Method for early detection of inter-turn short circuit in stator winding of induction motor based on voltage signal

Abstract

The application discloses a method for early detection of turn-to-turn short circuit of a stator winding of an induction motor based on a voltage signal, and comprises the following steps: collecting three-phase stator winding voltage signals of an induction motor to be detected during operation; performing time-frequency analysis to obtain time-frequency energy; constructing a cost function, and initializing a time-frequency ridge line of the voltage signal; updating the time-frequency ridge line to realize accurate estimation of the time-frequency ridge line of the voltage signal; calculating three-phase voltage symmetrical components, performing time-varying band-pass filtering, and obtaining fundamental waves of the three-phase symmetrical components; calculating amplitudes of the three-phase symmetrical component fundamental waves, constructing an extended zero-sequence voltage factor, and realizing real-time detection of a turn-to-turn short circuit fault; and constructing a fault phase index to realize identification of a turn-to-turn short circuit phase. The application can effectively detect an early turn-to-turn short circuit fault, improves the accuracy of online detection, reduces the hardware cost of online detection, improves the robustness of online detection under non-stationary conditions, reduces the complexity of data acquisition and signal processing, and improves the practicability of intelligent health management.

Description

Technical Field

[0001] This invention relates to the field of fault detection and health management of induction motors, and in particular to an early detection method for inter-turn short circuits in the stator windings of an induction motor based on voltage signals. Background Technology

[0002] Modern economies rely on the reliable and uninterrupted operation of manufacturing, energy, petrochemical, transportation, and defense equipment. Low-cost, durable, high power-to-weight ratio, and high energy conversion efficiency motors have gradually become core drive equipment in various industries. Statistics show that stator faults account for approximately 37% of induction motor failures. The main cause of stator faults is inter-turn short circuit (ITSC) faults, a common and highly dangerous type of stator fault. In the early stages of an ITSC fault, if it is not addressed promptly, the increased current in the short-circuit portion will lead to localized overheating of the coil, thereby damaging the insulation layer of adjacent coils. Subsequently, the number of short-circuited turns continues to increase, leading to more serious faults such as phase-to-phase short circuits and phase-to-ground short circuits. Studies have shown that the insulation of the windings can break down in a very short time. Therefore, researching early ITSC fault detection methods is of great significance for ensuring the safe and reliable operation of motors.

[0003] Because current and voltage signal acquisition is non-invasive, the signals are pure, and they do not interfere with the original system, research based on current and voltage signals is the most common. Voltage imbalance produces characteristics similar to inter-turn short circuits in the current signal; therefore, using only the current signal cannot effectively detect inter-turn short circuits under voltage imbalance conditions. Methods based on voltage signal analysis often require a tachometer to achieve online detection under non-stationary operating conditions, and research on fault phase identification using only voltage signals has not been found. Using both voltage and current signals can overcome the above shortcomings, but it will increase the hardware cost of online detection. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an early detection method for inter-turn short circuits in the stator windings of an induction motor based on voltage signal processing. This method suppresses the influence of factors such as non-stationary operating conditions and voltage imbalance, effectively detects early inter-turn short circuit faults in the stator windings of an induction motor, and identifies the phase of the fault without adding additional sensors, thereby reducing the cost of online detection and providing more usable information for subsequent maintenance.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] An early detection method for inter-turn short circuits in the stator winding of an induction motor based on voltage signals includes the following steps:

[0007] Step 1: Collect the three-phase stator winding voltage signal during the operation of the induction motor under test, and proceed to Step 2 and Step 5 respectively;

[0008] Step 2: Perform time-frequency analysis on a single-phase voltage signal based on short-time Fourier transform to obtain time-frequency energy and proceed to step 3;

[0009] Step 3: Construct a cost function using time-frequency energy, initialize the time-frequency ridge of the voltage signal, and proceed to Step 4;

[0010] Step 4: Continuously update the time-frequency ridge line based on the iterative amplitude modulation and frequency modulation model to achieve accurate estimation of the voltage signal time-frequency ridge line, then proceed to Step 5;

[0011] Step 5: Calculate the three-phase voltage symmetrical components. Perform time-varying bandpass filtering on the three-phase symmetrical components based on the Volk-Kalman filter and time-frequency ridge to obtain the fundamental frequency of the three-phase symmetrical components. Proceed to Step 6 and Step 7 respectively.

