System and method for detecting broken bar faults in squirrel cage induction motors - Patents.com

Abstract

A computer-implemented method for detecting broken bar faults in an induction motor during operation is provided, comprising the steps of injecting a frequency modulated continuous wave (FMCW) voltage signal into a voltage source to power the motor, acquiring, in the time domain, signals of stator currents powering the induction motor via an interface, performing a Fourier transform (FT) on the stator currents and the injected FMCW signal to obtain a spectrum of the stator currents and a spectrum of the injected signal, calculating a cross-correlation between the spectrum of the injected signal and the spectrum of the stator currents, and calculating the cross-correlation function at a frequency f=±2(1-s)f 0 and detecting a broken bar fault in the induction motor if the magnitude of the fault signature is greater than a threshold.

Description

[Technical field]

[0001] The present invention relates generally to the field of monitoring electric machines, and more specifically to broken bar fault detection in induction motors using (FMCW) signal injection. [Background technology]

[0002] Broken rotor-bar (BRB) is one of the most common faults in squirrel-cage induction motors. Although BRB failures do not generally lead to immediate failure of the induction motor, they can have serious secondary effects such as poor starting performance, excessive vibration, and torque fluctuations. In some cases, broken pieces can strike the stator windings at high speed, causing catastrophic failure of the winding insulation. Therefore, it is very important to detect BRB failures and perform timely repairs or maintenance.

[0003] To detect BRB faults, motor current signature analysis (MCSA) method is widely used because it is non-invasive and low-cost. When one or more rotor bars break in a squirrel-cage induction motor, the rotor will induce extra frequency components in the stator current during operation due to the rotor asymmetry caused by the broken bars. Therefore, BRB fault detection can be realized by detecting the characteristic frequency components.

[0004] However, there are three major problems that hinder the detection performance. First, the magnitude of the characteristic frequency is relatively small depending on the total number of rotor bars. Second, the characteristic frequency is very close to the power supply frequency, so it is difficult to distinguish the fault signature from the dominant operating frequency components. Third, background noise hinders the detection performance. Due to these practical issues, the characteristic frequency may be buried in the side lobe or noise of the power supply frequency components. Therefore, it is difficult to detect broken bar faults.

[0005] Over the past decades, all kinds of MCSA methods have been developed to improve the detection performance. For example, researchers use signal processing techniques such as ESPRIT, MUSIC, and compressed sensing to achieve high-resolution frequency spectrums that can better separate the feature frequency components. These methods typically require a high signal-to-noise ratio and may not work well in strong noise conditions. As another example, researchers exploit the transient starting process of a motor to detect broken bar faults. In this case, the rotation speed is much lower, so the feature frequency components are better separated from the fundamental frequency. However, this method requires the motor to be restarted, which makes it unsuitable for online monitoring. In addition, the feature frequency also changes during the starting process, so it is difficult to capture the fault feature frequency components in a short time.

[0006] Signal injection methods are widely used for fault detection. For example, Jordi Cusido et al. propose injecting a wideband signal into a motor to measure the system response. Depending on the change in the impulse response, motor faults can be detected. However, this signal injection method lacks theoretical support and physical modeling. In practice, it is unclear how to tell whether the change is due to a fault or noise.

[0007] Therefore, there is a need for a method and system for detecting broken bar faults in squirrel cage induction motors that has improved detection performance. Summary of the Invention

[0008] It is an object of some embodiments of the invention to provide a system and method suitable for performing broken bar fault detection in an induction motor based on analysis of the stator currents powering the induction motor under varying speed and load operation, such that broken bar fault detection can be performed continuously concurrently with the operation of the induction motor without the need to restart the induction motor.

[0009] The main differences between our method and other existing methods are as follows. First, our method is an active sensing method that actively monitors the induced stator current of an injected frequency modulation continuous wave (FMCW) signal, whereas most of the existing methods are passive methods that do not inject a signal. Second, our injected signal is an FMCW signal, whereas other signal injection methods mainly inject narrow pulses rather than FMCW signals. Third, our method aims to extract fault signatures based on physical analysis of motor dynamics and signal processing techniques, and shows superior performance by increasing the magnitude of the fault signature in very noisy conditions, whereas other detection methods rely on very weak fault signatures or changes in stator currents that may be due to noise or other interferences.

[0010] According to some embodiments of the present invention, a method for extracting motor fault signatures by actively injecting an FMCW signal can be provided. The FMCW signal has a small magnitude and a frequency band higher than the fundamental frequency. Since the FMCW signal has a small magnitude, it will not interfere with the operation of the motor. Under broken bar fault conditions, the injected signal will induce another FMCW signal whose frequency band is lower than that of the injected signal. By analyzing the cross-correlation between the injected signal and the induced signal in the frequency domain using signal processing techniques, the fault signature can be robustly extracted even in noisy conditions.

