of each round; A nonlinear function characterizing the power-law properties of superconducting materials, used according to the first... Critical current of each cycle Power Law and measuring current Calculate and generate the first Dynamic resistance of each round ; For the first Inductance in each round; For the first DC bias voltage for each round; For the first Critical current for each cycle; For the first The power law number of each round; The first noise driving matrix is ​​preset; This is the preset first process noise vector.

[0040] It should be noted that, It is a function describing the nonlinear power-law relationship (EJ Power Law) between voltage and current in superconducting materials under quasi-steady-state conditions. The specific calculation formula is as follows: In the formula, For the current round (the 1st round) The predicted dynamic resistance value at each sampling time; The preset superconducting critical voltage criterion constant (usually taken as...) (Total length of coil) This is the measured current value from the previous round (at the (n-1)th sampling time). This is the critical current estimate in the first best estimated state vector of the previous round; This is the power law estimate in the first best estimated state vector of the previous round.

[0041] This formula is based on the current-voltage characteristic equation of high-temperature superconductors. This is derived. In the quasi-steady-state model, we represent it as an equivalent resistance, i.e. .therefore, Essentially, it is calculating the current given... Critical current Power Law Index The nonlinear equivalent resistance value exhibited by the superconducting magnet.

[0042] For ease of mathematical description, this embodiment defines... The deterministic state transition function in the first state equation is defined by the first state equation, which does not contain noise terms. The deterministic mapping part is defined as the deterministic state transition function, i.e. It characterizes the evolution of the system state from the previous time step to the current time step, ignoring the influence of noise. This function is derived from the first state equation describing the nonlinear characteristics of the dynamic resistance. It also consists of linear transitive terms describing the random walk characteristics of the remaining variables. Specifically, for this function... Regarding the state variables from the previous round Taking the partial derivatives yields the Jacobian matrix, which is the first state transition matrix for the current round. The specific calculation formula is as follows: Further solving for the partial derivatives yields the specific matrix form: In the formula, For the first The first state transition matrix of each round, i.e., the first state transition matrix of the current round; The first deterministic state transition function is a five-dimensional vector function. The dynamic resistance is calculated based on the state of the previous round; The power law number of the previous round; This is the critical current for the previous round; This represents the measured current from the previous round. This matrix clearly describes how minute perturbations in the critical current and power law number propagate and affect the change in dynamic resistance at the current moment.

[0043] Next, based on the first best estimated state vector from the previous round and the preset first state equation, the first predicted state vector for the current round is calculated and generated. The specific calculation process is as follows: The first best estimated state vector in the previous round The vector structure is specifically represented as: In the formula, This is the first best estimated state vector from the previous round; This is the best estimate of the dynamic resistance from the previous round; This is the best estimate of the inductance from the previous round; This is the best estimate of the DC bias voltage from the previous round; This is the best estimate of the critical current for the previous round; This is the best estimate of the power law number from the previous round.

[0044] Subsequently, based on the preset first state equation, the first best estimated state vector from the previous round is mapped to the first predicted state vector for the current round. This process utilizes the physical property functions of superconducting materials. The dynamic resistance is updated, while the remaining parameters follow a random walk model to maintain numerical propagation. The specific computational generation process is described by the following state transition equation: In the formula, For the current round (the 1st round) The first predicted state vector at each sampling time; This is a preset nonlinear state transition function; This is the measured current value from the previous round; This is a preset superconducting critical voltage criterion constant.

[0045] It should be noted that the first row of the matrix represents the dynamic resistance prediction value for the current round calculated based on the best estimate of the critical current, the best estimate of the power law number, and the measured current from the previous round; the last four rows of the matrix represent that the inductance, DC bias voltage, critical current, and power law number follow a random walk model in the prediction step, that is, their predicted values ​​are considered to be numerically equal to the best estimate value at the previous moment.

[0046] Furthermore, the random walk model refers to the discretized modeling assumptions used for state variables with unmodeled time-varying characteristics, such as inductance, DC bias voltage, critical current, and power law. Due to the sampling time interval... The time intervals are extremely short, and the parameters mentioned above exhibit thermal inertia or magnetic hysteresis as they change with ambient temperature or magnetic field. Therefore, it is assumed that the parameters maintain a basic continuity of value between two adjacent sampling times, with their tiny numerical drift driven by Gaussian white noise (process noise).

[0047] Subsequently, based on the first state transition matrix of the current round, the first covariance matrix of the previous round, and the preset process noise matrix, the first prediction covariance matrix of the current round is calculated and generated. This step aims to quantify and convey the uncertainty of the system state, projecting the estimation error left over from the previous time step onto the current time step through the linearized state transition matrix, and superimposing the system process noise introduced by the random walk model, thereby determining the confidence interval of the predicted state at the current time step. The specific calculation formula is as follows: In the formula, The first prediction covariance matrix of the current round represents the uncertainty of the system state estimate before the current observation data is fused; This is the first state transition matrix for the current round; This is the first covariance matrix of the previous round; This is the transpose of the first state transition matrix for the current round; The first process noise matrix is ​​a pre-defined matrix, which is a diagonal matrix. The diagonal elements represent the random walk variance of the inductance, DC bias voltage, critical current, and power law number in the discrete time step, respectively. The first noise driving matrix is ​​a preset value used to map the four-dimensional process noise vector to the five-dimensional state space. Considering that the dynamic resistance is determined by other state variables through algebraic equations and there is no independent process noise, therefore... It is typically configured as a vector with all zeros in the first row and the remaining four rows as an identity matrix. It is the transpose of the first noise driving matrix.

[0048] By using this step to extrapolate the covariance, the error limit of the state estimation can be dynamically maintained, providing a statistical basis for the subsequent calculation of the Kalman gain, thereby preventing state divergence caused by over-reliance on model predictions.