[0012] Step 6: Calculate the fundamental amplitude of the three-phase symmetrical components using the envelope method, construct the extended zero-sequence voltage factor, and detect inter-turn short-circuit faults in real time. Proceed to Step 7.

[0013] Step 7: Construct a fault phase index based on the fundamental phase of the zero-sequence voltage component and the fundamental phase of the three-phase original voltage to identify the inter-turn short circuit phase.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. This invention can effectively detect early inter-turn short circuit faults and is not affected by power supply voltage imbalance, thus avoiding false alarms and improving the accuracy of online detection;

[0016] 2. This invention can accurately estimate the instantaneous frequency of the voltage signal without relying on a tachometer, thereby determining the motor speed information and reducing the hardware cost of online detection;

[0017] 3. This invention takes into account the non-stationary characteristics of signals and constructs a fault detection index that is less affected by rotational speed, thereby improving the robustness of online detection under non-stationary operating conditions;

[0018] 4. This invention does not rely on current sensors; it can accurately determine the phase of an inter-turn short circuit using only voltage signals, reducing the complexity of data acquisition and signal processing and improving the practicality of intelligent health management. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the method of the present invention.

[0020] Figure 2Results of early fault detection for inter-turn short circuits: (a) Three-phase stator voltage (b) Zero-sequence voltage (c) Zero-sequence voltage spectrum under healthy conditions (d) Zero-sequence voltage spectrum under inter-turn short circuit conditions (e) Fault detection index EZVF

[0021] Figure 3 Results of inter-turn short circuit detection under voltage imbalance: (a) Zero-sequence voltage (b) Zero-sequence voltage spectrum under voltage imbalance (c) Zero-sequence voltage spectrum under the combined effects of voltage imbalance and inter-turn short circuit (d) Fault detection index EZVF

[0022] Figure 4 Results of inter-turn short circuit detection for phase A: (a) Zero-sequence voltage (b) Fault detection index EZVF (c) Fault phase index

[0023] Figure 5 Results of inter-turn short circuit detection for phase B: (a) Zero-sequence voltage (b) Fault detection index EZVF (c) Fault phase index

[0024] Figure 6 Results of inter-turn short circuit detection under step speed: (a) Zero-sequence voltage (b) Actual speed vs. estimated speed (c) Fault detection index EZVF (d) Fault phase index

[0025] Figure 7 Results of inter-turn short circuit detection under gradually varying speeds: (a) Zero-sequence voltage (b) Actual speed vs. estimated speed (c) Fault detection index EZVF (d) Fault phase index Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0027] Example

[0028] like Figure 1 As shown, this invention provides an early detection method for inter-turn short circuits in the stator winding of an induction motor based on voltage signals. Without loss of generality, this technique specifically includes the following steps:

[0029] Step 1: Collect the three-phase stator winding voltage signal during the operation of the induction motor under test.

[0030] Step 2: Perform time-frequency analysis on a single-phase voltage signal based on short-time Fourier transform to obtain time-frequency energy. This includes the following steps:

[0031] Step 201: Set the window width W and the number of Fourier points N, and construct the short-time Fourier transform function STFT(t);

[0032] Step 202: Perform a Fourier transform on a phase voltage signal using the function to obtain the time-frequency energy E(t,f).

[0033] Step 3: Construct a cost function using time-frequency energy to initialize the time-frequency ridge of the voltage signal, specifically including the following steps:

[0034] Step 301: Calculate the maximum value of the time-frequency energy E(t,f) mentioned in step 202, and denote the time and frequency here as t. base f base ;

[0035] Step 302: Using t base Starting from the initial time, cost functions are constructed along the time axis to both sides. The expression for the cost function at each time step is as follows:

[0036]

[0037] In the formula, E(t) i ,f j ) represents the time spectrum t i At frequency f j The energy at the point, J represents the sampling frequency of the input data, c1 represents the coefficient of the time-frequency energy, and c2 represents the coefficient of the frequency change rate;

[0038] Step 303: Calculate the minimum value of the cost function at each time moment, and take the frequency corresponding to the cost function value as the instantaneous frequency at that time moment;

[0039] Step 304: After calculating the instantaneous frequency at a given moment, denote the instantaneous frequency as f. base Step 303 is repeated until the instantaneous frequencies of all times are obtained. These instantaneous frequencies are then connected in a time series to form the initial time-frequency ridge.

