Judgment method for jamming state of GIS (Gas Insulated Switchgear) isolation switch

Abstract

The invention belongs to the technical field of electric power, and discloses a method for judging the jamming state of a GIS (Gas Insulated Switchgear) isolation switch, which is characterized by comprising the following steps of: constructing a transfer function of a mechanical system driven by a motor, converting the transfer function into a transfer function form and simplifying the transfer function form, reversely describing a transfer function response curve, and judging the jamming state of the GIS isolation switch. And a step of identifying a jam defect. The method has the main beneficial technical effects that the dynamic characteristics of the motor are directly associated, the system model is more accurate, the change of voltage and current is sensitive to the change of the system state, the analysis universality and applicability are wider, the data analysis is more flexible, and the extra cost is remarkably reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of electric power, and in particular relates to a method for judging a stuck state of a GIS isolating switch. Background Art

[0002] Gas-insulated switchgear (GIS) is a key component for separating and isolating electrical equipment in power systems. However, the mechanical structure of GIS disconnectors is susceptible to assembly errors and structural damage from prolonged use, leading to failures. Improper opening and closing pose the greatest threat to power systems and personnel safety.

[0003] Due to the enclosed structure of GIS disconnectors, the open and closed positions can typically only be confirmed using the open and close indicator signs linked to the operating mechanism. However, the information on these signs cannot effectively identify faults such as phase loss in the conductive part or broken connecting rods that could cause inadequate opening and closing of the disconnector. While auxiliary detection methods, such as microswitches and posture sensors, can detect faults in the operating mechanism and the transmission path, they also cannot reliably determine the open and closed positions of the GIS. Therefore, there is an urgent need in the industry for a reliable method to detect the open and closed positions of GIS disconnectors.

[0004] To address this issue, researchers and engineers have actively explored and developed various technologies for detecting the open and closed positions of GIS disconnectors in recent years. One key approach utilizes advanced sensing technologies, such as drive motor power and vibration signal sensing, to monitor the position and status of GIS internal components in real time. These sensors can accurately detect the open and closed positions and detect structural defects that could lead to non-positioning problems. In addition to sensing technologies, methods based on image processing and pattern recognition have also been applied to detecting the open and closed positions of GIS disconnectors. By installing cameras inside the GIS and transmitting real-time images to a computer system, image processing algorithms and pattern recognition techniques enable intelligent analysis and determination of the position of GIS internal components. This method is non-contact, highly real-time, and can accurately determine whether the open and closed positions are correct. However, in power systems, once the disconnector opening and closing instructions are issued, the key focus is whether the device completes the corresponding operation and whether any abnormal disconnector position status can be detected promptly to avoid potential operational accidents. This is crucial for the safe and stable operation of the power system. As a key component in the power system, the disconnector's opening and closing operations must be precise and reliable. If the equipment fails to complete the corresponding action after receiving an opening / closing instruction, it may cause abnormal circuit connections in the power system, even leading to major accidents. Therefore, it is imperative to ensure that the opening and closing positions of the disconnector accurately respond to instructions to ensure the normal operation of the power system. Furthermore, it is crucial to promptly detect abnormal opening and closing conditions of the disconnector. During operation, the disconnector may malfunction or damage, resulting in inaccurate opening and closing positions. Continuing to operate the power system in this abnormal state can lead to serious consequences such as circuit disconnection, overload, short circuit, and even fire and explosion. Therefore, it is essential to be able to promptly detect these abnormal conditions, halt operation, and take appropriate measures to ensure the safety of the power system.

[0005] To achieve this goal, power systems should be equipped with specialized monitoring and protection devices that can monitor the operation of disconnectors in real time, ensuring accurate opening and closing operations and responding promptly to abnormal situations.

[0006] CN214069363U discloses a device for mounting a posture sensor in GIS switchgear, suitable for use in substation GIS switchgear. The device comprises a mounting bracket, which includes a mounting plate. The mounting plate comprises a first end, a second end, and a connecting portion connecting the first and second ends. The mounting plate is provided with a connecting structure and a sensor fixing structure, respectively located at the first and second ends. The connecting structure comprises a sleeve welded to the first end, which is adapted to fit over a GIS switch operating rod. Clamping bolts are threadedly connected to opposing sides of the sleeve, securing the GIS switch operating rod. A through-hole is also provided in the first end for the GIS switch operating rod to pass through. This device allows for quick and reliable installation of posture sensors in GIS switchgear, offering high versatility and low application costs.

