A method for diagnosing and locating inter-turn short circuit faults in a permanent magnet synchronous motor

Abstract

This invention discloses a method for diagnosing and locating inter-turn short-circuit faults in permanent magnet synchronous motors. This invention requires no additional hardware; it can accurately diagnose whether an inter-turn short-circuit fault has occurred in the motor, quantitatively characterize the severity of the fault, and precisely locate the fault phase based solely on voltage and current signals in the two-phase stator coordinate system (α-β coordinate system). This invention does not require precise models or large amounts of data, is unaffected by environmental interference, provides accurate location, is simple to implement, and has high real-time performance.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet motor fault diagnosis technology, specifically to a method for diagnosing and locating inter-turn short-circuit faults in permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in electric vehicles, rail transportation, aerospace, and other fields due to their high efficiency, high power density, and high torque density. However, high-load operation and the high switching frequency of wide-bandgap devices increase mechanical, thermal, and electrical stresses, leading to frequent inter-turn short circuit faults (ITSFs). Failure to diagnose these faults in a timely manner can result in performance degradation or system downtime, causing economic losses. Therefore, efficient and accurate fault diagnosis methods are crucial for the reliable operation of motors.

[0003] Currently, the diagnosis of inter-turn short-circuit faults in motors mainly includes three methods: mathematical model-based, data-driven, and signal analysis. Mathematical model-based diagnosis compares the expected and actual operating conditions by accurately modeling the motor. Theoretically, if a precise theoretical model of the motor can be constructed, this difference analysis can effectively locate inter-turn short-circuit faults. However, this method is limited by the accuracy of the motor model; changes in motor parameters during operation due to load and temperature can easily lead to model deviations, affecting the accuracy of the diagnosis. In contrast, the data-driven method does not rely on a precise physical model of the motor. Instead, it uses a large amount of data from permanent magnet synchronous motors under various fault levels and operating conditions as its core, employing machine learning or data mining algorithms to uncover potential patterns and regularities in the data, thereby establishing a mapping relationship between data features and fault type and severity. This method depends on the quality and quantity of data and is a black-box model, making it difficult to interpret the diagnostic basis. Signal analysis-based diagnosis utilizes the time-domain and frequency-domain characteristics of electrical, magnetic, force, and thermal signals, analyzing the characteristic signals of the motor through mathematical transformations to determine whether a fault has occurred. This method does not require a large amount of data and an accurate model, but electromagnetic interference in the motor operating environment and the sensor's own error drift can affect the extraction of fault feature signals, leading to misjudgment or missed judgment of faults. Furthermore, the fault location accuracy is limited, making it difficult to accurately determine the specific fault location. Especially in the case of minor faults in multi-phase windings or complex motor structures, it is often necessary to combine it with other methods to increase the complexity and cost of diagnosis. Summary of the Invention

[0004] In view of this, the present invention provides a method for diagnosing and locating inter-turn short-circuit faults in permanent magnet synchronous motors. This method requires no additional hardware and can accurately diagnose whether an inter-turn short-circuit fault has occurred in the motor, quantitatively characterize the severity of the fault, and precisely locate the fault phase based solely on voltage and current signals in the two-phase stator coordinate system (α-β coordinate system). The present invention does not require precise models or large amounts of data, is unaffected by environmental interference, provides accurate location, is simple to implement, and has high real-time performance.

[0005] The method for diagnosing inter-turn short-circuit faults in a permanent magnet synchronous motor according to the present invention includes:

[0006] S1, sample the three-phase current of the motor and transform it to the stator two-phase coordinate system to obtain i α i β ;

[0007] S2, extract i α i β The fundamental wave i α1 i β1 ;

[0008] S3, i α1 Delay by 90° to obtain i α1 e -j90° ;

[0009] S4, calculate the fault factor FI, where the fault factor FI is: i α1 e -j90° with i β1 The absolute value of the difference in one current cycle T s The average of the inner integrals;

[0010] If the fault factor FI is greater than the set threshold Th, it is determined that an inter-turn short circuit fault has occurred.

[0011] Preferably, in S4, the integration operation is implemented using a low-pass filter with a transfer function of 1 / (Ts+1), where s is the Laplace operator and T is the integration time constant.

[0012] Preferably, in step S4, the current frequency of the motor is extracted, and its reciprocal is taken to obtain the period T. S .

