Diagnosis of open‑phase faults for a five‑phase PMSM Fed ...

This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.

Diagnosis of open‑phase faults for a five‑phasePMSM Fed by a closed‑loop vector‑controlleddrive based on magnetic field pendulousoscillation technique

Chen, Hao; He, Jiangbiao; Demerdash, Nabeel A. O.; Guan, Xing; Lee, Christopher Ho Tin

2021

Chen, H., He, J., Demerdash, N. A. O., Guan, X. & Lee, C. H. T. (2021). Diagnosis ofopen‑phase faults for a five‑phase PMSM Fed by a closed‑loop vector‑controlled drivebased on magnetic field pendulous oscillation technique. IEEE Transactions On IndustrialElectronics, 68(7), 5582‑5593. https://dx.doi.org/10.1109/TIE.2020.3000109

https://hdl.handle.net/10356/151765

https://doi.org/10.1109/TIE.2020.3000109

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Abstract—An on-line diagnostic approach of

open-phase faults for a five-phase permanent magnet synchronous motor (PMSM) fed by a closed-loop vector-controlled drive is presented in this paper. This approach is accomplished based on the magnetic field pendulous oscillation (MFPO) phenomenon, in which a significant “swing-like” pendulous oscillation in the magnetic field is observed in case of open-phase faults. According to analysis of the signatures of MFPO patterns under faulty conditions, all possible open-phase faults are detected, including single-phase open faults, two-adjacent phase open faults, and two-nonadjacent phase open faults. Moreover, this approach is capable of localizing the faulted phase/phases by further extracting the phase angle features of MFPO angular position waveforms under faulty conditions. Meanwhile, in order to minimize the number of sensors to reduce the implementation cost of this diagnostic approach, a phase-locked loop (PPL) technique is developed to overcome the fault masking difficulties associated with the compensation action of the closed-loop vector-controlled drive. As a result, this diagnostic approach only requires four current sensors and a speed sensor, which are typically already available in

Manuscript received January 8, 2020; revised March 25, 2020 and

May 2, 2020; accepted May 23, 2020. This work was supported in part by the SEMPEED Consortium at Marquette University through its member corporations, viz. Motor Design Ltd., Kollmorgen Corp., Regal Beloit America Inc., Grundfos Corp., and MTS System Corp, and in part by the Start-up Grant from Nanyang Technological University under Grant M4082346.040.601001. (Corresponding author: Christopher H. T. Lee.)

H. Chen is with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53233 USA, and also with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]).

J. He is with the Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA (e-mail: [email protected]).

N. A. O. Demerdash is with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53233 USA (e-mail: [email protected]).

X. Guan is with the School of Automation, Beijing Institute of Technology, Beijing 100081, China (e-mail: [email protected]).

C. H. T. Lee is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]).

five-phase PMSM drive systems for control purpose. Finally, experimental results demonstrate the effectiveness of the presented approach.

Index Terms—Fault diagnosis, magnetic field pendulous oscillation (MFPO), open-phase fault, permanent magnet synchronous motor (PMSM).

NOMENCLATURE

ang_dif Angular difference. fn Stator magnetomotive forces (MMFs) of phases A,

B, C, D, E, respectively. Fs Total stator MMF. →

Fs Total stator MMF space-vector. in Currents of phases A, B, C, D, E, respectively. i1, i1 Stator currents in subspace 1-1 reference frame. id1, iq1 Stator currents in subspace d1-q1 reference frame. Im Magnitude of phase currents. →

s Current space-vector.

∠→

s Current space-vector angle.

Ns Number of effective turns per phase. P Number of rotor poles. Rs Stator phase resistance. Te Electromagnetic torque. →

Vs Voltage space-vector. Complex space-vector operator, =e

j(2π/5). Magnetic field pendulous oscillation (MFPO)

angular position. Δs Magnitude of MFPO angular position waveform. Phase angle of MFPO angular position waveform. Electrical angular position. Output angular position of phase-locked loop. ωs Synchronous speed in electrical rad/s. →s Stator flux linkage space-vector. ’ Superscript “ ’ ” means variables under faulty

condition. b Subscript “b” means backward component. f Subscript “f ” means forward component.

Diagnosis of Open-Phase Faults for a Five- Phase PMSM Fed by a Closed-Loop

Vector-Controlled Drive Based on Magnetic Field Pendulous Oscillation Technique

Hao Chen, Member, IEEE, JiangBiao He, Senior Member, IEEE, Nabeel A. O. Demerdash, Life Fellow, IEEE,

Xing Guan, Student Member, IEEE, and Christopher H. T. Lee, Senior Member, IEEE


I. INTRODUCTION

HE RELIABILITY of motor-drive systems is of significant importance in safety-critical applications, e.g., aircraft,

ship propulsion, and electric vehicles. Compared to the conventional three-phase permanent magnet synchronous motor (PMSM) drive systems, five-phase counterparts have exhibited the advantages of high torque density and improved fault-tolerance capability [1], [2]. Hence, a five-phase PMSM drive system is investigated in this paper.

Five-phase PMSMs are not immune to all electrical faults. Due to the destructive nature and potential propagation of the faults, it is essential to diagnose these faults in an incipient stage. Consequently, further damage to the motor-drive system could be prevented, and preferably a remedial fault-tolerance control strategy could be triggered to maintain the system functionality as much as possible [3], [4]. Among all the electrical faults in PMSM drive systems, the open-phase fault is one of the most common faults, which could be caused by two switch failures of the same phase leg in the inverter, external cable connection failures, or internal stator winding ruptures [5].