[0049] During the correction phase, to correct the predicted values ​​using new measurement data, an observation matrix needs to be calculated. Based on the measured current values ​​from the current cycle and the previous cycle, the rate of change of current for the current cycle is calculated. Subsequently, based on the measured current values ​​and the rate of change of current for the current cycle, the first observation equation is linearized to determine the first observation matrix for the current cycle. This matrix characterizes the sensitivity of the observed voltage to each state variable, and its expression is: In the formula, This is the first observation matrix for the current round; This represents the measured current for the current round. This represents the rate of change of current in the current cycle. The last two terms in the matrix being 0 indicate that, in the observation equation at the current moment, the critical current and power law number do not directly generate voltage, but rather act indirectly through the dynamic resistance.

[0050] Based on this, the first observation matrix of the current round, the first prediction covariance matrix of the current round, and the preset observation noise matrix (characterizing the measurement noise of the voltage sensor) are used to calculate the first Kalman gain matrix of the current round. This gain matrix determines whether to place more weight on the model predictions or the corrected values ​​from the measured data during the estimation process. The specific calculation formula is as follows: In the formula, For the current round (the 1st round) The first Kalman gain matrix (at each sampling time) is used to map the voltage observation residuals back to the five-dimensional state space; The first prediction covariance matrix of the current round represents the uncertainty of the prior estimate based on the state of the previous time step to the current time step; This is the first observation matrix for the current round, i.e., the Jacobian matrix of the first observation equation with respect to the state variables; This is the transpose of the first observation matrix in the current round; The first observation noise matrix is ​​a preset value, typically a scalar or... The matrix, the value of which is determined by the statistical variance of the voltage sensor and the intensity of environmental electromagnetic interference; This represents the operation of inverting a matrix.

[0051] Understandably, this step is the most critical correction stage in the Kalman filter algorithm, aiming to calculate an optimal weight coefficient matrix that minimizes the posterior error covariance. This gain matrix determines whether to place more trust in the model's predictions or the corrected values ​​from the measured data during the estimation process: when the preset observation noise is large, the value of the gain matrix tends to be small, favoring the preservation of the model's prediction path; conversely, when the model's prediction covariance is large, the value of the gain matrix tends to be large, relying more on the current voltage measurement deviation to correct the state variables.

[0052] Then, the first predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round are substituted into the first observation equation to calculate the predicted voltage value of the current round. The predicted voltage value of the current round is then compared with the actual measured voltage value to calculate and generate the voltage deviation value of the current round.

[0053] Finally, based on the first Kalman gain matrix of the current round, the first best estimated state vector of the current round is calculated and generated according to the voltage deviation value of the current round and the first predicted state vector of the current round, thus completing the optimal estimation of the state at the current moment.

[0054] Specifically, the difference between the measured voltage and the predicted voltage (i.e., the voltage deviation) is considered as "innovation." This scalar voltage innovation is weighted and mapped back to a multidimensional state space using the Kalman gain matrix. The required correction for each state variable is calculated and superimposed onto the prior predicted state vector, thus obtaining the posterior state estimate with the smallest statistical mean square error (i.e., the first best estimated state vector). This correction step can eliminate the accumulated error caused by model parameter drift or initial value deviation in real time. The specific calculation formula is as follows: In the formula, For the current round (the 1st round) The first best estimated state vector (at each sampling time) contains the corrected dynamic resistance, inductance, DC bias voltage, critical current and power law number. This is the first predicted state vector for the current round; This is the first Kalman gain matrix for the current round, used to adjust the correction weight of the voltage deviation on the state vector; This is the voltage deviation value for the current cycle, which is the scalar difference obtained by subtracting the predicted voltage value from the measured voltage value.

[0055] At the same time, it is determined whether the current round is the last sampling time. If not, the covariance matrix is ​​updated and rolled to the next time.

[0056] Specifically, when the current round is not the last sampling time, the statistical description of the current state estimation error must be updated to support state recursion for the next time step. At this point, the first updated covariance matrix for the current round is calculated based on the first Kalman gain matrix, the first observation matrix, and the first prediction covariance matrix for the current round. This step reflects the increased confidence in the state estimation results (i.e., reduced uncertainty) after incorporating the latest voltage measurement information.

[0057] By subtracting the information gain from the measurement from the predicted covariance, the posterior covariance matrix is ​​obtained, and this matrix is ​​used as the baseline covariance matrix for the next prediction step, thus forming a closed-loop recursive estimation algorithm. The specific calculation formula is as follows: In the formula, For the current round (the 1st round) The first updated covariance matrix (at each sampling time) represents the posterior state estimation error covariance after fusing the measurement data; The identity matrix is ​​a preset matrix whose dimensions are consistent with the dimensions of the system state vector (in this embodiment, it is...). ); This is the first Kalman gain matrix for the current round; This is the first observation matrix for the current round; This is the first prediction covariance matrix for the current round.

[0058] This recursive filtering based on electromagnetic physics mechanisms can effectively extract key internal states such as dynamic resistance and critical current from voltage signals that are overwhelmed by noise, providing high-confidence initial conditions for subsequent risk prediction.