[0011] Some embodiments of the present invention are based on the recognition that motor broken bar fault signatures in stator currents are difficult to extract because their magnitude is small and close to the operating frequency. The present invention can provide a broken bar fault detection method that improves detection performance and sensitivity by injecting a frequency modulated continuous wave (FMCW) signal into the stator voltage. Under broken bar fault conditions, this injected signal will induce another FMCW signal in a certain frequency band that is coherent with the injected signal in the frequency domain but has a lower frequency than that of the injected signal. By analyzing the cross-correlation between the injected signal and the induced signal, the fault signature can be robustly extracted even under strong noise conditions.

[0012] Some embodiments of the computer-implemented method use a dynamic model with a multi-loop equivalent circuit to simulate the stator currents, in which the broken bar fault is modeled by an open circuit of the corresponding branch. The injection signal is simulated by adding an extra term to the stator voltage, and the stator current is simulated and monitored using the dynamic model. We then develop signal processing techniques to extract the fault signature by analyzing the stator current. Simulation results demonstrate that our approach can effectively detect the broken bar fault even in noisy conditions.

[0013] To detect Broken Rotor Bar (BRB) faults, the Motor Current Signature Analysis (MCSA) method can be used because it is non-invasive and low cost. When one or more rotor bars break in a squirrel cage induction motor, the rotor generates a frequency component f in the stator current during operation due to rotor asymmetry. b =(1±2κs)f0, where s is the slip speed, f0 is the power supply frequency, and κ is the harmonic frequency index. Among these extra induced components, the (1-2s)f0 component is the strongest and is typically treated as the characteristic frequency of BRB faults. Therefore, BRB fault detection is realized by detecting the characteristic frequency component (1-2s)f0.

[0014] In addition, there are three major problems that hinder the detection performance. First, the magnitude of the characteristic frequency is relatively small, depending on the total number of rotor bars. For example, for a squirrel-cage motor with 30 rotor bars, the fault component is typically 30-40 dB lower than that of the fundamental power frequency. Second, the characteristic frequency is very close to the power frequency f0. Under steady-state operating conditions, the slip speed s typically ranges from 0.005 to 0.05. For a power supply of f0=50 Hz, the difference between the characteristic frequency and the fundamental frequency f0 can be as small as 0.01 f0=0.5 Hz, so it is difficult to distinguish the fault signature from the dominant operating frequency component. Third, background noise hinders the detection performance. From these practical issues, the characteristic frequency may be buried in the side lobe or noise of the power supply frequency component. Therefore, it is difficult to detect the broken bar fault.

[0015] Some embodiments of the present invention are based on the recognition that under fault conditions, the resulting stator currents powering an induction motor are sparse in the frequency domain because they contain the fundamental frequency of the power source generating the stator current, its harmonics, and fault frequency components caused by the fault.

[0016] According to an embodiment of the present invention, a broken bar fault detection method is provided, which improves the detection performance by injecting an FMCW signal into the stator voltage. Based on the equivalent circuit model, when a broken bar fault occurs in a squirrel-cage induction motor, this injected signal will induce another FMCW signal in a certain frequency band. By analyzing the cross-correlation of the signals, the fault signatures can be well separated and effectively extracted even in strong noise conditions. Simulation results demonstrate that our proposed method can significantly improve the broken bar fault detection performance.

[0017] Additionally, some embodiments of the present invention provide a computer-implemented fault signal measurement method for detecting broken bar faults during operation of an induction motor powered by a stator voltage. In this case, the method uses a processor coupled to a memory storing instructions implementing the method, which when executed by the processor performs steps of the method, the steps including injecting an FMCW signal into the induction motor via an interface, the FMCW signal being modulated such that the FMCW signal is superimposed on a fundamental frequency of the stator voltage, and the method steps further include obtaining, via the interface, a response current signal generated from the induction motor in response to the injected FMCW signal during a frequency sweep period; performing a spectral analysis of the injected FMCW signal and the response current of the induction motor; calculating a cross-correlation between a stator current frequency spectrum of the induction motor and a frequency spectrum of the injected FMCW voltage signal; extracting a fault signature of a broken bar fault from a result of the calculated cross-correlation; and determining that a broken bar fault has occurred in the induction motor if a magnitude of the fault signature is greater than a threshold value.

