Open Phase Fault Detection of a Five-Phase Permanent Magnet Assisted Synchronous Reluctance Motor based on Symmetrical Components Theory

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—This paper presents a novel approach for open phase fault detection of a five-phase permanent magnet assisted synchronous reluctance motor (PMa-SynRM). Under faults, the five-phase PMa-SynRM is expected to run at fault tolerant control (FTC) mode,
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  0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2017.2682016, IEEETransactions on Industrial Electronics Open Phase Fault Detection of a Five-PhasePermanent Magnet Assisted SynchronousReluctance Motor based on SymmetricalComponents Theory AKM Arafat,  Student Member, IEEE,  Seungdeog Choi,  Senior Member, IEEE   Jeihoon Baek,  Member, IEEE  Abstract   —This paper presents a novel approach foropen phase fault detection of a five-phase permanent mag-net assisted synchronous reluctance motor (PMa-SynRM).Under faults, the five-phase PMa-SynRM is expected to runat fault tolerant control (FTC) mode, otherwise it drawsa large amount of current with a significant reduction inthe reluctance torque. To successfully achieve FTC op-eration of five-phase PMa-SynRM, the accurate detectionof a fault condition has to be preceded. With the bestof these authors knowledge, the detection of faults hasbeen limitedly studied for five-phase motors. The analy-sis of open phase fault in five-phase machine involvescomplicated conditions including single-phase open fault(SPF),two-phaseadjacentfault(TPAF),andtwo-phasenon-adjacent fault (TPNF). To perform the timely fault tolerantoperation, those faults have to be accurately analyzed anddetected. In this paper, a novel symmetrical components(SCs) analysis is utilized to extract the feature of thosefault conditions. This analysis will provide the types offaults by logically analyzing the pattern of magnitude andphase angle changes of the fundamental signal in the SCs.The proposed method has been comprehensively analyzedthrough theoretical derivation, finite element simulations,and experimental testing through a 5hp PMa-SynRM con-trolled by TI-DSP F28335. Index Terms   —Fault detection, Fault diagnosis, Symmet-rical components (SCs), Finite element method (FEM). I. I NTRODUCTION E XTENSIVE research has been accomplished to improvethe reliability of electric machines under critical serviceapplications such as aerospace, automotive, etc. [1]. Especially,electric motors have been popularly applied to the hybrid andelectric vehicles where the reliable operation is mandatory. Forsuch critical applications, advanced fault detection and faulttolerant operation of electric machine has been predominantlyrequired.To maximize the fault tolerance capability, a multi-phasemotor system has been suggested in [2]–[4]. Among all Manuscript received August 29, 2016; revised October 20, 2016 andJanuary 13, 2017; accepted February 16, 2017. AKM Arafat and Se-ungdeog Choi are with the School of Electrical and Computer Engineer-ing, University of Akron, Akron, Ohio (e-mail: aa188@zips.uakron.eduand schoi@uakron.edu). Jeihoon Baek is with the School of Elec-trical, Electronics and Communication Engineering, Korea Univer-sity of Technology and Education, Cheonan, Korea (e-mail: jh-baek@koreatech.ac.kr). the multi-phase motor families, a five-phase system is theminimum configuration that inherits greater fault tolerancecapability than a conventional three-phase system [5]–[7]. Onthe other hand, a system with higher than 5-phase, wouldhave to deal with more power switches failure in operationwhich could potentially increase the complexity in the faultdetection and fault tolerant control. In a five-phase machine,the increased degree of freedom with additional phase con-nections compared to single or three-phase machine can beutilized to enhance the dependability of the drive. Theseredundant electric phases can also be utilized to providehigher flexibility and accuracy in the fault detection procedure.Among many types of five-phase motors, a PMa-SynRM hasbeen considered as one of the most promising technologydue to its many benefits in terms of robust