[0059] In a preferred embodiment, when the high-temperature superconducting magnet is operating under transient conditions, based on a preset transient electromagnetic dynamic model, and according to the measured voltage and the measured current, the internal state variables of the high-temperature superconducting magnet are generated, including: When the high-temperature superconducting magnet is in a transient operating condition, the preset transient electromagnetic dynamic model is used as the second observation equation. Repeat the second state estimation operation until the second state estimation operation has been performed at all sampling times to generate the internal state variables of the high-temperature superconducting magnet; The second state estimation operation includes: Based on the second best estimated state vector from the previous round, the partial derivatives of the preset second state equation are calculated to generate the second state transition matrix for the current round; wherein, the initial round is the first sampling time; the second best estimated state vector is the best estimated value of the second system state vector; the second system state vector consists of a resistor auxiliary variable, an inductor, and a DC bias voltage; the best estimated value of the second system state vector from the previous round in the initial round is a preset value; the resistor auxiliary variable is the square root of the dynamic resistance; Based on the second best estimated state vector from the previous round and the preset second state equation, the second predicted state vector for the current round is calculated and generated; wherein, the second predicted state vector is the predicted value of the second system state vector; The second prediction covariance matrix for the current round is calculated and generated based on the second state transition matrix of the current round, the second covariance matrix of the previous round, and the preset process noise matrix; wherein, the second covariance matrix of the previous round of the initial round is a preset value. The current change rate for the current round is calculated based on the measured current value of the current round and the measured current value of the previous round. Based on the measured current value of the current round, the resistance auxiliary variable in the second predicted state vector of the current round, and the current change rate of the current round, the second observation equation is linearized to determine the second observation matrix of the current round. The second Kalman gain matrix for the current round is calculated and generated based on the second observation matrix of the current round, the second prediction covariance matrix of the current round, and the preset observation noise matrix. Substitute the second predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round into the second observation equation to calculate the predicted voltage value of the current round. Based on the predicted voltage value of the current cycle and the measured voltage value of the current cycle, the voltage deviation value of the current cycle is calculated and generated; Based on the second Kalman gain matrix of the current round, the second best estimated state vector of the current round is calculated and generated according to the voltage deviation value of the current round and the second predicted state vector of the current round. If the current sampling time is the last sampling moment, then the dynamic resistance is calculated based on the resistance auxiliary variable in the second best estimated state vector of the current sampling time, and the dynamic resistance, the inductance and the DC bias voltage in the second best estimated state vector of the current sampling time are determined as the internal state variables of the high-temperature superconducting magnet. If not, then the second updated covariance matrix of the current sampling time is calculated based on the second Kalman gain matrix, the second observation matrix and the second prediction covariance matrix of the current sampling time. The next sampling moment is updated to the next sampling time, the second best estimated state vector of the current sampling time is updated to the second best estimated state vector of the previous sampling time in the next sampling time, and the second updated covariance matrix of the current sampling time is updated to the second covariance matrix of the previous sampling time in the next sampling time.

[0060] In one specific embodiment, when the high-temperature superconducting magnet operates under transient conditions, based on a preset transient electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated according to the measured voltage and the measured current. This process is a special handling mechanism for magnets operating under high-frequency power fluctuations or rapid charging and discharging conditions. Because the physical properties of superconducting materials no longer simply follow the steady-state DC power-law relationship under such conditions, and to prevent negative dynamic resistance estimates due to noise interference during numerical calculations (which violates physical principles), this embodiment introduces an auxiliary resistance variable. (i.e., the square root of the dynamic resistance) serves as the core state to be evaluated.

[0061] First, under the transient operating condition of the high-temperature superconducting magnet, a pre-defined transient electromagnetic dynamic model is used as the second observation equation. This equation establishes a nonlinear mapping relationship between the internal state and the terminal voltage, with the resistance auxiliary variable as the core. Subsequently, an iterative loop is entered, repeatedly executing the second state estimation operation until all sampling times have been completed.

[0062] The preset transient electromagnetic dynamic model is specifically as follows: In the formula, For the first transient condition The predicted voltage value at the nth sampling time, i.e., the voltage value at the nth sampling time under transient conditions. The predicted voltage values ​​for each round; For the first The resistance auxiliary variable at each sampling time. Used to characterize the Dynamic resistance at each sampling time; For the first The measured current value at each sampling time; For the first Inductance at each sampling time; The sampling time interval; For the first DC bias voltage at each sampling time; For the first The rate of change of current at each sampling time.

[0063] Specifically, in the prediction phase, the state transition matrix is ​​first calculated. Since the internal parameters of the magnet change drastically in the transient state and there is no clear analytical formula for the physical evolution, this embodiment assumes that each state variable (including the resistance auxiliary variable, inductance and DC bias voltage) follows a random walk model within a small time step.

[0064] Therefore, based on the second best estimated state vector from the previous round, the partial derivatives of the preset second state equation are calculated to generate the second state transition matrix for the current round. This step aims to obtain the gradient information of the system state evolution under transient conditions. The specific calculation process is as follows: The preset second state equation is specifically as follows: in, For the first The second system state vector for each round; For the first Resistance auxiliary variables for each round; For the first Inductance at each sampling time; For the first DC bias voltage for each round; This is a preset second noise driving matrix; This is the preset second process noise vector.

[0065] The pre-defined second state equation essentially describes the time evolution of the state variables. To perform linearization derivation for Kalman filtering, this equation is delimited from noise terms. The deterministic mapping part is defined as the deterministic state transition function, i.e. This function indicates that, under the random walk assumption of transient conditions, the prior predicted values ​​of the resistance auxiliary variable, inductance, and DC bias voltage are directly inherited from the state values ​​of the previous round. Therefore, by examining this state transition function... Taking the partial derivative of the state vector from the previous round yields the Jacobian matrix (i.e., the second state transition matrix), which describes the propagation characteristics of the state error. The result is a constant identity matrix. The specific calculation formula is as follows: In the formula, Current round (number) The second state transition matrix (at each sampling time); The deterministic state transition function in the predefined second state equation represents The state from the previous moment The part that is decided, namely ; For the previous round (the first) The second system state vector (at each sampling time) includes resistance auxiliary variables. ,inductance and DC bias voltage ; The resistance auxiliary variable from the previous round; The inductor from the previous round; The DC bias voltage of the previous round.

[0066] It is understandable that the elements in the matrix This indicates that in the random walk model, the propagation coefficient of each state variable with respect to itself is 1 (i.e., perfectly positively correlated); the elements in the matrix This indicates that the state variables are independent of each other during the time recursion process, and there are no cross-coupling terms.

[0067] Based on this, according to the second best estimated state vector from the previous round and the preset second state equation, the second predicted state vector for the current round is calculated and generated. This process is the direct transfer of state values. In the formula, This is the second predicted state vector for the current round, containing the predicted resistance auxiliary variable. ,inductance and DC bias voltage ; The second best estimated state vector from the previous round.

[0068] Simultaneously, based on the second state transition matrix of the current round, the second covariance matrix of the previous round, and the preset process noise matrix, the second prediction covariance matrix of the current round is calculated and generated to quantify the uncertainty of state prediction. In the formula, This is the second prediction covariance matrix for the current round; This is the second covariance matrix from the previous round; The second process noise matrix is ​​a preset value, which characterizes the random fluctuation variance of the resistor auxiliary variable, inductance, and DC bias voltage in the transient state.

