A method for analyzing inter-turn short circuit fault characteristics of a parallel-winding permanent magnet synchronous motor

Abstract

The application discloses a method for analyzing inter-turn short circuit fault characteristics of a parallel winding permanent magnet synchronous motor, and comprises the following steps: step one, obtaining the parameter relationship of each branch circuit according to the equivalent circuit of the PCW PMSM under the ITSC; step two, selecting the negative sequence voltage component, the three-order harmonic of the phase current and the circulating current as the fault characteristics and constructing the model of the negative sequence voltage, the three-order harmonic of the phase current and the circulating current; step three, analyzing the influence of the parallel winding on the ITSC characteristics according to the model of the negative sequence voltage component, the three-order harmonic of the phase current and the circulating current, then analyzing the influence of the fault mode on the phase current and phase voltage characteristics and the influence of the short circuit position on the phase current and phase voltage characteristics according to the model of the negative sequence voltage and the three-order harmonic of the phase current, and finally analyzing the circulating current fault characteristics according to the model of the circulating current. The method has the beneficial effects that the winding configuration, the fault mode and the short circuit position of the ITSC characteristics can be accurately detected, and the evaluation accuracy of the ITSC is improved.

Description

Technical Field

[0001] This invention relates to the field of inter-turn short-circuit fault analysis technology for permanent magnet synchronous motors, and in particular to a method for analyzing the characteristics of inter-turn short-circuit faults in parallel-winding permanent magnet synchronous motors. Background Technology

[0002] In high-power permanent magnet synchronous motors (PMSMs), the stator windings are typically connected in parallel to reduce inverter output voltage and increase power density. Inter-turn short circuit (ITSC) faults are among the most common failures in PMSMs. In PMSMs with parallel windings (PCW), fault currents and circulating currents flow in the phase windings with ITSCs, ultimately leading to additional copper losses, torque ripple, magnet demagnetization, and machine failure. These degrade the reliability of PCW PMSMs in practical applications. Therefore, it is necessary to evaluate ITSCs in PCW PMSMs.

[0003] Motor voltage characteristic analysis (MVSA) and motor current characteristic analysis (MCSA) are widely used in motor condition monitoring and fault detection due to their non-invasiveness, wide adaptability, and ease of characteristic signal acquisition. The magnetomotive force of a short-circuited coil introduces harmonics into the air gap magnetic field of the motor, resulting in fault characteristic harmonics in the phase current and phase voltage that match the number of pole pairs. Regardless of the winding configuration, the third harmonic in the phase current can be used to detect in-terminal fault syndrome (ITSC) with a short-circuited turns percentage of only 2-3%. Furthermore, when ITSC occurs, the ninth harmonic in the phase current increases, and its increment is unaffected by the severity of the fault. On the other hand, the imbalance in stator winding impedance and back electromotive force (EMF) caused by ITSC introduces negative sequence components into the motor phase current and voltage.

[0004] With a reasonable detection threshold, the aforementioned features can detect ITSC in PMSMs with series windings (SCW). However, in the case of PCW PMSMs, the PCW configuration affects the amplitude of the ITSC characteristics in the current and voltage, making it difficult to determine the detection threshold in practical applications. Therefore, the detection methods based on MCSA and MVSA described above perform poorly in PCW PMSMs. Due to the circulating current (icir) and fault current (if) in the ITSC fault phase, the currents in different branches of the fault phase may have different amplitudes and phase angles. Therefore, it is unreasonable to equate PCW with SCW in winding fault analysis. Furthermore, there are two fault modes in PCW PMSMs. One is that the ITSC occurs in a single branch (single-branch fault), and the other is that the ITSC occurs between different branches (branch-branch fault). Therefore, each branch belonging to the fault phase winding should be modeled separately, and the influence of PCW must be considered to determine the detection threshold.