[0007] CN206412278U discloses a composite GIS switch and grounding knife mechanical position indicator device, comprising a switch and grounding knife position indicator, a mounting bracket, and a reflector rotatably mounted on the mounting bracket. The switch and grounding knife position indicator comprises an indicator panel located outside the switch being measured, and a closing and opening travel switches fixed to the switch's transmission mechanism. The indicator panel is electrically connected to the closing and opening travel switches, respectively. A collision member is fixedly connected to the transmission mechanism and moves with the transmission mechanism. When the switch is in the closed position, the collision member presses against the closing travel switch contacts; when the switch is in the open position, the collision member presses against the opening travel switch contacts. Using this device, the actual position of switch and grounding knife, whose positions are difficult to directly inspect, can be quickly and accurately determined at the GIS site, facilitating personnel inspections and improving the safety of switching operations.

[0008] CN113933567A discloses an online monitoring system for the opening and closing status of a GIS disconnector. The system comprises a Hall sensor for acquiring the motor current value of the disconnector under test. The motor current value includes the motor current value when the disconnector under test moves from the open position to the closed position, and the motor current value when the disconnector under test moves from the closed position to the open position. A monitoring device is connected to the Hall sensor via a shielded cable and an aviation connector. The monitoring device receives the motor current value and converts it into a current-time waveform. A data analysis and diagnostic instrument is wirelessly connected to the monitoring device. The data analysis and diagnostic instrument acquires the current-time waveform and compares it with a normal current-time waveform pre-stored in the monitoring device to obtain a status determination result. This accurately determines the opening and closing status of the GIS disconnector, thereby ensuring the safety of electrical equipment.

[0009] CN115201673A provides an online monitoring system for abnormal vibration of disconnect switches in GIS equipment, relating to the field of substation equipment monitoring. The system comprises a vehicle body, and a data processing module, a data output module, and an image acquisition module, all mounted on the vehicle body. The image processing module is used to capture images of the disconnect switches and transmit them to the data processing module. The data processing module analyzes and determines the position of the disconnect switches and their switching trends, converts the results of the analysis and determination into switch position and status signals, and marks these signals. The data output module transmits these marks to a mobile terminal. This system ensures accurate disconnect switch operation, reduces manual workload, improves work efficiency, and reduces the risk of misoperation and accidents.

[0010] Direct detection is not suitable for GIS disconnectors due to their enclosed structure, narrow internal space, compact transmission mechanism, and operation in a high-voltage, high-current environment. Sensors are introduced at high potential, signal lines are difficult to extract, and signals are subject to strong electromagnetic interference, which can damage the sealing of the original structure and easily lead to insulation risks.

[0011] Both motor current-based and vibration signal-based state sensing methods theoretically provide complete information about the mechanical state of GIS disconnectors and can, in theory, monitor the contact state of GIS disconnectors. However, existing methods suffer from the following drawbacks: For motor current detection, they fail to reflect the phase relationship between voltage and current, and the motor currents of different motor models exhibit a certain degree of dispersion, resulting in unclear current characteristics. Even when current characteristics are relatively clear, existing diagnostic algorithms rely on physical analysis, analyzing the current envelope for defect analysis and threshold determination. This approach presents two problems. First, the threshold setting for different disconnectors is difficult to quantify directly, requiring expert intervention to perform physical analysis of the disconnector's motion before assigning a threshold. Furthermore, it is difficult to adapt to the varying thresholds that occur in industrial environments due to the discrete mechanical state of the disconnectors. For vibration signal detection, these methods only consider the disconnector's vibration frequency under electromagnetic force, ignoring the natural frequency of the GIS disconnector's structure. This results in a conclusion that is difficult to reconcile with the measured signal. The resulting data volume is large, signal transmission time is long, and storage space is intensive.