[0069] During the correction phase, the observation equations must be linearized to integrate the observation data. Based on the measured current value of the current cycle and the measured current value of the previous cycle, the current change rate for the current cycle is calculated. Subsequently, based on the measured current value of the current cycle, the resistance auxiliary variable in the second predicted state vector of the current cycle, and the current change rate of the current cycle, the partial derivative of the second observation equation is taken to determine the second observation matrix for the current cycle. In the formula, This is the second observation matrix for the current round; The resistance auxiliary variable in the current round of prediction; This is the measured current value for the current round; This represents the rate of change of current in the current cycle.

[0070] The first item of the matrix This demonstrates how the gradient information of dynamic resistance can be nonlinearly transformed into the gradient information of auxiliary variables by introducing auxiliary variables.

[0071] Next, based on the second observation matrix of the current round, the second prediction covariance matrix of the current round, and the preset observation noise matrix, the second Kalman gain matrix of the current round is calculated and generated: In the formula, This is the second Kalman gain matrix for the current round; This is the preset second observation noise matrix.

[0072] Subsequently, the second predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round are substituted into the second observation equation to calculate the predicted voltage value of the current round, and the voltage deviation value is calculated in combination with the measured voltage. Based on the second Kalman gain matrix of the current round, the second best estimated state vector of the current round is calculated and generated according to the voltage deviation value of the current round and the second predicted state vector of the current round. In the formula, This is the second best estimated state vector for the current round; The measured voltage value for the current round; The predicted voltage value for the current round is calculated using the following formula: .

[0073] Finally, determine if the current round is the last sampling time. If so, then based on the resistance auxiliary variable in the second best estimated state vector of the current round, perform a square operation ( The dynamic resistance is calculated and generated, and the dynamic resistance, the inductance in the second best estimated state vector of the current round, and the DC bias voltage are determined as the internal state variables of the high-temperature superconducting magnet. If not, the second updated covariance matrix of the current round is calculated and generated based on the second Kalman gain matrix, the second observation matrix of the current round, and the second prediction covariance matrix of the current round. In the formula, This is the second updated covariance matrix for the current round, used for the recursion in the next time step; It is a third-order identity matrix.

[0074] It's understandable that it's third-order (3-dimensional) because, under transient conditions, our second system state vector... It includes three state variables, namely, the resistance auxiliary variable. ,inductance and DC bias voltage Therefore, the relevant covariance matrix and Kalman gain With observation matrix The product results are all The matrix. For performing matrix subtraction. An identity matrix of the same dimension must be used. .

[0075] Through the special modeling and estimation algorithm for transient conditions described above, this embodiment can ensure the non-negativity constraint of dynamic resistance by utilizing the numerical characteristics of square root filtering when the magnet's state fluctuates drastically. This effectively avoids algorithm divergence and significantly improves the robustness and accuracy of the system in assessing the potential thermal effects inside the magnet under extreme conditions.

[0076] Step S3: Input the planned power value sequence and the internal state variables into a preset magnet state prediction model, so that the magnet state prediction model generates a predicted sequence of internal state variables and a predicted sequence of current for the high-temperature superconducting magnet in the future control cycle based on the planned power value sequence and the internal state variables.

[0077] In a preferred embodiment, a pre-defined magnet state prediction model is trained in the following manner: Obtain a magnet state prediction dataset; wherein, the magnet state prediction dataset includes several historical planned power value sequences, historical initial internal state variables, and corresponding magnet state prediction labels; the magnet state prediction labels are historical internal state variable sequences and historical current sequences; The magnet state prediction dataset is randomly divided into several batches of training samples according to a preset number; Training samples from each batch are sequentially input into the magnet state prediction model to train it until a preset number of training iterations are reached. Each time a batch of training samples is received, the magnet state prediction model outputs a predicted sequence of internal state variables and a predicted current sequence. Based on the predicted internal state variables, the predicted current sequence, and the corresponding magnet state prediction labels, a loss function value is calculated. The magnet state prediction model is then updated based on the loss function value.

[0078] Specifically, the preset magnet state prediction model employs a recurrent neural network architecture (such as LSTM or GRU) with long short-term memory capabilities to adapt to the time-dependent and dynamic nonlinear characteristics present in the operation of high-temperature superconducting magnets. In this step, the internal state variables generated in step S2 at the current moment (including dynamic resistance, inductance, DC bias voltage, etc.) are used as the initial hidden state or initial input vector of the magnet state prediction model, and the planned power value sequence of the high-temperature superconducting magnet in the future control period (i.e., the next N time steps) is used as the time-varying driving input of the model. Since the magnet power... ,Voltage With current There is a physical coupling relationship between them, that is The magnet state prediction model, by learning the evolution patterns of historical data, can implicitly or explicitly infer future terminal voltage changes based on the input power sequence. It then combines this with the current internal state to iteratively calculate the future current response and internal state evolution. Finally, the model outputs a predicted sequence of internal state variables (with a focus on the predicted trajectory of dynamic resistance) and a predicted current sequence for the next N control cycles, providing forward-looking data support for subsequent risk assessment.

[0079] Step S4: Based on the predicted dynamic resistance value in the internal state variable prediction sequence and the current prediction sequence, determine whether the high-temperature superconducting magnet has a risk of quenching or thermal instability in the future control cycle.