[0013] Preferably, the motor current frequency is obtained by converting the actual speed of the motor, performing phase-locked loop operation on the motor current signal, or by performing Fourier transform on the motor current signal and selecting the frequency component with the largest amplitude.

[0014] Preferably, in step S4, the threshold Th is determined in the following manner:

[0015] When the motor is running without faults, multiple sets of data are collected to calculate FI, and the mean value μ of FI is statistically analyzed.FI Standard deviation σ FI Calculate the initial threshold TH0 = μ FI +kσ FI Where k is 2 to 3;

[0016] Based on motor parameters, operating conditions, and minimum short-circuit fault turns ratio μ min Based on the voltage equations of a three-phase permanent magnet motor, estimate I under minimum fault conditions. fmin Based on the failure factors FI and I fmin The relationship FI = 4μI f / 3π is used to calculate FI at the minimum fault condition. min ;

[0017] The set threshold TH is greater than the initial threshold TH0 and less than the minimum fault FI. min .

[0018] Ideally, the severity of inter-turn short-circuit faults can be determined based on the magnitude of the fault factor FI: the larger the fault factor FI, the more severe the inter-turn short-circuit fault.

[0019] Preferably, in step S2, the fundamental frequency is extracted using a bandpass filter, a signal phase-locked loop, or a wavelet transform.

[0020] The present invention also provides a method for locating inter-turn short-circuit faults in a permanent magnet synchronous motor, comprising:

[0021] S-1, sample the dq axis voltage of the motor and transform it to the stator two-phase coordinate system to obtain u. α u β ;

[0022] S-2, extract u α u β fundamental wave u α1 u β1 And by delaying the phase by 90° respectively, u is obtained. α1 e -j90° ,u β1 e -j90° ;

[0023] S-3, u α1 e -j90° and u α1 Convert to DC model to obtain u1, u2; then convert u β1 e -j90° and u β1 Convert to DC model numbers to obtain u3 and u4;

[0024] S-4, calculate the fault factors FI1, FI2, and FI3 as follows:

[0025]

[0026] The fault factors are then labeled to obtain sign(FI1), sign(FI2), and sign(FI3);

[0027] S-5, judged based on the sign of the fault factor:

[0028] When sign(FI1) is greater than 0 and sign(FI2) is less than 0, an inter-turn short circuit fault occurs in phase A.

[0029] When sign(FI2) is greater than 0 and sign(FI3) is greater than 0, an inter-turn short circuit fault occurs in phase B.

[0030] When sign(FI1) is less than 0 and sign(FI3) is less than 0, an inter-turn short circuit fault occurs in phase C.

[0031] Preferably, in S-2, the fundamental frequency is extracted by using a bandpass filter, a signal phase-locked loop, or wavelet transform.

[0032] Preferably, in S-2, an all-pass filter or Hilbert transform is used to achieve a 90° delay in the voltage signal.

[0033] Beneficial effects:

[0034] 1. The fault diagnosis method in this invention uses a current sensor from a conventional motor driver, eliminating the need for additional observers. It diagnoses short-circuit faults solely through the current signal in the two-phase stator coordinate system (α-β coordinate system), thus improving versatility. In signal processing, the Clark transformation is first performed to the α-β coordinate system. Then, the α-axis current is processed with a 90-degree lag to extract fault features. By comparing these features with a preset threshold, the fault can be accurately diagnosed and its severity determined. The diagnostic sensitivity is related to the preset threshold. In practical implementation: signal processing is simple, and some signal processing is necessary for the motor control algorithm, resulting in lower computational load and more efficient real-time performance; the absence of additional sensors reduces hardware costs and interference; and the sensitivity of the method can be adjusted by changing the preset threshold.

[0035] 2. Based on diagnosis, this invention generates a DC signal by delaying the voltage signal output by the current controller by 90 degrees and performing a Park transformation. It defines fault factors (FI1, FI2, FI3) and accurately locates the phase of the motor short circuit fault according to their polarity combination. The signal noise output by the controller is lower, which has less impact on phase judgment. The calculation and judgment rules are simple, which effectively improves the real-time performance of the system.

[0036] 3. This invention integrates diagnosis and location processes. It integrates diagnosis and location through a unified signal processing process, and shares the signal acquisition and processing module with the normal drive control part of the motor, which simplifies the system design. It can also locate the fault phase while diagnosing the fault. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of an inter-turn short circuit in phase A of a permanent magnet synchronous motor.

