Variable working condition dual three-phase motor weak inter-turn short circuit fault diagnosis method based on VMD-SST

Abstract

The VMD-SST-based variable working condition dual three-phase motor weak inter-turn short circuit fault diagnosis method belongs to the motor fault diagnosis technical field, and aims to solve the problems that the traditional method is difficult to accurately track time-varying fault characteristics under variable working condition, the dual three-phase motor harmonic suppression characteristics result in that the weak fault signal is difficult to extract, and the single-turn short circuit fault is easily submerged by noise under low signal-to-noise ratio. The mechanism that the fault generates 4 times and 6 times electric frequency harmonic components in the fifth harmonic space is deduced by establishing a fault mathematical model, and accordingly, the fifth harmonic space d-axis and / or q-axis current is selected as a characteristic signal; the characteristic signal is subjected to variational mode decomposition, and a target mode is selected from multiple mode components; the target mode is subjected to synchronous compression wavelet transform to obtain a time-frequency diagram; a time-frequency ridge line is extracted, if the ridge line frequency is 4 times and / or 6 times electric frequency, then it is judged that an inter-turn short circuit fault occurs, and the starting time of the ridge line is taken as a fault occurrence time.

Description

Technical Field

[0001] This invention belongs to the field of motor fault diagnosis technology, specifically relating to a method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST (Adaptive Variational Mode Decomposition and Synchronous Compressed Wavelet Transform). Background Technology

[0002] Dual three-phase motors, as a typical multiphase motor topology, have gained widespread attention and engineering applications in recent years for high-reliability and high-power-density applications. Compared to traditional three-phase motors, dual three-phase motors typically employ two sets of independent three-phase windings with a 30° electrical phase shift, offering the following significant technical advantages: First, through reasonable winding distribution and control strategies, 5th and 7th spatial harmonics can be effectively canceled, significantly reducing torque ripple and electromagnetic noise, and improving operational smoothness. Second, they possess inherent fault-tolerant operation capabilities; when one set of windings experiences an open circuit or partial fault, the other set can maintain derating operation, effectively reducing the damage caused by motor failures to the system. Third, under the same volume and current rating, dual three-phase windings can achieve higher power density and better thermal field distribution. Based on these advantages, dual three-phase motors are widely applicable in fields with extremely high requirements for safety, redundancy, and energy efficiency, such as electric drive systems for new energy vehicles, aerospace servo systems, marine electric propulsion, and high-power wind turbine pitch systems.

[0003] However, under prolonged high loads, frequent start-stops, or harsh environmental conditions, the stator windings of dual-phase three-phase motors are highly susceptible to inter-turn short-circuit faults. Inter-turn short circuits are the most common early insulation faults in motor windings, accounting for over 60% of all winding faults. In its initial stage, this fault typically manifests as insulation degradation in a single turn or a few turns (i.e., a weak inter-turn short circuit). The short-circuited turn induces circulating currents far exceeding the rated value, causing a rapid local temperature rise. Simultaneously, it disrupts the spatial symmetry of the air gap magnetic field, inducing a negative-sequence magnetic field and additional harmonic torque, leading to phase current asymmetry, increased copper and iron losses, decreased efficiency, and intensified vibration and noise. If not diagnosed promptly, a weak inter-turn short circuit can quickly evolve into a severe phase-to-phase short circuit or ground fault, causing motor burnout or even paralysis of the entire drive system, resulting in significant economic losses and safety accidents. Therefore, early, accurate, and real-time diagnosis of inter-turn short-circuit faults in dual-phase three-phase motors is of significant engineering value for achieving condition-based maintenance, avoiding catastrophic failures, extending equipment service life, and ensuring safe equipment operation.

[0004] Although existing technologies have made some progress in diagnosing inter-turn short circuits under steady-state conditions, motors in actual engineering often operate under complex variable conditions such as frequent speed changes, drastic load fluctuations, and time-varying ambient temperatures. Existing methods face the following main technical challenges when applied to diagnosing weak inter-turn short circuit faults under variable conditions:

[0005] First, varying operating conditions undermine the fundamental assumptions of traditional diagnostic methods. Traditional frequency domain analysis methods based on Fourier transform are inherently suited to steady-state signals. When processing signals under varying operating conditions, they suffer from severe frequency ambiguity and energy leakage, failing to accurately track time-varying fault characteristic frequencies. While time-frequency analysis methods can provide some time-frequency joint information, under varying speed conditions, their frequency resolution is often insufficient to distinguish between weak fault harmonics and fundamental frequency fluctuations caused by speed variations.