control and lowcost design. The five-phase PMa-SynRM takes advantage of a synchronous reluctance machine (RSM) and a permanentmagnet synchronous machine (PMSMs) which has optimizedspeed, torque, and vibration characteristics [2], [3], [8].Many methods have been extensively studied in last fewdecades for the fault detection and diagnosis of electric motors[9], [10]. Fuzzy logic or neural network theory [11]–[15]is one of these conventional methods. This method requiresan expert system [16], [17] based on the rules set up fromthe accumulated experience. Open phase fault or short circuitfault has been analyzed with a motor dynamic model whichuses parameter estimation [18], [19] and state estimation [20],[21]. This method requires estimation of accurate physicalparameters to identify a precise system model. In [21], asimple diagnosis process has been proposed for three-phaseBLDC which analyzed the switching status during the faultconditions. In [22], a fault detection process has been analyzedwhich uses extra circuitry to identify the faults. Advance signalprocessing has been attempted for three-phase machines in[23]–[28]. In [25]–[27], along with a signal processing tech-nique, three-phase reference frame theory has been introducedto quantize the fault signature into a DC quantity.In recent years, advanced fault detection in three-phasemotor drives has received much attention. Motor currentsignature analysis using kernel density estimation has beendiscussed in [29]. A mixed logical dynamic motor drive modelhas been discussed in [30]. Extended form of the Kalmanfilter associated to an appropriate model of permanent magnetsynchronous machine has been discussed in [31]. Interturn  0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2017.2682016, IEEETransactions on Industrial Electronics short circuit faults are detected in [32]–[34]. In [32], [33],advanced analysis on the frequency pattern in motor currentand back electromotive force are analyzed to identify faults.In [34], injection of pulsating voltage which induced highfrequency current is suggested which is applicable for low-medium speed motor drive system. Intelligent particle filterwhich is applicable in a nonlinear system is discussed in [35].Until now, the fault detection and condition monitoringtheory has been commonly developed by assuming a three-phase system which may not be effectively applied for multi-phase machines. For a five-phase system and its diagnosis, anadvanced fault detection algorithm is required which considersa minimum of ten power switches and their combinationalcomplexities. Few studies have been made in [7], [36], [37]on fault detection in a five-phase motor. In [7], a model-basedobserver is proposed to estimate parameters to identify opentransistor faults in a five-phase permanent magnet motor drive.In [36], combined space vector spectrum analysis has beendone with a complex theoretical explanation for detecting in-terturn fault in a five-phase machine. In [37], a centroid basedswitch fault detection method has been discussed utilizing thereference frame theory in a five-phase system.To accommodate the theoretical complexities [36], [37] witheasier fault detection, the conventional SCs theory can beapplied as an excellent tool for the condition analysis of ageneral multi-phase system. The SCs theory has been utilizedas a powerful tool in stability calculations, which principallypermits the identification of any kind of unbalances in theelectrical power system [38], [39]. The detection procedure ismore intuitive and robust compared to those methods whichuse parametric system modeling [7], [17], [18] or complexsignal analysis [32]–[34]. The theory can be utilized to analyzethe system degradation if there is any kind of unbalancedcondition arises inside the machine. However, the applicationof SCs theory to five-phase system has been limitedly studiedand therefore requires further analysis.In this paper, the three-phase SCs theory has been math-ematically extended to the five-phase system. The proposeddetection algorithm can be easily embedded in a digital signalprocessor (no need an extra monitoring devices) with thecontrol program which helps to identify those