[0012] CN112710951A discloses a GIS disconnector status determination system and method, comprising: a sensor, a data transmission module, a data processing and storage module, and a human-computer interaction platform; the sensor is used to collect motor current, spindle torque, disconnector angle signal, and image signal; the data transmission module is used to transmit the collected data to a host computer for processing; the data processing and storage module is used to analyze and process the collected data to complete status evaluation and save the data; the human-computer interaction platform is used to display the collected waveforms, feedback evaluation results, and provide historical records. It can collect, display, and save disconnector waveforms and images in real time, perform disconnector status evaluation and send alarms, and can call and view historical disconnector opening and closing information and diagnostic results at any time.

[0013] CN112557895A discloses a multi-feature-based method for GIS disconnector fault diagnosis. This method requires collecting information about the GIS disconnector's motor current, spindle angle, and image. Two diagnostic procedures are required: the first, performed simultaneously with the GIS disconnector's operation, detects motor current and spindle angle signals to determine whether the disconnector has refused to open or close, leading to motor burnout. The second, performed after the GIS disconnector has completed opening and closing, processes, analyzes, and compares the collected current, angle, and image signals to determine whether the disconnector has problems such as jamming, loose fasteners, or improper opening and closing, and identifies the faulty area. This dual diagnostic approach effectively improves the reliability of disconnector fault diagnosis, ensuring timely detection and repair of faults and ensuring safe operation of GIS equipment.

[0014] In addition, the above-mentioned prior art still has room for improvement in determining the stuck state of the GIS disconnector. Summary of the Invention

[0015] In order to solve the above problems, the purpose of the present invention is to disclose a method for judging the stuck state of a GIS isolating switch, which is achieved by adopting the following technical solutions.

[0016] A method for determining a stuck state of a GIS disconnector is characterized in that the method comprises the following steps: constructing a transfer function of a mechanical system driven by a motor, converting the transfer function into a transfer function form and simplifying the form, inversely drawing a transfer function response curve, and identifying a stuck defect.

[0017] The above-mentioned method for determining the stuck state of a GIS disconnector is characterized in that the steps of constructing the transfer function of the mechanical system driven by the motor are: The basic equivalent circuit of an asynchronous motor includes stator resistance Rs, stator inductance Ls, rotor resistance Rr and rotor inductance Lr. In the equivalent circuit, the rotor resistance and inductance are adjusted by the slip ratio s to reflect the relative motion of the rotor. The voltage balance equation on the stator side is expressed as: V s =I s ·(R s +jωL s )+E Among them, V s is the stator voltage, Is is the stator current, Rs is the stator resistance, Ls is the stator inductance, j is the imaginary unit, j squared is equal to -1; ω is the angular frequency of the motor, E is the back electromotive force induced by the rotor motion, and the back electromotive force E on the rotor side is expressed as: Combining the circuit equations, substituting the back EMF equation on the rotor side into the voltage equation on the stator side, we get: Simplifying this equation, we get: The above-mentioned method for judging the stuck state of a GIS disconnector is characterized by converting it into a transfer function form and simplifying the steps into: To convert the above equation into transfer function form, first define the transfer function G(s) as the ratio of current to voltage: Solving the circuit equation for Is yields: The simplification process involves several steps: Ignore small quantities: If some parameters are small relative to other parameters, ignore them; Linearization: The behavior of the motor near its operating point is approximated as linear, and a linear model is used to approximate the nonlinear behavior; Parameter merging: Merge multiple related parameters into a single parameter to simplify the model; Narrow focus: focus on the most critical parts of the model; Through the above simplification process, a simpler first-order or second-order transfer function is obtained, depending on the key dynamic characteristics of the system. A common simplified form is the first-order transfer function: Where G(s) is the transfer function, s is the complex variable in the Laplace transform, K is the system gain, τ is the system time constant, and Rs is the stator resistance of the motor. It characterizes the dynamic response of the system. For asynchronous motors, the time constant τ is determined according to the electrical parameters of the motor. For a simplified model of a first-order linear system, the time constant τ is expressed as the ratio of the system inductance to resistance. For asynchronous motors, the expression for the time constant τ is used to consider the rotor time constant when analyzing motor starting or transient behavior.

