Aalborg Universitet Fault etection of a Five-Phase Permanent-Magnet Machine Bianchini, Clauio; Matzen, Torben.; Bianchi, icola; Fornasiero, Emanuele; Bellini, Alberto Publishe in: Proceeings of The 34th Annual Conference of IEEE Inustrial Electronics, 28. IECO 28 DOI (link to publication from Publisher): 1.119/IECO.28.4758125 Publication ate: 28 Document Version Publisher's PDF, also known as Version of recor Link to publication from Aalborg University Citation for publishe version (APA): Bianchini, C., Matzen, T.., Bianchi,., Fornasiero, E., & Bellini, A. (28). Fault etection of a Five-Phase Permanent-Magnet Machine. In Proceeings of The 34th Annual Conference of IEEE Inustrial Electronics, 28. IECO 28 (pp. 12-125). IEEE. https://oi.org/1.119/ieco.28.4758125 General rights Copyright an moral rights for the publications mae accessible in the public portal are retaine by the authors an/or other copyright owners an it is a conition of accessing publications that users recognise an abie by the legal requirements associate with these rights.? Users may ownloa an print one copy of any publication from the public portal for the purpose of private stuy or research.? You may not further istribute the material or use it for any profit-making activity or commercial gain? You may freely istribute the URL ientifying the publication in the public portal? Take own policy If you believe that this ocument breaches copyright please contact us at vbn@aub.aau.k proviing etails, an we will remove access to the work immeiately an investigate your claim. Downloae from vbn.aau.k on: ecember 28, 218
Fault etection of a Five-Phase Permanent-Magnet Machine Clauio Bianchini 1, Emanuele Fornasiero 2, Torben. Matzen 3, icola Bianchi 2, Alberto Bellini 1 1 DISMI - University of Moena an Reggio Emilia, Italy 2 DIE - University of Paova, Italy 3 IET - Aalborg University, Denmark I. ABSTRACT The paper focuses on the fault etection of a five-phase Permanent-Magnet (PM) machine. This machine has been esigne for fault tolerant applications, an it is characterise by a mutual inuctance equal to zero an a high self inuctance, with the purpose to limit the short circuit current. The effects of a limite number of short-circuite turns were investigate by theoretical an Finite Element (FE) analysis, an then a proceure for fault etection has been propose, focusing on the severity of the fault (i.e. the number of shortcircuite turns an the relate current). II. ITRODUCTIO The employment of multiphase machines (phase number greater than 3) fe by multiphase converters can introuce an improvement in the area of meium to high power size rives as they are characterise by a better efficiency, torque/weight an torque/volume ratio compare to three phase machines. With same voltage an power, the increase of the number of phases implies a reuction in the current per phase, thus the thermal stress on the power semiconuctors is inversely proportional to the number of phases. Hence high voltages IGBT can be use with higher switching frequency without parallelisation techniques. Fault-tolerant capability of electrical rives is an essential feature in applications such as automotive [1], aeronautic [2], an many others, where continuous operation is a manatory option. Although less stringent, fault tolerance is a positive feature also in the inustrial environment, ue to the relate prouctivity enhancement. A five-phase PM machine exhibits a high fault-tolerant capability [3], as it can be esigne to reuce the fault occurrence as well as to operate inefinitely in the presence of faults [4]. The egrees of freeom of a multiphase machine can be use to enhance the reliability of the rive, provie that electrical an mechanical fault iagnosis techniques are available. This reunancy might be use for iagnostic purposes. In fact a multiphase machine can continue to operate in case of a phase loss, with a suitable change of power supply, resulting in a reuce torque, but keeping control capabilities. Diagnosis techniques for three phase electric machine have