fault typesand fault location. In addition, in the proposed method, twodifferent magnitude indexes are used which would providea solid confirmation of the presence of the faults. Theseadvantages made the method more convincing and accuratein terms of fault information. In section II, the five-phase SCstheory has been established through mathematical modeling.The procedure to identify the types of faults and their locationof faults has been developed in the same section. In section III,the simulation and experimental validations with comparisontables have been provided. II. N EW  S YMMETRICAL  C OMPONENT  T HEORY FOR F IVE -P HASE  PM A -S YN RM  UNDER  F AULTS In this section, the SCs theory for a three-phase systemhas been extended to a five-phase system (without loss of generality). Fig. 1. Five-phase system showing different faults. A. Open Phase Faults in a Five-phase Machine System  In a five-phase system, the five phase currents (are 72 degreephase shifted from each other)can be derived as follows: I  sa  =  I  m 1 sin (2 πft ) I  sb  =  I  m 2 sin (2 πft − 2 π/ 5) I  sc  =  I  m 3 sin (2 πft − 4 π/ 5) I  sd  =  I  m 4 sin (2 πft − 6 π/ 5) I  se  =  I  m 5 sin (2 πft − 8 π/ 5) (1)where  I  sa ,I  sb ,I  sc ,I  sd ,I  se  are the five phases currents, and I  m 1 ,I  m 2 ,I  m 3 ,I  m 4 ,I  m 5  are magnitudes of each phase cur-rents, respectively.These five current variables can be effectively analyzed foradvanced fault detections in a five-phase machine. Fig.1 showsthe possible open phase faults in a five-phase system including(i) SPF (phase A=0), (ii) TPAF (phases AE=0), and (iii) TPNF(phases BE=0). These faults can be effectively detected usinga modified SCs theory. A Detailed analysis is done in thefollowing sections. B. Derivation of Symmetrical Components for a Five- phase system  Fundamentally, the number of phase sequences in a three-phase system is three which are positive sequence (PS),negative sequence (NS), and zero sequence (ZS) components.In a five-phase system, the number of phase sequence issignificantly increased due to larger phase combinations. Forexample, based on the phase rotation, a three-phase systemhas only two combinations (2x1). However, there are 24(=4x3x2x1) possible combinations of phase sequences in afive-phase system.To identify the proper phase sequences, each out of 24sequences has been evaluated based on ZS component. If theZS component become ideally zero, the sequence is selectedas one of phase sequence in a five-phase system. This has ledto the identification of four new sequences in five phase systemwhich are positive sequence 1 (PS1)  ( A → B  → C   → D  → E  ) , negative sequence 1 (NS1)  ( A  →  E   →  D  →  C   →  B ) ,positive sequence 2 (PS2)  ( A  →  C   →  E   →  B  →  D ) ,negative sequence 2 (NS2)  ( A  →  D  →  B  →  E   →  C  ) .These phase sequences are depicted in phasor diagram in Fig.2. These four sequences along with ZS makes a set of fiveSCs for a five-phase system.  0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2017.2682016, IEEETransactions on Industrial Electronics Fig. 2. Proposed symmetrical components for five-phase system. Base on identified five phase sequences, the currents of afive-phase system are decomposed as follows: I  sa  =   4 n =0 I  an I  sb  =   4 n =0 I  bn  =  I  a 0  + I  a 1 α 4 + I  a 2 α 1 + I  a 3 α 2 + I  a 4 α 3 I  sc  =   4 n =0 I  cn  =  I  a 0  + I  a 1 α 3 + I  a 2 α 2 + I  a 3 α 4 + I  a 4 α 1 I  sd  =   4 n =0 I  dn  =  I  a 0  + I  a 1 α 2 + I  a 2 α 3 + I  a 3 α 1 + I  a 4 α 4 I  se  =   4 n =0 I  en  =  I  a 0  + I  a 1 α 1 + I  a 2 α 4 + I  a 3 α 3 + I  a 4 α 2 (2)where  I  an ,I  bn ,I  cn ,I  dn ,I  en  (n=0,1,2,3 and 4) are the SCs of phase A, phase B, phase C, phase D, and phase E, respectively,and for phase A, the SCs are given as  I  a 0  (ZS),  I  a 1  (PS1), I  a 2  (NS1), I  a 3  (PS2), I  a 4  and (NS2), and  α  =   72 ◦ ) .Using (2), the five SCs can be found utilizing the transfor-mation matrix  ( T  )  as shown in (3).  