[0080] In a preferred embodiment, determining whether the high-temperature superconducting magnet faces quenching or thermal instability risk during future control cycles, based on the predicted dynamic resistance values ​​in the internal state variable prediction sequence and the current prediction sequence, includes: Extract the dynamic resistance prediction sequence for future control cycles from the internal state variable prediction sequence; Determine whether there is a dynamic resistance prediction value in the dynamic resistance prediction value sequence that is greater than a preset quench resistance threshold; if so, determine that the high-temperature superconducting magnet has a quench risk in the future control cycle; if not, determine that the high-temperature superconducting magnet does not have a quench risk in the future control cycle. Based on the predicted dynamic resistance sequence and the predicted current sequence, the AC loss power sequence of the high-temperature superconducting magnet in the future control cycle is calculated and generated. The AC loss power sequence is input into a preset magnet thermal model to calculate and generate a temperature rise prediction sequence for the high-temperature superconducting magnet in the future control cycle. Determine whether there is a temperature prediction value in the temperature rise prediction sequence that is greater than the preset thermal instability temperature threshold; if so, determine that the high-temperature superconducting magnet has a risk of thermal instability in the future control period; if not, determine that the high-temperature superconducting magnet does not have a risk of thermal instability in the future control period.

[0081] Specifically, first, the "quench risk" is identified, which is the risk that the superconducting material will suddenly lose its superconducting properties and revert to a normal resistive state. To this end, a sequence of dynamic resistance prediction values ​​for future control periods is extracted from the internal state variable prediction sequence. This sequence visually reflects the resistive evolution trajectory of the magnet over a future period. Then, it is determined whether any dynamic resistance prediction value in the sequence exceeds a preset quench resistance threshold. The preset quench resistance threshold is a safety boundary set based on the physical properties of the high-temperature superconducting tape (such as the resistance inflection point corresponding to the critical temperature and critical magnetic field). If any prediction value exceeds this threshold, it means that the magnet is about to enter an irreversible resistive heating state, confirming that the high-temperature superconducting magnet faces a quench risk within the future control period; otherwise, it is determined that there is no quench risk.

[0082] Furthermore, considering that even if the dynamic resistance does not reach a level of complete quenching, the continuous accumulation of small resistive heating may still cause the magnet temperature to gradually rise, thereby triggering the risk of thermal instability, it is necessary to evaluate the thermal effects in parallel. Based on the predicted dynamic resistance sequence and the predicted current sequence, the AC loss power sequence of the high-temperature superconducting magnet in the future control cycle is calculated using Joule's law. The specific calculation formula is as follows: In the formula, For the first time in the future control cycle Predicted AC power loss at each time step; This is the predicted value of the dynamic resistance corresponding to this time step; This is the predicted current value corresponding to this time step.

[0083] Subsequently, the AC loss power sequence is input into a preset magnet thermal model. In this embodiment, the preset magnet thermal model is a discrete-time iterative equation based on the first law of thermodynamics, used to describe the temperature evolution process of a high-temperature superconducting magnet under the combined effects of AC loss heating and cooling system heat dissipation. This model comprehensively considers the heat capacity characteristics of the magnet and the heat exchange efficiency with the low-temperature environment (such as a liquid nitrogen bath or a refrigerator cold head). The specific calculation formula is as follows: In the formula, The first in the future control cycle The predicted magnet temperature rise at each predicted time (i.e., the increase relative to the ambient reference temperature), in Kelvin (K). For the first time in the future control cycle The predicted temperature rise of the magnet at each predicted time point; for the first point in the prediction sequence, this value is the estimated actual temperature rise at the current time. The sampling time interval (or prediction step size) of the control system is expressed in seconds (s). Equivalent heat capacity of high-temperature superconducting magnets characterizes the ease with which the temperature of a magnet material rises after absorbing heat, and is expressed in joules per Kelvin (J / K). For the first time in the future control cycle The predicted AC power loss at each prediction time, in watts (W). The overall heat dissipation coefficient of the cooling system characterizes the ability of the magnet to dissipate heat to the low-temperature environment, and is measured in watts per Kelvin (W / K). This formula shows that the temperature rise at the current moment equals the temperature rise at the previous moment plus the temperature increase resulting from the net heat accumulation during this time step. This represents the net heat power within that time step, which is the heat generation power minus the heat dissipation power.

[0084] This model maps power loss to temperature changes, thereby generating a predicted temperature rise sequence for the high-temperature superconducting magnet during future control cycles. Finally, it determines whether any predicted temperature value in the predicted temperature rise sequence exceeds a preset thermal instability temperature threshold.

[0085] Step S5: If there is a risk of quenching or thermal instability in the high-temperature superconducting magnet during the future control period, adjust the planned power value sequence to generate an optimized power value sequence; use the optimized power value sequence as the target power value sequence of the high-temperature superconducting magnet during the future control period.

[0086] In a preferred embodiment, if the high-temperature superconducting magnet faces the risk of quenching or thermal instability during future control cycles, the planned power value sequence is adjusted to generate an optimized power value sequence, including: If the high-temperature superconducting magnet has the risk of quenching or thermal instability in the future control cycle, the power value correction operation is repeated until the high-temperature superconducting magnet has no risk of quenching or thermal instability in the future control cycle, and an optimized power value sequence is generated. The power value correction operation includes: Based on a preset adjustment strategy, the current power value sequence to be adjusted is adjusted to obtain the current candidate power value sequence; wherein, the initial power value sequence to be adjusted is the planned power value sequence; the preset adjustment strategy is to reduce the power change rate, limit the peak power value, or insert a low power value; The current candidate power value sequence and the internal state variables are input into a preset magnet state prediction model so that the magnet state prediction model generates a current internal state variable prediction sequence and a current current prediction sequence for the high-temperature superconducting magnet in a future control cycle based on the current candidate power value sequence and the internal state variables. Based on the predicted dynamic resistance value in the current internal state variable prediction sequence and the current prediction sequence, determine whether the high-temperature superconducting magnet has a risk of quenching or thermal instability in the future control cycle. If the high-temperature superconducting magnet does not have the risk of quenching or thermal instability in the future control cycle, then the current candidate power value sequence will be used as the optimized power value sequence. If the high-temperature superconducting magnet is at risk of quenching or thermal instability during future control cycles, the current candidate power value sequence will be updated to the current power value sequence to be adjusted.

[0087] Specifically, when the risk assessment logic in step S4 determines that there are potential safety hazards in the future, the control system will no longer directly execute the original planned power command. Instead, it will repeatedly execute the power value correction operation until the high-temperature superconducting magnet does not have the risk of quenching or thermal instability in the future control cycle, thereby generating the final optimized power value sequence.