[0018] The above-mentioned method for judging the stuck state of a GIS disconnector is characterized in that the step of reversely drawing the transfer function response curve is as follows: Collect time series data of the motor's input voltage V(t) and output current I(t) under different operating conditions; Perform data preprocessing: Data needs to be cleaned and preprocessed to remove noise and irrelevant information, including filtering, outlier removal, normalization, and other steps; Perform time domain analysis: Use statistical methods such as the least squares method to directly fit the parameters of the transfer function based on time domain data; Draw the response curve: After obtaining the transfer function, use the model to draw the response curve of the system. For a given input signal, use the transfer function to calculate the expected output. Use software tools: Leverage the system identification toolbox in MATLAB and Python software to simplify the process and use the functions and methods in the tool to perform system identification and model verification.

[0019] The above-mentioned method for judging the stuck state of a GIS disconnector is characterized in that the steps of identifying the stuck defect are: Parameter changes in the motor model: When a mechanical system driven by an asynchronous motor undergoes different mechanical state changes, these changes are reflected by parameter changes in the motor model. The following is a more detailed description of these changes using formulas: Assuming that the simplified model of the motor is a first-order linear system, the transfer function is expressed as: When the mechanical state changes due to increased friction caused by jamming, the stator resistance Rs or rotor resistance Rr of the motor increases, affecting the denominator of the transfer function, thereby reducing the overall gain of the transfer function; Changes in inductance: Changes in inductance value affect the time constant τr, where If the inductance Lr increases, the time constant τr will also increase, which will affect the dynamic response of the system; Changes in the torque-current relationship: The relationship between torque T and current I is expressed as: T=k·I Where k is a constant. If the motor requires more torque to maintain the same operating state due to increased friction or load, the current I will increase. This change is reflected in the output current of the transfer function. Changes in dynamic response: Changes in dynamic response are usually reflected at the extremes of the transfer function; Changes in efficiency and loss: Changes in efficiency are observed by comparing input power and output power, where input power Pin = V·I and output power Pout = T·ω.

[0020] The present invention has the following major beneficial technical effects: direct correlation with the dynamic characteristics of the motor, more accurate system model, sensitive response of voltage and current changes to system state changes, wider universality and applicability of analysis, more flexible data analysis, and significantly reduced additional costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A schematic block diagram of the invention.

[0022] Figure 2 Schematic diagram of dynamic response change-transfer function in this application.

[0023] Figure 3 Generate a schematic diagram of the motor's output current under normal conditions.

[0024] Figure 4 Generate a schematic diagram of the motor's output current in a stuck state.

[0025] Figure 5 The motor characteristic curves are in normal and stuck states. DETAILED DESCRIPTION

[0026] Please see Figure 1 and Figure 2 A method for judging the stuck state of a GIS disconnector is characterized in that the judgment method comprises the following steps: a step of constructing a transfer function of a mechanical system driven by a motor, a step of converting the transfer function into a form and simplifying the form, a step of reversely drawing a response curve of the transfer function, and a step of identifying a stuck defect.

