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Fault tolerant control of triple star-winding flux switching
permanent magnet motor drive due to open phase
Yu, F; Cheng, M; Hua, W; Chau, KT
The 10th International Conference on Ecological Vehicles and
Renewable Energies (EVER 2015), Monte Carlo, Monaco, 31
March-2 April 2015. In Conference Proceedings, 2015, p. 1-9
2015
http://hdl.handle.net/10722/217356
International Conference on Ecological Vehicles and Renewable
Energies (EVER). Copyright © IEEE.
2015 Tenth International Conference on Ecological Vehicles and Renewable Energies (EVER)
Fault Tolerant Control of Triple Star-Winding Flux
Switching Permanent Magnet Motor Drive Due to
Open Phase
Feng Yu, Ming Cheng, Wei Hua
K. T. Chau
School of Electrical Engineering
Southeast University
Nanjing, 210096, China
Email: mcheng@seu.edu.cn
Department of Electrical and Electronic Engineering
The University of Hong Kong
Porkfulam, Hong Kong
Abstract—The flux-switching permanent-magnet (PM)
(FSPM) motor is a new class of stator-PM brushless
machines, which offers the advantages of high reliability,
high power density, and high efficiency. In this paper, a
nine-phase FSPM motor with triple star-winding sets
spatially displaced by 40 degrees fed by three pulse-width
modulated voltage source inverters (VSIs) is proposed, and
the fault tolerant operation of the proposed FSPM motor is
addressed. The key of this paper is to investigate two
remedial strategies for fault-tolerant operation of the
FSPM motor drive under open-circuit fault. Firstly, by
isolating the faulty star-winding set, the torque pulsations
due to phase loss can be remedied, the so-called remedial
BLAC operation mode. Secondly, by injecting fifth and
seventh harmonic currents to reconstruct armature fields,
the low-frequency torque pulsation can also be remedied,
the so-called remedial BLAC with harmonic current
injection operation mode. Finally, these two remedial
operation modes are compared and verified by simulation
and experimental results, hence confirming the validity of
the proposed fault-tolerant FSPM motor drive.
investigated to supplement the average torque and offset
the harmonic torque under the open-circuit fault [5].
In general, multiphase motor offers higher faulttolerant capability. Hence, multiphase (such as five-phase,
nine-phase) FSPM motors have attracted more attention.
However, the multi-phase motors often need multiple
inverter legs, and this non-classical inverter structure could
increase the cost of the system, making it more difficult to
use them in industrial applications. In this respect, the
nine-phase FSPM motor with three separate star-winding
sets could be a preferred alternative, with each supplied by
a separate three-phase voltage source inverter (VSI) whose
volt-ampere rating corresponds to one-third motor power
as shown Fig. 1. Although some publications have studied
this kind of approach [6-7], the achievable performance in
fault-tolerant operation has remained unclear.
Keywords—flux-swiching permanent-magnet motor;
nine-phase; remedial strategies; harmonic currents;
BLAC; low-frequency.
I.
INTRODUCTION
The flux switching permanent magnet (PM) (FSPM)
motor is the most viable for fault-tolerant operation of
EVs, since it inherently offers high efficiency, high power
density, maintenance-free operation, insignificant thermal
influence on PMs and mechanically robust [1-3]. It has
been identified that the FSPM motor can offer some
degree of fault-tolerance, where magnetic field and
armature field are perpendicular to each other in fluxswitching motors, allowing them to have high force
density and immune to demagnetization due to unexpected
fault [4]. Moreover, a remedial control strategy has been
978-1-4673-6785-1/15/$31.00©2015 IEEE
Fig. 1: Triple star-winding FSPM motor supplied by three VSIs
connected to the same dc-source.
The purpose of this paper is to evaluate the
performance of a 36-slot 34-pole triple star-winding FSPM
(TSW-FSPM) motor with two fault-tolerant control
strategies duo to open phase. In the next section, the
modeling of TSW-FSPM motor leads us to deduce the
necessary condition in normal operating mode. Then, the
influence of open-circuit operation on the output torque is
II.