[0040] Step 4: Continuously update the time-frequency ridge line based on the iterative amplitude modulation and frequency modulation model to achieve accurate estimation of the voltage signal's time-frequency ridge line. This specifically includes the following steps:

[0041] Step 401: Initialize the Lagrange factor α, the filter cutoff frequency λ, and the minimum reconstruction error ε;

[0042] Step 402: The amplitude modulation and frequency modulation model of the voltage signal x(t) can be written as:

[0043] x(t)=A(t)cos(φ(t))=A(t)cos(2πf(t)t+φ0) (2)

[0044] In the formula, A(t) is the instantaneous amplitude of the signal x(t), φ(t) is the instantaneous phase of the signal, f(t) is the instantaneous frequency, and φ0 is the initial phase angle. The analytical form of the signal x(t) can be expressed using the Hilbert transform as follows:

[0045] x a (t)=A(t)exp(j(2πf(t)t+φ0)) (3)

[0046] Substituting the initial time-frequency ridge line described in step 3 into equation (3), we get:

[0047]

[0048] In the formula, P(t) represents the signal x. a Q(t) is the amplitude modulation component of the signal, and Q(t) is the frequency modulation component of the signal.

[0049] Step 403: To obtain the exact P(t) and Q(t), construct the Lagrange function as follows:

[0050]

[0051] In the formula, T() represents the differentiation operation, and α is the Lagrange factor. When When the time is right, the Lagrange function reaches its minimum value;

[0052] Step 404: Find the partial differential equation for P(t) in the Lagrange function:

[0053]

[0054]

[0055] In the formula, D is the improved second-order difference operator, () H The conjugate transpose operation is used to represent a matrix.

[0056] Step 405: Set the partial differential equation described in step 404 to zero, and obtain the frequency modulation component and amplitude modulation component in each iteration process as follows:

[0057]

[0058] P i (t)=(αD T D+I) -1 Q i (t) H x a (t) (9)

[0059] In the formula, I is the identity matrix, and i is the number of iterations;

[0060] Step 406: In each iteration, utilize the amplitude modulation component P i (t) The estimation error of the time-frequency ridge is calculated as follows:

[0061]

[0062] In the formula, Re(P) i (t)) and Im(P i (t) represent complex numbers P respectively. i The real and imaginary parts of (t);

[0063] Step 407: Since the instantaneous frequency should be a smooth function, a filter is used to filter Δfi to ensure high smoothness. The calculation method is as follows:

[0064]

[0065] In the formula, λ is the cutoff frequency of the filter;

[0066] Step 408: Update the time-frequency ridge line based on the estimation error described in step 407, calculated as follows:

[0067]

[0068] Step 409: Based on the updated time-frequency ridge reconstructed voltage signal from Step 408, calculate the error δ between the reconstructed signal and the original signal:

[0069]

[0070] Compare δ with the preset minimum reconstruction error ε. If δ is greater than the preset error ε, then continue to substitute the updated time-frequency ridge line into steps 405-409 to iteratively update the time-frequency ridge line; if δ is less than the preset error ε, then stop the iteration. The time-frequency ridge line at this point is the optimal solution, denoted as f. s It can be directly used for fault detection and fault phase identification.

[0071] Step 5: Calculate the symmetrical components of the three-phase voltage. Perform time-varying bandpass filtering on the symmetrical components using a Volk-Kalman filter and a time-frequency ridge to obtain the fundamental frequency of the symmetrical components. This includes the following steps:

[0072] Step 501: Perform a symmetrical transformation on the three-phase stator winding voltage described in Step 1 to obtain the positive-sequence voltage, negative-sequence voltage, and zero-sequence voltage. The formula for the symmetrical transformation is:

[0073]

[0074] In the formula, a = e j2π / 3 U + U- U0 and U1 are the positive-sequence, negative-sequence, and zero-sequence voltages, respectively.

[0075] Step 502: Set the Volk-Kalman filter bandwidth b and cutoff frequency to the values ​​described in step 4. s Time-varying bandpass filtering is performed on the three-phase symmetrical voltages to obtain the fundamental components of the three-phase symmetrical voltages.