[0006] Secondly, the harmonic suppression characteristics of dual three-phase motors increase the difficulty of fault feature extraction. Under healthy conditions, the fifth harmonic space dq-axis currents of a dual three-phase motor cancel each other out due to the winding phase-shifting structure, resulting in a significant reduction in amplitude. However, after a fault occurs, harmonic components of 4th and 6th times the electrical frequency are generated in this harmonic space. This mechanism provides a diagnostic basis for this invention, but it also means that fault feature signals appear in the originally extremely low-energy harmonic space, and their absolute values ​​are very weak, easily drowned out by environmental noise and measurement errors.

[0007] Third, the signal-to-noise ratio of weak inter-turn short-circuit faults is extremely low. The fault current generated by a single-turn short circuit is typically only on the order of one percent of the rated current, and the corresponding fault characteristic harmonic component amplitude is very small. Existing methods, such as directly analyzing the current waveform or using simple threshold judgment, are difficult to achieve reliable diagnosis under interference such as load fluctuations and inverter switching noise, resulting in high missed detection rates and false alarm rates.

[0008] To address the aforementioned issues, recent studies have attempted to use variational mode decomposition (VMD) to adaptively decompose motor currents and extract fault-related intrinsic mode functions (EMFs). VMD has a more robust mathematical foundation and better resistance to mode aliasing compared to empirical mode decomposition (EMD). However, standard VMD still suffers from insufficient time-frequency convergence when processing strongly non-stationary variable operating condition signals, making it difficult to simultaneously achieve high time and frequency resolution. Synchronous compressed wavelet transform can sharpen time-frequency ridges by redistributing wavelet coefficients, but it is sensitive to noise when used alone and lacks the ability to adaptively select effective modes.

[0009] In summary, existing technologies lack a method that can effectively integrate the adaptive denoising advantages of variational mode decomposition with the high time-frequency focusing capability of synchronous compressed wavelet transform, specifically for the sensitive and accurate diagnosis of weak inter-turn short-circuit faults in dual three-phase motors under varying operating conditions (variable speed, variable load). This invention addresses this technological gap. Summary of the Invention

[0010] To address the challenges of accurately tracking time-varying fault characteristics under varying operating conditions using traditional methods, the difficulty in extracting weak fault signals due to the harmonic suppression characteristics of dual-three-phase motors, and the ease with which single-turn short-circuit faults are drowned out by noise under low signal-to-noise ratios, this invention provides a method for diagnosing weak inter-turn short-circuit faults in dual-three-phase motors under varying operating conditions based on VMD-SST.

[0011] The present invention describes a method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST. This method includes the following steps:

[0012] S1. Obtain the current signal of the dual three-phase motor, and extract the fifth harmonic space current from the current signal as a feature signal.

[0013] S2. Perform variational mode decomposition on the feature signal to obtain... One modal component;

[0014] S3, from the above Select the target mode from the modal components;

[0015] S4. Perform synchronous compressed wavelet transform on the target mode to obtain the time-frequency diagram;

[0016] S5. Determine whether an inter-turn short circuit fault has occurred and the time of occurrence of the fault based on the time-frequency ridge line in the time-frequency diagram.

[0017] Preferably, the fifth harmonic spatial current in step S1 is a time-varying signal of the fifth harmonic spatial d-axis current. Time-varying signal of and / or fifth harmonic space q-axis current .

[0018] Preferably, the mathematical model for variational mode decomposition in step S2 is as follows:

[0019] First, construct the variational constraint problem:

[0020] ;

[0021] In the formula, The number of decomposed modes, For the first One eigenmode function ; For the first The center frequencies of the eigenmode functions The extracted fifth harmonic spatial current time-varying signal. or , The unit impulse function;

[0022] Then, a penalty factor is introduced. and Lagrange multipliers The variational constraint problem is transformed into the following augmented Lagrangian function:

[0023] ;

[0024] Finally, the augmented Lagrangian function is solved iteratively using the alternating direction multiplier method.

[0025] Preferably, the number of decomposition modes in the variational mode decomposition is... =6, penalty factor =2000.

[0026] Preferably, the selection rule for the target mode in step S3 is: for The amplitudes of each modal component curve under healthy conditions were detected, and modal components with amplitudes below 0.02A under healthy conditions were selected. As the target mode.