[0018] Further, in accordance with some embodiments of the present invention, there is provided a fault detection apparatus for detecting a broken bar fault during operation of an induction motor powered by a stator voltage, the fault detection apparatus including an interface connected to a Frequency Modulated Continuous Wave (FMCW) generator and configured to cause a controller of the induction motor to add an FMCW signal to the stator voltage via the FMCW generator, a memory configured to store instructions of a computer-implemented fault signal measurement method for detecting a broken bar fault during operation of an induction motor powered by a stator voltage, and a processor coupled to the memory, the processor configured to execute the instructions implementing the method, the instructions, when executed by the processor, perform steps of the method, the method steps including injecting the FMCW signal into the stator voltage of the induction motor via the interface, the FMCW signal being injecting a signal from the FMCW generator into the stator voltage of the induction motor. The FMCW signal is modulated so as to be superimposed on a fundamental frequency of the stator voltage, and the method steps further include: acquiring a response current signal generated from the induction motor in response to the injected FMCW signal during a frequency sweep period via the interface connected to a sensor disposed in the induction motor; performing a spectral analysis of the injected FMCW signal and the response current of the induction motor; calculating a cross-correlation between a stator current frequency spectrum of the induction motor and a frequency spectrum of the injected FMCW signal; extracting a fault signature of a broken bar fault from a result of the calculated cross-correlation; and determining that a broken bar fault has occurred in the induction motor if the magnitude of the fault signature is greater than a threshold value.

[0019] The presently disclosed embodiments will be further described with reference to the accompanying drawings, in which the drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. [Brief description of the drawings]

[0020] [Figure 1] 1 is a schematic diagram of a system for controlling an induction motor according to an embodiment of the invention. [Figure 2A] FIG. 2 is a diagram showing an equivalent circuit of a stator winding and a rotor in a squirrel-cage induction motor in a normal, healthy state according to an embodiment of the invention. [Figure 2B] FIG. 2 is a diagram showing an equivalent circuit of a stator winding and a rotor in a squirrel-cage induction motor in a normal, healthy state according to an embodiment of the invention. [Figure 2C] FIG. 13 illustrates an equivalent circuit for a broken bar fault condition, according to an embodiment of the invention. [Figure 3A] 5A-5D show stator current spectra for a single high frequency (HF) signal injection under healthy and fault conditions, respectively, according to an embodiment of the invention. [Figure 3B] 5A-5D show stator current spectra for a single high frequency (HF) signal injection under healthy and fault conditions, respectively, according to an embodiment of the invention. [Figure 4A] FIG. 13 is an exemplary plot of stator voltage with and without FMCW signal injection powering an induction motor in a zoomed-in view of time and voltage according to an embodiment of the invention. [Figure 4B] FIG. 13 is an exemplary plot of stator voltage with and without FMCW signal injection powering an induction motor in a zoomed-in view of time and voltage according to an embodiment of the invention. [Figure 5A] 5A-5C are exemplary plots of stator current spectra with FMCW injection under healthy and fault conditions, respectively, according to an embodiment of the invention. [Figure 5B] 5A-5C are exemplary plots of stator current spectra with FMCW injection under healthy and fault conditions, respectively, according to an embodiment of the invention. [Figure 5C] 5A-5C are exemplary plots of spectra processed using cross-correlation analysis for fault signature extraction in healthy and faulty conditions, respectively, according to an embodiment of the invention. [Figure 5D] 5A-5C are exemplary plots of spectra processed using cross-correlation analysis for fault signature extraction in healthy and faulty conditions, respectively, according to an embodiment of the invention. [Figure 6] FIG. 2 is a block diagram of a method for detecting faults in an induction motor in accordance with an embodiment of the present invention. [Figure 7] FIG. 4 is a block diagram of a method for automatically detecting faults in an induction motor according to another embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0021] Description of the embodiments Various embodiments of the present invention will now be described with reference to the drawings. It should be noted that the drawings are not drawn to scale, and that elements of similar structure or function are indicated by similar reference numerals throughout the drawings. It should also be noted that the drawings are intended only to facilitate the description of certain embodiments of the present invention. They are not intended to be exhaustive or to limit the scope of the invention. In addition, aspects described in the context of a particular embodiment of the present invention are not necessarily limited to that embodiment, but may also be practiced in other embodiments of the present invention.

[0022] 1 is a schematic diagram of a fault detection system configuration 10 illustrating an exemplary squirrel cage induction motor according to one embodiment of the invention. The squirrel cage induction motor 100 includes a squirrel cage rotor assembly 102, a stator assembly 104, a main shaft 106, and a main bearing 108. In this example, the induction motor 100 is a squirrel cage induction motor. Broken rotor bars of assembly 102 are a common fault in such induction motors.