NINE-PHASE FSPM MOTOR MODEL
A. Topology and Features
A concentrated winding FSPM motor with 34-rotorpole and 36 slots-stator-tooth has been proposed, featuring
only odd-order harmonics in the air-gap magneto-motive
force (MMF) distribution, as shown in Fig. 2 (a). The
stator consists of “U-shaped” laminated segments,
between which circumferentially magnetized magnets are
sandwiched and the direction of magnetization is reversed
from one magnet to the next. Each stator tooth comprises
two adjacent laminated segments and one magnet. There
are four coils in each phase, e.g., four coils marked as A1
for phase A1, and each coil surrounding only one tooth.
The simplified stator winding structure of the proposed
motor is shown in Fig. 2 (b). The notation represents the
phase name and the star-winding set number. For example,
B3 stands for the B-phase of the third star-winding set.
The adjacent star-winding sets are spatially displaced by
2π/9 rad. The resultant MMF waveform will be established
by nine equally spaced phase windings.
Harmonic content (%)
frequency of torque pulsation; improving noise
characteristics; and reducing the stator copper losses [8].
Voltage (V)
discussed in Section III. For this faulty operation mode,
two different control methods reducing the torque
oscillations are studied. The first method is simpler, but
the second makes it possible to reduce considerably the
copper losses of the motor and well-suited for real-time
implementation. In Section IV, the TSW-FSPM motor
control strategy is presented. Furthermore, in Section V,
simulation and experimental results will be presented to
verify the proposed fault-tolerant operation of the motor
drive. Finally, the conclusions will be drawn in Section VI.
Fig. 3: Back EMF at no load. (a) Waveform. (b) FFT results.
Finite-element (FE) method is used to calculate the
back electro-motive force (EMF) of the TSW-FSPM
motor. Fig. 3 (a) shows the back-EMF waveform at no
load. The amplitude of the back-EMF is 288V, and the
waveform is very symmetrical. A fast Fourier Transform
(FFT) is carried out to obtain its frequency components in
Fig. 3 (b). It is found that the most significant component
in the back-EMF waveform is the fundamental component
while the higher order harmonics are relatively low.
Therefore, this kind of TSW-FSPM motor can be driven as
a brushless ac (BLAC) motor. Neglecting the influence of
the higher order harmonics, the simplified phase backEMF can be obtained as:
⎧e A1 = E1 sin(ωt )
⎪
⎪e A2 = E1 sin(ωt − 2π )
⎪
9
⎨
#
⎪
⎪
16π
)
⎪eC 3 = E1 sin(ωt −
9
⎩
(1)
where ω is the angular frequency of the fundamental
component (the electrical rotor speed), and E1 is the
amplitude of the fundamental back EMF.
B. D-Q Model of the TSW-FSPM Motor
Fig. 2: 36-slot 34-pole TSW-FSPM motor. (a) Cross section. (b)
Simplified winding.
Due to the fact that there are no magnets, brushes, nor
windings in the rotor, the TSW-FSPM motor offers the
advantages of simple structure and mechanical robustness.
Compared with traditional three-phase FSPM motor, the
benefits gained from the TSW-FSPM motor drives are:
reducing the stator current per phase without increasing
the voltage per phase; increasing the power density;
reducing the amplitude of current per phase, increasing the
Many papers have been published describing the model
of multiple stator star-winding sets, particularly for dual
star-winding motors [9]. There are two main approaches to
model a dual star-winding motor: The first is through
extension of the three-phase model, and the second is
through the vector space decomposition (VSD).
According to the multiple three-phase model, the ninephase currents can be expressed as a combination of triple
three-phase sets, which are coupled to each other. Thus,
synchronous-frame current controllers can be applied to
each three-phase model with three-phase decoupling
scheme, and the stator voltage equations can be expressed
in the triple d-q reference frames [10]. However, this
model neglects the freedom of control due to harmonic
current components. Therefore, imbalance among inverter
systems or asymmetry among the star-winding sets can
cause an imbalance in the current transient response.
Especially, a large amount of imbalance is likely to exist
under faulty operation.
To reject the disturbances due to manufacturing
tolerance and control imbalance, another modeling
approach is the VSD theory. The 9-D current space can be
divided into four orthogonal subspaces. Harmonics of
different orders are mapped into different subspaces, i.e.,
the α1-β1, α3-β3, α5-β5, and α7-β7 subspaces as shown in Fig.