[0088] Furthermore, for the adjustment strategy to reduce the rate of power change, a slope-limiting algorithm is used to smooth the current power value sequence to be adjusted. First, a maximum allowable rate of power change threshold is set. This threshold is determined by the maximum withstand current change rate and inductance value of the high-temperature superconducting magnet. Subsequently, each power value to be adjusted in the power sequence is traversed in chronological order. If the power value at the current moment The power value has been corrected compared to the previous time. The absolute value of the difference exceeded If so, the range of change will be forcibly limited. The specific calculation formula is as follows: In the formula, This is the corrected power value at the current moment; It is a symbolic function; This is a function designed to minimize the value of the minimum value. This strategy effectively reduces high-frequency spikes in power commands and suppresses eddy current losses within the magnet caused by drastic current fluctuations.

[0089] For adjusting peak power values, an amplitude clamping algorithm is used. A preset safe power amplitude upper limit is established. This upper limit is typically based on the critical current of the magnet. The corresponding power value setting. Examine each value in the power sequence; once the absolute power value at a certain moment is found... Exceed If the boundary value is not reached, it will be truncated directly to the boundary value. The specific calculation logic is as follows: This strategy directly prevents the magnet's operating current from approaching the critical region, thereby reducing the risk of quenching at its source.

[0090] The adjustment strategy for inserting low-power values ​​primarily addresses the risk of thermal instability. When it is predicted that the cumulative temperature rise over a future period will exceed a threshold, segments of the power sequence that are continuously operating at high power are identified, and a segment with a duration of [duration missing] is forcibly inserted into them. The zero-power or low-power range (e.g., 5% of rated power), that is to say (when This is equivalent to artificially creating a "cooling window," using the continuous cooling capacity of the cooling system to dissipate the accumulated heat, thereby pulling the magnet temperature back below the safe line.

[0091] By applying the above three strategies individually or in combination, it is possible to generate an optimized power value sequence that satisfies physical security constraints and approximates the original scheduling intent as closely as possible.

[0092] Step S6: If there is no risk of quenching or thermal instability in the high-temperature superconducting magnet during the future control period, the planned power value sequence shall be used as the target power value sequence of the high-temperature superconducting magnet during the future control period.

[0093] Specifically, if the high-temperature superconducting magnet faces no risk of quenching or thermal instability during future control cycles, it indicates that the magnet is currently operating well and the scheduling commands issued from the upper level do not exceed the safety margin, requiring no additional intervention or derating. In this case, the planned power value sequence is directly confirmed as the target power value sequence for the high-temperature superconducting magnet during future control cycles for subsequent execution. This approach ensures that, while meeting safety requirements, the superconducting energy storage device maintains high accuracy and efficiency in responding to upper-level power scheduling commands.

[0094] Step S7: Control the high-temperature superconducting magnet according to the target power value sequence.

[0095] Specifically, the high-temperature superconducting magnet is controlled according to the target power value sequence. Specifically, the final determined target power value sequence is used as the execution reference. By adjusting the voltage applied across the high-temperature superconducting magnet or the current flowing through it in real time, the magnet is driven to strictly follow the optimized power operation, ensuring that the magnet remains in a safe and stable physical state throughout the entire operating cycle.

[0096] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0097] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for controlling a high-temperature superconducting magnet, characterized in that, include: The measurement voltage, measurement current, and planned power value sequence of the high-temperature superconducting magnet in the future control cycle are obtained. Based on the measured voltage, the measured current, and the preset electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated; the internal state variables include dynamic resistance. The planned power value sequence and the internal state variables are input into a preset magnet state prediction model so that the magnet state prediction model generates a predicted sequence of internal state variables and a predicted sequence of current for the high-temperature superconducting magnet in the future control cycle based on the planned power value sequence and the internal state variables. Based on the predicted dynamic resistance values ​​in the internal state variable prediction sequence and the current prediction sequence, it is determined whether the high-temperature superconducting magnet is at risk of quenching or thermal instability in future control cycles. In the event that the high-temperature superconducting magnet faces the risk of quenching or thermal instability during future control cycles, the planned power value sequence is adjusted to generate an optimized power value sequence; the optimized power value sequence is then used as the target power value sequence for the high-temperature superconducting magnet during future control cycles. If there is no risk of quenching or thermal instability in the future control cycle of the high-temperature superconducting magnet, the planned power value sequence will be used as the target power value sequence of the high-temperature superconducting magnet in the future control cycle. The high-temperature superconducting magnet is controlled according to the target power value sequence.

2. The control method for a high-temperature superconducting magnet as described in claim 1, characterized in that, Based on the measured voltage, the measured current, and the preset electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated, including: The operating conditions of the high-temperature superconducting magnet are determined based on the measured voltage and the measured current; the operating conditions are either quasi-steady-state or transient. When the high-temperature superconducting magnet is operating under quasi-steady-state conditions, based on a preset quasi-steady-state electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated according to the measured voltage and the measured current; wherein, when the high-temperature superconducting magnet is operating under quasi-steady-state conditions, the internal state variables also include inductance, DC bias voltage, critical current, and power law number. When the high-temperature superconducting magnet is operating under transient conditions, based on a preset transient electromagnetic dynamic model, the internal state variables of the high-temperature superconducting magnet are generated according to the measured voltage and the measured current; wherein, when the high-temperature superconducting magnet is operating under transient conditions, the internal state variables also include inductance and DC bias voltage.

