Abstract â This paper examines winding faults as short circuit for permanent magnet synchronous motor (PMSM). The study is carried out by means of stator ...
On the short-circuiting Fault Detection in a PMSM by means of Stator Current Transformations J.A. Rosero, L. Romeral, J. Cusidó, A. Garcia, J.A. Ortega MCIA Research Group. Universitat Politècnica de Catalunya. C. Colom 1. 08222 Terrassa. Catalunya. Spain Abstract – This paper examines winding faults as short circuit for permanent magnet synchronous motor (PMSM). The study is carried out by means of stator current harmonic analysis. dq0 current transformation is also used to diagnose the state of the machine, and Wavelet approach is proposed to extend the analysis to the transitory of the failure. Experimental results for the full range of speeds have been obtained, which demonstrate the claims of the paper.
with an appropriate post-control system are main issues of the research. In this paper is carried out the analysis of short circuit failure in the stator winding for 4, 8 and 12 turns; the analysis combine FFT and Wavelet transformations for stator current, and q-axis current, for high, medium and low operation speeds.
Index Terms - PMSM Drives, Fault Detection, Short Circuiting, FFT, Wavelet.
II. MOTOR’S HARMONICS
I. INTRODUCTION
In many applications the failure of a drive has a serious impact on the operation of the system. In some cases the failure results in lost production, whilst in others it may jeopardize human safety. In such applications it is advantageous to use a drive capable of continuing to operate in the presence of any single point failure [1], [2]. Such a drive is termed fault tolerant and the development of a fault tolerant drive is the final aim of the research presented here. Synchronous-type electric motor drives are now extensively used in many industrial applications requiring high system reliability, high efficiency and extended high-speed operation. Such applications include power steering in automotive vehicles, aerospace / aircrafts, robotics and military power drive applications. In many of these critical drive applications, it is required that the drive comprising the motor and the converter, under fault conditions, operates stably and meets base drive needs for a period of time before the system can be (self) – repaired [3]. Stator or armature faults are usually related to insulation failure. In common parlance, they are generally known as phase-to-ground or phase-to-phase faults. It is believed that these faults start as undetected turn-to-turn faults that finally grow and culminate into major ones. In critical applications the drive has to be designed to ensure that it is possible to continue to operate with the fault until the faulted unit can be replaced. Appropriate post fault control must prevent fault propagation and minimize the impact of the fault on the dc link and shaft torque. Short circuit failures are the most important in PMSM [4], thus, that is the biggest failure cause and also for the damages that it would make in the applications of PMSM. In high security applications short circuit fault current in the machine is limited to rated value by designing the machine with a high. phase inductance [1]. This type of failure recaptures a special attention for the fault tolerant drives, and early detection and isolation of faults
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The main harmonics of PMSM become present for the constructive form of electrical machines. These harmonics will have bigger relevance for the case of short circuit in turns of winding; due to the short circuit current breeds an asymmetry in the turnings fields, and induces revolving electromagnetic fields in the air gap. A. Stator harmonics It is well know that is possible to obtain a sinusoidal turning field from n sinusoidal pulsating fields shifted in space and time 2S/n, where the amplitude of the turning field is n/2 times the amplitude of one of the pulsating fields. By this way is possible to obtain a progressive wave. In case of three-phase pulsating fields the next positive and progressive field is obtained, the negative one is cancelled. It is also well know that in systems without neutral point the third harmonic and his multiples became cancelled, and for mechanical and electromagnetically symmetries the pair harmonics are cancelled as well. Other resulting harmonics correspond to teeth spatial distribution, and they produce winding’s pulsating torques, which are called harmonics for stator slots. They are placed in:
f slot
f s (6v r 1)
fv
f · § vp¨ nf s r s ¸ v ¹ ©
(1) fs is the frequency supply and v is an entire number. The main resulting harmonics are 5th, 7th, 11th, 13th, 17th and 19th. The positive sign shows a clockwise sense and for anticlockwise the negative sign is used. Considering a sinusoidal grid supply, with frequency supply fs, a spatial harmonic v has a space period v times lower. The v-spatial harmonic frequency seen from the rotor could be expressed as [5]:
(2) n is the fs frequency supply harmonic and p the pair of poles. The slots harmonics 5th and 7th are seen turning at 6 fs, 11th and 13th turn at 12 fs, etc.