[0027] Preferably, step S4 specifically includes: performing a synchronous compressed wavelet transform on the target mode selected in step S3, and using the transformed time-frequency coefficients as output to obtain the time-frequency diagram of the target mode; the mathematical model of the synchronous compressed wavelet transform is:

[0028] ;

[0029] In the formula, For modal components The time-frequency coefficients after synchronous compressed wavelet transform. For the modal components Continuous wavelet transform function under the mother wavelet For wavelet scale, , b The translation amount, This is an estimate of the instantaneous frequency. This refers to the instantaneous frequency.

[0030] Preferably, for the modal components Wavelet coefficients obtained by synchronous compressed wavelet transform The expression is:

[0031] ;

[0032] In the formula, It is the complex conjugate of the continuous wavelet transform function under the mother wavelet.

[0033] Preferably, the instantaneous frequency estimate The expression is:

[0034] ;

[0035] In the formula, This indicates taking the real part.

[0036] Preferably, the specific method for determining whether an inter-turn short circuit fault has occurred and the time of fault occurrence in step S5 is as follows: extract the time-frequency ridge line from the time-frequency diagram. If the frequency corresponding to the extracted time-frequency ridge line is 4 times the electrical frequency and / or 6 times the electrical frequency, it is determined that an inter-turn short circuit fault has occurred in the dual three-phase motor, and the starting time of the time-frequency ridge line is taken as the time of fault occurrence.

[0037] Preferably, the 4th and / or 6th times the electrical frequency is derived from the following mathematical model:

[0038] When a two-phase three-phase motor experiences an inter-turn short-circuit fault, let the proportion of the faulty part in the faulty phase be . The short-circuit current is The additional voltage caused by the fault for:

[0039] ;

[0040] In the formula, For phase resistance, For the sake of self-reflection, The electric frequency of the motor. The mutual inductance between two phase windings that are spatially separated by 30 electrical degrees is given. Mutual inductance between two phase windings that are spatially separated by 60 electrical degrees;

[0041] Additional voltage for the fault Perform a harmonic space Clark-Park transform, the transform matrix is: ,get:

[0042] ;

[0043] In the formula, Short-circuit current amplitude, For electrical angle, Short-circuit current The phase angle;

[0044] The transformation result includes Item and The terms correspond to the 4th and 6th harmonic components of the electrical frequency, respectively.

[0045] The beneficial effects of this invention are:

[0046] 1. Clear fault characteristic frequencies are given, providing a theoretical basis for diagnosis.

[0047] By establishing a mathematical model of weak inter-turn short-circuit faults in a dual-phase three-phase motor under varying operating conditions and performing a harmonic space Clark-Park transform on the fault voltage, this invention theoretically reveals that inter-turn short-circuit faults generate 4th and 6th harmonic components in the fifth harmonic space. This conclusion transforms the fault diagnosis problem into the detection problem of specific harmonic frequencies, avoiding blind feature extraction and pointing the way for subsequent signal processing.

[0048] 2. Applicable to varying operating conditions, with good diagnostic robustness.

[0049] To address the challenge of time-varying fault characteristic frequencies under varying operating conditions, which traditional frequency domain methods struggle to adapt to, this invention employs variational mode decomposition to adaptively decompose the characteristic signals, selecting the optimal parameter combination (…). =6, =2000), effectively separating fault-related modes from healthy modes and environmental noise; then, combined with synchronous compressed wavelet transform, the dispersed wavelet coefficients are compressed to the instantaneous frequency point, significantly improving the clustering of the time-frequency plot. Experimental results show that under variable speed and variable load conditions, this method can obtain clear time-frequency ridges of 4 times / 6 times the electrical frequency, achieving accurate tracking of time-varying fault characteristics.

[0050] 3. High sensitivity, capable of detecting weak short-circuit faults in a single turn.

[0051] To address the issues of low signal-to-noise ratio and susceptibility to noise masking in weak inter-turn short-circuit faults, this invention employs VMD adaptive decomposition to remove high-frequency small-amplitude fluctuations and environmental noise, retaining low-frequency modes containing fault characteristics. This is followed by SST energy redistribution, allowing the weak fault characteristic energy to be concentrated and manifested. Experiments demonstrate that even under extremely weak fault conditions with only one short-circuit turn (fault current approximately one percent of the rated current), this method can still accurately identify the fault characteristic frequency and pinpoint the fault occurrence time (50ms), significantly improving early fault diagnosis capabilities.

[0052] 4. Able to pinpoint the exact time of the fault.