3. The control method for a high-temperature superconducting magnet as described in claim 2, characterized in that, Based on the measured voltage and the measured current, the operating conditions of the high-temperature superconducting magnet are determined, including: Extract the measured voltage values ​​at each sampling time from the measured voltage; Extract the measured current values ​​at each sampling time from the measured current; Based on the measured voltage value and the measured current value at the last sampling moment, the operating power of the high-temperature superconducting magnet at the last sampling moment is calculated and generated. Based on the measured voltage value at the previous sampling time and the measured current value at the previous sampling time, the operating power of the high-temperature superconducting magnet at the previous sampling time is calculated. The rate of change of current at the last sampling moment is calculated based on the measured current value at the last sampling moment and the measured current value at the previous sampling moment. The power change rate at the last sampling time is calculated based on the operating power at the last sampling time and the operating power at the sampling time before the last sampling time. If the rate of change of current at the last sampling moment is less than the preset current change threshold and the rate of change of power at the last sampling moment is less than the preset power change threshold, the operating condition of the high-temperature superconducting magnet is determined to be the quasi-steady-state operating condition. If the rate of change of current at the last sampling moment is not less than the preset current change threshold, or the rate of change of power at the last sampling moment is not less than the preset power change threshold, the operating condition of the high-temperature superconducting magnet is determined to be the transient operating condition.

4. The control method for a high-temperature superconducting magnet as described in claim 3, characterized in that, Under the quasi-steady-state operating condition of the high-temperature superconducting magnet, based on a preset quasi-steady-state electromagnetic dynamic model, and according to the measured voltage and the measured current, the internal state variables of the high-temperature superconducting magnet are generated, including: Under the condition that the high-temperature superconducting magnet is in a quasi-steady-state condition, the preset quasi-steady-state electromagnetic dynamic model is used as the first observation equation; Repeat the first state estimation operation until the first state estimation operation has been performed at all sampling times to generate the internal state variables of the high-temperature superconducting magnet; The first state estimation operation includes: Based on the first best estimated state vector from the previous round, the partial derivatives of the preset first state equation are calculated to generate the first state transition matrix for the current round; wherein, the initial round is the first sampling time; the first best estimated state vector is the best estimated value of the first system state vector; the first system state vector consists of dynamic resistance, inductance, DC bias voltage, critical current, and power law; the best estimated value of the first system state vector from the previous round of the initial round is the preset value; Based on the first best estimated state vector from the previous round and the preset first state equation, the first predicted state vector for the current round is calculated and generated; wherein, the first predicted state vector is the predicted value of the first system state vector; The first prediction covariance matrix for the current round is calculated and generated based on the first state transition matrix of the current round, the first covariance matrix of the previous round, and the preset process noise matrix; wherein, the first covariance matrix of the previous round of the initial round is a preset value. The current change rate for the current round is calculated based on the measured current value of the current round and the measured current value of the previous round. Based on the measured current value and the current change rate of the current cycle, the first observation equation is linearized to determine the first observation matrix of the current cycle. The first Kalman gain matrix for the current round is calculated and generated based on the first observation matrix of the current round, the first prediction covariance matrix of the current round, and the preset observation noise matrix. Substitute the first predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round into the first observation equation to calculate the predicted voltage value of the current round. Based on the predicted voltage value of the current cycle and the measured voltage value of the current cycle, the voltage deviation value of the current cycle is calculated and generated; Based on the first Kalman gain matrix of the current round, the first best estimated state vector of the current round is calculated and generated according to the voltage deviation value of the current round and the first predicted state vector of the current round. Determine whether the current round is the last sampling time. If so, use the first best estimated state vector of the current round as the internal state variable of the high-temperature superconducting magnet. If not, calculate and generate the first updated covariance matrix of the current round based on the first Kalman gain matrix, the first observation matrix, and the first prediction covariance matrix of the current round. Update the next sampling time to the next round, update the first best estimated state vector of the current round to the first best estimated state vector of the previous round in the next round, and update the first updated covariance matrix of the current round to the first covariance matrix of the previous round in the next round.

5. The control method for a high-temperature superconducting magnet as described in claim 4, characterized in that, When the high-temperature superconducting magnet operates under transient conditions, based on a preset transient electromagnetic dynamic model, and according to the measured voltage and the measured current, the internal state variables of the high-temperature superconducting magnet are generated, including: When the high-temperature superconducting magnet is in a transient operating condition, the preset transient electromagnetic dynamic model is used as the second observation equation. Repeat the second state estimation operation until the second state estimation operation has been performed at all sampling times to generate the internal state variables of the high-temperature superconducting magnet; The second state estimation operation includes: Based on the second best estimated state vector from the previous round, the partial derivatives of the preset second state equation are calculated to generate the second state transition matrix for the current round; wherein, the initial round is the first sampling time; the second best estimated state vector is the best estimated value of the second system state vector; the second system state vector consists of a resistor auxiliary variable, an inductor, and a DC bias voltage; the best estimated value of the second system state vector from the previous round in the initial round is a preset value; the resistor auxiliary variable is the square root of the dynamic resistance; Based on the second best estimated state vector from the previous round and the preset second state equation, the second predicted state vector for the current round is calculated and generated; wherein, the second predicted state vector is the predicted value of the second system state vector; The second prediction covariance matrix for the current round is calculated and generated based on the second state transition matrix of the current round, the second covariance matrix of the previous round, and the preset process noise matrix; wherein, the second covariance matrix of the previous round of the initial round is a preset value. The current change rate for the current round is calculated based on the measured current value of the current round and the measured current value of the previous round. Based on the measured current value of the current round, the resistance auxiliary variable in the second predicted state vector of the current round, and the current change rate of the current round, the second observation equation is linearized to determine the second observation matrix of the current round. The second Kalman gain matrix for the current round is calculated and generated based on the second observation matrix of the current round, the second prediction covariance matrix of the current round, and the preset observation noise matrix. Substitute the second predicted state vector of the current round, the measured current value of the current round, and the current change rate of the current round into the second observation equation to calculate the predicted voltage value of the current round. Based on the predicted voltage value of the current cycle and the measured voltage value of the current cycle, the voltage deviation value of the current cycle is calculated and generated; Based on the second Kalman gain matrix of the current round, the second best estimated state vector of the current round is calculated and generated according to the voltage deviation value of the current round and the second predicted state vector of the current round. If the current sampling time is the last sampling moment, then the dynamic resistance is calculated based on the resistance auxiliary variable in the second best estimated state vector of the current sampling time, and the dynamic resistance, the inductance and the DC bias voltage in the second best estimated state vector of the current sampling time are determined as the internal state variables of the high-temperature superconducting magnet. If not, then the second updated covariance matrix of the current sampling time is calculated based on the second Kalman gain matrix, the second observation matrix and the second prediction covariance matrix of the current sampling time. The next sampling moment is updated to the next sampling time, the second best estimated state vector of the current sampling time is updated to the second best estimated state vector of the previous sampling time in the next sampling time, and the second updated covariance matrix of the current sampling time is updated to the second covariance matrix of the previous sampling time in the next sampling time.