[0027] The above-mentioned method for determining the stuck state of a GIS disconnector is characterized in that the steps of constructing the transfer function of the mechanical system driven by the motor are: The basic equivalent circuit of an asynchronous motor includes stator resistance Rs, stator inductance Ls, rotor resistance Rr and rotor inductance Lr. In the equivalent circuit, the rotor resistance and inductance are adjusted by the slip ratio s to reflect the relative motion of the rotor. The voltage balance equation on the stator side can be expressed as: V s =Is ·(R s +jωL s )+E Where V s is the stator voltage, Is is the stator current, Rs is the stator resistance, Ls is the stator inductance, ω is the angular frequency of the motor, and E is the back electromotive force induced by the rotor motion. The back electromotive force E on the rotor side can be expressed as: Combining the circuit equations, substituting the back EMF equation on the rotor side into the voltage equation on the stator side, we get: Simplifying this equation, we get: The above-mentioned method for judging the stuck state of a GIS disconnector is characterized by converting it into a transfer function form and simplifying the steps into: To convert the above equation into transfer function form, first define the transfer function G(s) as the ratio of current to voltage: Solving the circuit equation for Is yields: The simplification process involves several steps: Ignore small quantities: If some parameters are small relative to other parameters, they can be ignored. For example, if the effect of inductance is small relative to that of resistance, the inductance term can be ignored. Linearization: The behavior of the motor near its operating point can be approximated as linear, so a linear model can be used to approximate the nonlinear behavior. Parameter merging: Merge multiple related parameters into a single parameter to simplify the model, for example, combining the effects of resistance and inductance into a single time constant; Narrow focus: Concentrate on the most critical parts of the model. For example, if the analysis focuses on the stator behavior, the rotor parameters can be simplified or ignored. Through the above simplification process, a simpler first-order or second-order transfer function is obtained, depending on the key dynamic characteristics of the system. A common simplified form is the first-order transfer function: Where G(s) is the transfer function, s is the complex variable in the Laplace transform, K is the system gain, τ is the system time constant, and Rs is the stator resistance of the motor. It characterizes the dynamic response of the system. For asynchronous motors, the time constant τ can be determined based on the electrical parameters of the motor. Usually, for a simplified model of a first-order linear system, the time constant τ can be expressed as the ratio of the system inductance to resistance. For asynchronous motors, the expression for the time constant τ may not be directly obvious as it involves complex internal motor dynamics; however, a common approximation is to consider the rotor time constant, especially when analyzing motor starting or transient behavior.

[0028] The above-mentioned method for judging the stuck state of a GIS disconnector is characterized in that the step of reversely drawing the transfer function response curve is as follows: Collect time series data of the motor's input voltage V(t) and output current I(t) under different operating conditions; Perform data preprocessing: Data may need to be cleaned and preprocessed to remove noise and irrelevant information. This may include filtering, removing outliers, normalization, and other steps. Perform time domain analysis: Use statistical methods such as least squares to directly fit the parameters of the transfer function based on time domain data; Draw the response curve: Once the transfer function is obtained, the model can be used to draw the response curve of the system. For a given input signal, the transfer function can be used to calculate the expected output. Use software tools: This process can be greatly simplified by using system identification toolboxes in software such as MATLAB and Python. These tools provide convenient functions and methods to perform system identification and model verification.

[0029] The above-mentioned method for judging the stuck state of a GIS disconnector is characterized in that the steps of identifying the stuck defect are: Parameter changes in the motor model: When a mechanical system driven by an asynchronous motor undergoes different mechanical state changes, these changes can be reflected by parameter changes in the motor model. The following is a more detailed description of these changes using formulas: Assuming that the simplified model of the motor is a first-order linear system, the transfer function can be expressed as: When the mechanical state changes (such as increased friction due to jamming), the stator resistance Rs or rotor resistance Rr of the motor may increase, which will directly affect the denominator of the transfer function, thereby reducing the overall gain of the transfer function. Changes in inductance: Changes in inductance will affect the time constant τr (rotor time constant), where If the inductance Lr increases (perhaps due to damage or deformation of mechanical components), the time constant τr will also increase, which will affect the dynamic response of the system; Changes in the torque-current relationship: The relationship between torque T and current I can be expressed as: T=k·I Where k is a constant. If the motor requires more torque to maintain the same operating state due to increased friction or load, the current I will increase. This change will be reflected in the output current of the transfer function.

[0030] Changes in dynamic response: Changes in dynamic response are usually reflected in the extremes of the transfer function. For example, if the damping of the system is reduced (perhaps due to reduced internal friction), the extremes of the transfer function will move to the left, which means that the system responds faster. Changes in efficiency and losses: Changes in efficiency can be observed by comparing input power and output power. Input power Pin = V·I, while output power Pout = T·ω. If efficiency decreases, the same input power will produce lower output power, which may be reflected in a decrease in the gain of the transfer function.

[0031] To test the entire process, a simplified scenario is used for verification, in which a motor and transfer function parameters are used to simulate the GIS disconnector stuck state judgment method. This includes the following steps: Define basic parameters: Stator resistance = 0.5Ω Rs=0.5Ω Stator inductance = 0.0015 Ls=0.0015H Rotor resistance = 0.3Ω Rr=0.3Ω Rotor inductance = 0.001H Lr=0.001H Slip ratio = 0.05 s=0.05 Motor angular frequency = 314 rad / s ω=314rad / s (power frequency is 50Hz) The input voltage V(t) is a sine wave with a peak value of 220V.