4. This approach gives an alternative motor description,
which is useful for the TSW- FSPM motor control and for
development of the pulse-width modulation (PWM)
techniques. The relationship between VSD variables and
phase variables for the TSW-FPSM motor with three
isolated neutrals is given with:
cos γ
⎡ 1
⎢ 0
sin γ
2⎢
⎢ ...
...
9⎢
⎢ 0 sin 7γ
⎢⎣1 / 2 − 1 / 2
cos 2γ
...
sin 2γ
...
...
...
sin 14γ
1/ 2
...
...
cos 8γ ⎤ ⎡i A1 ⎤ ⎡i1α ⎤
⎢ ⎥ ⎢ ⎥
sin 8γ ⎥⎥ ⎢i A2 ⎥ ⎢i1β ⎥
... ⎥ ⎢... ⎥ = ⎢... ⎥
⎥⎢ ⎥ ⎢ ⎥
sin 56γ ⎥ ⎢iC 2 ⎥ ⎢i7 β ⎥
1 / 2 ⎥⎦ ⎢⎣iC 3 ⎥⎦ ⎢⎣0 ⎥⎦
(2)
where γ=2л/9, and i1α, i1β, i3α,…, i7β are the α-, and β-axis
components of stator currents in α1-β1, α3-β3, α5-β5 and α7β7 plane respectively. The first two rows in (2) define
stator fundamental current components that will lead to
fundamental flux and torque production, while the last row
defines the zero-sequence component. In between, there
are 3 pairs of rows, which define 3 pairs of stator harmonic
current components, called further on third, fifth and
seventh harmonic current components.
Considering the drive where the stator star-winding
sets are not electrically isolated and no common return
path is present, the summation of the phase currents in
each star-winding set should satisfy the following
constraints:
⎧i A1 + i B1 + iC1 = 0
⎪
⎨i A2 + i B 2 + iC 2 = 0
⎪i + i + i = 0
⎩ A3 B 3 C 3
Hence, the third harmonic current components can be
deduced as:
i3α = 0 , i3 β = 0
(4)
As will be shown shortly, the third-harmonic current will
not flow in the drive system.
Due to the sinusoidal distribution of the MMF around
the air-gap for the TSW-FSPM motor, only the α1-β1
current components contribute to effective electromechanical energy conversion, while the α5-β5 and α7-β7
current components only produce losses. To explore the
controller design, a rotational transformation Rh(θ) is used
to transform αh-βh components into the general
synchronous reference frame dh-qh components, where the
d1-axis is taken to be aligned with magnet flux linkage, as
in conventional PM motors, and the induced back EMF is
aligned to the q1-axis. The dh-qh currents are deduced from
αh-βh currents by applying a rotation of θ as:
⎡ cos hθ
Rh (θ ) = ⎢
⎣− sin hθ
sin hθ ⎤
cos hθ ⎥⎦
(5)
where h=1, 3, 5 and 7. Through the VSD strategy, the
stator voltages in dh-qh reference frame can be expressed
as follow:
⎧u d 1 = Rs id 1 + Ld 1 did 1 dt − ωLq1iq1
⎪
⎪u q1 = Rs iq1 + Lq1diq1 dt + ω ( Ld 1id 1 + ψ m )
⎪u = R i + L di dt
⎪ d5
s d5
ls
d5
⎨
⎪u q 5 = Rs iq 5 + Lls diq 5 dt
⎪u = R i + L di dt
s d7
ls
d7
⎪ d7
⎪⎩u q 7 = Rs iq 7 + Lls diq 7 dt
Fig. 4: Four orthogonal subspaces: (a) α1-β1, (b) α3-β3, (c) α5-β5 and
(d) α7-β7.
(3)
(6)
where Ld1 and Lq1 are the stator inductance in d1-, q1-axis,
respectively, Rs is the phase resistance, Lls is the leakage
inductance and Ψm is the flux linkage amplitude. It can be
seen that stator resistance and stator leakage inductance
are the only motor parameters that appear in d5-q5 and d7q7 axis equations. The resultant d1-q1 axis equations are
identical to those of a corresponding three-phase motor.
Hence the basic vector control scheme will remain the
same as for a three-phase motor of the same type, where
the d1-, q1-axis current components can be easily
controlled by a pair of synchronous-frame current
controllers.