[0005] Compared to SCW PMSM, the total phase current of PCW PMSM is only slightly affected by the initial ITSC, meaning that ITSC becomes more difficult to detect. Furthermore, inter-branch short circuits are more difficult to detect than single-branch short circuits. Although some PCW PMSM models with ITSC have been developed to evaluate fault current, torque ripple, and copper losses caused by ITSC, there are no corresponding methods for detecting ITSC characteristics in terms of winding configuration, fault mode, and short-circuit location. Summary of the Invention

[0006] The purpose of this invention is to solve the above-mentioned problems by designing a method for analyzing the inter-turn short-circuit fault characteristics of a parallel-winding permanent magnet synchronous motor.

[0007] The technical solution of the present invention to achieve the above objectives is a method for analyzing the characteristics of inter-turn short-circuit faults in parallel-winding permanent magnet synchronous motors, the method comprising the following steps:

[0008] Step 1: Obtain the parameter relationships of each branch circuit based on the equivalent circuit of PCW PMSM under ITSC;

[0009] Step 2: Select the negative sequence voltage component, the third harmonic of the phase current, and the circulating current as fault characteristics, and construct models of the negative sequence voltage, the third harmonic of the phase current, and the circulating current based on the parameter relationships of each branch circuit of the equivalent circuit of PCW PMSM under ITSC.

[0010] Step 3: Analyze the impact of parallel windings on ITSC characteristics based on the models of negative sequence voltage components, third harmonic of phase current, and circulating current. Then, analyze the impact of fault modes on phase current and phase voltage characteristics, as well as the impact of short-circuit location on phase current and phase voltage characteristics, based on the models of negative sequence voltage and third harmonic of phase current. Finally, analyze the characteristics of circulating current faults based on the model of circulating current.

[0011] The parameter relationships of each branch circuit in step one are as follows:

[0012] (1)

[0013] In the formula, u represents the number of branches, S1 and S2 represent the faulty branches of phase A, S3 represents the remaining u-2 healthy branches, and r a1 r a2 and r a3 Representing the resistances of S1, S2, and S3 respectively, r s L represents the phase resistance. a1 L a2 and L a3 Let L and S1 represent the inductances of S1, S2, and S3, respectively. sLet e ​​represent the phase inductance, α be a unit vector with a phase of 120°, and e be the phase inductance. a1 e a2 and e a3 These represent the back electromotive forces of the S1, S2, and S3 branch windings, respectively. a e b and e c These represent the back electromotive force of the three-phase windings, ω e λ represents electric angular velocity. pm This indicates the magnetic flux linkage of a permanent magnet.

[0014] The process of constructing the negative sequence voltage component model in step two includes:

[0015] The PCW PMSM model under ITSC is as follows:

[0016] (2)

[0017] Among them, i a1 i a2 and i a3 Let i and represent the currents in S1, S2, and S3, respectively. a i b and i c and -i f This represents the currents of phases a, b, and c, and the fault current, v a1 v a2 and v a3 and represent the voltages of S1, S2, and S3, respectively, v a v b and v c and -v f This represents the voltages of phases a, b, and c, and the voltage of the short-circuit coil, e. af Let L represent the back electromotive force of the short-circuit coil, and j represent the imaginary part. The inductance matrix L and the resistance matrix R are shown in equations (3) and (4), respectively.

[0018] (3)

[0019] (4)

[0020] (5)

[0021] Where x and y range from 0 (neutral point N) to 1 (power supply side), representing the ratio of the number of turns from the neutral point to the short circuit point on branches S1 and S2 to the total number of turns in the branches, which can be used to indicate the short circuit location, M a1a2 M a1a3 M a2a3 M a3af Represents the mutual inductance between the branches of phase a winding, Ma1ha1f M a2ha2f The mutual inductance between the healthy winding and the short-circuited winding of the faulty branch, r a1f L a1f r a2f L a2f These represent the resistance and inductance of the short-circuited windings of S1 and S2, respectively. a1h L a1h r a2h L a2h These represent the resistance and inductance of the healthy windings of S1 and S2, respectively. a3 Indicates the resistance of branch S3;