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B. Teeth wave harmonics. The harmonic order is directly related with the slot number twice the polar step, and his magnitude depends on the distribution winding factor [6], [7]. Every stator harmonic creates synchronous torques. These kinds of harmonics are in the order: ª Z º (3) f slot f s «v 1 r 1» p ¬ ¼ Z1 is the stator slots number. C. Asynchronous Parasitic Torques The v harmonic turns at fsQ= r fs/Q from main frequency (fs) and the harmonic slip could be expressed: f sv f r (4) sv 1r v r f sv sv is the harmonic’s v slip and fr is the rotor’s frequency. The induced rotor current frequency for the v harmonic flux from stator back-fem is determined by:
f 2v
f s >1 r v @
(5)
D. Synchronous Harmonics These harmonics appear for mutual action between stator and rotor harmonics having the same order from v and k integer umbers, and then turning with synchronism regarding rotor speed. Particularly, synchronism of teeth harmonics from rotor and stator must be considered, which is expressed by expression (6). Z Z (6) vZ 1 kZ 2 r2 p v 1 r1 k 2 r1 p p Z2 are the rotor slots.
Some experiments have been carried out for different motors with short turns on phase A; the motors were driven at nominal, medium and low speed. TABLE 1 shows the parameters of the motors, which were controlled by a power converter running the control scheme shown in Fig. 1. For tests execution has been manipulated a special winding of the same characteristics of the original and additional outlets in the phase A for 4, 8, and 12 turns. For the motor considered in Table I, power supply from the inverter (for instance, 150 Hz) is three times the rotor frequency in Hz, which is equal to rotor speed (3000 rpm) in rpm divided by sixty. All the following harmonic representations have been related to the base rotor frequency, which changes for every rotor speed. The experiment starts driving the motor to the nominal operation, and then closing the external switch to provoke a short circuiting; after stabilizing the transitory, stator current and speed are measured, and acquisition and processing are done by means Labview application. Figure 2 shows the change in stator current after a short circuit involving 12 windings turns with the motor running at 1500 rpm. Although the stator current increases in only 20%, short circuit current grows more than sixth times the nominal stator current. This value is high enough to affect the operation, and can provoke permanent damage of the motor, even permanent demagnetization. TABLE 1. PMSM NOMINAL DATA
Voltage Speed Torque Pair pole Z1 Z2 Current Resistance Inductance Moment of Inertia Back EMF Constant
III. EXPERIMENTAL RESULTS. The experimental rig for the diagnosis was built with a commercial power converter, running a vector control with magnetizing current id = 0 on a PMSM. Position and speed closed loops were included in the control, as well as data acquisition and supervision (Fig. 1). Man machine interface and diagnostics system was made with Labview software. Signal processing, current transformations, monitoring and data storing were also programmed with the same software.
380 6000 2.3 3 6 18 2.9 2.6 9.6
V rpm N.m
0.000235
kgm²
57.6
Vrms/krpm
poles slots A : mH
Stator current harmonics regarding base rotor speed and main harmonics amplitude are shown in Fig. 3 to Fig. 5, with machine running at nominal torque and 3000 rpm, 1500 rpm and 300 rpm respectively.
Fig. 1. Scheme of a vector control and supervision of PSMM.
Stator harmonics matching (6) are bigger than the rest of teeth’s harmonics, which are the third and fifth (v =2), seventh and fifth again (v=3), and seventh and ninth (v=4), among others. Regarding base rotor speed, these harmonics are the ninth, the fifteenth, the twenty first and the twenty ninth. Apart from mains harmonics sixth, twelfth, and eighteenth (in rotor frequency based spectra), these synchronous harmonics are the most evident in stator current spectra depicted in Fig. 3 to Fig.5.
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Among these series of harmonics, the first synchronous harmonic, the number nine, shows the highest difference regarding main harmonic in a short-circuited machine, even at a low speed.