In recent years, the development of open-phase fault diagnosis for electric machines has received considerable attention. In [6], Gajanayake et al. diagnosed open-phase faults by calculating the root-mean-square (RMS) value of phase currents. This method is straightforward, while it has a relatively slow fault detection speed (usually requires more than 3 electrical cycles), and imposes a heavy computational burden (CPU resource and memory-consuming), as well as facing the possibility of false alarms. In [7], Kuruppu et al. presented a single-phase open fault diagnostic method for a three-phase PMSM based on the d-q current signatures. By comparing the phase shift in the fault diagnosis signal with respect to the actual electrical angle, this method is capable of identifying the faulted phase. Compared to the aforementioned phase current RMS value calculation method, this method exhibits a rapid fault diagnosis capability. In [8], Freire et al. adopted an open-phase fault diagnostic method based on the derivative of the absolute current Park’s vector, which exhibits a high immunity to false alarms. In [9], Yang et al. presented an on-line open-phase fault diagnostic method via analysis of the neutral-point voltage characteristics. This method exhibits satisfactory fault diagnosis performance, especially for the operating conditions with low fault harmonic magnitudes, e.g., light load conditions, since the fault harmonic in the neutral-point voltage results in reduced effects on sensor measurement errors and torque loads. In [10], Hang et al. developed a zero-sequence voltage component (ZSVC) based method to diagnose open-phase faults for PMSM drive systems. With the combined analysis of the fundamental component of the ZSVC and the initial phase angle difference of stator currents, this method can not only diagnose open-phase faults, but also discriminate fault types (two switch failures of the same phase leg in the inverter or internal stator winding ruptures). It should be noted that for both of the methods presented in [9] and [10], an accessible neutral-point of stator windings and an additional resistance network are needed, which might not be feasible in most industrial applications. Up to date, most of the existing methods focused

on three-phase motor-drive systems, in which the open-phase fault results in a symmetry in the remaining two phase currents with the same magnitude and an 180-degree phase shift in between. By contrast, an asymmetry appears between the remaining four phase currents in five-phase motor-drive systems with an open-phase fault, due to the compensation action of closed-loop vector-controlled drives [11], [12]. Hence, many of these effective diagnostic approaches developed for three-phase counterparts would be invalid in five-phase PMSM drive systems.

More recently, few methods have been developed to diagnose open-phase faults in five-phase motor-drive systems. In [13], Salehifar et al. presented a current signal-based method to diagnose open-phase faults in a five-phase PMSM drive system via analysis of the particular characteristics of currents in a subspace d-q reference frame. Since the fault localization is conducted for each phase of the motor separately, this method is inefficient during execution, and a time delay has to be considered to avoid false alarms. In [14], Trabelsi et al. developed a centroid-based diagnostic method of open-phase faults for five-phase PMSMs. It was found that the current locus in a subspace reference frame is a point under normal condition, while it is an ellipse-like shape under open-phase fault condition. It should be noted that for the work presented in both [13] and [14], only one type of open-phase faults, i.e., single-phase open faults, is taken into account. In [15], Arafat et al. presented an open-phase fault diagnostic method for a five-phase PMSM based on symmetrical component theory. With analysis of the magnitude and phase angle of the fundamental currents in the five symmetrical component sequences, both of the different open-phase fault types and localization of the faulted phase/phases are effectively identified. The limitation of this method comes from the fact that the phase angle of currents in the remaining phases is assumed as constant before and after the open-phase faults. In fact, both of the magnitude and phase angle of currents in the remaining phases will change, after open-phase faults occur in the motor fed by a closed-loop vector-controlled drive with the voltage source inverter (VSI), which is adopted in most of the high-performance industrial applications [16], [17].

Differing from the previous diagnostic methods for open-phase faults in five-phase PMSM drive systems, this paper brings new contributions with further extension of the work in [18] to present a comprehensive study on diagnosis of open-phase faults for a five-phase PMSM fed by a closed-loop vector-controlled drive based on a so-called magnetic field pendulous oscillation (MFPO) technique. The basic principle of the MFPO phenomenon was originally presented in [19]. It was subsequently developed for diagnosis of rotor broken-bar faults in [20]-[22] and stator interturn faults in [23], [24] for three-phase induction machines. Conventionally, the sensing of both the phase currents and voltages is needed to monitor the resultant magnetic field affected by a broken-bar or an interturn fault. Accordingly, for the five-phase motor-drive system investigated in this paper, at least four current sensors and four voltage sensors would be needed to implement the diagnostic approach, which will increase the system cost and physical volume. On the other hand, the three-phase induction machines investigated in [19]-[24] are fed by open-loop drives. In this

T


paper, the MFPO technique is re-developed for diagnosis of open-phase faults for a five-phase PMSM fed by a closed-loop vector-controlled drive. Moreover, in order to reduce the hardware complexity and implementation cost, a phase-locked loop (PLL) technique is developed, by which no additional sensors and/or related signal conditioning circuits are needed. Finally, the effectiveness of the presented diagnostic approach is verified by experimental results.

II. MFPO PHENOMENON IN PMSMS

The schematic diagram of the investigated five-phase PMSM drive system is shown in Fig. 1. It contains a five-leg VSI drive and a five-phase PMSM. The motor-drive system is operated with a closed-loop vector-controlled strategy, in which the reference stator voltages in the d-q rotating reference frame are generated by the associated proportional-integral (PI) regulators based on the difference between the commanded signals, i.e., the current and the speed, and their corresponding measured signals [25]. The specifications of the motor-drive system are listed in Table I. It should be noted that in order to guarantee the safety of the system when testing a faulted machine in Section IV, as well as for the sake of consistency throughout this paper, the five-phase PMSM is operated at a low operating point of 6 Nm at 100 r/min, which is different from that in [18].

Under normal condition, the ideal five-phase currents can be expressed by eq. (1). These currents are sequentially shifted by 72 electrical degrees, i.e., 2π/5, from phase-A to phase-E as:

cos( )

cos( 2 5)

cos( 4 5)

cos( 6 5)

cos( 8 5)

a m s

b m s

c m s

d m s

e m s

i I t

i I t

i I t

i I t

i I t

(1)

The fundamental component of the stator magnetomotive forces (MMFs) can be expressed as:

1 2 cos cos( )

1 2 cos( 2 5) cos( 2 5)

1 2 cos( 4 5) cos( 4 5)

1 2 cos( 6 5) cos( 6 5)

1 2 cos( 8 5) cos( 8 5)

a s m s

b s m s

c s m s

d s m s

e s m s

f N I t

f N I t

f N I t

f N I t

f N I t

(2)

The total stator MMF can be expressed as:

5 4 cos( )e

s n s m sn a

F f N I t

(3)

The total stator MMF space-vector can be expressed as:

sj ts fF F e

(4)

As can be seen, the locus of the total stator MMF space-vector is a circle. The electromagnetic torque can be expressed as:

5 4 ( )e s sT P I

(5)

( )s s s sV R I dt (6)

Under faulty condition, e.g., an open-phase fault occurred in

5-Phase PMSMT1 T2 T3 T4 T5

T6 T7 T8 T9 T10

A

B

C

D E

n

G

Vbus

IGBT Driver

Controller (FPGA)

Currents Measurement

Speed Measurement

Speed Command

Gate Driving Signals

Fig. 1. Schematic diagram of the five-phase motor-drive system.

