Coil-turn short-circuit of PMSM influence on the transformed phase voltage frequency pattern

Transcription

1 Adam BIERNAT Warsaw University of Technoogy, Institute of Contro and Industria Eectronic doi:0.599/ Coi-turn short-circuit of PMSM infuence on the transformed phase votage freuency pattern Abstract. In the paper the possibiity of detection of PMSM stator winding turn short-circuit based on changes in transformed phase votage in generating no-oad state of operation is discussed. For this purpose anaysis of induced votage space phasor magnitude time change is used. Diagnostic data is obtained from experimenta testing of PMSM designed for eectrica car appication. Streszczenie. W artyue przeanaizowano możiwość diagnozowania zwarcia zwojowego maszyny synchronicznej z magnesami trwałymi w oparciu o zmiany zachodzące w transformowanym napięciu fazowym podczas pracy generatorowej w stanie jałowym. Anaizie poddana została zmienność czasowa modułu fazora przestrzennego napięcia induowanego. Pomiary diagnostyczne zostały zreaizowane podczas testów aboratoryjnych sinia synchronicznego zaprojetowanego do bezpośredniego napędu samochodu eetrycznego. (Wpływ zwarcia zwojowego na podstawie w Siniu Synchronicznym Magnesami trwałymi na obraz widma transformowanego napięcia fazowego. Keywords: permanent magnet synchronous machine, diagnostics, turn short-circuit faut detection, signa anaysis. Słowa uczowe: sini synchroniczny z magnesami trwałymi, diagnostya, wyrywanie zwarcia zwojowego, anaiza sygnału. Introduction Technica fitness of device and it s user safety coud be achieved by possiby freuent monitoring device technica condition. If technica device contains eectrica machine/machines it is necessary to encompass them by monitoring process. Periodic diagnostic tests (that enabe formuating proper diagnostic verdict and aunching if necessary emergency procedure reuire satisfying stationarity condition of diagnostic signa whie eeping possiby simiar extortions. For this reason diagnostic tests are performed in such a periods of variabe wor cyce that meet above reuirements. Suggested period of wor cyce in case of eectrica machine coud be for exampe oced rotor state [] or no oad state of operation. In the paper possibiity of PMSM winding turn short-circuit diagnosis in no oad generating state of operation is discussed. Diagnostic signa is instantaneous vaue of votage space phasor magnitude. Detection of coi-turn short-circuit on the base of induced votage dissymmetry Turn short-circuit is rated among most freuenty occurred eectrica machines faiure []. Owing to rapid deveopment of such faiure ony possiby eary detection aows to avoid machine breadown. On the other hand eary detection is troubesome due to the fact that in eary stage of deveopment turn short-circuit has negigibe infuence on machine operation. Turn short-circuit eads to oca air gap fux dissymmetry as a resut of appearance of short-circuit current in shorted winding turn forced by votage induced by resutant fux. This dissymmetry which coud be described by additiona forward and bacward rotating fux component that shoud appear aso in phase induced votage. Attention shoud be turned on fact that positive and negative component of particuar phase votage spectrum freuency caused by turn short-circuit reveas ony through the change of its ampitude (sma in the beginning of faiure deveopment that may ead to non unambiguous diagnostic verdicts. Induced votage dissymmetry reveas in deformation of space phasor oci [3] obtaining by transformation of three-phase votages u fa, u fb, u fc arrangement in to orthogona two-phase votage u d, u arrangement with fixed position of reference axes with respect to stator: ( { u fa, u fb, u fc} { u d, u } Deformation of space votage phasor oci reveas time and space variations of space phasor magnitude: ( u (, t ( u ( t ( u ( t d d Orthogona two-phase votage signa: (3 u d d ( t U cos( t u ( t U cos( t d, where: =,, 3,, U U ampitudes of freuency components of order, respectivey for orthogona signa of d and axes, ω, φ - pusation and phase of freuency components of order, contains freuency components that exists in three-phase signa. However space votage phasor magnitude contains new common-differentia freuency components: (4 f (, t A A ( A A d d A d d A A A d A cos( t cos(( t ( cos(( ( t A cos( t cos(( t ( d d ( A A A A cos(( ( t Components of euation (4 formed by difference of radian freuency describe positive whie sum of radian freuency negative components of space phasor. Negative and positive components appear as a resut of not ony PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 93 NR /07 5