[0053] By using high-resolution time-frequency ridge line analysis, this invention can not only determine whether an inter-turn short circuit has occurred, but also determine the fault occurrence time based on the start time of the time-frequency ridge line. This function has practical engineering value for fault tracing, condition-based maintenance decisions, and system fault-tolerant control.

[0054] In summary, this invention solves the problems of easily masked features, low signal-to-noise ratio, and insufficient model generalization ability in the diagnosis of weak inter-turn short circuit faults in dual three-phase motors under varying operating conditions. The robustness, sensitivity, and practicality of the diagnostic method are all improved, which is conducive to ensuring the safe and reliable operation of the motor. Attached Figure Description

[0055] Figure 1The equivalent circuit diagram for the inter-turn short-circuit fault section;

[0056] Figure 2 This is a waveform diagram of the motor phase current under variable speed operating conditions;

[0057] Figure 3 The waveform of the fifth harmonic space dq axis current amplitude under variable speed conditions;

[0058] Figure 4 The waveforms of the fifth harmonic spatial d-axis current modes under variable speed conditions are shown.

[0059] Figure 5 The time-frequency diagram of the fifth harmonic spatial d-axis current under variable speed conditions;

[0060] Figure 6 The waveforms of the fifth harmonic spatial q-axis current modes under variable speed conditions are shown.

[0061] Figure 7 The time-frequency diagram of the fifth harmonic spatial q-axis current under variable speed conditions;

[0062] Figure 8 The waveform diagram of the given torque under variable load conditions;

[0063] Figure 9 This is a waveform diagram of the motor phase current under variable load conditions;

[0064] Figure 10 The waveform of the fifth harmonic space dq axis current amplitude under variable load conditions;

[0065] Figure 11 The waveforms of the fifth harmonic spatial d-axis current modes under variable load conditions are shown.

[0066] Figure 12 Time-frequency diagram of the d-axis current of the fifth harmonic space under variable load conditions;

[0067] Figure 13 The waveforms of the fifth harmonic spatial q-axis current modes under variable load conditions are shown.

[0068] Figure 14 Time-frequency diagram of the q-axis current of the fifth harmonic under variable load conditions;

[0069] Figure 15 This is a flowchart of the method of the present invention. Detailed Implementation

[0070] 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.

[0071] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0072] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0073] Specific Implementation Method 1: The following is combined with... Figures 1 to 15 This embodiment describes the method for diagnosing weak inter-turn short circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST.

[0074] The main innovations of this invention are as follows: Addressing three technical challenges in diagnosing weak inter-turn short circuits (single-turn short circuits) in dual-phase three-phase permanent magnet synchronous motors under varying operating conditions (variable speed, variable load)—the time-varying fault characteristic frequency due to varying operating conditions, the weak fault characteristic signal due to the harmonic suppression characteristics of dual-phase three-phase motors, and the ease with which single-turn short circuit faults are drowned out by noise under low signal-to-noise ratio—this invention proposes a fault diagnosis method based on adaptive variational mode decomposition and synchronous compressed wavelet transform (VMD-SST). The main innovations of this invention are as follows:

[0075] 1. Theoretical innovation: Revealed the 4th / 6th harmonic characteristic mechanism of inter-turn short-circuit faults in the fifth harmonic space.

[0076] By establishing a mathematical model of a weak inter-turn short-circuit fault in a dual three-phase permanent magnet synchronous motor under varying operating conditions, and performing a harmonic space Clark-Park transform on the fault's additional voltage, it was theoretically derived for the first time that an inter-turn short-circuit fault will generate harmonic components of the 4th and 6th harmonic frequencies in the fifth harmonic space. This discovery transforms the fault diagnosis problem into the detection problem of specific harmonic frequencies, providing a clear target frequency guide for subsequent signal processing.

[0077] 2. Methodological innovation: A fault diagnosis framework integrating VMD and SST was proposed.

[0078] To address the problem of time-varying fault characteristic frequencies under varying operating conditions and the difficulty of adapting to traditional frequency domain methods, variational mode decomposition (VMD) and synchronous compressed wavelet transform (VMD) are organically integrated. First, the adaptive decomposition capability of VMD is utilized, and then the parameter combination is optimized (…). =6, =2000) effectively separates fault-related modes from healthy modes and environmental noise; then, SST compresses the dispersed wavelet coefficients to the instantaneous frequency point, significantly improving the clustering of the time-frequency plot. The two complement each other, solving the problems of insufficient time-frequency clustering of VMD and the sensitivity of SST to noise.