[0038] Figure 2 This is a flowchart for diagnosing inter-turn short circuit faults in a permanent magnet synchronous motor.

[0039] Figure 3 A flowchart for locating inter-turn short-circuit faults in a permanent magnet synchronous motor. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0041] This invention provides a method for diagnosing and locating inter-turn short-circuit faults in permanent magnet synchronous motors.

[0042] 1. Diagnosis of inter-turn short circuit faults

[0043] This invention first analyzes the equivalent circuit model of a permanent magnet synchronous motor when an inter-turn short circuit fault occurs. Taking an inter-turn short circuit in phase A as an example, its equivalent circuit diagram is as follows: Figure 1 As shown, phase A winding is divided into a healthy section and a faulty section. The resistance, inductance, and back electromotive force of the healthy section are represented by R. ah L ah and e ah The resistance, inductance, and back electromotive force of the faulty component are represented by R. af L af and e af R f The contact resistance for inter-turn short-circuit faults, R, is used to characterize the degree of insulation degradation. f The smaller the value, the greater the degree of insulation damage. f Contact resistance R f The current in the branch. R x L x e x These represent the resistance, inductance, and back EMF of phase x of the motor, respectively. The short-circuit turns ratio is defined as μ = N. c / N s , indicating the number of turns where an inter-turn short-circuit fault occurred (N) c ) and the total number of turns of the motor phase winding (N) s The larger the value of μ, the deeper the short circuit fault.

[0044] When a short-circuit fault occurs in phase A of the motor, the voltage equation in the stator two-phase coordinate system can be expressed as:

[0045]

[0046] Among them, u α ,u β These are the α-β axis voltages of the motor, R s i is the phase resistance of the motor. α i β These are the α-β axis currents of the motor, L d Let θ be the inductance of the motor's direct shaft. e ω is the electrical angle of the motor. e Let ψ be the electrical angular velocity of the motor. f For permanent magnet flux linkage, i f The fault current of the motor is expressed as:

[0047]

[0048] The fault current i introduced by the inter-turn short circuit fault f This will cause distortion of the α-β plane current. Under fault-free conditions, the α-β axis currents are sinusoidal currents of equal amplitude and orthogonal to each other.

[0049]

[0050] Among them, i q This represents the q-axis current of the motor.

[0051] After a short circuit occurs between turns in phase A, the α-β axis currents are:

[0052]

[0053] Among them, i αh and i βh For the fault-free α-β plane current, i αf and i βf Let α be the plane current after an inter-turn short-circuit fault occurs in phase A. It can be seen that when an inter-turn short-circuit fault occurs in phase A of the motor, the α-axis current is equivalent to a superposition of (-2μ / 3)i in healthy mode. f The fault current is the β-axis current, while the β-axis current remains at the fault-free current value.

[0054] Considering only the fault current i f The fundamental component, the fault current expression is:

[0055] i f =-I f sin(θ e +θ k )

[0056] Among them, I f For fault current i f The amplitude, θ k (k = a, b, c) represents the phase of the fault current.

[0057] Based on the above analysis, the α-β plane current under phase A inter-turn short-circuit fault can be expressed as:

[0058]

[0059] Since the α-β axis currents are sinusoidal signals, directly extracting fault characteristics is difficult. However, by designing an all-pass filter, using Hilbert transform, or other methods, the phase of the α-axis current can be delayed by 90° to make it in phase with the β-axis current. Then, subtracting the β-axis current from the α-axis current with the 90° phase delay allows extraction of the relevant fault current I. f Fault characteristics.

[0060] will i α With a phase lag of 90°, we get:

[0061]

[0062] Among them, i α e -j90° This is the result of a 90° phase delay for the current along the α axis. At this point, i α e -j90° with i β If they are in phase, subtracting the two will yield the relevant fault current I. f The fault characteristics are shown in the following formula:

[0063]

[0064] To intuitively characterize the severity of the fault, the absolute values ​​of the above fault characteristics are taken and integrated over one current cycle, and the average is obtained to obtain the fault factor FI:

[0065]

[0066] The integral term in the above formula amplifies the low-frequency noise in the sampled current, causing some interference to the result. Therefore, a low-pass filter (transfer function 1 / (Ts+1)) is used to replace the integral (transfer function 1 / s), where T is the time constant, which is related to the bandwidth of the low-pass filter. It can be set according to the actual motor operating conditions to achieve a better integration effect without excessively amplifying the low-frequency noise of the current.