I  a 0 I  a 1 I  a 2 I  a 3 I  a 4  = 15  1 1 1 1 11  α 1 α 2 α 3 α 4 1  α 4 α 3 α 2 α 1 1  α 3 α 1 α 4 α 2 1  α 2 α 4 α 1 α 3      T   I  sa I  sb I  sc I  sd I  se  =  0 I  m 1 sin (2 πft )000  (3)In (3), the transformation matrix has been successfully derivedfor a five-phase system with the proposed SCs. In (3), onlythe PS1 component takes non-zero values, whereas all othercomponents take as zero values under healthy condition whichsatisfies the SCs theory. C. Symmetrical Components under Fault Conditions  This section provides the analysis of SCs under open phasefaults (SPF, TPAF, and TPNF). The Magnitudes and phasesof the SCs are analyzed under different fault conditions toidentify its pattern.When SPF occurs ( I  sa  = 0 ) the five SCs in (3) can bedriven as follows: Fig. 3. Proposed signal ratio (Magnitude index) under all possible openphase faults. I  a 0  =  K  01 sin (2 πft − arctan( B 01 /A 01 )) I  a 1  =  K  11 sin (2 πft ) I  a 2  =  K  21 sin (2 πft − arctan( B 21 /A 21 )) I  a 3  =  K  31 sin (2 πft − arctan( B 31 /A 31 )) I  a 4  =  K  41 sin (2 πft − arctan( B 41 /A 41 )) (4)When TPAF occurs (  I  sa  =  I  sb  = 0 ), the five SCs in (3)can be driven as follows: I  a 0  =  K  02 sin (2 πft − arctan( B 02 /A 02 )) I  a 1  =  K  12 sin (2 πft ) I  a 2  =  K  22 sin (2 πft − arctan( B 22 /A 22 )) I  a 3  =  K  32 sin (2 πft − arctan( B 32 /A 32 )) I  a 4  =  K  42 sin (2 πft − arctan( B 42 /A 42 )) (5)Where, K  n 1  = 4  n =0 ,n  =1 I  mn   ( A 2 n 1  + B 2 n 1 )      C  n 1 K  n 2  = 4  n =0 ,n  =1 I  mn   ( A 2 n 2  + B 2 n 2 )      D n 1  for  n  = 1 ,  C  n 1  =  D n 1  = 1 for  n   =  1,  C  n 1   =  D n 1   = 1 (6) K  n 1  and  K  n 2  are amplitudes of SCs under SPF and TPAF, I  mn  is the magnitude as in (1),  arctan( B n 1 /A n 1 )  and arctan( B n 2 /A n 2 )  are the phase angles of the other SCs inreference to the PS1,  B n 1  and  A n 1  are the summation of  sinσβ   and  cosσβ  , respectively  ( σ  = 0 , 1 , 2 ...,β   = 2 π/ 5) .Through (4) and (5), it has been comprehensively analyzedthat, the magnitudes and phase angles of the SCs underdeferent faults substantially changes with the mathematicalpattern. This can be effectively utilized to identify the typeof faults and location of the faults. D. Analysis of the Symmetrical Components - Amplitude  In this section, the magnitude of SCs will be utilized for thedetection of fault types. To comparatively analyze the signalmagnitude between SCs, two signal ratio indexes ( r 1 ,  r 2 ) havebeen proposed which is defined as follows: r 1  =  K  3 K  0 ,r 2  =  K  2 K  4 (7)where  K  0  ,  K  2  ,  K  3  , and  K  4  are the peak of ZS (  I  0  ), NS1(  I  2  ), PS2 (  I  3  ) and NS2 (  I  4  ), respectively.  0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2017.2682016, IEEETransactions on Industrial Electronics Fig. 4. Phase angles of SCs under all possible faults. Under SPF and TPAF in (4) and (5), the changes of   r 1  and r 2  have been presented in Fig. 3. In Fig. 3 the magnitudeindexes  r 1  and  r 2  are equal to one under any SPF (phasesA, B, C, D, E). The indexes,  r 1  and  r 2 , become lower thanone under any TPAF (phases AB, BC, CD, DE, and EA).Similarly, under any TPNF (phases AC, AD, BD, BE, CE)the indexes become higher than one. It can be seen that theindexes  r 1  and  r 2  clearly follow a pattern which is providingthe information of the types of faults as follows: r 1 ,r 2  <  1  ; Two-phase adjacent fault r 1 ,r 2  = 1  ; Single-phase fault r 1 ,r 2  >  1  ; Two-phase non-adjacent fault(8) E. Analysis of the Symmetrical Components - Phase  In this section, the phase of SCs will be utilized for detectingthe fault locations. The phase angle changes of SCs underfaults also have a valuable information on the location of faults. Fig. 4 shows the MATLAB simulation results of phaseangle changes under different fault conditions. In Fig. 4,leading phase (w.r.t. PS1) is colored as red and lagging phase(w.r.t. PS1) is colored as blue. Other than, in-phase or outof phase (w.r.t. PS1) is colored as green. Fig. 4 shows that,the change of phases of those sequences shows unique patternunder different fault condition (SPF, TPAF, and TPNF). F. Overall Detection Scheme  The overall block diagram of the detection procedure isshown in Fig. 5. The motor is run with field orient controlstrategy at maximum torque per ampere condition. Underfault conditions, the