[0023] The controller 110 is powered by the power source 120 and can be used to monitor and control the operation of the induction motor 100 in response to various inputs according to embodiments of the present invention. For example, a controller coupled to the induction motor 100 can control the speed of the induction motor based on inputs received from a sensor 130 configured to obtain data regarding the operating conditions of the induction motor 100. According to certain embodiments, the electrical signal sensors can be current and voltage sensors for obtaining current and voltage data regarding the induction motor 100. For example, the current sensor senses current data from one or more of a plurality of phases of the induction motor. More specifically, if the induction motor is a three-phase induction motor, the current and voltage sensors sense current and voltage data from three phases of the three-phase induction motor. Although certain embodiments of the present invention are described with respect to a multi-phase induction motor, other embodiments of the present invention are applicable to other multi-phase electric machine machines.

[0024] The FMCW generator 140 generates an FMCW voltage signal that is small in magnitude (approximately 2% of the power supply voltage). The controller 110 injects the FMCW voltage signal into the power supply signal (FIG. 4A) to power the induction motor 100 for diagnosing the induction motor 100.

[0025] Some embodiments of the present invention describe a system for detecting broken bar faults in an electric machine, such as an induction motor 100. The system configured for detection includes a fault detection module 200 for detecting the presence of fault conditions in various components, including the rotor bars, within an induction motor assembly. The fault detection module 200 can be referred to as a fault detection device. In one embodiment, the fault detection module 200 is implemented as a subsystem of the controller 110. In an alternative embodiment, the fault detection module 200 is implemented using a separate processor. The fault detection module 200 can be a hardware circuit module operably connected to the controller 110. In some implementations, the fault detection module 200 and the controller 110 can share information. For example, the fault detection module 200 can reuse sensor data used by the controller to control the operation of the induction motor.

[0026] Furthermore, the fault detection module 200 includes a processor 210, a memory 220, and a fault detection program 230, which is stored in a storage and uploaded to the memory 220 when instructions of the program 230 are executed by the processor 210. The module 200 further includes an interface 250 configured to acquire signals from the sensor 130. The interface 250 includes the processor 210, the memory 220, the fault detection program 230, a user interface 240, and an A / D (analog / digital) converter and an A / D (analog / digital) converter for data communication with the sensor 130. The processor 210 may be multiple processors, and the memory 220 may be a memory module including multiple memories. The user interface 240 is configured to connect to a keyboard and a display configured to show normal / fault status information of the induction motor 100 in response to an output of the fault detection module 200.

[0027] The presence of a broken bar in induction motor 100 reduces rotor torque and increases reliance on other rotor bars of induction motor 100 to provide the desired current. Increased reliance on other rotor bars causes the other rotor bars to deteriorate at a faster rate, thus affecting the overall performance of the induction motor.

[0028] In one embodiment of the present invention, the current and voltage sensors detect stator current and stator voltage data, respectively, from the stator assembly 104 of the induction motor 100. The current and voltage data obtained from the sensors are communicated to the controller and / or fault detection module for further processing and analysis. The analysis includes performing a motor current signature analysis (MCSA) to detect faults in the induction motor 100 using a cross-correlation based method. In some embodiments, upon detecting a fault using the fault detection module 200, the controller 110 receives a fault detection signal via the interface 250 of the fault detection module 200 and stops operation of the induction motor by sending an interruption signal of the stator voltage of the induction motor 100 to the controller 110 for further inspection or repair. In some cases, the sensor 130 may include a controller interface (not shown) configured to receive the fault detection signal from the interface 250 and send a fault condition signal to the controller 110 such that the controller 110 interrupts the stator voltage of the induction motor 100 to stop operation of the induction motor 100. If the sensor 130 does not include a controller interface, the interface 250 may be configured to connect to the controller 110 such that the controller 110 interrupts the stator voltage of the induction motor 100 to stop operation of the induction motor 100 in response to a fault detection signal from the fault detection module 200 via the interface 250.

[0029] The system also includes a memory for storing the signal measurements, the injected signal, and various parameters and coefficients for performing the cross-correlation analysis, and the system can include a user interface for indicating a fault when a peak component at a frequency near f=-2(1-s)f0 of the cross-correlation function is detected as a fault signature.

[0030] Broken rotor bars (BRB) are one of the most common faults in squirrel cage induction motors. Although BRB failures do not generally lead to immediate failure of the induction motor, they can have serious secondary effects such as poor starting performance, excessive vibration, and torque fluctuations. In some cases, the broken pieces may strike the stator windings at high speed, causing catastrophic failure of the winding insulation. Therefore, it is very important to detect BRB faults and perform timely maintenance.

[0031] To detect BRB faults, the motor current signature analysis (MCSA) method is widely used because it is non-invasive and low-cost. When one or more rotor bars break in a squirrel-cage induction motor, the rotor exhibits a frequency component f in the stator current during operation due to rotor asymmetry. b =(1±2κs)f0, where s is the slip speed, f0 is the power supply frequency, and κ is the harmonic frequency index. Among these extra components, the (1-2s)f0 component is the strongest and is typically treated as the characteristic frequency of BRB faults. Therefore, BRB fault detection using the MCSA method is realized by detecting the characteristic frequency component (1-2s)f0.