[0067] On the other hand, during the operation of the motor, the time T of one current cycle S It may not be possible to determine precisely, but it can be estimated based on the motor's current frequency. Estimate TS The main methods are: (1) Utilizing the relationship between motor speed and current frequency, measure the actual speed of the motor, convert it to the current frequency of the motor, and take the reciprocal to obtain the period T. S (2) The current frequency can be extracted by performing a phase-locked loop operation on the motor current signal, and the period T can be obtained by taking the reciprocal. S (3) The motor current signal can be Fourier transformed, and the frequency component with the largest amplitude can be selected to obtain the fundamental frequency of the current. Taking the reciprocal gives the period T. S .

[0068] This fault factor is only related to the short-circuit turns ratio and the magnitude of the fault current, where T s This is one current cycle, and this is a constant value. The above analysis is derived using an inter-turn short-circuit fault in phase A as an example. Due to the symmetry of the three phases of the motor, it is easy to obtain that when inter-turn short-circuit faults occur in phases B and C, i... α e -j90° -i β The value of the fault factor FI is 4μI, which is the product of the fault current and the fundamental frequency cosine function, which is 2μ / 3 times the absolute value of the product. f / 3π. This indicates that regardless of which phase of the three-phase permanent magnet motor experiences an inter-turn short-circuit fault, as long as the fault severity is the same, i.e., μ and R... f If the fault factor FI is the same, it will show the same value. Therefore, the fault factor FI can be used as a fault indication to diagnose whether an inter-turn short circuit fault has occurred in the motor and to determine the severity of the motor fault.

[0069] In practical judgment, a preset threshold TH can be used to compare the calculated FI with TH for judgment. However, the value of TH determines the sensitivity of this method. When TH is too high, its sensitivity is low, and it may miss minor faults. When TH is too low, the method is highly sensitive and easily affected by signal noise, thus leading to false fault reports.

[0070] The goal of setting up a TH (Head of Detection) is to distinguish between normal operating conditions (no faults, FI≈0) and fault conditions (FI>0), while balancing false alarm rate and false negative rate. Below are the specific methods and considerations for setting up a TH:

[0071] 1. First, in the fault-free state, μ and I... f All values ​​are 0, and theoretically FI is 0 at this point. However, in practice, due to noise, sensor errors, and system non-ideals, FI may not be 0. The motor can be run without faults, and multiple sets of data can be collected to calculate FI. The mean value μ of FI can then be calculated. FI Standard deviation σ FI Set the initial threshold TH0 = μ FI +kσ FIk can be selected from 2 to 3 (for confidence intervals of 95% to 99%) to avoid false alarms.

[0072] 2. Determine the minimum level of fault that TH can detect (i.e., the minimum μ and I). f First, based on the motor parameters and operating conditions, estimate I during the minimum fault condition. f Calculate the FI at the corresponding minimum fault. min .

[0073] In summary, TH is set slightly higher than the initial threshold TH0, but lower than the minimum fault FI. min Furthermore, the operating results of the motor under different working conditions can be appropriately adjusted based on the above.

[0074] 2. Phase location of inter-turn short circuit fault

[0075] To locate the fault phase, this invention utilizes α-β plane voltage signals for analysis. In the absence of a fault, the α-β plane voltage signals are sinusoidal signals with equal and orthogonal amplitudes, corresponding to the following α-β plane voltage expression:

[0076]

[0077] in, θ e For the electrical angle of the motor; u d u q These are the voltages on the direct shaft and quadrature shaft of the motor, respectively; This represents the phase of the voltage.

[0078] Based on the above formula, the α-β plane voltages when inter-turn short-circuit faults occur in phases A, B, and C are expressed as follows:

[0079] Phase A short circuit fault:

[0080]

[0081] Phase B short circuit fault:

[0082]

[0083] C-phase short circuit fault:

[0084]

[0085] in, R s ω is the stator resistance of the motor. e L is the electrical angular velocity of the motor. d The inductance of the motor is the quadrature axis inductance.