five-phase currents are initially fed to alow pass filter to remove higher order harmonics. Only thefundamental current components are considered during thedetection procedure. The filtered phase signals are multipliedby the five-phase transformation matrix ( T  ) as shown in(3) to identify five SCs. The magnitudes and phases of thefive SCs have been measured. Utilizing these magnitude and Fig. 5. Overall fault detection process.TABLE IS PECIFICATION OF THE  PM A -S YN RM Parameter SpecificationsNumber of slot/poles 15/4Rated current (rms)(A) 15.17Rated voltage (rms) (V) 67Power (kW) 2.83Rated speed (rpm) 1800Rated Torque (Nm) 15Phases 5 phase information, the magnitude indexes and phase patternhave been identified (7). Finally, the type and location of theopen phase fault have been effectively identified by using (8)and Fig. 4. This fault information can be sent to the motorcontroller to activate fault tolerant control strategy [5]. III. S IMULATION  R ESULTS A. Simulation Environment  Finite element analysis (FEA) has been performed to provethe performance of the proposed method. The five-phasemachine in Table. I, has been utilized under the tests. Themotor parameters are derived through the differential evolutionoptimization through Lumped Parameter Model and FiniteElement Method (FEM) [6].The simulation has been performed under different faultconditions, including SPF, TPAF, and TPNF. Detailed finiteelement analysis (FEA) has been done to the motor in Table.I to observe the pattern identified in Fig. 3 and Fig. 4 undernon-linear operating conditions of the machine. B. Phase Currents under Different Open Phase Faults  Fig. 6 shows the phase currents (A, B and D) under TPNF(C and E). It can be seen that, the phase B current becomessubstantially distorted causing THD as 37%. The fundamentalcomponent which is shown in Fig. 6 is obtained throughfiltering to evaluate the comparative analysis. The p.u. valuesof the fundamental currents of the phases A, B, and D are 0.79,0.49, and 0.90, respectively. The Table II shows the summary  0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2017.2682016, IEEETransactions on Industrial Electronics Fig. 6. Currents (phase CE=0), (a) phase A, (b) phase B, (c) phase D.Fig. 7. Torque under different fault conditions. (a) (b)(c) (d) Fig. 8. SCs at 100% rated: (a) Healthy condition, (b) phase E=0, (c)phase DE=0, (d) phase CE=0. of p.u. values of the fundamental current under healthy andother possible fault conditions.The comparison of the torque and torque ripple underdifferent faults is given in Fig. 7. Fig. 7 shows the the averagetorques are 2 Nm, 1.88 Nm, 1.85 Nm and 1.65 Nm and thetorque ripples are 10%, 26%, 29%, and 31% under healthy,SPF, TPAF, and TPNF, respectively. C. Analysis of the Symmetrical Components - Amplitude  Using the proposed transformation matrix derived in SectionII, five SCs are shown in Fig. 8 and Fig. 10 for 100% and 30%rated conditions, respectively. Fig. 8a shows the SCs under Fig. 9. Signal ratio (magnitude index) under all possible open phasefaults. (a) (b)(c) Fig. 10. SCs at 30% rated: (a) phase D=0, (b) phase AB=0, (c) phaseAC=0.TABLE IIP ER  U NIT  V ALUES OF  F UNDAMENTAL  C URRENTS UNDER  F AULTS Operating Conditions p.u. values (Phases)A B C D EHealthy Condition 0.8 0.8 0.8 0.8 0.8E Open 0.74 0.55 0.88 0.88 0D and E Open 0.89 0.54 0.89 0 0C and E open 0.79 0.49 0 0.90 0 healthy conditions. It is observed in Fig. 8a that all the SCs(ZS, NS1, PS2, NS2) become zero except PS1.Fig. 8b shows the SCs under SPF (phase E=0) condition.The magnitudes of ZS, NS1, PS2, and NS2 are 0.3, 0.5,0.30,0.29 and 0.31, respectively.Fig. 8c shows the SCs under TPAF (phase D and E). Themagnitude of the ZS, NS1, PS2 and NS2 are 0.25, 0.23, 0.17,and 0.36, respectively.Fig. 8d shows the SCs under TPNF (Phase C and E). Themagnitude of the ZS, NS1, PS2 and NS2 are 0.19, 0.37, 0.4,and 0.18, respectively.Fig. 9 summarizes the magnitude index ( r 1  and  r 2 ) under allpossible open phase faults, including SPF, TPAF, and TPNF.Fig. 9 shows that, under SPF (phase A or B or C or D or E),the magnitude indexes,  r 1  and  r 2 , remain close to one ( = 1 ).
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