TABLE I SPECIFICATIONS OF THE INVESTIGATED MOTOR-DRIVE SYSTEM

Parameter Value Parameter Value

Supply voltage (VDC) 50 PM flux linkage (Wb) 0.037Number of stator slots 40 d-axis inductance (mH) 0.85Number of rotor poles 44 q-axis inductance (mH) 0.87

phase-A, the stator MMF of phase-A would be zero, i.e., fa = 0 in eq. (2). For better understanding about how the motor drive responds to this fault, assuming that the remaining four phase currents are not distorted at the first time-instant after the open-phase fault, the total stator MMF, F’

s, is re-presented as a combination of a forward component, F’

f, and a backward component, F’

b, as follows:

' ' 'cos( ) cos( )e

s n f bn b

F f F t F t

(7)

'f s mF N I (8)

' 1

4b s mF N I (9)

The total stator MMF space-vector is re-written as: 2' ' ' ' ' ' '( )s s s sj t j t j t j t

s f b f b f bF F e F e F F e e F F

(10)

As can be seen, due to the open-phase fault, the resultant stator MMF space-vector,

→

F's, is resolved into two components, i.e., a

strong forward component rotating counter clockwise (CCW) at synchronous speed,

→

F'f, and a weak backward component

rotating clockwise (CW) also at synchronous speed but in the opposite direction,

→

F'b. Based on eq. (6), the stator flux linkage

space-vector is controlled by the action of the VSI drive through the voltage space-vector, with the current space-vector as the system state variable. Hence, the resultant current space-vector,

→

Is', would also be resolved into two components,

i.e., a strong forward component rotating CCW at synchronous speed,

→

If', and a weak backward component rotating CW also at

synchronous speed, →

Ib', as expressed as follows: ' ' 's f bI I I

(11)

Substituting eq. (11) into eq. (5), the torque of the faulted motor can be expressed as:

' ' ' ' '5 4 [ ( )] 5 4 ( )e s f b s f s bT P I I P I I

(12)

The first term in eq. (12) represents a constant torque component, while the second term represents a torque ripple


component with a frequency equal to double of the fundamental operating frequency. It is expected that the compensation action of the closed-loop vector-controlled drive would tend to reduce the torque ripple by adjusting the voltage space-vector, which will directly impact the stator flux linkage space-vector [11], [26]. Due to this adjustment, both the voltage space-vector,

→ V 's,

and the stator flux linkage space-vector, → 's, would be resolved into two components, i.e., forward components,

→ V 'f and → 'f, and

backward components, →

V 'b and → 'b, as expressed by eq. (13) and eq. (14), respectively, as follows:

' ' 's f bV V V

(13)

' ' 's f b

(14)

Consequently, the torque in eq. (12) can be re-written as: ' ' ' ' '

' ' ' ' ' ' ' '

5 4 [( ) ( )]

5 4 [( ) ( ) ( ) ( )]

e f b f b

f f f b b f b b

T P I I

P I I I I

(15)

The first term in eq. (15) represents a constant torque which is the main developed toque of this motor. The second term and the third term represent torque ripples with a frequency equal to double of the fundamental operating frequency. The last term represents a constant torque with the opposite direction to the main torque in the first term, which results in a reduction of the average output torque of the motor-drive system. Responding to the torque reduction, the closed-loop vector-controlled drive would increase the magnitude of the forward current space-vector,

→

If' , to track the reference torque. Finally, at

steady-state operations after the open-phase fault, all the space-vectors can be re-written as a combination of a forward component and a backward component [27], [28]. More specifically, the resultant total stator MMF space-vector,

→

F's,

the resultant current space-vector, →

Is' , the resultant voltage

space-vector, →

V 's , and the resultant stator flux linkage space-vector, → 's, would be formulated as the same as they are previously expressed in eqs. (10), (11), (13), and (14), respectively, even though the resultant values may be different from those under the aforementioned assumption.

The simulated current and torque profiles before and after the phase-A open fault are shown in Fig. 2 and Fig. 3, respectively. In this case, the fault occurs at 0.25s. As can be seen, the average torque under faulty condition is the same as that under normal condition. This phenomenon is due to the compensation action of the closed-loop vector-controlled drive by re-configuring the currents, as depicted in Fig. 2. These results verify the correctness of the previously presented analysis.

The loci of the voltage, current, and stator flux linkage space-vectors under open-phase fault condition are depicted in Fig. 4. As can be seen, the asymmetry in the stator windings due to an open-phase fault disturbs the air-gap magnetic field, causing the air-gap magnetic field to form into two motions, i.e., one motion rotates at synchronous speed as the original rotation under normal condition, while the other motion oscillates around the original synchronously rotating axis. This is the so-called “magnetic field pendulous oscillation (MFPO)” phenomenon [19], [23]. In this paper, the MFPO phenomenon is utilized to diagnose the open-phase faults for a five-phase PMSM drive system.

Phase A Phase B Phase C Phase D Phase E

0.200 0.225 0.250 0.275 0.300 0.325

-6

-3

0

3

6

Pha

se c

urre

nts

(A)

Time (s)

Normal condition Phase-A open

Fig. 2. Current profiles when the phase-A open fault occurs.

0.200 0.225 0.250 0.275 0.300 0.3250

3

6

9 Torque

Tor

que

(Nm

)

Time (s)

Normal condition Phase-A open

Fig. 3. Torque profile when the phase-A open fault occurs.

s

s

s

s

locus of

locus of

locus of 's

'b

'f

'sI

'fI

'bI

'sd dt

's sR I

'sV

'fV

'bV

Fig. 4. Space-vector diagram of the closed-loop vector-controlled motor-drive system in case of an open-phase fault.

III. DIAGNOSIS OF OPEN-PHASE FAULTS BASED ON MFPO

As has been shown in [19]-[24], the MFPO can be observed by instantaneously monitoring the relative position of the stator voltage space-vector,

→ V 's, and the stator current space-vector,

→

Is' . However, for the investigated five-phase PMSM with

ungrounded star-connected windings, at least four voltage and four current measurements are required. In order to reduce the hardware complexity and implementation cost, a PLL technique is developed, as depicted in Fig. 5 [29], [30]. The gains of the PI controller in the PLL are obtained based on the symmetrical optimum method as shown in [29]. As a result, only measured four phase currents and measured speed are required, while these currents and speed are already available in the closed-loop vector-controlled motor drive. In other words, no additional sensors and/or related signal conditioning circuits are needed.