[0022] Each branch in the faulty phase has the same number of inductance voltage drops and back electromotive force terms; therefore, the voltage equation for the faulty phase branch simplifies to:

[0023] (6)

[0024] Where vβ represents the voltage drop across the inductance and back electromotive force, v a1 v a2 v a3 i a1 i a2 and i a3 Displayed as:

[0025] (7)

[0026] Substituting (1) and (7) into (6), we obtain the current in each branch of the faulty phase as follows:

[0027] (8)

[0028] As shown in equation (8), the current in different branches is determined by the total phase current i a and fault current i f Composition. Substituting (8) into (2), the fault current i f The voltage equation for a motor with ITSC is expressed as follows:

[0029] (9)

[0030] (10)

[0031] in

[0032] (11)

[0033] (12)

[0034] Where Δ represents the equivalent short-circuit turns ratio, and the severity of the ITSC fault is determined by Δ and the fault resistance r. f Sure;

[0035] Even under ITSC conditions, the three-phase currents can be considered balanced, and it can be derived that:

[0036] (13)

[0037] Through symmetrical component analysis, the negative sequence voltage component v can be obtained. – :

[0038] (14).

[0039] The process of constructing the third harmonic model of the phase current in step two includes:

[0040] Assuming the PMSM is powered by an ideal three-phase voltage source, the expression for the third harmonic voltage equation of the ITSC is derived as follows:

[0041] (15)

[0042] in

[0043] (16)

[0044] V a 3nd V b 3nd V c 3nd and i a 3nd i b 3nd i c 3nd ω represents the third harmonic of the phase voltage and current, respectively. 3e It is a cubic angular velocity, e a 3nd e b 3nd e c 3nd The third harmonic represents the phase back electromotive force. V a 3nd V b 3nd V c 3nd i a 3nd i b 3nd i c 3nd ea 3nd e b 3nd and e c 3nd It is shown in (17).

[0045] (17)

[0046] The third harmonic voltage equation for the faulty phase branch is derived as follows:

[0047] (18)

[0048] Among them, V a1 3nd V a2 3nd V a3 3nd i a1 3nd i a2 3nd i a3 3nd These represent the third harmonic of the branch voltage and the third harmonic of the branch current in branches S1, S2, and S3, respectively. β 3nd This represents the voltage drop caused by the inductance, and the back electromotive force and V a1 3nd V a2 3nd V a3 3nd i a1 3nd i a2 3nd i a3 3nd As shown in (19):

[0049] (19)

[0050] Substituting (18) and (19) into (15), we can obtain the third harmonic current of each branch of the faulty phase as follows:

[0051] (20)

[0052] Where i 3nd Representing the third harmonic current in the healthy branch, substituting equation (19) into equation (15), we can obtain the fault current i. f 3nd and fault phase current i a 3nd The third harmonic is:

[0053] (twenty one)

[0054] (twenty two).

[0055] The process of constructing the circulating current model in step two includes:

[0056] The circulating current i cir Defined as the unbalanced current between faulty phase branches, used to detect ITSC faults in PCW PMSMs, according to (8) and (20), the third harmonic of the circulating current i cir 3nd and fundamental component i cir 1st Export as:

[0057] (twenty three)

[0058] (twenty four).

[0059] In step three, the influence of the parallel winding on the ITSC characteristics is analyzed based on the model of negative sequence voltage component, third harmonic of phase current, and circulating current. This is achieved by using equations (14), (22), (23), and (24) to determine the influence of the number of PW branches on the ITSC characteristics in PCWPMSM. Among these equations, the negative sequence voltage (|v - |) and third harmonic current (|i a 3nd |) will decrease as the number of branches (u) increases.