[0076] Step 6: Calculate the fundamental amplitude of the three-phase symmetrical components using the envelope method, and construct the extended zero-sequence voltage factor to detect inter-turn short-circuit faults in real time. This includes the following steps:

[0077] Step 601: Establish an inter-turn short-circuit fault model for the induction motor, and derive that the zero-sequence voltage signal has the most significant impact on the fault response. The zero-sequence voltage signal is represented as:

[0078]

[0079] In the formula, μ represents the severity of the fault, and L 1s For stator leakage inductance, θ s,r R is the rotor position angle. s For the stator resistance, |I f | represents the magnitude of the short-circuit loop current, θ i,p Indicate I f The initial phase angle is also the initial phase angle of the p-phase current signal (p = a, b, c), β = arctan(L 1s / R s ), (β+π) is the initial phase difference between the fundamental component of the zero-sequence voltage and the fundamental component of the short-circuit loop current If;

[0080] Step 602: Calculate the envelope of the fundamental components of the three-phase symmetrical voltage described in Step 5 to obtain the fundamental amplitudes of the positive-sequence, negative-sequence, and zero-sequence voltages;

[0081] Step 603: Construct the extended zero-sequence voltage factor EZVF based on the symmetrical voltage fundamental amplitude from Step 602 to meet the fault detection requirements under non-stationary operating conditions. The EZVF is defined as follows:

[0082]

[0083] In the formula, r represents the current time, n represents the number of samples in the window, and |*| represents the amplitude of the symmetric component;

[0084] Step 604: Under healthy motor conditions, EZVF approaches zero; when an inter-turn short-circuit fault occurs, EZVF will change abruptly. The EZVF factor, constructed in step 603, is used to detect inter-turn short-circuit faults in the stator winding of the induction motor. If a fault is detected, proceed to step 7 to determine the fault phase.

[0085] Step 7: Construct a fault phase index based on the fundamental phase of the zero-sequence voltage component and the fundamental phase of the three-phase original voltage to identify the inter-turn short-circuit phase. This includes the following steps:

[0086] Step 701: Use the arctangent function to solve for the phase angle of the zero-sequence voltage fundamental component described in step 5, and then perform dewinding operation on these phase angles to obtain continuous zero-sequence voltage fundamental phase information.

[0087] Step 702: Calculate the fundamental phase information of the three-phase stator winding voltage collected using the same method as in step 701;

[0088] Step 703: Construct the inter-turn short-circuit phase identification index (PDI) based on the fundamental phase extracted in the above two steps. The index is defined as follows:

[0089]

[0090] In the formula, The power factor angle;

[0091] Step 704: The motor has inherent asymmetry, and during time-varying bandpass filtering, the phase of the filtered signal will shift slightly relative to the phase of the original signal. Considering the above issues, the PDI will also shift to some extent. Therefore, an interval is defined for each PDI index to address the signal phase shift. The PDI indices under different phase fault conditions are shown in Table 1;

[0092] Table 1. Inter-turn short circuit phase comparison table

[0093]

[0094] Step 705: Combine the phase identification index in step 703 and the lookup table in step 704 to identify the phase in which the inter-turn short circuit occurs.

[0095] The specific implementation results of the embodiment are as follows:

[0096] The parameters of the experimental motor are shown in Table 2. To verify the effectiveness of the proposed method in detecting minor faults, a slight inter-turn short-circuit fault with μ = 0.025 was injected into phase B. Figure 2 The original signal and analysis results of this fault are given at a speed of 40Hz and a load torque of 4Nm. An ITSC fault was injected into the stator winding at t=8.2s. Figure 2 (a) indicates that the time-domain waveform of the three-phase voltage signal does not change significantly after a minor fault occurs. After performing a symmetrical transformation on the voltage signal, the amplitude of the zero-sequence voltage signal changes slightly after the fault occurs, such as... Figure 2As shown in (b). Further analysis of the zero-sequence voltage signal reveals that the change in the zero-sequence voltage signal is mainly caused by the change in its fundamental component. The frequency domain analysis results of the zero-sequence voltage before and after the fault are as follows: Figure 2 As shown in (c)(d). Finally, the ITSC detection index EZVF was constructed using this data, as shown in (c)(d). Figure 2 As shown in (e), the EZVF was approximately 0.0005 before the fault occurred. Due to the inherent structural asymmetry of the motor, the EZVF value could not be exactly equal to 0 even when the motor was healthy. After the fault occurred, the EZVF value immediately changed to 0.007, which shows that the proposed method can effectively detect minor ITSC faults.