been extensively stuie in the last years with the purpose of etecting the fault at an early state an of compensating its negative effects uring scheule maintenance in orer to avoi unnecessary costs [5], [6]. A fault causes asymmetry in the machine, i.e. it prouces an electrical signal signature that can be etecte by non-invasive techniques base on time omain analysis, frequency analysis an time-frequency analysis. The most common technique, usually referre to as Motor Current Signature Analysis (MCSA), is base on the analysis of the harmonic spectrum of the stator current. It contains information (signature) univocally relate to the presence of electrical an mechanical faults [7] an permit a quantitative analysis of faults [8]. The faults of multiphase machines are similar to those of three-phase machines, they can be grossly classifie into mechanical (bearing failure), or electrical. The main electrical failures of a multiphase rive are Phase winings short-circuit Power switch open-circuit fault Phase open-circuit fault Some scientific papers have investigate the effects of faults in multiphase inverter, the methos of bypassing the faulte components an the compensation techniques to increase the reliability of the rive [9], [1], [11], [12]. However a general approach an a systematic analysis of fault effects an compensation is still not available. This paper proposes a novel fault etection metho for a five-phase PM machine, that is capable of an early etection of open an short circuit faults in a rive with current regulation. The avantages of the propose metho are that it is online an non-invasive an provies alert signals at an early stage. In fact it oes not require any eicate sensor for the fault etection. Moreover a iagnostic inex is propose that provies quantitative information about fault severity an the capability of ientifying the faulty phase in terms of electrical angle. The main rawbacks are that a in case of rives fe by PWM power converters a suitable processing is require to obtain supply voltages an that the measurements of all the phase voltages are require. Moreover the fault etection of this peculiar type of multiphase machine is an har task. Specifically short circuit faults are ifficult to etect, as the short current is limite by the wining resistance, the istortion of the flux is limite, an the asymmetry is very small in case of a low number of shorte turns. The structure of the paper is as follows, at first a moel of the faulty machine is introuce base on the equivalent
transformer moel. Then the accurate FE moelling of the machine is escribe, where FE results are use to compute the PM flux linkage in a faulty phase. Eventually the influence of the faults on machine electric quantities is investigate an a fault etection proceure is propose an valiate by simulation an experiments. III. MODELLIG OF FIVE-PHASE PM MACHIES A five-phase PM machine is use to valiate the propose fault etection metho. The machine features 2 stator slots an 9 magnetic pair poles without skewing. The stator turns are woun aroun the teeth with a single layer, [13]. Each phase has a total number of turns = 692. Fig. 1. Single layer wining istribution. Stator phases are woun with a sequence a, b, c, e, f, a, b, c, e, f an each of them occupies four slots. Each phase is fe by a eicate H-brige converter, Fig. 2. Rate spee an phase current are respectively 333 rpm an I M = 1.2 A. The photos of the five-phase machine stator an rotor are reporte in Fig. 3. Fig. 3. Photo of the stator (left) an rotor (right) of the the five-phase PM machine. with k=, 1,..., 4. λ mk (t) is obtaine from FE computations. Eventually the phase current is expresse by ( i k (t) = I M sin θ + 2 k π ) (3) 5 A current controlle multi-phase rive is use, where symmetrical sinusoial currents are force. Specifically each phase current is inepenently regulate by a hysteresis control that rives the H-brige switches, Fig. 2. IV. MODELLIG A PARTIAL COIL SHORT CIRCUIT FAULT The fault moele is the partial short circuit of a coil, where