[0086] Since the α-β plane voltages are mutually orthogonal sinusoidal quantities, they cannot be directly processed to extract fault features. Even after a 90° phase delay, the resulting variables are still sinusoidal and need to be converted into DC quantities for fault feature extraction, thereby distinguishing the different phases of short-circuit fault occurrence. The 90° voltage signal delay can be achieved by designing an all-pass filter, using Hilbert transform, or other methods.

[0087] Furthermore, regarding the u when an inter-turn short-circuit fault occurs in phases A, B, and C... α and u α e -j90° u β and u β e -j90° Perform the Park transformation as shown in the following equation.

[0088]

[0089] The results of u1, u2, u3, u4 corresponding to short-circuit faults in different phases are shown in Table 1.

[0090] Table 1

[0091]

[0092]

[0093] The failure factor is defined as shown in the following formula.

[0094]

[0095] The calculated failure factors FI1, FI2, and FI3 are shown in Table 2.

[0096] Table 2

[0097]

[0098] As can be easily seen from the results in Table 2, the phase in which the inter-turn short circuit occurs can be located based on the polarity of FI1, FI2, and FI3. When a short circuit fault occurs in phase A, FI1 is positive and FI2 is negative; when a short circuit fault occurs in phase B, FI2 and FI3 are positive; and when a short circuit fault occurs in phase C, FI1 and FI3 are negative.

[0099] 3. Implementation Steps

[0100] 3.1 Fault Diagnosis Process (See Reference) Figure 2 )

[0101] Step 1: Sample the three-phase current of the motor and obtain the two-phase stator current information i using Clark transform. α i β .

[0102] Step 2, extract i α i β The fundamental frequency signal is used to obtain i α1 i β1 .

[0103] Since the sampled current includes not only the fundamental signal but also interference from higher harmonics, if the sampled three-phase current signal contains too much interference, the transformed i α i β Errors may occur, affecting the accuracy of fault factor calculation. The calculation of the fault factor is related to the fundamental current signal, while higher harmonics or other irrelevant signal components are often unrelated to fault characteristics and may even obscure fault information. By extracting the fundamental signal, we can directly focus on the signal components most relevant to the fault, significantly reducing these interferences and ensuring the accuracy of signal processing. Methods for extracting the fundamental signal mainly include: designing bandpass filters near the fundamental, designing signal phase-locked loops, and wavelet transform.

[0104] Step 3, delay the current along the α-axis by 90 degrees to obtain i α1 e -j90° If a short circuit fault occurs at this time, i α1 e -j90° The difference between the current and the β-axis current should be:

[0105]

[0106] Step 3: Since the signal is still sinusoidal AC at this point, for ease of comparison, we take the absolute value of the above equation and integrate it to obtain the fault factor FI:

[0107]

[0108] Step 4: When a short-circuit fault occurs, the integral of the above equation should be 4μI. f / 3π, where μ represents the degree of short-circuit fault. Therefore, by setting a threshold TH, the result of the integral of the above formula can be compared with TH to determine whether a short-circuit fault has occurred.

[0109] 3.2 Fault Location Process (See Reference) Figure 3 )

[0110] Step 1: Extract the dq-axis voltage of the motor and perform an inverse Park transformation to obtain the voltage signal u in the two-phase stator coordinate system. α u β .

[0111] Step 2, extract the fundamental signal to obtain u α1 u β1 The two-phase fundamental voltage signals are used to obtain uα1 u β1 u is obtained by delaying the phase by ninety degrees respectively. α1 e -j90° and u β1 e -j90° .

[0112] The core of fault phase localization lies in converting the α-β plane voltage signal into a DC signal using the Park transform, and determining the phase of the fault based on the polarity of the fault factors (FI1, FI2, FI3). If the input signal contains high-frequency noise or harmonic components, the result of the Park transform may no longer be a stable DC signal, but rather a signal with fluctuations or distortions, which will interfere with the determination of the polarity of the fault factors. By extracting the fundamental frequency signal, the stability of the transformed signal can be ensured, thereby improving the calculation accuracy of the fault factors and the accuracy of fault phase localization. Methods for extracting the fundamental frequency signal mainly include: designing bandpass filters near the fundamental frequency, designing signal phase-locked loops, and wavelet transform.

[0113] Step 3, convert the two sets of AC signals that are 90° apart: u α1 e -j90° and u α1 u β1 e -j90° and u β1 Perform a Park conversion to obtain DC models u1, u2, u3, u4.