[0079] 3. Parameter innovation: The optimal combination of VMD parameters for weak inter-turn short circuit faults in dual three-phase motors is presented.

[0080] Through experimental verification, the optimal parameter combination suitable for this diagnostic task was determined: decomposition mode number. =6, penalty factor =2000. Under this parameter, modes 4 and 5 contain fault characteristic information, modes 1-3 are healthy high-frequency components, and mode 6 is a DC component, thus achieving effective separation of fault information and interference information.

[0081] 4. Functional innovation: It realizes accurate diagnosis and fault location of single-turn weak faults under varying operating conditions.

[0082] Under conditions where faults are difficult to identify due to varying speed and load, and even under extremely weak fault conditions with only one short-circuit turn (the fault current is approximately one percent of the rated current), this method can still obtain a clear time-frequency ridge line at 4 times / 6 times the electrical frequency, and accurately locate the fault occurrence time based on the ridge line's starting moment, thus possessing both high sensitivity and fault location capability.

[0083] Establishment of the fault mathematical model:

[0084] This embodiment takes a dual three-phase permanent magnet synchronous motor as the research object. The phases of the dual three-phase motor are ABCDEF, where phases ABC form one set of three-phase windings, and phases DEF form another set of three-phase windings. It is assumed that an inter-turn short-circuit fault occurs in phase A, and the proportion of the faulty portion in phase A is [missing information]. The equivalent circuit of the inter-turn short-circuit fault section is as follows: Figure 1 As shown.

[0085] The voltage equation for the dual three-phase motor is as follows:

[0086] (1)

[0087] In the formula, This is the voltage of phase A. The voltage of faulty section A. This refers to the voltage of the healthy portion of phase A. This refers to the fault current in phase A. This refers to the current in the healthy portion of phase A. The phase resistance, the resistance of the short-circuited part resistance of the healthy part , For self-inductance, the self-inductance of the short-circuited part Health part self-perception , The electric frequency of the motor. The back electromotive force of A is the back electromotive force of the short-circuited part. The back electromotive force of the healthy part , This is the matrix of remaining phase currents.

[0088] The mutual inductance matrix between the remaining phase and phase A is expressed as:

[0089] (2)

[0090] In the formula, For phases A and B to be mutually inducted, For AC phase mutual inductance. For alternating A and D inductance, For AE phase mutual inductance. For phase-to-phase mutual inductance (AF), to simplify calculations, the mutual inductance between two windings that are 30 electrical degrees apart in spatial position is: The mutual inductance between two phase windings that are 60 electrical degrees apart in spatial position is At this point, the mutual inductance matrix is:

[0091] (3)

[0092] Meanwhile, for phase A:

[0093] (4)

[0094] In the formula, This is the short-circuit current. This is the short-circuit resistor.

[0095] (1) and (4) are combined to obtain the voltage of phase A. :

[0096] (5)

[0097] Considering the entire motor winding, the voltage equation for a dual three-phase motor is:

[0098] (6)

[0099] In the formula, This is a phase voltage matrix for a dual three-phase motor. This is the back electromotive force matrix of a dual three-phase motor. This is the phase current matrix for a dual three-phase motor. It is a phase-to-phase mutual inductance matrix for a dual three-phase motor.

[0100] It can be seen that when a dual three-phase motor experiences an inter-turn short-circuit fault, the voltage equation, compared to the healthy state voltage, only has one additional voltage term. :

[0101] (7)

[0102] Derivation of fault characteristic frequencies and selection of characteristic signals:

[0103] Based on the winding phase-shifting characteristics of a dual three-phase motor, the dq-axis current components in the fifth harmonic space will cancel each other out under healthy conditions, resulting in a significant reduction in amplitude and only high-frequency fluctuations. This means that the fifth harmonic space has a low energy background under healthy conditions, providing an ideal observation window for fault characteristic detection.

[0104] Based on this, the fault additional voltage derived in the previous section... We perform the Clark-Park transform in harmonic space and analyze its behavior in the fifth harmonic space. The transform process is as follows:

[0105] (8)

[0106] In the formula, For electrical angle, Here is the Clark-Park transformation matrix for the harmonic space of a dual-phase three-phase motor:

[0107] (9)

[0108] short-circuit current Defined as sinusoidal alternating current form:

[0109] (10)

[0110] In the formula Short-circuit current amplitude, Short-circuit current The phase angle.