[0032] In practice, there are three major problems in detecting the characteristic frequency component. First, the magnitude of the characteristic frequency is relatively small, depending on the total number of rotor bars. For example, for a squirrel-cage motor with 30 rotor bars, the fault component is typically 30-40 dB lower than the fundamental power frequency component. The larger the number of rotor bars, the smaller the relative magnitude of the fault component. Second, the characteristic frequency is very close to the power frequency f0. Under steady-state operating conditions, the slip speed range is typically 0.005-0.05. For a power supply with f0=50 Hz, the difference between the characteristic frequency and the fundamental frequency f0 can be as small as 0.01 f0=0.5 Hz, making it difficult to distinguish the fault signature from the dominant operating frequency component. Third, background noise impedes the detection performance. Due to these practical problems, the characteristic frequency may be buried in the side lobes or noise of the power frequency components.

[0033] Over the past decades, researchers have developed all kinds of MCSA methods to improve the detection performance. For example, studies have used signal processing techniques such as ESPRIT, MUSIC, and compressed sensing to achieve high-resolution frequency spectrums that can well separate the characteristic frequency components. These methods typically require a high signal-to-noise ratio and may not work well in strong noise conditions. As another example, researchers use the starting process of a motor to detect broken bar faults. When the motor speed is increasing from zero to a constant asynchronous speed, the slip speed s decreases from 1 to a small number close to 0. In this case, the characteristic frequency components are well separated from the power frequency components in the frequency domain. However, this method requires the motor to be restarted, which is not favorable for online monitoring. In addition, the characteristic frequency also changes during the starting process, so it is difficult to capture the fault characteristic frequency components in a short time.

[0034] This disclosure proposes a method for extracting motor fault signatures by actively injecting a frequency modulated continuous wave (FMCW) signal. The FMCW signal has a small magnitude and a frequency band higher than the fundamental frequency. Since the FMCW signal has a small magnitude, it will not interfere with the operation of the motor. Under broken bar fault conditions, the injected signal will induce another FMCW signal whose frequency band is lower than that of the injected signal. By analyzing the cross-correlation between the induced and injected signals using signal processing techniques, the fault signature can be robustly extracted even in noisy conditions.

[0035] As an active sensing method, signal injection has been widely used for motor fault detection. For example, a high frequency (HF) sinusoidal signal can be injected into the stator to measure the induced harmonics to detect motor faults. The current spectrum for a healthy motor is shown in Figure 3A, and the current spectrum for a faulty motor is shown in Figure 3B. However, this high frequency signal injection method proves difficult to detect broken bar faults because the magnitude of the induced signal is too small to be detected. In Figure 3B, the magnitude of the fault signature is about 70 dB lower than the operating signal, making it very difficult to detect, especially in a noisy environment.

[0036] The main differences between our proposed method and other existing high-frequency signal injection methods are as follows. First, our injection signal is an FMCW signal, whereas other signal injection methods mainly inject a single high-frequency signal or a narrow-width time-domain pulse. Second, our fault signature extraction process is based on a physical model and signal cross-correlation analysis, rather than simply thresholding frequency components. Third, our fault signature frequencies are located at frequencies around f=±2(1-s)f0 of the cross-correlation function, whereas other MSCA-based methods seek fault signatures at frequency f=(1-2s)f0. In addition, our method exhibits robust performance in noisy environments.

[0037] To validate our method, we build a dynamic model of a squirrel-cage induction motor using a multi-loop equivalent circuit to represent the coupling between the stator and rotor. The stator currents in healthy and faulty conditions are simulated respectively by modifying the corresponding equivalent circuit. Then, we develop signal processing techniques to extract the fault signature. Simulation results demonstrate that our method improves the robustness of broken bar fault detection in strong noisy conditions. Dynamic Model of an Induction Motor

[0038] In a squirrel cage induction motor, the stator consists of three sinusoidally distributed windings, offset by 120° in space. The rotor contains longitudinal conductive bars connected at both ends by short-circuiting rings, giving it a squirrel cage shape. When an induction motor operates, the stator windings create a rotating magnetic field through the rotor, inducing currents in the rotor bars, which generate tangential forces perpendicular to the rotor, resulting in a torque that rotates the shaft.

[0039] In the remainder of this section, we first develop a dynamic model of the motor in normal healthy conditions and then extend it to fault conditions. For simplicity, we neglect magnetic saturation and assume linear magnetic characteristics. We use bold capital letters for matrices, regular capital letters for constant parameters, and lower case letters for time-varying parameters.