[0114] Step 4, calculate the fault factors FI1, FI2, and FI3 as follows:

[0115]

[0116] The fault factors are then labeled to obtain sign(FI1), sign(FI2), and sign(FI3).

[0117] Step 5: Determine the fault based on the sign of the fault factor: when sign(FI1) is greater than 0 and when sign(FI2) is less than 0, phase A has an inter-turn short circuit fault; otherwise, when sign(FI3) is greater than 0, phase B has an inter-turn short circuit fault; otherwise, phase C has an inter-turn short circuit fault.

[0118] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for diagnosing inter-turn short-circuit faults in a permanent magnet synchronous motor, characterized in that, include: S1, sample the three-phase current of the motor and transform it to the stator two-phase coordinate system to obtain i α i β ; S2, extract i α i β The fundamental wave i α1 i β1 ; S3, i α1 Delay by 90° to obtain i α1 e -j90° ; S4, calculate the fault factor FI, where the fault factor FI is: i α1 e -j90° with i β1 The absolute value of the difference in one current cycle T s The average of the inner integrals; If the fault factor FI is greater than the set threshold Th, it is determined that an inter-turn short circuit fault has occurred.

2. The method as described in claim 1, characterized in that, In S4, the integration operation is implemented using a low-pass filter, whose transfer function is 1 / (Ts+1), where s is the Laplace operator and T is the integration time constant.

3. The method as described in claim 1 or 2, characterized in that, In step S4, the current frequency of the motor is extracted, and its reciprocal is taken to obtain the period T. S .

4. The method as described in claim 3, characterized in that, The motor current frequency is obtained by converting the actual speed of the motor, performing phase-locked loop calculations on the motor current signal, or by performing a Fourier transform on the motor current signal and selecting the frequency component with the largest amplitude.

5. The method as described in claim 1, characterized in that, In step S4, the threshold Th is determined in the following manner: When the motor is running without faults, multiple sets of data are collected to calculate FI, and the mean value μ of FI is statistically analyzed. FI Standard deviation σ FI Calculate the initial threshold TH0 = μ FI +kσ FI Where k is 2 to 3; Based on motor parameters, operating conditions, and minimum short-circuit fault turns ratio μ min Based on the voltage equations of a three-phase permanent magnet motor, estimate I under minimum fault conditions. fmin Based on the failure factors FI and I fmin The relationship FI = 4μI f / 3π is used to calculate FI at the minimum fault condition. min ; The set threshold Th is greater than the initial threshold TH0 and less than the minimum fault FI. min .

6. The method as described in claim 1, characterized in that, The severity of inter-turn short circuit faults can be determined by the magnitude of the fault factor FI: the larger the fault factor FI, the more severe the inter-turn short circuit fault.

7. The method as described in claim 1, characterized in that, In S2, the fundamental frequency is extracted through a bandpass filter, a signal phase-locked loop, or wavelet transform.

8. A method for locating inter-turn short-circuit faults in a permanent magnet synchronous motor, characterized in that, include: S-1, sample the dq axis voltage of the motor and transform it to the stator two-phase coordinate system to obtain u. α u β ; S-2, extract u α u β fundamental wave u α1 u β1 And by delaying the phase by 90° respectively, u is obtained. α1 e -j90° ,u β1 e -j90° ; S-3, u α1 e -j90° and u α1 Convert to DC model to obtain u1, u2; then convert u β1 e -j90° and u β1 Convert to DC model numbers to obtain u3 and u4; S-4, calculate the fault factors FI1, FI2, and FI3 as follows: The fault factors are then labeled to obtain sign(FI1), sign(FI2), and sign(FI3); S-5, judged based on the sign of the fault factor: When sign(FI1) is greater than 0 and sign(FI2) is less than 0, an inter-turn short circuit fault occurs in phase A. When sign(FI2) is greater than 0 and sign(FI3) is greater than 0, an inter-turn short circuit fault occurs in phase B. When sign(FI1) is less than 0 and sign(FI3) is less than 0, an inter-turn short circuit fault occurs in phase C.

9. The method as described in claim 8, characterized in that, In S-2, the fundamental frequency is extracted through a bandpass filter, a signal phase-locked loop, or wavelet transform.

10. The method as described in claim 8 or 9, characterized in that, In S-2, an all-pass filter or Hilbert transform is used to achieve a 90° delay in the voltage signal.

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