a part of the turns in a coil is short-circuite ue to eterioration of the insulation. Uner these conitions the faulty phase can be moele aing a short-circuite ummy wining mutually couple to the remaining healthy part of the phase [15]. The moel of a healthy phase is escribe by v = Ri + L i t + λ pm, (4) t where v an i is the phase voltage an current, an the healthy phase parameters are: resistance R, inuctance L an the PM flux linkage λ pm. The partial short circuit is characterise by n, the number of short-circuite turns, where is the total number of turns of the phase. The electrical moel of the fault is shown in Fig. 4. For the ummy wining a linear relationship is assume i R 1 Fig. 2. Schematic representation of a phase of the PM machine. The special esign of Fig. 1 is characterise by a mutual coupling between phases equal to zero, even in the presence of iron saturation [14]. Hence each phase can be moele inepenently. The phase voltage can be expresse by v k (t) = e k (t) + R i k (t) + L i k(t) t the back emf is expresse by e k (t) = λ mk(t) t (1) (2) Fig. 4. fault. Short circuit + v i 2 t (λ pm,1) R 2 t (λ pm,2) L 1 L 2 M Turns: n Turns: n Phase moel of the five-phase PM machine in case of shorte turns between the number of shorte turns n an the resistance
an PM flux linkage, an a quaratic relationship between the number of shorte turns an the inuctance. The electrical parameters for the two winings in Fig. 4 can be expresse as R 1 L 1 λ pm,1 = R n ( = L n = λ pm n R 2 = R n ) 2 ( n L 2 = L (5) ) 2 (6) λ pm,2 = λ pm n. (7) It is assume that no leakage flux is present between the two parts of the coil, so that the mutual inuctance is M = L 1 L 2. Applying the equivalent transformer moel the reuce electrical circuit for the phase can be foun. The equivalent transformer moel is reporte in Fig. 5. + v Fig. 5. i R 1 R 2 t (λ pm,1) L 1 t (λ pm,2) Equivalent moel uner fault conitions. The magnetising inuctance of the moel is equal to the primary inuctance L 1 uner the assumption that no leakage flux is present. The resistance an PM flux linkage on the seconary sie (short-circuite part) referre to the primary sie are R 2 ( n)2 = R (8) n λ n pm,2 = λ pm. (9) A. Fault Influence From the equivalent moel it is possible to establish the parameters variation ue to a fault. The equivalent phase impeance Z eq = R eq + sl eq normalise with respect to the healthy resistance is reporte in Fig. 6 as boe iagrams. Magnitue [B] Phase [ ] 5 4 3 2 1 12 9 6 3 1 1 1 2 1 3 1 4 n=2 n=4 n=3 n=5 n= n=1 n= 1 1 1 2 1 3 1 4 Frequency [Hz] Fig. 6. Boe iagram of the phase impeance Zeq R. n=1 n=3 n=5 For frequencies ω R nl the phase impeance becomes ominantly resistive. For frequencies below, the impeance change are more attenuate. n Hence the etection of a small short circuit e.g. < 5% at low frequencies may be ifficult, as the electrical charateristic of the phase oes not change significantly. Using a high frequency signal (i.e. a frequency above R nl ) is it possible to etect small short circuit faults because the phase impeance angle changes significantly as observe in Fig. 6. n=2 n=4 V. FE MODELLIG OF THE FIVE-PHASE PM MACHIE Fluxes are obtaine from a two imensional Finite Element (FE) analysis [16], neglecting the en wining effects. A cross section of the machine is shown in Fig. 7. The moel of Fig. 5 can be rearrange by means of the Thevenin theorem. With simple computations the equivalent Thevenin parameters for a phase uner fault are obtaine: R eq (ω) = R n 1 + ω 2 L2 n R 2 1 + ω 2( ) nl 2 (1) R ( n ) 2 1 L eq (ω) = L ( ) 2 (11) 1 + ω 2 nl R n λ pm,eq (s) = λ pm 1 1 + nl R s (12) R nl For frequencies ω the resistance an PM flux linkage ecreases linearly an the inuctance quaratic with the number of short circuite turns n. Fig. 7. Cross section of the motor an flux plot.. FE simulation computes the magnetic flux linkages of the machine for each phase at no-loa. To this aim a zero wining current is force while the rotor spins with small angular steps δθ up to a polar pitch equal to 36 / p = 4 egrees.