[0097] Table 2 Design parameters of induction motor

[0098]

[0099] Figure 3 (a) The zero-sequence voltage is calculated from the original signal, with a rotational speed of 40 Hz and a load of 4 Nm. A voltage imbalance fault is injected at t = 6.3 s, an ITSC fault is injected at t = 11.9 s, and the supply voltage is restored to a balanced state at t = 17 s. The voltage imbalance degree is approximately 0.12, and the ITSC fault degree is 0.05. Figure 3 (b) and (c) show the spectral analysis results for voltage imbalance, ITSC, and simultaneous voltage imbalance, respectively. It can be observed that voltage imbalance slightly increases the amplitude of the zero-sequence voltage fundamental component, but the amplitude increment in this case is much smaller than that under ITSC. Therefore, the zero-sequence voltage fundamental component can still be used for ITSC detection under voltage imbalance. Figure 3 (d) It can be observed that at t = 6.3 s, the value of EZVF hardly changes; at t = 11.9 s, EZVF abruptly changes from 0.002 to 0.017; after removing the voltage imbalance (i.e., at t = 17 s), the change in EZVF is very small. These results indicate that voltage imbalance has little impact on the ITSC detection performance of the proposed method.

[0100] Figure 4 The zero-sequence voltage, turn-to-turn short circuit detection index, and phase identification index are given under phase A inter-turn short circuit (μ=0.05). Figure 4 (b) An inter-turn short-circuit fault was detected in the motor at t = 7.9 s. Subsequently, the phase detection index (PDI) was constructed using the phase information of the fundamental component of the zero-sequence voltage and the phase information of the three-phase voltage. Referring to Table 1, it can be found that the PDI... a The value after detecting ITSC is approximately 5°, falling within the fault range, such as... Figure 4 As shown in (c), the detected inter-turn short circuit phase is phase A, which is consistent with the actual fault phase.

[0101] Figure 5 The results shown are for a phase B inter-turn short circuit (μ = 0.025). The figure shows that at t = 9.1s, the PDI... b The value after detecting the ITSC is approximately 6°, falling within the fault range. This indicates that the detected inter-turn short circuit phase is phase B, which is consistent with the actual fault phase. The above verification shows that after detecting the ITSC, constructing the phase detection index (PDI) based on the phase information of the zero-sequence voltage fundamental component and the three-phase voltage phase information, and referring to Table 1, can effectively identify the phase of the ITSC fault.

[0102] Figure 6 The results of inter-turn short-circuit detection under step speed conditions are shown. Actual speeds are as follows: Figure 6 As shown by the red line in (b), the rotational speed suddenly changes from 31Hz to 41Hz at t=8.4s; increases to 45Hz at t=12.5s; and increases to 50Hz at t=16.6s. Figure 6 The green line in (b) represents the rotational speed estimated by the proposed method, which is basically consistent with the actual rotational speed, indicating that the proposed time-frequency ridge extraction method is effective under non-stationary operating conditions. Figure 6 (c) It can be seen that after the inter-turn short circuit occurs, EZVF abruptly changes from 0.002 to 0.0165. Subsequently, with changes in rotational speed, the ITSC detection index fluctuates slightly, but it remains essentially at the same level, indicating that the proposed ITSC detection index has strong robustness under non-stationary operating conditions. After detecting ITSC, the phase identification result of PDI also matches the actual result.

[0103] Figure 7 The results of inter-turn short-circuit detection under gradually varying speeds are shown. For example... Figure 7 As shown in (b), at t = 9.1s, the rotational speed steadily increased from 31Hz to 50Hz, and then steadily decreased to 35Hz. Under this condition, the estimated rotational speed remained very close to the actual value, and the ITSC detection index remained around 0.0165 with minimal fluctuation. These two sets of experiments demonstrate that the proposed time-frequency ridge extraction method and the ITSC fault detection index still exhibit high robustness under varying rotational speed conditions.