[0060] In step three, the analysis of the impact of fault modes on phase current and phase voltage characteristics based on the model of negative sequence voltage and phase current third harmonic is achieved by determining (14) and (22) that in the PCW PMSM, both the ITSC in a single branch and the branch ITSC of a certain phase can pass the third harmonic i in the phase current. a 3nd and negative sequence voltage v - To detect it.

[0061] In step three, the influence of the short-circuit location on the phase current and phase voltage characteristics is analyzed based on the model of negative sequence voltage and phase current third harmonic. This is determined by (14) and (22) that the ITSC will be affected by the short-circuit location. The closer the short-circuit location is to the middle of the winding, the higher the third harmonic i in the phase current. a 3nd and negative sequence voltage v - The smaller the amplitude.

[0062] In step three, the analysis of the circulating current fault characteristics based on the circulating current model is performed using equations (23) and (24) to determine |i cir 3nd The value of | is minimized when x = 0, while |i cir 3nd |Always higher than|i a 3nd |At different short-circuit locations, and it increases with x.

[0063] Beneficial effects

[0064] A method for analyzing the inter-turn short-circuit fault characteristics of a parallel-winding permanent magnet synchronous motor, prepared using the technical solution of the present invention, has the following advantages:

[0065] Since common fault characteristic signals such as dq voltage, second harmonic current, and second harmonic instantaneous reactive power are all derived from negative sequence voltage and third harmonic phase current, using negative sequence voltage components, third harmonic phase current, and circulating current as fault characteristics to analyze inter-turn short circuit (ITSC) faults in parallel-wound permanent magnet synchronous motors (PMSMs) is widely representative. Circulating current, as a unique stator inter-turn short circuit fault characteristic of parallel-wound permanent magnet synchronous motors, has advantages such as high signal-to-noise ratio and significant changes before and after the fault, which is beneficial for reliable stator inter-turn short circuit fault diagnosis. Attached Figure Description

[0066] Figure 1 This is a flowchart of a method for analyzing the inter-turn short-circuit fault characteristics of a parallel-winding permanent magnet synchronous motor, as described in this invention.

[0067] Figure 2 This is the equivalent circuit diagram of the PCW PMSM described in this invention;

[0068] Figure 3 This is a physical diagram of the experimental apparatus described in Embodiment 1 of the present invention;

[0069] Figure 4 This is the parameter table of the experimental apparatus described in Embodiment 1 of the present invention;

[0070] Figure 5 This is the experimental results table of health and failure labeled with H and F as described in Embodiment 1 of the present invention;

[0071] Figure 6 The different r described in Embodiment 1 of the present invention f Fault characteristic diagram (400 r / min, TL = 2 N∙m, fault severity: Δ = x – y = 1 / 6);

[0072] Figure 7This is a fault characteristic diagram at different speeds as described in Embodiment 1 of the present invention (TL = 2 N∙m. Fault severity: Δ = x – y = 1 / 6).

[0073] Figure 8 The fault characteristic diagrams under different x values ​​described in Embodiment 1 of the present invention are as follows (400 r / min, TL = 2 N∙m, fault severity: Δ = x – y = 1 / 6, rf = 0.1, 0.2Ω).

[0074] Figure 9 This refers to the different short-circuit locations and fault modes described in Embodiment 1 of the present invention. cir 1st (a), i cir 3nd and i a 3nd (b) Amplitude plot (400 r / min, TL = 2 N∙m, fault severity: Δ = x – y = 1 / 6, r f = 0.1Ω);

[0075] Figure 10 The diagram shows the phase current (a) and voltage (b) before and after the ITSC as described in Embodiment 1 of the present invention (400 r / min, TL = 10 N∙m, fault severity: Δ = x – y = 1 / 6, x = 2 / 3, y = 1 / 2, rf = 0.1Ω).