The choice of the angular step δθ is critical. In fact it is inferiorly limite by the resolution of results, an it is upperly limite by the size of the parts of the assembly. In fact a numerical high frequency noise woul be generate if a very small angular step is use. An angular step δθ =.2 mechanical egrees was chosen as an optimal trae-off. A ynamical moel is use for the machine simulation where the back emf are compute from the fluxes obtaine by FE simulations. The lumpe parameters of the machine, i.e. phase inuctance an resistance are obtaine from measurements. The ynamic moel allows to compute phase voltages as a function of the phase current force by the regulators. The spectral analysis of the voltages allows to compute the signatures in case of faulty conitions. FE simulations in case of shorte turns are mae forcing in the slots where shorte turns occur the short circuit current i 2 (see Fig. 4).The value of shorte current is change as a function of rotor position, as the shorte current epen on t (λ pm,2). Simulation parameters are tune so that the harmonics of the shorte current are the same of the back emf, i.e. funamental, 3r an 5th harmonics. VI. DIAGOSTIC IDEX A solily built iagnostic inex shoul give information about occurring faults in the machine, here consiering asymmetry ue to a partial short circuit. The inex shoul not give a false inication on e.g. healthy harmonic components. It is sensible to analyze the influence cause by a partial coil short circuit using stator fixe orthogonal components. Introucing the transformation from phase components to orthogonal components by the matrix p2o The voltage space vector in αβ system is efine as: v a (t) sv αβ = [ a a 1 a 2 a 3 a 4] v b (t) v c (t) (16) v (t) v e (t) while in α 2 β 2 system it is efine as: sv α2β 2 = [ a a 2 a 4 a 6 a 8] v a (t) v b (t) v c (t) v (t) v e (t) where v i (t) are the phase voltage waveforms. VII. SIMULATIO AD EXPERIMETAL RESULTS A. FE results (17) In case of shorte turns the negative sequence component is increase. In case of open circuit the current of the open phase vanishes, hence the current regulation will try to force all the available voltage, i.e. the DC bus voltage. The fault etection proceure shoul simply monitor the voltages in orer to monitor overcomes the average of the current of a suitable threshol. Simulations were mae relying on the proceure escribe in the previous section, that uses ata from FE computations to provie back emf waveforms to the ynamic simulations. Results valiate the use of the spectrum of the five-phase space vector as a reliable iagnostic inex. Re ( a a 1 a 2 a 3 a 4) p2o = 2 Im ( a a 1 a 2 a 3 a 4) 5 Re ( a a 2 a 4 a 6 a 8) Im ( a a 2 a 4 a 6 a 8), (13) 1 2 1 2 1 2 1 2 1 2 where a = e j 2π 5. Then the orthogonal components v {α,β,α2,β 2,} are obtaine from the phase values as [ vα v β v α2 v β2 v ] T = p2o [ v a v b v c v v e ] T, For frequency analysis in αβ an α 2 β 2 space, the following two complex values are efine as v αβ = v α + jv β (14) v α2β 2 = v α2 + jv β2. (15) There are ifferent variations of the transformation in literature, in particular of the secon set [v α2 v β2 ]. Here the secon set is base on ouble incrementation of a similar to [17]. The other variation is where a triple incrementation of a is use instea [18]. The ifference between using ouble or triple incrementation is inversion of the frequency observe in α 2 β 2 i.e. f α2β 2 = f α3β 3. Besies this, the two variations contains the same information, so they are ientical from the frequency analysis point of view. Fig. 8. Spectrum of sv αβ for the five-phase PM machine in case of healthy machine (blue soli line), n/ = 3 % shorte turns (re soli line), in case of n/ = 6 % shorte turns (green soli line) an n/ = 9 % shorte turns (black soli line). Fig. 8 shows the spectrum of the space vector of sv αβ for the five-phase PM machine in case of healthy machine (main part of the figure) an in case of machine with 2, 4 an 6 shorte turns (on the little winow on the upper left sie of the figure, that is the enlargement of the behaviour aroun the frequency f). Being = 692 it turns out that the percentage of shorte turns is of about 3%, 6% an 9% respectively.