Then, the electromagnetic torque can be written as:
Te =
∂Wco 9
= p (ψ m iq1 + ( Ld 1 − Lq1 )id 1iq1 )
∂θ r
2
It is obvious that for balanced star-winding sets and for
a given torque, the losses are minimized if stator d1-axis
current and the fifth, seventh harmonic currents are equal
to zero. Hence, the torque can be rewritten as:
9
9
pψ miq1 = pψ m (iq′1 + iq′′1 + iq′′1′ )
2
2
(8)
where iq′1 , iq′′1 and iq′′′1 are the q1-axis current components of
the first, second and third star-winding set contributing to
the torque-producing, respectively. In normal operation,
we have:
iq′1 = iq′′1 = iq′′′1 =
III.
iq*1
3
When there is open-circuit fault in phase A1, the
current circulating in the remaining two phases of this
winding set is:
(7)
where Wco is the co-energy, θr is the mechanical rotor
angle, and p is the number of pole-pairs. The electromagnetic torque is composed of two parts. The first part is
the PM torque which arises from the interaction between
the flux linkage and q1-axis stator current component. The
second part is the reluctance-torque component caused by
inductance variation as a function of the rotor positions.
Te =
A. Remedial BLAC Operation
(9)
OPERATION UNDER OPEN FAULT CONDITION
Open-circuit faults that occur in the TSW-FSPM motor
drive can be classified as the winding open-circuit and
power device open-circuit, both resulting in disabling of
the faulty phase. Consequently, the motor drive needs to
work at fault-tolerant operations. Therefore, the study of
fault-tolerant performance of the TSW-FSPM motor under
open-circuit fault is necessary.
Once an open-circuit fault is detected with an
acceptable delay, the current control strategy must be
modified to reduce the torque pulsations due to phase loss.
The first stage is to isolate the faulty phase by keeping
open the corresponding two power switches. Then, the
second step is to reduce, or remove if possible, these lowfrequency torque pulsations. A simple solution is to make
the supply balanced by opening all the switches of the VSI
connecting to the faulty star-winding set of the TSWFSPM motor. Consequently, only two star-winding sets
remain supplied and the torque pulsations disappear in this
manner. Another solution, proposed here, is based on the
VSD theory. The main idea is to compensate the torque
pulsations by injecting fifth and seventh harmonic currents
to neutralize the large low-frequency pulsating torque so
as to permit smooth drive operation.
iB1 = −iC1 = I m cos(θ )
(10)
where Im is the magnitude of phase current. Then, d1-q1
components of the first star-winding set contributing to the
torque-producing current are written as follow:
⎡id′ 1 ⎤ 2 ⎡ cos θ
⎢′ ⎥= ⎢
⎣iq1 ⎦ 9 ⎣− sin θ
cos(θ − 3γ )
− sin (θ − 3γ )
⎡0⎤
cos(θ − 6γ ) ⎤ ⎢ ⎥
i B1
− sin (θ − 6γ )⎥⎦ ⎢ ⎥
⎢⎣iC1 ⎥⎦ (11)
I m ⎛ sin(2θ ) ⎞
⎜⎜
⎟⎟
3 3 ⎝ cos(2θ ) + 1⎠
The torque expression becomes:
=−
Te =
⎞
⎛
I
9
pψ m1 ⎜⎜ iq′′1 + iq′′1′ − m (cos(2θ ) + 1)⎟⎟
2
3 3
⎠
⎝
(12)
It is known that the faulty star-winding set currents will
lead to an oscillating i'q1 giving an oscillating torque
according to (12). To decrease the torque pulsation and the
mutual influence between phases, all the switches of the
VSI connected to the faulty star-winding set are opened. In
this manner, the TSW-FSPM motor becomes a dual starwinding FSPM motor and its vector control consists of
controlling the d1-q1 current components of the two
remaining healthy star-winding sets. As usual, the d1-axis
current component is fixed to zero for minimizing the
losses and the motor torque is controlled by the q1-axis
current component. Hence, the torque in the post fault
operation can be expressed as:
Te =
9
pψ m1 (iq′′1 + iq′′1′ )
2
(13)
Therefore, this kind of TSW-FSPM motor can be
driven in the remedial BLAC operation mode.