[0076] Figure 11 This is the fundamental component table of the circulating current described in Embodiment 1 of the present invention;

[0077] Figure 12 This is a table showing the ratio of characteristics under fault conditions to characteristics under healthy conditions under operating conditions of 400 r / min and TL = 10 N∙m, as described in Embodiment 1 of the present invention. Detailed Implementation

[0078] Example 1

[0079] The following describes Embodiment 1 of the present invention in detail with reference to the accompanying drawings, such as... Figure 1-11 As shown;

[0080] Build such Figure 3 The experimental setup is shown. The machine load is provided by a magnetic powder brake controlled by a tension controller. Machine parameters (parallel windings) are as follows: Figure 4 As shown.

[0081] The phase winding of the machine under test consists of two coil groups that can be connected in series or parallel. To simulate ITSC, the two coil groups of phase A are divided into six sub-coils, and the two ends of each sub-coil are led out and connected to a junction box. Then, the sub-coils of each coil group are connected in series, and different ITSC severity levels are simulated by shorting different sub-coils with variable resistors.

[0082] A. Evolution of fault characteristics under different winding configurations

[0083] The machine under test operates in constant speed mode under magnetic field orientation control, and ITSCs are simulated under SCW (Case I) and PCW (Case II) respectively.

[0084] The experimental results for health and failure labeled with H and F are as follows: Figure 5 As shown, Case I and Case II have the same fault severity (the ITSC in Case II is a single-branch fault). It can be seen that the phase current and voltage characteristics of the PCW PMSM are not significantly different from those of the SCW PMSM, which is consistent with theoretical analysis.

[0085] PCW PMSM can reduce the demand on inverter output voltage, but it makes ITSC testing more difficult. Therefore, for critical machines, the determination of winding configuration requires a trade-off between inverter output voltage and operational reliability.

[0086] B. Evolution of Fault Characteristics under Different Fault Modes

[0087] To investigate the impact of fault modes on ITSC characteristics, the phase windings of the test machine were connected in parallel. Figure 6 shows the characteristics of single-branch faults and inter-branch faults with the same fault severity, where x = 1 / 6, y = 0 (single-branch fault) and x = 1 / 3, y = 1 / 6 (inter-branch fault). f The minimum value is set to 0.1Ω to avoid motor damage due to excessive fault current. f The maximum value is set to 1Ω to ensure that the ITSC characteristics are sufficiently obvious for easy analysis.

[0088] In Figure 6, it can be seen that |v - |and|i a 3nd |in the range of 0.1 to 1Ω r f Within the range, the single-branch ITSC is higher than the multi-branch ITSC. Therefore, the latter will be more difficult to detect using the characteristics of phase current and voltage, and the determination of the detection threshold should consider the impact of fault modes on ITSC characteristics. Furthermore, when r f When set to 0.1Ω, |v –The difference between |i and |i a 3nd The currents for these two ITSC modes are 0.22V and 0.33A, respectively. However, when r f When set to 1Ω, |v – | Differences and |i a 3nd The currents between these two ITSC modes are 0.02V and 0.03A, respectively, which are close to zero. Therefore, it is difficult to distinguish between the two fault modes in the early stages of ITSC.

[0089] The evolution of ITSC characteristics at different speeds is shown in Figure 10. It can be seen that within the speed range of 100 to 700 rpm, |v - The difference in voltage between the two ITSC modes increases from 0.11V to 0.72V. a 3nd The current increased from 0.09 to 0.37A. The different speed behaviors of these two ITSC modes, to some extent, validate the analysis of the fault current path.

[0090] It is worth noting the |v of the branch fault. - | and |i a 3nd |Always lower than a single fault, with no intersection points, such as Figure 7 As shown. Therefore, ITSC detection thresholds based on branch faults will be effective because they are sensitive to single-branch faults at different speeds. Conversely, detection thresholds based on single-branch faults have higher amplitudes and cannot indicate branch faults.