0
Amplitude (dB)
-20
With more than ten decibels of difference between healthy and faulty machine, its evaluation and quantification seems promising criteria for a fault detection. Whilst it is recognised that stator current harmonics depend on constructive characteristics and power converter and modulation used to drive the motor, the analysis of lower synchronous harmonics can help to a supervisory system to determine the health of the machine, detecting failures in a simple way.
M Healthy M 4 Short turns on phase A M 8 Short turns on phase A M 12 Short turns on phase A
w=300 rpm
-40 -60 -80 0
2
4
6
8
10 12 Harmonics
14
16
18
20
22
Fig. 5. Stator current harmonics for PMSM. 300 rpm.
Figure 6 shows the effect of the short circuit of 12 turns on the q-axis current, with the machine running at 3000 rpm. 50 Hz oscillations are on the q-axis current, and over current spikes appear at frequency of 100 Hz. These effects are not present in a healthy machine, and hence clearly reflect the presence of a short circuit failure in the motor windings. Taking advantage of this effect, q-axis stator current could be analyzed instead of stator current. As short circuiting will lead to higher losses, it seems likely that the system's analysis can be extended to an active q-current. Fig. 7 to Fig. 9 depict q-axis stator current harmonics for a range of rotor speed. It is shown that active current present higher total harmonics distortion than stator current for a faulty motor, for every harmonic considered and for the full range of speed. Current oscillations showed in Fig. 4 provoke torque oscillations, and as a consequence speed oscillations appear as well. FFT of rotor speed could give also information about the failure in the motor, especially at a low seed (Fig. 10).
Fig. 2. PMSM short circuit current. 12 turns shorted, 1500 rpm.
0 w=3000 rpm
M M M M
Amplitude (dB)
-10 -20
Healthy 4 Short turns on phase A 8 Short turns on phase A 12 Short turns on phase A
-30 -40 -50 -60 0
2
4
6
8
10 12 Harmonics
14
16
18
20
22
Fig. 3. Stator current harmonics for PMSM. 3000 rpm. Fig. 6. PMSM q axis current. 12 turns shorted, 3000 rpm. w=1500 rpm
Am plitude (dB)
-10
10
M Healthy M 4 Short turns on phase A M 8 Short turns on phase A M 12 Short turns on phase A
-20 -30
0
Amplitude (dB)
0
-40 -50 -60 -70 0
w=3000 rpm
M Healthy M 4 Short turns M 8 Short turns M 12 Short turns
-10 -20 -30 -40 -50
2
4
6
8
10 12 Harmonics
14
16
18
20
-60 0
22
2
4
6
8
10 12 Harmonics
14
16
18
Fig. 3. q - axis current harmonics for PMSM. 3000 rpm.
Fig. 4. Stator current harmonics for PMSM. 1500 rpm.
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20
22
0 -10
w=1500 rpm
M M M M
Amplitude (dB)
-20 -30
Figure 11 shows the short circuit current harmonics that have been read from the shorted turns. The spectra are referred again to the base rotor speed.
Healthy 4 Short turns 8 Short turns 12 Short turns
Here again the ninth harmonic, which is the first synchronous harmonic of this machine, shows the higher amplitude of the spectra, and it is as high as 20% of the short circuit current.
-40 -50 -60 -70 0
2
4
6
8
10 12 Harmonics
14
16
18
20
22
Fig. 4. q axis current harmonics for PMSM.1500 rpm. 0 -10
w=300 rpm
M M M M
Amplitude (dB)
-20 -30
Detection of short circuit occurrence can be also be done by Discrete Wavelet Transform analysis.
Healthy 4 Short turns 8 Short turns 12 Short turns
The discrete version of Wavelet Transform, DWT, consists in sampling neither the signal nor the transform but sampling the scaling and shifted parameters.
-40
This results in high frequency resolution for lower frequencies and high time resolution for higher frequencies.
-50 -60 -70 0
The previous analysis proves that identification and diagnosis of short circuit turns in stator windings can be done by analyzing synchronous harmonics of the machine, those produced by interaction between stator and rotor teeth harmonics.