The five phase currents are obtained from the four measured current signals due to the ungrounded star-connected winding configuration, i.e., ∑(ia+ib+ic+id+ie)=0. Then, the currents are transformed to the stationary reference frame with the conventional utility angular position, , e.g., i1=Im‧cos and i1=Im‧sin. Furthermore, these currents are transformed to the synchronously rotating d-q reference frame with the output


PI controller

0

Δ * Integrator

sincos

ParkTransformation

ClarkeTransformation

iaib

+-

++

icidie

1i 1i 3i 3i 0i

*1 0qi

1qi

Fig. 5. Block diagram of the five-phase PLL structure. angular position of the PLL, , instead of , as expressed as follows:

** *1 1

** *1 1

cos( )cos sin

sin( )sin cosd m

q m

i i Ii i I

(16)

By setting iq1=0 as the input of the PLL, this offers immediate possibility to lock onto the utility current. It should be noted that the rotating d-q reference frame is synchronized to the fundamental output frequency of the drive. The output angular position of the PLL, , would not be affected by any oscillation caused by an open-phase fault [31]. Hence, the output angular position of the PLL, , can be used as a reference, which is rotating CCW at synchronous speed. Accordingly, the aforementioned MFPO phenomenon can be measured by the oscillation of the stator current space-vector,

→

Is', with respect to

the output angular position of the PLL, , which is defined as “MFPO angular position” as depicted in Fig. 6.

The presented diagnostic approach of open-phase faults includes three steps as follows: Step 1: Detection of any open-phase fault from normal

condition. Step 2: Classification of different types of open-phase faults.

Due to the limitation of zero neutral-point current, the five-phase PMSM cannot operate under three-phase open fault condition [17]. Hence, three types of open-phase faults are investigated in this paper, namely, single-phase (SP) open faults, two-adjacent-

phase (TAP) open faults, and two-nonadjacent-phase (TNP) open faults.

Step 3: Localization of the faulted phase/phases.

A. Detection of Open-Phase Faults

The stator current space-vector is obtained by the measured currents as follows:

2 3 4( ) 2 5 [ ( ) ( ) ( ) ( ) ( )]s a b c d eI t i t i t i t i t i t

(17)

It should be noted that only fundamental components are taken into account in this paper. The MFPO angular position, (t), is expressed as:

*( ) ( ) ( )st I t t

(18)

Under normal condition, the MFPO angular position, (t), is theoretically calculated as zero, i.e., (t)=0. By contrast, under open-phase fault condition, as aforementioned in section II, an oscillating motion appears around the original synchronously rotating axis with a frequency equal to double of the fundamental operating frequency. Hence, the MFPO angular position, (t), under faulty condition, can be expressed as:

locus of

locus of

locus of 's

'sI

'sd dt

's sR I

'sV

MFPO angular position

*

Fig. 6. Re-defined MFPO in space-vector diagram.

( ) cos(2 )s st t (19)

The MFPO angular position, (t), under both normal and open-phase fault conditions, is plotted in a polar coordinate manner as shown in Fig. 7. For any point (r, ) in these polar plots, the radius is calculated by r(t)=│Re[

→

s(t)]│. As can be

seen, the locus/trace of the →

r (t)=r(t)∠(t) vector shows a

straight line under normal condition, while the loci/traces show unfilled-petal shapes under open-phase fault conditions. These different shape signatures can be used for detection of open-phase faults.

B. Classification of Open-Phase Fault Types

The MFPO angular position waveforms under the conditions of the three different open-phase fault types are shown in Fig. 8. For the sake of generality, the waveform of (t) under normal condition is included in Fig. 8(a). The results of the magnitude of the MFPO angular position waveform, Δs, are listed in Table II.

As can be seen, the Δs under normal condition stays almost zero [refer to Fig. 8(a)]. By contrast, under faulty condition, SP open faults have the smallest value, i.e., ≈2.5 (refer to Table II), while TAP open faults have the largest value, i.e., ≈15.2. It indicates that compared to the other two types of the investigated fault scenarios, TAP open faults are the most serious faults. Moreover, the values of Δs for each type of faults stay almost the same regardless of the faulted phase leg/legs. Hence, the significantly different values of Δs with different open-phase fault types can be used to classify the fault types.

It should be noted that in order to be more practical, typical lower and upper bounds are set for each type of open-phase faults. More specifically, 50% of the magnitude of the MFPO angular position waveform, Δs, under SP faults is set as the lower bound for SP faults, i.e., 2.5×50%=1.25. This value is also set as the threshold for the detection of any open-phase fault from normal condition. The average value of Δs under SP faults and that under TNP faults is set as the upper bound for the SP faults and the lower bound for the TNP faults, i.e., (2.5+5.9)/2=4.2. The average value of Δs under TNP faults and that under TAP faults is set as the upper bound for the TNP faults and the lower bound for the TAP faults, i.e., (5.9+15.2)/2=10.55. These bounds are marked in Fig. 8. If the value of Δs is within the region between the lower and upper bounds, the specific type of open-phase faults can be identified. In addition, it is interesting to note that the MFPO angular


1(A) SP fault

TAP fault

TNP fault

Zoom-in plot2(A)

3(A)90°

180° 0°

270°

Normal

Fig. 7. Polar coordinate plot (r, ) under normal and faulty conditions.

0 90 180 270 360

-20

-10

0

10

20

Upper bound

Lower bound

Phase-A Phase-B Phase-C Phase-D Phase-E Normal

MFP

O a

ngul

ar p

osit

iond

eg.

Time (ele. deg.)

445.46 452.27 459.09 465.91 472.73Time (ms)

72 deg.

(a)

0 90 180 270 360

-20

-10

0

10

20

MF

PO a

ngul

ar p

ositi

ond

eg.

Time (ele. deg.)

Phase-A&B Phase-B&C Phase-C&D Phase-D&E Phase-E&A

72 deg.

445.46 452.27 459.09 465.91 472.73Time (ms)

Lower bound

(b)

0 90 180 270 360

-20

-10

0

10

20

MF

PO

ang

ular

pos

itio

nd

eg.

Time (ele. deg.)

Phase-A&C Phase-B&D Phase-C&E Phase-D&A Phase-E&B

72 deg.