[0040] FIG. 2A shows the equivalent circuit of the stator windings, and FIG. 2B shows the equivalent circuit of the rotor in a squirrel-cage induction motor. Assuming there are n rotor bars, the squirrel-cage rotor can be modeled as n+1 independent current loops, of which n are identical circuit loops in the ideal case, each loop consisting of two adjacent rotor bars connected by two end ring sections. The remaining circuit loop is formed by one of the end rings. The rotor current distribution can therefore be expressed in terms of (n+1) independent loop currents, i.e., the n rotor bar loop currents i j (1≦j≦n) one end ring loop current i eIt can be specified in terms of the sum of the above.

number

[0041] It is important to note that while the stator winding resistance in (7) and the stator inductance in (8) are constant under our assumptions, the stator-rotor mutual inductance in (9) varies with the angular position of the rotor, because the mutual inductance is associated with the relative position between the stator windings and the rotor bars, which changes during operation.

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[0042]

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[0043] In summary, equations (1)-(19) form a dynamic model of an induction motor with unknown stator and rotor currents. Given the motor parameters, standard methods such as the fourth-order Runge-Kutta method for solving differential equations can be used to simulate the stator currents during dynamic operation. Fault condition model

[0044] A computer-implemented method according to some embodiments is based on a dynamic model using a multi-loop equivalent circuit to simulate the stator currents of an induction motor. In this case, a broken bar fault is modeled by an open circuit in the corresponding branch. The injection signal is simulated by adding an extra term to the stator voltages, and the stator currents are simulated and monitored using the dynamic model.

[0045] When one bar breaks completely, the associated branch becomes an open circuit. Then, the two associated loops are replaced by a new loop with twice the end ring segments, so the total number of circuit loops is reduced by one. The equivalent circuit of the rotor under fault condition is shown in Figure 2C. As a result, in (11)-(16), the corresponding loops need to be deleted or reconstructed with equivalent parameters.

[0046] Compared with other models such as the dq model, this equivalent circuit model is easier to understand and can flexibly simulate intermediate fault conditions. Motor parameters

[0047] In normal healthy conditions, the inductances and resistances of (7), (8), (9), (15), and (16) can be calculated. We omit the details of the parameter calculations. Instead, we use publicly available parameters in our simulations. FMCW injection based broken bar fault detection

[0048] In this section, we ignore the detailed hardware implementation and focus on fault signature extraction from a signal processing perspective. FMCW signal

[0049]

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[0050]

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[0051]

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[0052] amplitude U iis selected to fold two sides. On the one hand, the amplitude must be small enough so that the injection signal does not interfere with the motor operation. On the other hand, the signal must be large enough so that the induced signal can be detected.

[0053] Figures 4A and 4B are exemplary plots of the stator voltage u a0 (t) in (20) without signal injection for power supply to the induction motor and the stator voltage u a (t) in (23) with FMCW signal injection in the enlarged views of time and voltage according to some embodiments of the invention. It can be seen from Figure 4B that when the FMCW signal is injected into the power supply voltage, the power supply waveform is slightly distorted. Since U i <<U0, the extremely small distortion caused by the injection signal does not affect the motor operation.

[0054] [Number]

[0055] [Number]

[0056] When f1 = 0, that is, when f min = f max = f2, the injection signal becomes a single-frequency signal having a frequency f2, and f2 > f0. Figures 3A and 3B are exemplary plots of the current spectra with and without single-frequency signal injection for power supply to the induction motor according to some embodiments of the invention. However, it has been found that with this high-frequency signal injection method, it is difficult to detect broken bar faults because the magnitude of the induced signal is too small to be detected. In Figure 3B, the magnitude of the fault signature is about 70 dB lower than that of the operating signal, so detection is very difficult especially in a noisy environment.

[0057] [Number]

[0058] If the kth harmonic amplitude is much greater than that of the fundamental frequency, the motor will accelerate to a much higher speed. Since the amplitude of the kth harmonic is not large enough to accelerate the motor speed, the motor will always run at a constant low speed during the starting process.

[0059]

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[0060] When k>>1, the absolute value of the induced frequency is 2(1-s)f0 lower than the injection frequency. Note that this frequency shift 2(1-s)f0 between the injected and induced signals does not depend on the frequency of the injected signal. The magnitude of the induced signal is very small and difficult to detect, but this property can be used to detect faults. When an FMCW voltage signal of a certain band is injected, the frequency band of the induced signal will shift by 2(1-s)f0 to a lower frequency band. Next, the cross-correlation between the injected signal spectrum and the induced signal spectrum is calculated by integrating all frequency components. It is expected that a peak component can be detected at the frequency shift f=-2(1-s)f0.

[0061]

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[0063]

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[0064] Typically, I F,f < i,f and I F,f ​<<I0, that is, the magnitude of the induced fault signal is much smaller than the magnitude of the injection signal and the magnitude of the operating signal.