[0091] C. Evolution of fault characteristics at different short-circuit locations

[0092] To investigate the impact of short-circuit location on inter-branch fault characteristics, ITSC was introduced at x = 1 / 6, 1 / 3, 1 / 2, 2 / 3, 5 / 6, and 1, where Δ = x – y = 1 / 6. a 3nd The evolution of | and |v – The short circuit location is shown in Figure 8. It can be seen that the ITSC short circuit occurs near the electrical center of the winding. - |and|i a 3nd The lowest level means that these faults are more difficult to detect due to their weaker characteristics.

[0093] |i a 3nd The evolution of | and |v –The experimental results showed good agreement between different short-circuit locations and theoretical analyses.

[0094] In practical applications, weaker ITSCs require lower detection thresholds. To detect all possible ITSCs in a PCW PMSM, more sophisticated detection methods may be needed, where determining appropriate detection thresholds is crucial. These thresholds should be high enough to exclude noise and low enough to detect inter-branch short-circuit faults occurring near the electrical midpoint of the winding.

[0095] D. Experimental evaluation of circulating current for fault detection

[0096] The circulating current is measured by a sensor installed on the power supply side of the stator winding. Figure 9 It shows |i cir 1st |、|i cir 3nd |and|i cir 3nd |, where ITSC settings and Figure 11 Same. It can be seen that |i cir 3nd | Always higher than |i a 3nd Even near the neutral point where the difference between them is minimal, |i cir 3nd | Gundam | i a 3nd | is 1.54 times, therefore, |i c ir 3nd Due to its high signal-to-noise ratio, it is more suitable as an indicator for accurately detecting ITSCs.

[0097] As shown in Figure 9(b), when x changes from 1 / 6 to 1, |i cir 3nd The value increases from 0.17A to 4.82A, which is a monotonic relationship, where x = 1 / 6 indicates that the ITSC occurs within a single branch, and x = 1 / 3 indicates that the ITSC occurs between branches. Therefore, |i cir 3nd |More sensitive to inter-branch faults. When x = 1 / 2 and x = 2 / 3, |i cir 3nd The values ​​of | are 1.18A and 1.13A, respectively. Due to their high amplitude and reliable detection, they can effectively indicate inter-branch faults occurring near the electrical midpoint of the phase winding. The experimental results of circulating current characteristics for different fault modes and short-circuit locations agree well with the theoretical analysis results.

[0098] Based on the above analysis, the performance of MCSA and MVSA in detecting PCW PMSMs using ITSCs is limited. As shown in Figure 10, ITSCs occurring near the electrical midpoint of the phase winding only cause slight interference to the motor phase voltage and current. However, the fundamental component of the circulating current is as high as 10.93A, such as... Figure 11 As shown, this leads to significant torque ripple. The characteristics of the ITSC in terms of phase current, phase voltage, and circulating current are shown in Table 3, where healthy and faulty are marked with H and F, respectively. It can be seen that |i a 3nd | Increased from 0.12 to 0.18A and |v – | Under ITSC conditions, the voltage increases only from 0.45 to 0.46 V. (Compared to |v) – | Compared to, |i a 3nd It seems more suitable as a fault detection indicator.

[0099] To further illustrate |v – |and|i a 3nd | When testing the performance of the ITSC, under operating conditions of 400 r / min and TL = 10 N∙m, the ratio of the characteristics under fault conditions to those under healthy conditions is as follows: Figure 12 As shown, it can be seen that |i a 3nd | and |v–| perform well in detecting single-branch faults (x = 0, x = 1), which is attributed to their significant magnitude variations. At this point, |i a 3nd The minimum change rate of | is 1.5, which means that it is possible to monitor |i a 3nd All possible faults were detected, although its low signal-to-noise ratio requires a high-precision current measurement sensor. However, due to |v – The ratio of |v is close to 1, making it impossible to monitor |v|. – | To detect ITSC (x = 1 / 2, x = 2 / 3) occurring near the electrical center of the winding.

[0100] It is worth noting that |i cir 3nd |Increased from 0.33A to 1.17A, and |i cir 1st | Increased from 1.06A to 10.93A, such as Figure 11As shown, this is reliable for fault detection. Without considering the difficulty in measurement, circulating current will be a more reliable indicator of ITSC fault detection than phase current.