445.46 452.27 459.09 465.91 472.73Time (ms)

Lower bound

Upper bound

(c)

Fig. 8. MFPO angular position waveforms with different types of open-phase faults. (a) SP faults (the result under normal condition is included). (b) TAP faults. (c) TNP faults.

TABLE II VALUE OF ΔS FOR ALL POSSIBLE OPEN-PHASE FAULTS

SP faults Δs TAP faults ΔS TNP faults ΔS

Phase-A 2.5 Phase-A&B 15.2 Phase-A&C 5.9Phase-B 2.5 Phase-B&C 15.2 Phase-B&D 5.8Phase-C 2.5 Phase-C&D 15.3 Phase-C&E 5.8Phase-D 2.6 Phase-D&E 15.2 Phase-D&A 5.9Phase-E 2.5 Phase-E&A 15.2 Phase-E&B 5.9

position waveforms consist of two cyclic periods in one electrical cycle, which confirmed the second-harmonic nature

of the MFPO phenomenon as previously mentioned [refer to eq. (19)].

C. Localization of the Faulted Phase/Phases

As observed in Fig. 8, for each type of open-phase faults, e.g., SP faults in Fig. 8(a), there is a 72-degree phase shift between the five scenarios from phase-A fault through phase-E fault. More specifically, the MFPO angular position waveform of phase-A fault is leading that of phase-B fault by 72 degrees, and so forth. The same rule can also be observed in the other two open-phase fault types, as marked in Fig. 8(b) and (c), respectively. Hence, for each type of faults, with the knowledge of the faulted phase/phases in one of the five scenarios, the localization of the faulted phase/phases in the other four scenarios can be successfully targeted by the 72-degree phase shift.

In this paper, the challenge of the prerequisite mentioned above is overcome by the phase angle analysis of the MFPO angular position waveform with respect to the output angular position of the PLL, (refer to Fig. 5). As previously concluded, the MFPO angular position waveform alternates with a frequency equal to double of the fundamental operating frequency, while the output angular position of the PLL, has been locked onto the utility current and synchronized to the fundamental operating frequency. Hence, the half phase angle of the MFPO angular position waveform, , will synchronize with the output angular position of the PLL, More specifically, the angular difference between and the at the first time-instant, i.e., (1), will be constant, and is defined as follows:

*_ 2 (1)ang dif (20)

The calculated values of the angular difference, ang_dif, for all case-studies are listed in Table III. With the specific value of ang_dif for each open-phase fault case-study, the localization of the faulted phase/phases can be identified.

It should be noted that in practice, typical angular regions around the specific value of ang_dif are set based on the results in Table III, as depicted in Fig. 9. Taking SP faults as an example, if the value of ang_dif is within the red region of Fig. 9(a), the faulted phase, i.e., phase-A, can be identified. The same rule can also be observed in the case-studies from phase-B through phase-E faults, as well as in the case-studies of TAP and TNP faults shown in Fig. 9(b) and (c), respectively. In addition, it is interesting to note that there is also an approximate 72-degree difference between the results of two adjacent case-studies for each type of faults, e.g., the difference between the ang_dif of phase-A fault and that of phase-B fault is -4.2°-(-75.9°)=71.7°≈72°.

The overall open-phase fault diagnosis procedure/algorithm including the flowchart and the fault diagnosis process is shown in Fig. 10. As can be seen from Fig. 10(b), the presented diagnostic approach is non-invasive since the diagnosis process within the red dashed line just extracts information of measured currents and speed, which does not interfere the vector-controlled algorithm within the blue dashed line. The control algorithm will not be changed during the diagnosis process. Moreover, the current signals over only one electrical cycle are needed. Hence, the diagnosis speed of this approach is


TABLE III

VALUE OF ang_dif FOR ALL POSSIBLE OPEN-PHASE FAULTS

SP faults ang_dif TAP faults ang_dif TNP faults ang_dif

Phase-A -4.2° Phase-A&B -51.8° Phase-A&C 10.7°Phase-B -75.9° Phase-B&C -124.2° Phase-B&D -60.8°Phase-C -148.7° Phase-C&D -195.9° Phase-C&E -133.7°Phase-D -220.6° Phase-D&E -267.9° Phase-D&A -205.3°Phase-E -293.4° Phase-E&A -340.0° Phase-E&B -277.3°

Phase-E

Phase

-DPh

ase-

C

Phase-B

Phase-A

0°

-4°(356°)

-76°(284°)-148°(212°)

-220°(140°) -292°(68°)

72°

(a)

Phase-A&B

Phase-E&

A

Phas

e-C

&D

Phase-B

&C

Phase-D&E

0°

-52°(308°)-124°(236°)

-196°(164°)

-268°(92°)

-340°(20°)

(b)

Phase-A&

C

Phase-E&B

Phas

e-C&

E

Phase-B&D

Phas

e-D

&A

0°

-61°(299°)-133°(227°)

-205°(155°)

-277°(83°)

11°

(c)

Fig. 9. Typical angular regions for localization of the faulted phase/ phases. (a) SP faults. (b) TAP faults. (c) TNP faults.

fast since it takes only one electrical cycle (fundamental period) to recognize the fault occurrence if the required time for signal processing is negligible, as long as the motor-drive system is under steady-state operation condition. It should be noted that this is an on-line diagnostic approach. No matter when the sampling of current signals starts, if a specific feature of the fault indicators, i.e., the magnitude of the MFPO angular position waveform, Δs, and the angular difference, ang_dif, shows up during the operation, such an open-phase fault can be diagnosed and reported.

The real-time simulated results of the fault indicators, i.e., Δs and ang_dif, from normal condition to faulty condition under SP fault in phase-A, TAP fault in phase-A&B, and TNP fault in phase-A&C, are shown in Fig. 11. In these cases, open-phase faults occur at 27.27ms. As can be seen, the results under steady-state operation condition are maintained almost constant as expected. In Fig. 11 (a), all the results of Δs for the three case-studies are within their corresponding lower and upper bounds, which have been shown in Fig. 8. In Fig. 11(b), the results of ang_dif for SP fault in phase-A, TAP fault in

Localize the faulted phase/phases based on eq. (18)

Save these signals over one electrical cycle

Obtain the output angular position of the PLL, (refer to Fig. 5)

Filter the current signals

Measure the four current signals and obtain the five-phase currents

Δs >Threshold?No

Yes

Start

Calculate the magnitude of the MFPO angular position waveform, Δs , based on the eqs. (15)-(17)

Classify the open-phase fault types, i.e., SP, TAP, or TNP open faults

“Alarm” Specify the open-phase fault type and the faulted phase/phases

Steady-state ?Yes

No

(a)

Calculate MFPO characteristics, Δs and ang_dif

ia ~ ie

PI regulator+-

iq*+-

+-

n*

d/dt

Inverter

id* = 0

A

B

C

D E

n

PI regulator

PI regulator

Xdq

X

SVPWM

Filter

Vd*

Vq*

V*

V*

Xdq

Xabcde

5-Phase PMSM

PLL

Fundamental components of stator currents

“Alarm”Decision making

(b)

Fig. 10. (a) Algorithmic flowchart of the diagnostic approach. (b) Overall fault diagnosis process.

phase-A&B, and TNP fault in phase-A&C, are within the red regions in Fig. 9(a), (b), and (c), respectively.