[0104] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for early detection of inter-turn short circuits in the stator winding of an induction motor based on voltage signals, characterized in that, Includes the following steps: Step 1: Collect the three-phase stator winding voltage signal during the operation of the induction motor under test, and proceed to Step 2 and Step 5 respectively; Step 2: Perform time-frequency analysis on a single-phase voltage signal based on short-time Fourier transform to obtain time-frequency energy and proceed to step 3; Step 3: Construct a cost function using time-frequency energy, initialize the time-frequency ridge of the voltage signal, and proceed to Step 4; Step 4: Continuously update the time-frequency ridge line based on the iterative amplitude modulation and frequency modulation model to achieve accurate estimation of the voltage signal time-frequency ridge line, then proceed to Step 5; Step 5: Calculate the three-phase voltage symmetrical components. Perform time-varying bandpass filtering on the three-phase symmetrical components based on the Volk-Kalman filter and time-frequency ridge to obtain the fundamental frequency of the three-phase symmetrical components. Proceed to Step 6 and Step 7 respectively. Step 6: Calculate the fundamental amplitude of the three-phase symmetrical components using the envelope method, construct the extended zero-sequence voltage factor, and detect inter-turn short-circuit faults in real time. Proceed to Step 7. Step 7: Construct fault phase indices based on the fundamental phase of the zero-sequence voltage component and the fundamental phase of the three-phase original voltage to identify the inter-turn short-circuit phase. Step 7 includes: Step 701: Use the arctangent function to solve for the phase angle of the zero-sequence voltage fundamental component in step 5, and then perform dewinding operation on these phase angles to obtain continuous zero-sequence voltage fundamental phase information. Step 702: Calculate the fundamental phase information of the three-phase stator winding voltage collected using the same method as in step 701; Step 703: Construct the inter-turn short-circuit phase identification index (PDI) based on the fundamental phase extracted in the above two steps. The index is defined as follows: (17) In the formula, θ δ =φ+β+π , φ The power factor angle; Step 704: The motor has inherent asymmetry, and during time-varying bandpass filtering, the phase of the filtered signal will shift slightly relative to the phase of the original signal; define an interval for each PDI index to address the signal phase shift; the PDI indexes under different phase fault conditions are shown in Table 1. Table 1. Inter-turn short circuit phase comparison table Step 705: Combine the phase identification index in step 703 and the lookup table in step 704 to identify the phase in which the inter-turn short circuit occurs.

2. The method as described in claim 1, characterized in that, Step 2 includes: Step 201: Set the window width W and the number of Fourier points N, and construct the short-time Fourier transform function STFT(t); Step 202: Perform a Fourier transform on a phase voltage signal using the function to obtain the time-frequency energy. E(t, f).

3. The method as described in claim 2, characterized in that, Step 3 includes: Step 301: Calculate the time-frequency energy mentioned in step 202. E(t, f) The maximum value, where the time and frequency are denoted as . t base , f base ; Step 302: with t base Starting from the initial time, cost functions are constructed along the time axis to both sides. The expression for the cost function at each time step is as follows: (1) In the formula, E(t i , f j ) In the time spectrum t i At all times in frequency f j The energy at the location, J Indicates the sampling frequency of the input data. c 1 represents the coefficient of time-frequency energy. c 2 represents the coefficient of the rate of change of frequency; Step 303: Calculate the minimum value of the cost function at each time moment, and take the frequency corresponding to the cost function value as the instantaneous frequency at that time moment; Step 304: After calculating the instantaneous frequency at a given moment, record the instantaneous frequency as... f base Step 303 is repeated until the instantaneous frequencies of all times are obtained. These instantaneous frequencies are then connected in a time series to form the initial time-frequency ridge. .