[0065] Figures 5A and 5B are exemplary plots of the stator current spectrum in the healthy and faulty states, respectively, for FMCW injection according to some embodiments of the present invention, using an injection signal frequency band of 650 Hz to 750 Hz, or the 13th to 15th harmonics of k = 13. It is clear that the magnitude of the induced fault signal of 550 Hz to 650 Hz is more than 20 dB lower than the magnitude of the injection signal, and at 50 Hz it is more than 80 dB lower than the magnitude of the operating signal. Since the magnitude of the fault signal is small, detection is difficult, especially in noisy measurements.

[0066]

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[0068] Figure 6 is a block diagram showing the steps of a fault signal measurement method implemented by a computer for automatically detecting a broken bar fault during the operation of an induction motor powered by a stator voltage. The fault signal measurement method implemented by a computer includes at least the step of injecting an FMCW signal into the stator voltage at 610, the step of receiving a measured value of the stator current at 620, the step of spectral analysis and signal processing at 630, and the step of determining a fault when a fault signature is extracted at 640.

[0069] First, in step 610, an FMCW signal (FIGS. 4A and 4B) is injected into the stator voltage to power a squirrel cage induction motor. During operation, the stator current is measured as shown in equations (32) and (33). Then, the method analyzes the frequency spectrum of the stator current in step 630, as shown in FIG. 5A for a healthy motor and in FIG. 5B for a faulty motor. The cross-correlation between the stator current spectrum and the injected signal spectrum is calculated according to equation (35), and the results are shown in FIG. 5C for a healthy motor and in FIG. 5D for a faulty motor. The fault signature at the frequency f=±2(1-s)f0 of the cross-correlation function is extracted for further evaluation.

[0070] FIG. 7 is a block diagram illustrating the process steps of a computer-implemented fault signal measurement method (fault detection program 230) for automatically detecting faults in an induction motor in accordance with another embodiment of the present invention.

[0071] An FMCW signal is injected into the power supply voltage and the stator current is monitored as shown in equations (32) and (33). In step 730, the frequency spectrum of the stator current (FIG. 5A for healthy motor and FIG. 5B for faulty motor) and the frequency spectrum of the injected signal are analyzed. In step 720, the cross-correlation between the injected signal spectrum and the stator current spectrum is calculated as shown in FIG. 5C for healthy motor and FIG. 5D for faulty motor. Then, the method extracts a fault signature at the frequency f=±2(1-s)f0 of the cross-correlation function in step 740. If the magnitude of the fault signature is greater than the threshold in step 710, a broken bar fault is detected in step 770. In other words, the system determines that a broken bar fault has occurred. Otherwise, the system continues to monitor the stator current for analysis in step 750. In some cases, the threshold can be defined around −50 dB compared to the maximum cross-correlation value.

[0072] The above-described embodiments of the present invention can be implemented in any of numerous ways. For example, the embodiments can be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether located on one computer or distributed across multiple computers, for example in a computer cloud. Such multiple processors can be implemented as an integrated circuit, with one or more processors in an integrated circuit component. However, a processor can be implemented using circuitry in any suitable format.

[0073] Further, it should be understood that the computers may be embodied in any of a number of forms, such as a rack-mounted computer, a desktop computer, a laptop computer, a minicomputer, or a tablet computer. Such computers may be interconnected by one or more networks of any suitable form, such as a local area network or a wide area network, such as an enterprise network or the Internet. Such networks may be based on any suitable technology and may operate according to any suitable protocol, and may include, for example, wireless networks, wired networks, or fiber optic networks.

[0074] Also, embodiments of the invention may be embodied as a method, an example of which is provided. The order of steps performed as part of this method may be determined in any suitable manner. Thus, embodiments may be configured to perform operations in an order different from that illustrated, including performing some operations simultaneously, although in the illustrated embodiment they are shown as a sequence of operations.

[0075] Although the invention has been described in terms of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. It is therefore the object of the appended claims to cover all such variations and modifications which come within the true spirit and scope of the invention.

Claims

1. 1. A computer-implemented fault signal measurement method for detecting broken bar faults during operation of an induction motor powered by a stator voltage, the method using a processor coupled to a memory storing instructions implementing the method, the instructions, when executed by the processor, perform steps of the method, the steps of the method including: injecting a frequency modulated continuous wave (FMCW) signal into the induction motor during operation via an interface, the FMCW signal being modulated such that the FMCW signal is superimposed on a fundamental frequency of the stator voltage, the method steps further comprising: acquiring, via the interface, a response current signal generated by the induction motor in response to the injected FMCW signal during a frequency sweep period; performing a spectral analysis of the injected FMCW signal and the response current of the induction motor; calculating a cross-correlation between a stator current frequency spectrum of the induction motor and a frequency spectrum of the injected FMCW signal; extracting a fault signature of a broken bar fault from the calculated cross-correlation results; and determining that a broken bar fault has occurred in the induction motor if a magnitude of the fault signature is greater than a threshold.