It should also be noted that the specific results including the magnitude of the MFPO angular position waveform, Δs, in Table II and the angular difference, ang_dif, in Table III, are obtained at one specific operating point. Taking a SP fault in phase-A as an example, the fault indicators, i.e., Δs and ang_dif, with load and speed variations are shown in Fig. 12 and Fig. 13, respectively. As can be seen, with the load increasing, the magnitude of the MFPO angular position waveform, Δs, and the angular difference, ang_dif, increase. By contrast, with the speed increasing, Δs changes little while ang_dif reduces. These results make heuristic sense, because the open-phase fault occurred in larger load case means more impact on the air-gap magnetic field so that more significant MFPO phenomenon is observed. Since most of the motor-drive systems in common industrial applications, fans and pumps, etc., are operated at one operating point (the so-called rated operating point), the presented diagnostic approach is effective, low-cost, and practical. On the other hand, for the motor-drive systems which have more than one operating point, e.g., electric vehicles, the open-phase faults can also be successfully


0

5

10

15

20

25

Faulty conditionNormal condition

Time (ele. deg.)0 360 720 1080 1440 1800

Time (ms)0 27.27 54.55 81.82 109.09 136.36

SP fault (Phase-A) TAP fault (Phase-A&B) TNP fault (Phase-A&C)

Mag

nitu

de o

f th

e M

FPO

ang

ular

pos

itio

n w

avef

orm

, s

, (de

g.)

Lower bound(SP faults)

Upper bound(TNP faults)&Lower bound(TAP faults)Upper bound(SP faults)&Lower bound(TNP faults)

(a)

-180

-135

-90

-45

0

45

90

Ang

ular

dif

ferr

ence

, ang

_dif,

(de

g.)

SP fault (Phase-A) TAP fault (Phase-A&B) TNP fault (Phase-A&C)

Time (ms)0 27.27 54.55 81.82 109.09 136.36

Time (ele. deg.)0 360 720 1080 1440 1800

Normal condition

Faulty condition

Red region in Fig. 9(a)

Red region in Fig. 9(b)

Red region in Fig. 9(c)

(b)

Fig. 11. Real-time simulated results. (a) Magnitude of the MFPO angular position waveform, Δs. (b) Angular difference, ang_dif.

4 6 8 10 120

2

4

6

Load (Nm)Mag

nitu

de o

f th

e M

FP

O a

ngul

ar

pos

ition

wav

efor

m,

s , (

deg.

)

4 6 8 10 12

-20

-10

0

10

20

Ang

ular

dif

ferr

ence

, ang

_dif,

(de

g.)

Load (Nm) (a) (b)

Fig. 12. Fault indicators with load variation. (a) Δs vs. load. (b) ang_dif vs. load.

50 75 100 125 1500

2

4

6

Speed (r/min)Mag

nitu

de o

f th

e M

FP

O a

ngul

ar

pos

itio

n w

avef

orm

,

s , (

deg.

)

50 75 100 125 150

-20

-10

0

10

20

Ang

ular

dif

ferr

ence

, ang

_dif,

(de

g.)

Speed (r/min) (a) (b)

Fig. 13. Fault indicators with speed variation. (a) Δs vs. speed. (b)

ang_dif vs. speed.

diagnosed using this diagnostic approach with look-up tables [32].

IV. EXPERIMENTAL VALIDATION

To validate the effectiveness of the presented diagnostic approach, a five-phase motor prototype which is a dual-rotor surface-mounted PMSM with high torque density, was used for the experimental setup as shown in Fig. 14. More details about

Stator Rotor

Inverter IGBT driver

FPGA-based controller

(a) (b)

Prototype LoadTorque

transducer(c)

Fig. 14. Test hardware setup. (a) Prototype of the five-phase PMSM. (b) Five-phase drive. (c) Test bench of the five-phase motor-drive system. this motor can be found in [33]. A commercially available FPGA (Altera-Cyclone III EP3C25Q240, 50-MHz, 24,624-Logic Elements, 508-KB-RAM) with embedded processors, is used as the microcontroller for vector control purpose and signal processing.

As previously analyzed, the effectiveness of the PLL is the prerequisite of the presented diagnostic approach. The

measured current space-vector angle, ∠→

s(t), and the output

angular position of the PLL, t, in a certain electrical cycle are shown in Fig. 15. It should be noted that in order to illustrate the MFPO phenomenon more explicitly, the results are obtained with a TAP fault in phase-A&B. As can be seen, with

the time increasing, the current space-vector angle, ∠→

s(t), increases with oscillation, while the output angular position of the PLL, t, increases linearly without any oscillation resulting from the open-phase fault. These experimental results verify the effectiveness of the PLL.

The MFPO angular position waveforms under normal condition, as well as under SP fault in phase-A, TAP fault in phase-A&B, and TNP fault in phase-A&C, are shown in Fig. 16(a), (b), (c), and (d), respectively. The measured magnitude of the MFPO angular position waveform, Δs, and the angular difference, ang_dif, for all case-studies are listed in Table IV (in comparison with the simulation results in Table II) and Table V (in comparison with the simulation results in Table III), respectively. As can been seen, the simulation results and experimental results are in good agreement. There is a negligible discrepancy which may be due to the fact that the measurement interferences of current sensors and the saturation of the motor are not taken into account in the simulations.

It should be noted that the experimental signals in Fig. 16 are sampled in the same electrical cycle with the simulation counterparts as depicted in Fig. 8. In practice, for an on-line diagnostic approach, the signals can be sampled at any time. Hence, to further verify this approach, the real-time experimental results of diagnosis process under SP fault in phase-A, TAP fault in phase-A&B, and TNP fault in phase-A&C, are shown in Fig. 17. It should be noted that these


Current space-vector angle, Output angular position of PLL,

0 90 180 270 360-180

-90

0

90

180

Time (ms)

Ang

le (

deg.