4. The method as described in claim 3, characterized in that, Step 4 includes: Step 401: Initialize the Lagrange factor α, the filter cutoff frequency λ, and the minimum reconstruction error ε; Step 402: Voltage signal x(t) The amplitude modulation and frequency modulation model is denoted as: (2) In the formula, A(t) is the instantaneous amplitude of the signal x(t). Let f(t) be the instantaneous phase of the signal, and f(t) be the instantaneous frequency. The initial phase angle is used; the signal is transformed using the Hilbert transform. x(t) The analytical form is expressed as: (3) Substituting the initial time-frequency ridge line described in step 3 into equation (3), we get: (4) In the formula, P(t) is the signal. x a (t) The amplitude modulation component, Q(t), is the frequency modulation component of the signal; Step 403: To obtain the exact P(t) and Q(t), construct the Lagrangian function as follows: (5) In the formula, T() represents the differentiation operation, and α is the Lagrange factor; when When the time is right, the Lagrange function reaches its minimum value; Step 404: Find the partial differential equation for P(t) in the Lagrange function: (6) (7) In the formula, D is the improved second-order difference operator, () H The conjugate transpose operation is used to represent a matrix. Step 405: Set the partial differential equation described in step 404 to zero, and obtain the frequency modulation component and amplitude modulation component in each iteration process as follows: (8) (9) In the formula, I is the identity matrix, and i is the number of iterations; Step 406: In each iteration, utilize the amplitude modulation component P i (t) The estimation error of the time-frequency ridge is calculated as follows: (10) In the formula, Re(P) i (t)) and Im(P i (t) represent complex numbers P respectively. i The real and imaginary parts of (t); Step 407: Since the instantaneous frequency should be a smooth function, to ensure high smoothness, a filter is used to filter Δfi. The calculation method is as follows: (11) In the formula, λ is the cutoff frequency of the filter; Step 408: Update the time-frequency ridge line based on the estimation error described in step 407. The calculation method is as follows: (12) Step 409: Based on the updated time-frequency ridge reconstructed voltage signal from Step 408, calculate the error δ between the reconstructed signal and the original signal: (13) Compare δ with the preset minimum reconstruction error ε. If δ is greater than the preset error ε, continue to substitute the updated time-frequency ridge line into steps 405-409 to iteratively update the time-frequency ridge line; if δ is less than the preset error ε, stop the iteration. The time-frequency ridge line at this point is the optimal solution, denoted as δ. f s It is directly used for fault detection and fault phase identification.

5. The method as described in claim 4, characterized in that, Step 5 includes: Step 501: Perform a symmetrical transformation on the three-phase stator winding voltage described in Step 1 to obtain the positive-sequence voltage, negative-sequence voltage, and zero-sequence voltage. The formula for the symmetrical transformation is: (14) In the formula, U + U - U0 and U1 are the positive-sequence, negative-sequence, and zero-sequence voltages, respectively. Step 502: Set the Volk-Kalman filter bandwidth b and cutoff frequency as described in step 4. f s Time-varying bandpass filtering is performed on the three-phase symmetrical voltages to obtain the fundamental components of the three-phase symmetrical voltages.

6. The method as described in claim 5, characterized in that, Step 6 includes: Step 601: Establish an inter-turn short-circuit fault model for the induction motor, and derive that the zero-sequence voltage signal has the most significant impact on the fault response. The zero-sequence voltage signal is represented as: (15) In the formula, μ The severity of the fault, L 1s For stator leakage, θ s,r The rotor position angle, R s For stator resistance, | I f | indicates the magnitude of the short-circuit loop current. θ i,p express I f The initial phase angle is also the initial phase angle of the p-phase current signal. p=a,b,c ), β =arctan(L 1s / R s ) , ( β+π The zero-sequence voltage fundamental component and the short-circuit loop current If are the initial phase differences between them. Step 602: Calculate the envelope of the fundamental components of the three-phase symmetrical voltage described in Step 5 to obtain the fundamental amplitudes of the positive-sequence, negative-sequence, and zero-sequence voltages; Step 603: Construct the extended zero-sequence voltage factor EZVF based on the symmetrical voltage fundamental amplitude in Step 602 to meet the fault detection requirements under non-stationary operating conditions; EZVF is defined as follows: (16) In the formula, r represents the current time, n represents the number of samples in the window, and |*| represents the amplitude of the symmetric component; Step 604: When the motor is in good condition, EZVF approaches zero; when an inter-turn short circuit fault occurs, EZVF will change abruptly; based on the EZVF constructed in step 603, an inter-turn short circuit fault in the stator winding of the induction motor is detected; if a fault is detected, proceed to step 7 to determine the fault phase.

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