B. Remedial BLAC with Harmonic Current Injection
Operation
Contrary to the first method, the two remaining phases
of the faulty star-winding set are supplied to track a nonsinusoidal reference current to reduce the torque
oscillations [11]. The key is to sum the measured q1-axis
current component (i'q1+i''q1+i'''q1) to be controlled to a
non-oscillating reference value. However, it is an openloop technique where the currents are determined (based
on motor fault models) for each fault scenario and the
harmonic current content in each orthogonal subspace is
not quantified.
According to amplitude invariant criterion, the inverse
Park transformation of (2) can be deduced as:
⎡ i′A1 ⎤
⎢i′ ⎥ ⎡ 1
⎢ A 2 ⎥ ⎢ cos γ
⎢i′A3 ⎥ ⎢
⎢ ⎥ = ⎢cos 2γ
⎢ iB′ 1 ⎥ ⎢ ...
⎢ ... ⎥ ⎢
⎢ ⎥ ⎢⎣ cos 8γ
⎢⎣iC′ 3 ⎥⎦
0
sin γ
1
cos 3γ
...
...
sin 2γ
...
cos 6γ
...
...
...
sin 8γ
cos 24γ
...
⎡ i1α ⎤
⎢i ⎥
1β
0 ⎤⎢ ⎥
⎢
0⎥
sin 7γ ⎥⎥ ⎢ ⎥
0
sin 14γ ⎥ ⎢⎢ ⎥⎥ (14)
⎥ i5α
... ⎥ ⎢ ⎥
⎢i5 β ⎥
sin 56γ ⎥⎦ ⎢ ⎥
i
⎢ 7α ⎥
⎢⎣i7 β ⎥⎦
where ik′ (k=A1, A2,…, C2, C3 or 1,2,..9) is the remaining
phase current under faulty condition.
After loss of phase A1, the relationship between
currents i'B1 and i'C1 according to (10) and (14) can be
obtained as:
2 cos 3γ ⋅ i1α + 2 cos 3γ ⋅ i5α + 2 cos 3γ ⋅ i7α = 0 (15)
From (15), it turns out that the fifth and seventh
harmonic current components are not independent any
more and positive to maintain the torque-producing
current i1α due to phase loss, hence keeping the
undisturbed MMF in the post fault operation. This means
that the torque linearity in a steady state can be guaranteed
even under asymmetric fault conditions. Therefore, the
harmonic currents should be quantified to keep the torqueproducing current invariant when the rotor angle is known,
what is called the remedial BLAC with harmonic current
injection operation.
It is well known that the loss results in temperature rise,
which is a critical issue for high-reliability operation. To
minimize the motor losses for a given torque, the fifth and
seventh harmonic current components in relations with
(15) are degrees of freedom which can be used. The
copper losses during the remedial BLAC with harmonic
current injection operation can be calculated as:
9
Rs ((i12α + i12β ) + (i52α + i52β ) + (i72α + i72β ))
(16)
2
Using Lagrangian multiplier λ for constrain (15), the
objective function P for the system can be formed as:
pj =
P (i5α , i5 β , i7α , i7 β , λ ) = p j + λ (i1α + i5α + i7α )
(17)
Zeroing the derivatives of the Lagrange function with
respect to i5α, i5β, i7α, i7β, and λ leads to the following
results:
∂P
∂P
∂P
= 0 , ...,
=0
=0,
∂i5α
∂i5 β
∂λ
(18)
Then, the quantified harmonic current components can
be obtained as:
⎧i5α = i7α = − i1α 2
⎨
⎩i5 β = i7 β = 0
(19)
Based on the equations above, the same operation can
be applied to the loss of any other phase. Similarly, the
reconstructed fifth and seventh harmonic current
components can be calculated as:
−1
⎞
⎡ihα ⎤
⎛
cos 2 (h( k − 1)γ ) + sin 2 (h(k − 1)γ ) ⎟⎟ ⋅
⎢i ⎥ = −ξ ⎜⎜
⎣ hβ ⎦
⎠
⎝ h =5 , 7
∑[
]
⎡cos(h( k − 1)γ )cos(( k − 1)γ ) cos(h( k − 1)γ )sin (( k − 1)γ )⎤ ⎡i1α ⎤
⎢ sin (h( k − 1)γ )cos(( k − 1)γ ) sin (h( k − 1)γ )sin (( k − 1)γ )⎥ ⎢i ⎥
⎣
⎦ ⎣ 1β ⎦
(20)
where ξ is a faulty condition quantity and its value is 1 or
0, corresponding to faulty or healthy mode, respectively.