[0111] Combining equations (8) and (10), we get:

[0112] (11)

[0113] Due to electrical angle The above formula contains Item and The terms correspond to the 4th and 6th harmonic components of the electrical frequency, respectively. This means that when a two-phase three-phase motor experiences an inter-turn short circuit fault, harmonic components of the 4th and 6th electrical frequencies will be generated in the fifth harmonic space.

[0114] Based on the above theoretical derivation, this invention selects the time-varying signal of the fifth harmonic spatial d-axis current. Time-varying signal of and / or fifth harmonic space q-axis current As a diagnostic feature signal, the presence of harmonic components at 4 times and / or 6 times the electrical frequency is used to determine whether a fault has occurred.

[0115] Variational Mode Decomposition (VMD) Denoising:

[0116] After extracting the feature signal and / or Next, the signal needs to be decomposed and denoised to extract weak fault features. This invention employs variational mode decomposition to adaptively decompose the feature signal, solves the variational constraint problem, and uses the alternating direction multiplier method to avoid mode aliasing. The mathematical model of variational mode decomposition is as follows:

[0117] First, construct the variational constraint problem:

[0118] (12)

[0119] In the formula, The number of decomposed modes, For the first One eigenmode function ; For the first The center frequencies of the eigenmode functions The extracted fifth harmonic spatial current time-varying signal. or , The unit impulse function;

[0120] Then, a penalty factor is introduced. and Lagrange multipliers The variational constraint problem is transformed into the following augmented Lagrangian function:

[0121] (13)

[0122] Finally, the augmented Lagrangian function is solved iteratively using the alternating direction multiplier method.

[0123] The augmented Lagrangian function is solved iteratively using the alternating direction multiplier method, continuously updating each modal component. Center frequency and Lagrange multipliers Until the convergence condition is met, the original signal is finally... Decomposed into A discrete modal component.

[0124] Optimal parameter selection: Through experimental verification, the optimal parameter combination selected in this invention is: decomposed mode number. =6, penalty factor =2000.

[0125] Target mode selection:

[0126] After VMD decomposition, six modal components are obtained. Further identification is needed to determine which of these modal components contain fault information and which are background components in a healthy state. The selection rule proposed in this invention is: to detect the amplitude of each modal component curve in a healthy state, and select the modal components with amplitudes below 0.02A in a healthy state as target modes. This is because these modes have very low energy in a healthy state, contributing little to the healthy signal, but are sensitive to fault signals—a fault will generate significant harmonic components in these modes.

[0127] Taking variable speed operation as an example, VMD decomposition of the fifth harmonic spatial d-axis current yields 6 modes, such as... Figure 4 As shown in the diagram, the first three modal signals contain higher harmonics and show little change before and after the fault, containing the main information under healthy conditions. Mode 6 mainly contains DC components. Modes 4 and 5 contain low-frequency harmonics, generating a series of harmonic components after the fault, containing motor fault information. Based on the above selection rules, the mode with an amplitude below 0.02A under healthy conditions (mode 4 in this example) is selected as the target mode for subsequent synchronous compressed wavelet transform.

[0128] The same processing was applied to the q-axis current of the fifth harmonic space, resulting in 6 modes, as follows: Figure 6 As shown, mode 4 is also selected as the target mode.

[0129] Synchronous Compressed Wavelet Transform (SST) and Time-Frequency Plot Generation:

[0130] After selecting the target mode, its time-frequency characteristics need to be further analyzed to identify the fault characteristic frequency. Because the motor operates under varying conditions, the frequency components are complex, and the modes obtained from VMD decomposition may still have some mode aliasing issues, resulting in insufficient clarity when directly observing the time-frequency diagram. Therefore, this invention performs synchronous compressed wavelet transform on the selected target mode, obtaining a high-resolution time-frequency representation through energy redistribution to extract clear signal time-frequency ridges.

[0131] First, for the target mode The expression for continuous wavelet transform is as follows:

[0132] (14)

[0133] In the formula, For the modal components Continuous wavelet transform function under the mother wavelet For wavelet scale, , b The translation amount, It is the complex conjugate of the continuous wavelet transform function under the mother wavelet.

[0134] Then, instantaneous frequency estimation is performed:

[0135] instantaneous frequency estimate It can be represented as:

[0136] (15)

[0137] In the formula, This indicates taking the real part.