that in this case, the component at 3f increases almost proportionally with the number of the shorte turns. Fig. 9. Polar representation of the space vector sv αβ in case of healthy machine (blue, curve (a)), machine with a short circuit (1%) in the phase 1 (green, curve (b)) an with a short circuit (1%) in the phase 4 (re, curve (c)). B. Experimental results Some experimental tests were mae to valiate the equivalent moel. A prototype five-phase machine was mae where 4 turns have been ae in a coil of one phase, 2 woun in a irection an 2 in the other. In this manner 2 little winings have been introuce, an they have been connecte in series with the main phase wining. In this way the short circuit current an the inuce voltages can be measure in only a portion of the wining. The motor have been spinne at various spee, starting from zero up to 6 rpm. Experiments confirm that for a low number of shortcircuite turns, the circuit impeance is mainly resistive. Fig. 11 shows the measure short circuit current in 2 shortcircuite turns an the inuce voltage in the other 2 opene turns, with a rotating spee of 6 rpm (i.e. about 565.5 ra/s). Inuce voltage an current are in phase, in nice agreement with the moel results. Hence with a low number of shorte turns the reactive part of the impeance is negligible. Short circuit current (A pk ) 5.5 5.1.2.3.4.5 Time (s) Back emf (V) Fig. 11. Short circuit current an back emf with a 2 turns fault Fig. 1. Spectrum of sv α2 β 2 for the five-phase PM machine in case of healthy machine (blue soli line), n/ = 3 % shorte turns (re soli line), in case of n/ = 6 % shorte turns (green soli line) an n/ = 9 % shorte turns (black soli line). Results show that the amplitue of the component at f (in Fig. 8 the supply frequency is f = 5 Hz) increases almost proportionally with the number of shorte turns. On the contrary, the amplitue of other components, at ifferent frequencies, yiel no useful informations for a reliable fault etection. Since the variation of the amplitue of the component at f of sv αβ is significant, it can be an efficient quantitative iagnostic inex. Together with the fault etection, this inex can yiels informations about its severity (i.e. the number of short-circuite turns). The ientification of the faulty phase is possible referring to the polar representation of the space vector sv αβ ; this representation is an ellipse that change the position of its axis accoring to the faulty phase, as Fig. 9 highlights (curve (a) refers to healthy machine, curve (b) to a 1% short circuit on phase 1, curve (c) to a 1% short circuit on phase 4). Fig. 1 shows the spectrum of the sv α2β 2. Results show Full-fault short circuit current an voltage were measure at various spee, connecting the two terminal of the phase uner stuy. Fig. 12 shows a nice agreement between the phase equivalent moel an the measure peak current an voltage in this conition. In first part of Fig. 12 the measure back-emf ecreases more than the moel at spees higher than about 45 rpm. This eviation is probably ue to ey currents. In secon part of Fig. 12 the measure I cc ecreases more than the moel. This eviation is probably ue to a little increase of L 1, moving away from the saturation. In fact, with the whole wining short circuite, the inuce current causes a flux that rives own the PM flux. At high spee, i.e. for high ω, the short circuit current behavior is linear accoring to the equation I cc = λ pm /L 1. In Fig. 13 the whole wining short circuit current an the inuce voltage waveforms in the little wining of 2 turns can be observe at 6 rpm. The phase isplacement between them confirms that with a large number of short-circuite turns the inuctance cannot be neglecte. VIII. COCLUSIOS A five-phase PM machine has been esigne for fault tolerant applications. It is characterise by a mutual inuctance
Bemf Short circuit current (A pk ) Short circuit current (A pk ).35.3.25.2.15.1.5 Measure bemf Compute bemf 1 2 3 4 5 6 3.5 3 2.5 2 1.5 1.5 Measure I cc Compute I cc ω (ra/s) 1 2 3 4 5 6 5 Fig. 13. Fig. 12. ω (ra/s) Short circuit current versus rotation spee.2 5.1.2.3.4.4 Time (s) Short circuit current an back emf with a whole wining fault equal to zero an a high self inuctance, in orer to limit the short circuit current. However, with a limite number of shortcircuite turns the current in the short-circuite turns increases with ω an the behavior is almost purely resistive, so that back emf an current are in phase. Only the resistance limits the short circuit current, thus it is manatory to etect quickly the fault in case of a limite number of short-circuite turns. A eicate moel was evelope to investigate the behavior of the machine uner these conitions, an experiments were mae to valiate it. The etection of short circuit faults was investigate relying on the frequency analysis of the phase voltages for a current-controlle rive. Symmetrical components transformation were investigate in orer to seek for the most robust inicator. It is prove that the partial short circuit fault can be efficiently etecte by monitoring the amplitue of the harmonic component of voltage space vector in the αβ an α 2 β 2 space at the frequency f an 3f respectively. The above mentione amplitue can be use to monitor the fault severity, an the faulty phase can be ientifie, relying on the polar representation of the voltage space vector..2 Back emf (V) REFERECES [1] D. Diallo, M. E. H. Benbouzi, an A. Makouf, A fault-tolerant control architecture for inuction motor rives in automotive applications, IEEE Trans. on Vehicular Technology, vol. 53, no. 6, pp. 1847 1855, ov. 24. [2] J. A. Haylock, B. C. Mecrow, A. G. Jack, an D. J. 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