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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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