[0138] Finally, perform synchronous compression transformation:

[0139] The energy of traditional wavelet transform is distributed across different scales. The above methods cannot simultaneously and accurately display both the fault time and the fault characteristic frequency. Therefore, this invention employs synchronous compressed wavelet transform to convert the frequency contributed to the same instantaneous frequency. The wavelet coefficients are compressed to the same point on the frequency axis:

[0140] (16)

[0141] In the formula, For modal components The time-frequency coefficients after synchronous compressed wavelet transform. It is a unit impulse function.

[0142] Through synchronous compression transformation, energy is redistributed to the vicinity of the instantaneous frequency point, thereby obtaining a high-resolution time-frequency map of the target mode.

[0143] Fault diagnosis and fault location:

[0144] After obtaining the high-resolution time-frequency map, fault diagnosis is required. Time-frequency ridges are extracted from the time-frequency map obtained after synchronous compressed wavelet transform to acquire the instantaneous frequency trajectory of energy accumulation. It is then determined whether the frequency corresponding to the extracted time-frequency ridge is 4 times and / or 6 times the current electrical frequency.

[0145] If a time-frequency ridge appears in the time-frequency graph, and its frequency changes with time and always maintains a 4-fold relationship with the current electrical frequency, then it is determined that there is a 4-fold electrical frequency harmonic component in the d-axis current of the fifth harmonic space.

[0146] If a time-frequency ridge appears in the time-frequency graph, and its frequency changes over time and always maintains a relationship of 6 times with the current electrical frequency, then it is determined that there is a harmonic component of 6 times the electrical frequency in the q-axis current of the fifth harmonic space.

[0147] When the presence of a 4th harmonic component and / or a 6th harmonic component is detected, an inter-turn short-circuit fault is determined to have occurred in the dual three-phase motor. Simultaneously, the starting time of the time-frequency ridge line in the time-frequency diagram is taken as the time of occurrence of the inter-turn short-circuit fault.

[0148] Experimental verification:

[0149] (I) Variable speed operating condition test

[0150] This embodiment was conducted on a dual three-phase permanent magnet synchronous motor experimental platform. The motor was set to run under variable speed conditions, and a single-turn inter-turn short circuit fault (1 turn short-circuited) was artificially set for phase A at 50ms.

[0151] Fault diagnosis is performed according to the method of the present invention:

[0152] 1. Signal Acquisition: Acquire motor phase current, such as... Figure 2 As shown, it is difficult to directly identify faults from the current waveform.

[0153] 2. Feature Extraction: Extract the time-varying signal of the fifth harmonic spatial d-axis current. Time-varying signal of the fifth harmonic space q-axis current ,like Figure 3 As shown, the signal fluctuates after the fault.

[0154] 3. VMD decomposition: for VMD decomposition was performed (K=6, α=2000), resulting in 6 modes ( Figure 4 The first three modes contain higher harmonics and do not change significantly before and after the fault, containing the main information under healthy conditions. Mode 6 mainly contains DC components. Modes 4 and 5 contain low-frequency harmonics, generating a series of harmonic components after the fault, containing motor fault information. When selecting a mode, it should be ensured that the mode contains as little information as possible under healthy motor conditions. Therefore, modes with amplitudes below 0.02A under healthy conditions are selected for fault diagnosis. In this example, mode 4 is selected for synchronous compressed wavelet transform.

[0155] 4. SST Transform: Perform synchronous compressed wavelet transform on mode 4 to obtain a high-resolution time-frequency diagram. Figure 5In the figure, even under a weak inter-turn fault at variable speed, the 5th harmonic space d-axis current still shows a clear time-frequency ridge, and the frequency of the time-frequency ridge changes with the motor's electrical frequency. This indicates that under the condition of a short-circuit fault at variable speed, the 5th harmonic space d-axis current generates a harmonic signal that is a fixed multiple of the electrical frequency. The frequency of the time-frequency ridge changes with the motor's electrical frequency, and is calculated to be 4 times the electrical frequency.

[0156] 5. Fault diagnosis: Based on the time-frequency ridge line characteristics, it is determined that an inter-turn short circuit fault has occurred. The fault start time is approximately 50ms, which is consistent with the setting.

[0157] right Perform the same processing ( Figure 6 , Figure 7 Similarly, a clear time-frequency ridge at 6 times the electrical frequency appeared after the fault, further verifying the effectiveness of the method.

[0158] (II) Variable load test

[0159] This embodiment is performed under variable load conditions, with the given torque waveform as follows: Figure 8 As shown, the same fault is set at 50ms.