6. The control method for a high-temperature superconducting magnet as described in claim 5, characterized in that, The preset quasi-steady-state electromagnetic dynamic model is specifically as follows: In the formula, For the first quasi-steady-state condition The predicted voltage value at the nth sampling time, i.e., the voltage value at the quasi-steady-state condition. The predicted voltage values ​​for each round; For the first Dynamic resistance at each sampling time; For the first The measured current value at each sampling time; For the first Inductance at each sampling time; The sampling time interval; For the first DC bias voltage at each sampling time; For the first The rate of change of current at each sampling time; The preset transient electromagnetic dynamic model is specifically as follows: In the formula, For the first transient condition The predicted voltage value at the nth sampling time, i.e., the voltage value at the nth sampling time under transient conditions. The predicted voltage values ​​for each round; For the first The resistance auxiliary variable at each sampling time. Used to characterize the Dynamic resistance at each sampling time; For the first The measured current value at each sampling time; For the first Inductance at each sampling time; The sampling time interval; For the first DC bias voltage at each sampling time; For the first The rate of change of current at each sampling time.

7. The control method for a high-temperature superconducting magnet as described in claim 6, characterized in that, The preset first state equation is specifically as follows: in, For the first The first system state vector of each round; A nonlinear function characterizing the power-law properties of superconducting materials, used according to the first... Critical current of each cycle Power Law and measuring current Calculate and generate the first Dynamic resistance of each round ; For the first Inductance in each round; For the first DC bias voltage for each round; For the first Critical current for each cycle; For the first The power law number of each round; The first noise driving matrix is ​​preset; This is the preset first process noise vector; The preset second state equation is specifically as follows: in, For the first The second system state vector for each round; For the first Resistance auxiliary variables for each round; For the first Inductance at each sampling time; For the first DC bias voltage for each round; This is a preset second noise driving matrix; This is the preset second process noise vector.

8. The control method for a high-temperature superconducting magnet as described in claim 7, characterized in that, The pre-defined magnet state prediction model is trained using the following method: Obtain a magnet state prediction dataset; wherein, the magnet state prediction dataset includes several historical planned power value sequences, historical initial internal state variables, and corresponding magnet state prediction labels; the magnet state prediction labels are historical internal state variable sequences and historical current sequences; The magnet state prediction dataset is randomly divided into several batches of training samples according to a preset number; Training samples from each batch are sequentially input into the magnet state prediction model to train it until a preset number of training iterations are reached. Each time a batch of training samples is received, the magnet state prediction model outputs a predicted sequence of internal state variables and a predicted current sequence. Based on the predicted internal state variables, the predicted current sequence, and the corresponding magnet state prediction labels, a loss function value is calculated. The magnet state prediction model is then updated based on the loss function value.

9. The control method for a high-temperature superconducting magnet as described in claim 8, characterized in that, Based on the predicted dynamic resistance values ​​in the internal state variable prediction sequence and the current prediction sequence, determine whether the high-temperature superconducting magnet faces quenching or thermal instability risks during future control cycles, including: Extract the dynamic resistance prediction sequence for future control cycles from the internal state variable prediction sequence; Determine whether there is a dynamic resistance prediction value in the dynamic resistance prediction value sequence that is greater than a preset quench resistance threshold; if so, determine that the high-temperature superconducting magnet has a quench risk in the future control cycle; if not, determine that the high-temperature superconducting magnet does not have a quench risk in the future control cycle. Based on the predicted dynamic resistance sequence and the predicted current sequence, the AC loss power sequence of the high-temperature superconducting magnet in the future control cycle is calculated and generated. The AC loss power sequence is input into a preset magnet thermal model to calculate and generate a temperature rise prediction sequence for the high-temperature superconducting magnet in the future control cycle. Determine whether there is a temperature prediction value in the temperature rise prediction sequence that is greater than the preset thermal instability temperature threshold; if so, determine that the high-temperature superconducting magnet has a risk of thermal instability in the future control period; if not, determine that the high-temperature superconducting magnet does not have a risk of thermal instability in the future control period.

10. The control method for a high-temperature superconducting magnet as described in claim 9, characterized in that, In the event of a risk of quenching or thermal instability during future control cycles of the high-temperature superconducting magnet, the planned power value sequence is adjusted to generate an optimized power value sequence, including: If the high-temperature superconducting magnet has the risk of quenching or thermal instability in the future control cycle, the power value correction operation is repeated until the high-temperature superconducting magnet has no risk of quenching or thermal instability in the future control cycle, and an optimized power value sequence is generated. The power value correction operation includes: Based on a preset adjustment strategy, the current power value sequence to be adjusted is adjusted to obtain the current candidate power value sequence; wherein, the initial power value sequence to be adjusted is the planned power value sequence; the preset adjustment strategy is to reduce the power change rate, limit the peak power value, or insert a low power value; The current candidate power value sequence and the internal state variables are input into a preset magnet state prediction model so that the magnet state prediction model generates a current internal state variable prediction sequence and a current current prediction sequence for the high-temperature superconducting magnet in a future control cycle based on the current candidate power value sequence and the internal state variables. Based on the predicted dynamic resistance value in the current internal state variable prediction sequence and the current prediction sequence, determine whether the high-temperature superconducting magnet has a risk of quenching or thermal instability in the future control cycle. If the high-temperature superconducting magnet does not have the risk of quenching or thermal instability in the future control cycle, then the current candidate power value sequence will be used as the optimized power value sequence. If the high-temperature superconducting magnet is at risk of quenching or thermal instability during future control cycles, the current candidate power value sequence will be updated to the current power value sequence to be adjusted.

Images