2. The method of claim 1 , wherein the FMCW signal is a modulated frequency continuous sine wave signal.

3. The method of claim 1 , wherein the frequency range of the FMCW signal is configured to be greater than an operating frequency of the induction motor.

4. The method of claim 1 , wherein the induction motor is a squirrel cage induction motor.

5. The method of claim 1 , further comprising the step of interrupting the supply of the stator voltage if the determining step indicates the occurrence of the broken bar fault.

6. 2. The method of claim 1, wherein the acquiring step is performed at a sampling rate of at least twice the highest frequency of the injected FMCW signal, and the acquiring step is performed on a uniform grid to generate a set of samples of a grid of frequencies.

7. The method of claim 1 , wherein the broken bar fault is modeled by an open circuit in a corresponding branch of an equivalent circuit of a rotor in the induction motor.

8. If the equivalent circuit represents n rotor bars, the squirrel cage rotor can be modelled as n+1 independent current loops, of which n are identical circuit loops in the ideal case, each loop consisting of two adjacent rotor bars connected by two end ring sections, and the remaining circuit loops are formed by one of the end rings, so that the rotor current distribution can be modelled in terms of n+1 independent loop currents, i.e., n rotor bar loop currents i ｊ (1≦j≦n) current i of one of the end rings ｅ The method of claim 1 , wherein the method is specified in terms of:

9. The method of claim 1 , wherein the threshold is defined around −50 dB compared to a maximum cross-correlation value. 【Request 10】 【Number 1】 【Request 11】 【Number 2】

12. 1. A fault detection apparatus for detecting a broken bar fault during operation of an induction motor powered by a stator voltage, comprising: an interface connected to a frequency modulated continuous wave (FMCW) generator and configured to cause a controller of the induction motor to add an FMCW signal to the stator voltage via the FMCW generator; a memory configured to store instructions for a computer-implemented fault signal measurement method for detecting a broken bar fault during operation of an induction motor powered by the stator voltage; a processor coupled to the memory, the processor configured to execute the instructions implementing the method, the instructions, when executed by the processor, performing steps of the method, the steps of the method including: injecting the FMCW signal into the stator voltage of the induction motor via the interface, the FMCW signal being modulated such that the FMCW signal is superimposed on a fundamental frequency of the stator voltage, the method steps further comprising: acquiring, during a frequency sweep period, a response current signal generated by the induction motor in response to the injected FMCW signal via the interface connected to a sensor disposed within the induction motor; performing a spectral analysis of the injected FMCW signal and the response current of the induction motor; calculating a cross-correlation between a stator current spectrum of the induction motor and a current spectrum of the injected FMCW signal; extracting a fault signature of a broken bar fault from the calculated cross-correlation results; and determining that a broken bar fault has occurred in the induction motor if the magnitude of the fault signature is greater than a threshold.

13. 13. The fault detection apparatus of claim 12, wherein the FMCW signal is a modulated frequency continuous sine wave signal.

14. The fault detection apparatus of claim 12 , wherein the frequency range of the FMCW signal is configured to be greater than an operating frequency of the induction motor.

15. 13. The fault detection apparatus of claim 12, wherein the induction motor is a squirrel cage induction motor.

16. The fault detection apparatus of claim 12 further comprising the step of interrupting the supply of the stator voltage if the determining step indicates the occurrence of the broken bar fault.

17. 13. The fault detection apparatus of claim 12, wherein the acquiring step is performed at a sampling rate at least twice the highest frequency of the injected FMCW signal, and the acquiring step is performed on a uniform grid to generate a set of samples of a grid of frequencies.

18. The fault detection apparatus of claim 12 , wherein the broken bar fault is modeled by an open circuit in a corresponding branch of an equivalent circuit of a rotor in the induction motor.

19. If the equivalent circuit represents n rotor bars, the squirrel cage rotor can be modelled as n+1 independent current loops, of which n are identical circuit loops in the ideal case, each loop consisting of two adjacent rotor bars connected by two end ring sections, and the remaining circuit loops are formed by one of the end rings, so that the rotor current distribution can be modelled in terms of n+1 independent loop currents, i.e., n rotor bar loop currents i ｊ (1≦j≦n) current i of one of the end rings ｅ 13. The fault detection device of claim 12, wherein the fault detection device is specified in terms of:

20. The fault detection device according to claim 12, wherein the threshold value is defined to be around −50 dB compared to a maximum cross-correlation value. 【Request 21】 【Number 3】 【Request 22】 【Number 4】

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