2 ampitude difference of adeuate freuency components of three phase signa u fa, u fb, u fc, but aso as a resut of three phase signa adeuate freuency component mutua phase shift change. The ast pecuiarity expain different sensitiveness of space phasor magnitude time change on three phase votage dissymmetry than singe phase time change. Disregarding space variation aows to treat signa u d (α,t as time depending signa shifted in freuency domain by fundamenta harmonic freuency f [4]: jft (5 ud (, t ud ( t e Freuency domain signa u d (t shift by fundamenta harmonic freuency f effectuate in mutua shifting of positive and negative components that exist in phase votage by freuency f. Simpe simuations show proportionaity of negative and positive freuency components ampitude both to chosen phase freuency component ampitude change or to chosen phase freuency component phase change. In case of phase votage odd freuency components divisibe by three ony negative and positive freuency components appear. In case of phase votage odd freuency components non divisibe by three negative or positive freuency components are over imposed on existing freuency component that may ead to ampitude modifications. Comparison of spectrum freuency components ampitude of diagnostic signa for heathy motor and motor with turn short-circuit coud be repaced by finding differences in picture that presents freuency-freuency map (F-F map []. F-F map is created by presentation of spectrum parts in cascade way [4]: (6 X n, m X ( n ( m M ( p where: n =,, 3 N p, eement of spectrum part, N p number of eements in spectrum part, m =,, 3... M p spectrum part, M p number of spectrum parts, whie height of freuency components are mared by appropriatey chosen contour ines. Idea of creation if F-F map is expained on figure. -D map is created on the base of 3-D map by representing ampitude as contour ines. Fig.. Idea of creation of F-F map: a assembing of signa spectrum parts, b resutant 3-D F-F map Spectrum part range is a chosen characteristic freuency f char (ordinate axe describes subseuent spectrum part, abscissa axe describes freuency range of spectrum part. As a measure of F-F map structure reguarization, the mean ampitude vaue of freuency components of range 0 f char and its higher harmonics spaced by f char : M p (7 X sum ( n Γ[ X ( n ( m N p ] M p m where: Γ scae change operation of spectrum freuency components ampitude, determined on the base of spectrum F-F map is proposed [4]. Thus defined ampitude mean vaue is euivaent to synchronous averaging in freuency domain. Motivation for determining mean ampitude vaue of freuency components is attempt to create diagnostic measure that characterize high sensitiveness to chosen freuency component and their higher harmonics ampitude change. It is worth to mention that proposed measure comparativey es sensitive to individua component ampitude change. Anaysis of transformed votage signa of PMSM turn short-circuit Subject of anaysis is ow rotationa speed, three phase synchronous motor with permanent magnets and outer rotor with p = 7 pair of poes (number of rotor permanent magnets is N =34 and N =36 stator teeth [5]. Experiment was performed for heathy and motor and turn short-circuit of one concentrated winding coi. Votage was measured using votage/votage sensors with gavanic separation and freuency range 0 0 Hz for rotationa speed 300 rpm. Fig.. Votage space phasor oci of PMSM: a heathy motor, b motor with turn short-circuit of one concentrated winding coi Mentioned above wea conditionaity dependence between device state feature (arising short-circuit and diagnostic signa parameters confirms comparison of space phasor oci in case of heathy and fauty motor (fig.. Anaysis of votage space phasor magnitude time variation reveas appearance of side bands distant from fundamenta freuency component and it higher harmonics by freuency N f determined by tooth-grove stator 6 PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 93 NR /07