[0101] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, the phrase "comprising an element defined as..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0102] The above technical solutions only embody the preferred technical solutions of the present invention. Any modifications that may be made by those skilled in the art to certain parts thereof embody the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method of analyzing inter-turn short circuit fault signature of a parallel wound permanent magnet synchronous machine characterized by, The method comprises the following steps: Step one, obtaining the parameter relationship of each branch circuit according to the equivalent circuit of PCW PMSM under ITSC; Step two, selecting the negative sequence voltage component, the third harmonic of phase current and the circulating current as the fault characteristics, and constructing the model of the negative sequence voltage, the third harmonic of phase current and the circulating current based on the parameter relationship of each branch circuit of the equivalent circuit of PCW PMSM under ITSC, wherein the circulating current is the unbalanced current between the branch circuits of the fault phase; Step three, analyzing the influence of parallel windings on the ITSC characteristics according to the model of the negative sequence voltage component, the third harmonic of phase current and the circulating current, then analyzing the influence of the fault mode on the characteristics of phase current and phase voltage and the influence of the short-circuit position on the characteristics of phase current and phase voltage according to the model of the negative sequence voltage and the third harmonic of phase current, and finally analyzing the fault characteristics of the circulating current according to the model of the circulating current.

2. A method of analyzing inter-turn short circuit fault characteristics of a parallel wound permanent magnet synchronous machine according to claim 1, characterized in that, The parameter relationship of each branch circuit in the step one is: (1) where u denotes the number of branches, S1 and S2 represent the faulty branches of phase A, S3 represents the remaining u-2 healthy branches, r a1 , r a2 , and r a3 represent the resistances of S1, S2, and S3, respectively, r s represents the phase resistance, while L a1 , L a2 , and L a3 represent the inductances of S1, S2, and S3, respectively, L s represents the phase inductance, α is a unit vector with a phase of 120°, e a1 , e a2 , and e a3 represent the counter-electromotive forces of S1, S2, and S3, respectively, e a , e b , and e c represent the counter-electromotive forces of the three-phase winding, ω e represents the electrical angular velocity, and λ pm represents the permanent magnet flux linkage.