[0032] Motor model: Using the above parameters, construct the equivalent circuit model and transfer function of the motor.

[0033] Data generation: Using this model, generate the output current of the motor in normal and jammed states, see Figure 3 and Figure 4 The motor characteristic curves in normal and jammed states are shown in Figure 5 .

[0034] In a motor, or any inductive load, the observed decrease in current when resistance increases or the motor enters a jammed state is expected. This is because the overall circuit impedance increases. The following explains why this happens: Impedance Increases: Resistance and inductive reactance combine to define the total impedance of the motor. Resistance and inductive reactance are the two components of the complex impedance: resistance R contributes to the real part, and inductive reactance jωL contributes to the imaginary part. The total impedance Z is composed of the stator and rotor impedances: Z = R + jωL. R includes the stator resistance, Rs, and the rotor resistance, Rr, and the inductive reactance includes the contributions of the stator inductance and the rotor inductance, Lr.

[0035] In the stuck state, if the resistance R increases (for example due to mechanical wear or poor electrical contact caused by the sticking), the total impedance also increases.

[0036] Ohm's Law: According to Ohm's Law, the current I is determined by the voltage V and the impedance Z: I = ZV. If the impedance Z increases, the current I will decrease. This is why when the motor enters a jammed state, the current flowing through the motor will decrease even if the input voltage remains unchanged.

[0037] Motor efficiency and dynamic characteristics: A jammed state can also affect the motor's dynamic characteristics, such as starting and running characteristics. Increased resistance causes motor efficiency to decrease because more electrical energy is converted to heat rather than mechanical energy.

[0038] The method of the present invention has the following advantages: From the perspective of transfer function, the system identification method based on voltage and current data is used to analyze the motor drive system. Compared with the method based on vibration analysis, it has the following advantages: (1) Direct correlation with motor dynamic characteristics and system behavior mapping: Voltage and current data are directly related to the electrical dynamic characteristics of the motor, making it possible to more directly map the system behavior when analyzing from the perspective of transfer function. Accurate system model: The transfer function analyzed through voltage and current data can provide an accurate mathematical model of the motor system, which helps to better understand the inherent dynamic characteristics of the system.

[0039] (2) Sensitivity and responsiveness, rapid response to changes: Voltage and current changes are sensitive to changes in system status and can quickly detect small changes in system performance.

[0040] Frequency domain analysis capability: Transfer functions allow for convenient frequency domain analysis, which is particularly important for understanding and diagnosing resonance and stability issues in motor systems.

[0041] (3) Universality and wide applicability of analysis: Almost all motor systems can have their transfer functions analyzed using voltage and current data without considering specific conditions in vibration analysis, such as installation location, environmental interference, etc.

[0042] (4) Flexibility in data analysis and diverse analysis methods: Voltage and current data allow for the use of a variety of data processing and system identification techniques, such as time series analysis and frequency domain analysis, providing greater flexibility. Adaptability to complex scenarios: Under complex operating conditions such as variable speed operation and load changes, voltage and current data can still be effectively used for transfer function analysis.

[0043] (5) Cost-effectiveness: Reduced additional costs: Compared with vibration-based methods, the use of voltage and current data avoids the need for additional vibration monitoring equipment, thereby reducing costs.

[0044] The present invention has the following major beneficial technical effects: direct correlation with the dynamic characteristics of the motor, more accurate system model, sensitive response of voltage and current changes to system state changes, wider universality and applicability of analysis, more flexible data analysis, and significantly reduced additional costs.

[0045] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions described in the claims, including equivalent alternatives to the technical features of the technical solutions described in the claims. Equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for determining a stuck state of a GIS isolating switch, characterized by: The judgment method includes the following steps: constructing a transfer function of a mechanical system driven by a motor, converting it into a transfer function form and simplifying it, reversely drawing a transfer function response curve, and identifying a jam defect.