2
4
6
8
10 12 Harmonics
14
16
18
20
22
0.35 4.8 5.4 0.3
Amplitude (pu)
Fig. 5. q axis current harmonics for PMSM. 300 rpm. 0 w=300 rpm
Amplitude (dB)
-20
-40
M Healthy M 16 Short turns on phase A M 32 Short turns on phase A
0.2 0.15 0.1 0.05
M M M M
-60
-80 0
0.25
w=1500 rpm
2
4
6
8
10 12 Harmonics
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics
Healthy 4 Short turns on phase A 8 Short turns on phase A 12 Short turns on phase A
14
16
18
20
Fig. 6. Short circuit current harmonics for PMSM.1500 rpm. 22
Fig.10. Speed harmonics for PMSM. 300 rpm.
Yet, the speed oscillations will depend on the bandwidth of speed controllers [8], which can attenuate or modify the effect of the failure. A. Short Circuit Transient To analyze the behaviour of the machine when the sort circuit is appearing, this is provoked after the machine achieves the nominal state, by short circuiting a number of stator turns. The dynamical signal acquired during the pass from normal state to short circuited one is analyzed by means of Meyer Wavelet Transform with seven details. As it has been well demonstrated [9] [10] this transformation is useful in case of variations of base frequency or current amplitude. In these cases, standard FFT can not obtain accurate values of the frequencies in the spectra.
Wavelet transformation can concentrate signal analysis in high frequencies (harmonic fault frequencies) with enough accuracy to detect the fault. Wavelet details 1 to 7 for the short circuit transition are shown in Fig. 12. The motor is running at 300 rpm, and the short circuit appears at 0.7s after data acquisition starting. Although the change in amplitude is very small in acquired signal s (stator current), it is confident the effect on details one to three. The same concussion is obtained from Fig. 13, with the motor running at 1500 rpm. Once again, short circuiting can be diagnosed by analyzing the lower details. As complementary information for fault detection, module of the Continuous Wavelet Transform can be used also to detect the failure, because it increments in more than 40% after the short circuit (Fig. 14).
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TABLE II. RMS VALUE OF LOWER WAVELET DETAILS FOR A SHORT CIRCUIT FAILURE OF 8 SHORTED TURNS.
Speed
Detail 1
Detail 2
Detail 3
rpm
Healthy
Faulty
Healthy
Faulty
Healthy
Faulty
300 1500 3000
0.01 0.04 0.04
0.04 0.09 0.09
0.01 0.04 0.09
0.03 0.08 0.14
0.22 0.17 0.05
0.50 0.25 0.14
V. CONCLUSION
Fig. 12. Wavelet transform from stator current of PMSM with 12 turns shorted at 0.7 sec. 300 rpm.
In Table II is shown as a summary the Wavelet lower details for short circuit failure of 8 turns. It is concluded that these details can be processed during supervision to diagnose and identify short circuit failures in a PMSM.
Short circuit fault detection in a PMSM stator winding has been presented in this paper. Theoretical analysis of the stator current spectra has been presented, and synchronous harmonics have been defined. Experimental results support the claims made in the paper and they prove that these synchronous harmonics are more adequate to detect short circuit failures, especially those of the lower order. By using digital or analogue pass band on-line tuned filter, these harmonics can be used to on-line diagnosis of the machine. Oscillations of q-axis current can be also used to diagnose a short circuit in the motor, although the effects of control loops in these oscillations have not been well analyzed yet. On the other hand, Wavelet analysis of the acquired stator current has proved to be a useful tool for detecting short circuiting appearance, especially by considering lower details of the Wavelet decomposition. In a post fault data processing, an indication of the time occurrence and fault magnitude can be obtained by this way. It is concluded that signal processing of stator harmonics can give accurate information about the faulty or healthy state of the machine, and thus it can be used for fault diagnosis and fault tolerance PMSM electrical drives.
Fig.14. Continuous wavelet modulation from stator current of PMSM with12 short turns. 1500 rpm.
ACKNOWLEDGEMENT
Fig. 13. Wavelet transform coefficients from stator current of PMSM with12 turns shorted. 1500 rpm.
The authors would like to acknowledge the economic support received from the Spanish Ministry of Science and Technology for realizing this work under the DPI 2004-03180 Research Project. Also, the work was supported by the Programme Alban, the European Union Programme of High Level Scholarships for Latin America, scholarship No.E04D027632CO, Mr. J.A. Rosero.
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