)

Time (ele. deg.)

( )sI t

*( )t

0 6.82 13.64 20.45 27.27

Fig. 15. Validation of the effectiveness of PLL.

0 90 180 270 360

-20

-10

0

10

20

MF

PO

ang

ular

pos

itio

nd

eg.

Normal (Simulation) Normal (Experiment)

Time (ele. deg.)

0 6.82 13.64 20.45 27.27Time (ms)

(a)

0 90 180 270 360

-20

-10

0

10

20

MF

PO a

ngul

ar p

osit

iond

eg.

SP fault in phase-A (Simulation) SP fault in phase-A (Experiment)

Time (ele. deg.)

0 6.82 13.64 20.45 27.27Time (ms)

(b)

SP fault in phase-A&B (Simulation) SP fault in phase-A&B (Experiment)

0 90 180 270 360

-20

-10

0

10

20

MF

PO a

ngul

ar p

osit

iond

eg.

Time (ele. deg.)

0 6.82 13.64 20.45 27.27Time (ms)

(c)

0 90 180 270 360

-20

-10

0

10

20

MF

PO a

ngul

ar p

osit

iond

eg.

SP fault in phase-A&C (Simulation) SP fault in phase-A&C (Experiment)

Time (ele. deg.)

0 6.82 13.64 20.45 27.27Time (ms)

(d)

Fig. 16. Comparison of simulated and measured MFPO angular position waveforms. (a) Normal condition. (b) SP fault in phase-A. (c) TAP fault in phase-A&B. (c) TNP fault in phase-A&C.

TABLE IV EXPERIMENTAL VALUE OF ΔS FOR ALL POSSIBLE OPEN-PHASE FAULTS

SP faults Δs TAP faults ΔS TNP faults ΔS

Phase-A 2.9 Phase-A&B 16.7 Phase-A&C 5.6Phase-B 2.7 Phase-B&C 17.1 Phase-B&D 5.7Phase-C 2.8 Phase-C&D 16.6 Phase-C&E 5.5Phase-D 2.8 Phase-D&E 16.9 Phase-D&A 5.5Phase-E 2.7 Phase-E&A 17.2 Phase-E&B 5.6

TABLE V EXPERIMENTAL VALUE OF ang_dif FOR ALL POSSIBLE OPEN-PHASE FAULTS

SP faults ang_dif TAP faults ang_dif TNP faults ang_dif

Phase-A -4.1° Phase-A&B -53.9° Phase-A&C 10.4°Phase-B -77.3° Phase-B&C -127.2° Phase-B&D -61.1°Phase-C -147.6° Phase-C&D -199.8° Phase-C&E -133.8°Phase-D -220.4° Phase-D&E -271.0° Phase-D&A -202.0°Phase-E -292.4° Phase-E&A -344.1° Phase-E&B -276.5°

0

5

10

15

20

25

Lower bound (TAP faults)

Mag

nitu

de o

f th

e M

FP

O a

ngul

ar

pos

ition

wav

efor

m, s

, (de

g.) SP fault (Phase-A)

TAP fault (Phase-A&B) TNP fault (Phase-A&C)

Lower bound (SP faults)

Upper bound (SP faults)

Lower bound (TNP faults)

Upper bound (TNP faults)

Time (ms)0 13.64 27.27 40.91 54.55 68.18 81.82

(a)

-90

-45

0

45

90

Red region in Fig. 9(c)

81.8268.1854.5540.91Ang

ular

dif

ferr

ence

, ang

_dif

, (de

g.) SP fault (Phase-A)

TAP fault (Phase-A&B) TNP fault (Phase-A&C)

Time (ms)0 13.64 27.27

Red region in Fig. 9(a)

Red region in Fig. 9(b)

(b)

Fig. 17. Real-time experimental results. (a) Magnitude of the MFPO angular position waveform, Δs. (b) Angular difference, ang_dif.

results are obtained at steady-state operation of the motor-drive system. As can be seen, for all open-phase fault case-studies including SP fault in phase-A, TAP fault in phase-A&B, and TNP fault in phase-A&C, the fault indicators, i.e., the magnitude of the MFPO angular position waveform, Δs, and the angular difference, ang_dif, are maintained almost constant as expected. Even though slight pulsation can be observed in the results under TAP fault in phase-A&B, this is due to the fact that the TAP open faults are the most serious faults, which inevitably lead to mechanical vibration and measurement difficulties. In Fig. 17(a), all the results of Δs for the three case-studies are within their corresponding lower and upper bounds, which are set based on the simulated results as previously shown in Fig. 8. In Fig. 17(b), the results of ang_dif for SP fault in phase-A, TAP fault in phase-A&B, and TNP fault in phase-A&C, are within the red regions in Fig. 9(a), (b),


and (c), respectively.

In companion with the simulated results in Fig. 12 and Fig. 13, the experimental validation of the presented diagnostic approach under SP fault in phase-A for different operating points, i.e., load and speed variations, are listed in Table VI and Table VII, respectively. As can be seen, the simulated results are also in acceptable agreement with the experimental results. These results further verified the effectiveness of the presented diagnostic approach.

V. CONCLUSION

An on-line open-phase fault diagnostic approach based on the MFPO phenomenon for a five-phase PMSM fed by a closed-loop vector-controlled drive, was developed in this paper. The MFPO concept was introduced and demonstrated to effectively explain how the magnetic field is affected by the open-phase faults in a five-phase motor-drive system. Based on the theoretical analysis, as well as the simulation and experimental results, the following conclusions can be inferred: 1) Unlike the circularly rotating magnetic field under normal

condition, the open-phase fault disturbs the air-gap magnetic field, which leads it into two motion components, i.e., one motion component rotates at synchronous speed, while the other motion component oscillates around the original synchronously rotating axis with a frequency equal to double of the fundamental operating frequency.

2) With the PLL technique, a reference can be found, i.e., the output angular position of the PLL, , which would not be affected by any oscillation caused by an open-phase fault. Moreover, the hardware complexity and implementation cost of the diagnostic approach was significantly reduced. As a result, only the measurement of four phase currents and speed is required. These currents and speed are already available in such a motor-drive system. In other words, no additional sensors and/or related signal conditioning circuits are needed.