[0160] Phase current acquisition ( Figure 9 Time-varying signals of the fifth harmonic space d-axis current Time-varying signal of the fifth harmonic space q-axis current ( Figure 10 ), respectively for and Perform VMD-SST processing. Figure 11-14 The results show that even under drastic load changes... and The time-frequency ridges caused by the fault can still be clearly identified in the time-frequency diagram (4 times and 6 times the electrical frequency, respectively), and the fault time is accurately located.

[0161] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST, characterized in that, The method includes the following steps: S1. Obtain the current signal of the dual three-phase motor, and extract the fifth harmonic space current from the current signal as a feature signal. S2. Perform variational mode decomposition on the feature signal to obtain... One modal component; S3, from the above Select the target mode from the modal components; S4. Perform synchronous compressed wavelet transform on the target mode to obtain the time-frequency diagram; S5. Determine whether an inter-turn short circuit fault has occurred and the time of occurrence of the fault based on the time-frequency ridge line in the time-frequency diagram. The specific method for determining whether an inter-turn short circuit fault has occurred and the time of fault occurrence in step S5 is as follows: extract the time-frequency ridge line from the time-frequency diagram. If the frequency corresponding to the extracted time-frequency ridge line is 4 times the electrical frequency and / or 6 times the electrical frequency, it is determined that an inter-turn short circuit fault has occurred in the dual three-phase motor, and the starting time of the time-frequency ridge line is taken as the time of fault occurrence. The 4th and / or 6th times the electrical frequency are derived from the following mathematical model: When a two-phase three-phase motor experiences an inter-turn short-circuit fault, let the proportion of the faulty part in the faulty phase be . The short-circuit current is The additional voltage caused by the fault for: ； In the formula, For phase resistance, For the sake of self-reflection, The electric frequency of the motor. The mutual inductance between two phase windings that are spatially separated by 30 electrical degrees is given. Mutual inductance between two phase windings that are spatially separated by 60 electrical degrees; Additional voltage for the fault Perform a harmonic space Clark-Park transform, the transform matrix is: ,get: ； In the formula, Short-circuit current amplitude, For electrical angle, Short-circuit current The phase angle; The transformation result contains Item and The terms correspond to the 4th and 6th harmonic components of the electrical frequency, respectively.

2. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 1, characterized in that, The fifth harmonic spatial current mentioned in step S1 is a time-varying signal of the fifth harmonic spatial d-axis current. Time-varying signal of and / or fifth harmonic space q-axis current .

3. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 2, is characterized in that... The mathematical model for variational mode decomposition described in step S2 is as follows: First, construct the variational constraint problem: ； In the formula, The number of decomposed modes, For the first One eigenmode function ; For the first The center frequencies of the eigenmode functions The extracted fifth harmonic spatial current time-varying signal. or , The unit impulse function; The imaginary unit; Then, a penalty factor is introduced. and Lagrange multipliers The variational constraint problem is transformed into the following augmented Lagrangian function: ； Finally, the augmented Lagrangian function is solved iteratively using the alternating direction multiplier method.

4. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 3, is characterized in that, The number of decomposition modes in the variational mode decomposition =6, penalty factor =2000.

5. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 4, characterized in that, The selection rule for the target mode in step S3 is as follows: for The amplitudes of each modal component curve under healthy conditions were detected, and modal components with amplitudes below 0.02A under healthy conditions were selected. As the target mode.

6. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 5, is characterized in that, Step S4 specifically includes: performing a synchronous compressed wavelet transform on the target mode selected in step S3, and using the transformed time-frequency coefficients as output to obtain the time-frequency diagram of the target mode; the mathematical model of the synchronous compressed wavelet transform is: ； In the formula, For modal components The time-frequency coefficients after synchronous compressed wavelet transform. For the modal components Continuous wavelet transform function under the mother wavelet For wavelet scale, , The translation amount, This is an estimate of the instantaneous frequency. This refers to the instantaneous frequency.

7. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 6, is characterized in that, For the modal components Wavelet coefficients obtained by synchronous compressed wavelet transform The expression is: ； In the formula, It is the complex conjugate of the continuous wavelet transform function under the mother wavelet.

8. The method for diagnosing weak inter-turn short-circuit faults in a dual three-phase motor under varying operating conditions based on VMD-SST according to claim 6, is characterized in that, Instantaneous frequency estimate The expression is: ； In the formula, This indicates taking the real part.

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