3 structure (on fig. 3b ony the side bands of fundamenta freuency f are mared. Attention shoud be turned to existence of third and ninth fundamenta freuency harmonic in votage space phasor magnitude time variation. This indicate that three phase system deveops ampitude differences and possiby own mutua non-zero phase shift of odd, divisibe by three harmonics due to basic motor dissymmetry. In the PMSM dominant basic dissymmetry is rotor magnetic circuit dissymmetry deveoped by toerance of each individua magnet manufacture. That means that as characteristic freuency common-differentia main freuency components (in this case eua to the product of rotationa freuency f w and number of stator teeth N coud be adopted. On figure 3 ampitude spectrum of phase votage and magnitude of votage space phasor ampitude spectrum with freuency domain shift correction is presented. Freuency shift faciitate comparison with phase votage ampitude spectrum. Fig.3. Heathy motor: a ampitude spectrum of phase votage, b spectrum of magnitude of votage space phasor On figure 4 F-F maps of votage space phasor magnitude ampitude spectrum determined according to ( and ( for heathy and faied motor, shifted by fundamenta freuency f are presented. As characteristic freuency of presented F-F maps doube of common-differentia freuency components of fundamenta freuency f =f w p and rotationa freuency f w that is eua to of product of rotationa freuency and number of stator teeth (p+f w =(N +f w =N f w is adopted. For adopted characteristic freuency F-F maps show highest eve of structure reguarization. Freuency components distant by characteristic freuency form side bands of different intenseness (in the picture of F-F map side bands are visibe as vertica structures distant from each other by rotationa freuency f w and it mutipes. In the spectrum of votage space phasor magnitude apart of above mentioned freuency components, freuency components (mared by gray area that create diagona structure appears. Freuency components that create diagona structure are distant from each other by mutipe of fundamenta freuency f =pf w. They originate in mutua moduation of fundamenta and higher phase votage harmonics. Freuency of dominating diagona structure freuencies are as foow: 6f =5f +f =7f f commondifferentia freuency components of fundamenta and fifth bacward rotating time harmonic or seventh forward rotating time harmonic and f that is common-differentia freuency components of first and eeventh or thirteenth time harmonics Stator turn short-circuit of concentrated coi eads to change in tooth saturation and in conseuence increase of stator dissymmetry. Deepening of stator dissymmetry resuts in ampitude modification of aready existing freuency components and appearance of new ones in form of side bands distant by rotationa freuency f w that are grouped in the centre of gray area. What confirms that discussed stator faiure deepens ampitude differences between phases odd, divided by three harmonics (in this case ninth. On the figure 5 the fragment of 3D F-F map containing freuency components that are subject of greatest modifications is presented. Changes in ampitude spectrum originated in turn short-circuit revea presented on figure 6, determined on the base of F-F map fragment (fig. 5 according to (7 mean vaues of freuency component ampitude ogarithms distant by characteristic freuency. White arrows indicate increase of mean ampitude ogarithm vaues of ninth harmonic of fundamenta freuency and its side bands distant by rotationa freuency f w, proving stator dissymmetry increase. It is interesting that some (indicated by bac arrows mean ampitude ogarithm vaues of freuency components (synchronous with freuency (N +f w as expained earier decrease. PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 93 NR /07 7

4 Fig.4. F-F map of magnitude of votage space phasor spectrum: a heathy motor, b motor with turn short-circuit of one concentrated winding coi Fig.5. Fragment of 3D F-F map with eft sided bands distant by rotationa freuency f w : a heathy motor, b motor with turn short-circuit of one concentrated winding coi (arrows indicate side bands which ampitude changes substantiay 8 PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 93 NR /07

5 Fig.6. Mean vaues of freuency component ampitude ogarithms distant by characteristic freuency: a heathy motor, b Motor with turn short-circuit of one concentrated winding coi Summary Presented in the paper method of diagnostics signa anaysis enabe detection of turn short circuit utiizing measurement of induced votage in no-oad state of operation. Despite of wea conditionaity dependence between turn short-circuit and diagnostic signa parameters proposed F-F map of votage space phasor magnitude spectrum aows to find and interpret signa differences of heathy and fauty motor by narrowing search to particuar map area. Diagnostic measure based on mean vaue of ampitude of freuency components distant by characteristic freuency shows adeuate sensitiveness to anayzed machine faut. Author: dr inż. Adam Biernat, Warsaw University of Technoogy, Institute of Contro and Industria Eectronic, Division of Eectrica Machines, u. Koszyowa 75, Warszawa, E-mai: adam.biernat@ee.pw.edu.p. REFERENCES [] Toiyat H. A., Handi S., Choi S., Meshgin-Ke H.: Eectric Machines modeing, condition monitoring, and faut diagnosis. CRC Press, pp 0-, pp 6-3 ISBN [] Kiman G. B., Premerani W. J., Koeg R. A., Hoeweer D.: A New approach to on-ine turn faut detection in Ac motors. IEEE Transactions on Energy Conversion, Vo. 9 Issue 3 (004 pp [3] Dencer A., Jare T.: Eectric Anaiza drgań prądnicy z magnesami trwałymi na podstawie generowanego napięcia. ogistya 6/04, pp ] Biernat A.: Anaiza sygnałów diagnostycznych maszyn eetrycznych. Oficyna Wydawnicza Poitechnii Warszawsiej, Warszawa 05, ISBN pp [5] Szczypior J., Jaubowsi R., Biernat A.: Eomobiność Innowacyjne i eoogiczne środi transportu, Konstruacja maszyny eetrycznej do bezpośredniego napędu samochodu, Badania maszyny eetrycznej. Wydawnictwa Komuniacji i Łączności, Warszawa 05, ISBN , pp PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 93 NR /07 9