3) Different open-phase fault types, i.e., SP, TAP, and TNP faults, result in significantly different values of the magnitude of the MFPO angular position waveform, Δs. This phenomenon indicates that Δs is a feasible option to be a fault indicator to detect the existence of open-phase faults and classify the open-phase fault types.

4) For each type of such open-phase faults, each open-phase fault case-study has a specific value of the angular difference, ang_dif, which can be utilized to localize the faulted phase/phases. More interestingly, there is an approximate 72-degree difference of the ang_dif between two adjacent case-studies for each type of open-phase faults.

5) The fault indicators, i.e., Δs and ang_dif, are not affected by the variation of sampling instants. Hence, the presented diagnostic approach is effective, reliable, and practical.

The main limitation of the presented diagnostic approach is that the diagnosis process is implemented under steady-state operation condition. The improvement on the robustness of the diagnostic approach during fast speed and load dynamics/transients, the discrimination of open-switch faults and open-phase faults to avoid the risk of misdiagnosis, as well as the fault-tolerant control strategy with the obtained fault information, will be investigated in future work.

TABLE VI EXPERIMENTAL VALIDATION WITH LOAD VARIATION (SP FAULT IN PHASE-A)

Case-studies ΔS ang_dif

Simulation Experiment Simulation ExperimentCase-I (6Nm, 100r/min)

2.5 2.9 -4.2° -4.1°

Case-II (9Nm, 100r/min)

3.3 3.6 -1.4° -1.8°

TABLE VII

EXPERIMENTAL VALIDATION WITH SPEED VARIATION (SP FAULT IN PHASE-A)

Case-studies ΔS ang_dif

Simulation Experiment Simulation ExperimentCase-I (6Nm, 100r/min)

2.5 2.9 -4.2° -4.1°

Case-II (6Nm, 140r/min)

2.7 3.3 -10.2° -11.6°

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Hao Chen (M’19) received the B.Sc. degree in electrical engineering from the School of Electrical Engineering, Beijing Jiaotong University, Beijing, China, in 2012, and the Ph.D. degree in control science and engineering from the School of Automation, Beijing Institute of Technology, Beijing, China, in 2019.

From 2016 to 2018, he was with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI, USA, as a joint Ph.D. student. He is currently a Postdoctoral Research Fellow with the School of Electrical and Electronic

Engineering, Nanyang Technological University, Singapore. His research interests include design and optimization of electric machines,

power electronic drives and motor control.

JiangBiao He (M’15–SM’16) is an Assistant Professor in power energy area with the Department of Electrical and Computer Engineering, University of Kentucky. He previously worked in industry, most recently as a Lead Engineer with GE Global Research, Niskayuna, New York. He also worked with Eaton Corporation and Rockwell Automation before he joined GE in 2015. He received the Ph.D. degree in electrical engineering from Marquette University,

Milwaukee, Wisconsin. His research interests include high-performance propulsion drives for

electric transportation, renewable energies, and fault-tolerant operation of power conversion systems for safety-critical applications. He has authored more than 70 technical papers and 10 patent applications in power electronics and motor drives areas.

Dr. He is an IEEE Senior Member, and has served as an Associate Editor for several prestigious IEEE journals in electric power area. He also served in the organizing committees for various IEEE international conferences (IEMDC-2017, ECCE-2018, ITEC-2019, etc.), and has been an active member of multiple IEEE standards working groups. He is a recipient of the 2019 IEEE IAS Outstanding Young Member Achievement Award.

Nabeel A. O. Demerdash (M’65–SM’74–F’90–LF’09) received the B.Sc.E.E. degree (distinction with first-class Hons.) from Cairo University, Giza, Egypt, in 1964, and the M.S.E.E. and Ph.D. degrees from the University of Pittsburgh, Pittsburgh, PA, USA, in 1967 and 1971, respectively.

From 1968 to 1972, he was a Development Engineer in the Large Rotating Apparatus Development Engineering Department, Westinghouse Electric Corporation, East Pittsburgh.

From 1972 to 1983, he was an Assistant Professor, an Associate Professor, and then a Professor in the Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA. From 1983 to 1994, he was a Professor in the Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY, USA. Since 1994, he has been a Professor with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI, USA, where he was the Department Chair from 1994 to 1997. He is the Director of the SEMPEED Consortium at Marquette University. He is the author or co-author of more than 125 papers published in various IEEE TRANSACTIONS. His current research interests include power electronic applications to electric machines and drives, electromechanical propulsion and actuation, computational electromagnetics in machines and drives, and fault diagnostics and modeling of motor-drive systems.


Prof. Demerdash is a member of the Electric Machines Committee of the

IEEE Industry Applications Society, the American Society of Engineering Education, Sigma Xi, and the Electromagnetics Academy. He has received the 1999 IEEE Nikola Tesla Technical Field Award for pioneering contributions to electric machine and drive system design using coupled finite-element and electrical network models. He has also received two 1994 Working Group Awards and two 1993 Prize Paper Awards from the IEEE Power and Energy Society (PES) and its Electric Machinery Committee, and a 2012 Prize Paper Award from the PES, as well as a 2012 Prize Paper Award from the IEEE Industry Applications Society Electric Machines Committee and the 2015 Marquette University Lawrence G. Haggerty Faculty Award for Research Excellence.

Xing Guan was born in Jilin, China. He received the B.Sc. degree in electrical engineering from Beijing Institute of Technology of Beijing, China in 2013. He is currently working toward the Ph.D. degree at the School of Automation, Beijing Institute of Technology (BIT), Beijing, China.

His research interests include electric machines and drive systems, motor design and control, energy conversion.

Christopher H. T. Lee (M’12-SM’18) received the B.Eng. (Hons.) and Ph.D. degrees in electrical engineering from the Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong, in 2009 and 2016, respectively.

He currently serves as an Assistant Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, a Visiting Assistant Professor at Massachusetts Institute of Technology, Cambridge, MA, USA, and

an Honorary Assistant Professor in his alma mater. His research interests include electric machines and drives, renewable energies, and electric vehicle technologies. In these areas, he has published one book, three book chapters, and about 70 referred papers.

Dr. Lee received many awards, including the Nanyang Assistant Professorship, the Li Ka Shing Prize (the best Ph.D. thesis prize) and Croucher Foundation Fellowship to support his postdoctoral research. He is also an Associate Editor of IEEE ACCESS and IET Renewable Power Generation.

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