2. A method for determining a stuck state of a GIS isolating switch according to claim 1, characterized in that: The steps to construct the transfer function of a mechanical system driven by a motor are: The basic equivalent circuit of an asynchronous motor includes stator resistance Rs, stator inductance Ls, rotor resistance Rr and rotor inductance Lr. In the equivalent circuit, the rotor resistance and inductance are adjusted by the slip ratio s to reflect the relative motion of the rotor. The voltage balance equation on the stator side is expressed as: V s =I s ·(R s +jωL s )+E Among them, V s is the stator voltage, Is is the stator current, Rs is the stator resistance, Ls is the stator inductance, j is the imaginary unit, ω is the angular frequency of the motor, and E is the back electromotive force induced by the rotor motion. The back electromotive force E on the rotor side is expressed as: Combining the circuit equations, substituting the back EMF equation on the rotor side into the voltage equation on the stator side, we get: Simplifying this equation, we get:

3. A method for determining a stuck state of a GIS isolating switch according to claim 2, characterized in that: Convert it into the form of transfer function and simplify the steps as follows: To convert the above equation into transfer function form, first define the transfer function G(s) as the ratio of current to voltage: Solving the circuit equation for Is yields: The simplification process involves several steps: Ignore small quantities: If some parameters are small relative to other parameters, ignore them; Linearization: The behavior of the motor near its operating point is approximated as linear, and a linear model is used to approximate the nonlinear behavior; Parameter merging: Merge multiple related parameters into a single parameter to simplify the model; Narrow focus: focus on the most critical parts of the model; Through the above simplification process, a simpler first-order or second-order transfer function is obtained, depending on the key dynamic characteristics of the system. A common simplified form is the first-order transfer function: Where G(s) is the transfer function, s is the complex variable in the Laplace transform, K is the system gain, τ is the system time constant, and Rs is the stator resistance of the motor. It characterizes the dynamic response of the system. For asynchronous motors, the time constant τ is determined according to the electrical parameters of the motor. For a simplified model of a first-order linear system, the time constant τ is expressed as the ratio of the system inductance to resistance. For asynchronous motors, the expression of the time constant τ is used to consider the rotor time constant when analyzing motor starting or transient behavior.

4. A method for determining a stuck state of a GIS isolating switch according to claim 1 or 3, characterized in that: The steps to reverse plot the transfer function response curve are: Collect time series data of the motor's input voltage V(t) and output current I(t) under different operating conditions; Perform data preprocessing: Data needs to be cleaned and preprocessed to remove noise and irrelevant information, including filtering, outlier removal, normalization, and other steps; Perform time domain analysis: Use statistical methods such as the least squares method to directly fit the parameters of the transfer function based on time domain data; Draw the response curve: After obtaining the transfer function, use the model to draw the response curve of the system. For a given input signal, use the transfer function to calculate the expected output. Use software tools: Leverage the system identification toolbox in MATLAB and Python software to simplify the process and use the functions and methods in the tool to perform system identification and model verification.

5. A method for determining a stuck state of a GIS isolating switch according to claim 1 or 4, characterized in that: The steps for identifying a jam defect are: Parameter changes in the motor model: When a mechanical system driven by an asynchronous motor undergoes different mechanical state changes, these changes are reflected by parameter changes in the motor model. The following is a more detailed description of these changes using formulas: Assuming that the simplified model of the motor is a first-order linear system, the transfer function is expressed as: When the mechanical state changes due to increased friction caused by jamming, the stator resistance Rs or rotor resistance Rr of the motor increases, affecting the denominator of the transfer function, thereby reducing the overall gain of the transfer function; Changes in inductance: Changes in inductance value affect the time constant τr, where If the inductance Lr increases, the time constant τr will also increase, which will affect the dynamic response of the system; Changes in the torque-current relationship: The relationship between torque T and current I is expressed as: T=k·I Where k is a constant. If the motor requires more torque to maintain the same operating state due to increased friction or load, the current I will increase. This change is reflected in the output current of the transfer function. Changes in dynamic response: Changes in dynamic response are usually reflected at the extremes of the transfer function; Changes in efficiency and loss: Changes in efficiency are observed by comparing input power and output power, where input power Pin = V·I and output power Pout = T·ω.

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