3. The method of claim 1, wherein, The process of constructing the model of the negative sequence voltage component in the step two comprises: The PCW PMSM model under ITSC is: (2) where i a1 , i a2 , and i a3 represent the currents of S1, S2, and S3, respectively, i a , i b , and i c represent the currents of a-phase, b-phase, and c-phase, respectively, and i f represents the fault current, v a1 , v a2 , and v a3 represent the voltages of S1, S2, and S3, respectively, v a , v b , and v c represent the voltages of a-phase, b-phase, and c-phase, respectively, and v f represents the short-circuit coil voltage, e af represents the counter electromotive force of the short-circuit coil, j represents the imaginary part, the inductance matrix L and the resistance matrix R are shown in equations (3) and (4), respectively, (3) (4) (5) where x and y range from 0 (neutral point N) to 1 (power supply side), representing the ratio of the number of turns from the neutral point to the short-circuit point on the S1 and S2 branches to the total number of branch turns, can be used to represent the short-circuit position, M a1a2 , M a1a3 , M a2a3 , M a3af represent the mutual inductance between the branches of the a-phase winding, M a1ha1f , M a2ha2f represent the mutual inductance between the healthy part of the fault branch winding and the short-circuit winding, r a1f , L a1f , r a2f , L a2f respectively represent the resistance and inductance of the short-circuited part of the S1 and S2 windings, r a1h , L a1h , r a2h , L a2h respectively represent the resistance and inductance of the healthy part of the S1 and S2 windings, r a3 represents the resistance of the S3 branch; Each branch in the fault phase has the same number of inductance voltage drops and back electromotive force items, therefore, the branch voltage equation of the fault phase is simplified as: (6) where vβ represents the voltage drop of the inductance and back electromotive force, v a1 , v a2 , v a3 , i a1 , i a2 and i a3 are shown as: (7) Substitute (1) and (7) into (6), and the current of each branch of the fault phase is obtained as: (8) As shown in equation (8), the currents of different branches are composed of total phase current i a and fault current i f Substitute equation (8) into equation (2), the fault current i f and the motor voltage equation with ITSC are represented as: (9) (10) Wherein (11) (12) where Δ represents the equivalent short-circuit turn ratio, and the fault severity of ITSC is determined by Δ and the fault resistance r f determined; Even under the condition of ITSC, the three-phase current can be considered to be balanced, and it can be derived that: (13) By symmetrical component analysis, the negative sequence voltage component v – : (14)。 4. The method of claim 1, wherein, The process of constructing the model of the third harmonic of phase current in the step two comprises: Assuming that the PMSM is supplied by an ideal three-phase voltage source, the third harmonic voltage equation expression of ITSC is derived as: (15) Wherein (16) V a 3nd V b 3nd V c 3nd and i a 3nd i b 3nd i c 3nd ω represents the third harmonic of the phase voltage and current, respectively. 3e It is a cubic angular velocity, e a 3nd e b 3nd e c 3nd The third harmonic representing the phase back electromotive force, V a 3nd V b 3nd V c 3nd i a 3nd i b 3nd i c 3nd e a 3nd e b 3nd and e c 3nd It is shown in (17), (17) The third harmonic voltage equation of the branch of the fault phase is derived as: (18) where V a1 3nd , V a2 3nd , V a3 3nd , i a1 3nd , i a2 3nd , i a3 3nd denote the branch voltage third harmonic, the branch current third harmonic of S1, S2, S3, respectively, v β 3nd denote the voltage drop caused by the inductance, and the back electromotive force and V a1 3nd , V a2 3nd , V a3 3nd , i a1 3nd , i a2 3nd , i a3 3nd As shown in (19): (19) Substitute (18) and (19) into (15), and the third harmonic current of each branch of the fault phase can be obtained as: (20) where i 3nd The third harmonic of the fault current i f 3nd and the fault phase current i a 3nd is (21) (22)。 5. The method of claim 1, wherein, The process of constructing the model of the circulating current in the step two comprises: The circulating current i cir defined as the unbalanced current between the faulted phase branches, for detecting the ITSC fault of the PCPMSM, the circulating current third harmonic i cir 3nd and the fundamental component i cir 1st is derived as: (23) (24)。 6. The method of claim 1, wherein, The step three is to analyze the influence of parallel winding on ITSC characteristics according to the model of negative sequence voltage component, three harmonic of phase current and circulating current, which is to determine the influence of PW branch number on ITSC characteristics in PCW PMSM by formula (14), formula (22), formula (23) and formula (24), wherein the negative sequence voltage (|v - ) and the third harmonic current (|i a 3nd ) will decrease with the increase of branch number (u).

7. The method of claim 1, wherein, The step three is to analyze the influence of fault mode on the characteristics of phase current and phase voltage according to the model of negative sequence voltage and third harmonic of phase current. The ITSC in a single branch and the branch ITSC of a certain phase in PCW PMSM can be detected by the third harmonic of phase current i a 3nd and negative sequence voltage v - .

8. The method of claim 1, wherein, According to the model of the third harmonic of the negative sequence voltage and the phase current, the influence of the short-circuit position on the characteristics of the phase current and the phase voltage is analyzed. It is judged from (14) and (22) that the ITSC will be affected by the short-circuit position, and the closer the short-circuit position is to the middle of the winding, the smaller the amplitude of the third harmonic i a 3nd and the negative sequence voltage v - is.

9. The method of claim 1, wherein, The step three is analyzed by formula (23) and formula (24) according to the model of the circulating current, and the value of |i cir 3nd The value of |i cir 3nd The value of |i a 3nd The value of |i

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