IV.
MOTOR CONTROL STRATEGY
Since the traditional rotor-flux-oriented control strategy
cannot be applied to the TSW-FSPM motor directly, a
stator-flux-oriented (SFO) dq equation of the motor in the
rotor reference frame is developed [12]. It can be found
that the rotor position of the maximum PM flux linkage is
defined as the d1-axis, while the q1-axis advances the d1axis by 90° electrical degrees (equivalent to 2.64° in
mechanical degree). The development of the d1-q1 axis is
crucial for the development of this SFO fault-tolerant
control strategy. It has been known that the q1- and d1-axis
components of armature currents correspond to the
production of torque and flux, respectively. When the d1axis component of armature current is maintained, the
stator-PM flux-linkage will be constant.
Fig. 5 shows the control block diagram of the TSWFSPM motor drive, in which the SFO fault-tolerant control
is incorporated. By employing a proportional-integral (PI)
regulator, the difference between the reference speed and
the actual speed determines the reference electromagnetic
torque, which is directly proportional to the q1-axis
component of armature current. Note that the nine-phase
decoupling transform is carried out, and thus, the magnetic
interaction between the star-winding sets is decoupled.
Finally, a hysteresis controller is employed to drive the
three VSIs. The controller can use ξ to control the scheme
selection and activation. Switching to healthy operation
mode, the reference value of the torque-producing current
component is calculated by the control system in order to
satisfy the demand of torque, whereas the remaining
harmonic current components are restricted to zero. As to
the fault-tolerant implementation, the fifth and seventh
harmonic current components are online calculated by (20)
R1−1 (θ )
i1*β
i5*α
i5*β
ωr
i7*α
iA* 1 ~
iC* 3
i7*β
Fig. 5: Control block diagram for the TSW-FSPM motor supplied by
three VSIs.
V.
SIMULATION AND EXPERIMENTS
A. Simulation
For the work undertaken here, a physical phase
variable model of the TSW-FSPM motor was incorporated
into a Matlab/Simulink model of the full motor-drive
system. Vector-control algorithm orientated with the
stator-PM flux linkage and a mechanical load model are
also incorporated. The VSIs in this case have been
modeled by ideally controlled voltage sources but could
easily be extended to incorporate real device models if
required. The electromagnetic performance is investigated
when the TSW-FSPM motor is operated in normal and
faulty mode. To assess the level of the torque ripple under
various conditions, a torque ripple factor is defined as [13]:
K T = (Tmax − Tmin ) Tav × 100%
(21)
where Tmax, Tmin and Tav are the maximum, minimum, and
average values of the output torque, respectively.
The motor parameters are the same as in the experimental setup and are given in Table 1.
TABLE 1: MOTOR PARAMETERS
Rated output power
Rated current (rms)
Rated frequency
Rated speed
No. of pole-pairs in rotor
No. of pole-pairs in stator
Resistance per coil
D-axis inductance
Q-axis inductance
D-axis magnetic flux
Rotary inertia
10 kW
4.83 A
283 Hz
500 rpm
34
36
1.3 Ω
16 mH
18 mH
0.224 Wb
0.05 kg.m2
Current (A)
id*1
Torque (Nm)
i1*α
iq*1
Under the normal condition, the TSW-FSPM motor
drive operates in the nine-phase BLAC mode. Fig. 6 (a)
shows the motor phase current and torque waveforms. The
corresponding average torque and torque ripple of the
motor drive are 50N·m and 2%, respectively. It should be
noted that the torque ripple is caused by the cogging
torque. Fig. 6 (b) shows the motor phase current and
torque with phase A1 in the open-circuit fault. After the
fault occurs, phase A1 current drops to zero, and phases
B1 and C1 become equal and opposite to each other. The
torque- and flux-producing currents will become
disturbed, since the first star-winding is effectively
behaving as a single-phase winding in this mode. As
expected, the phase currents of the triple star-winding sets
become uncontrollable and a torque ripple of 10% exists
under such open-circuit fault condition. Pulsation with
double fundamental frequency is observed in the torque, in
accordance with (12).
Current (A)
ω
*
r
There are two stages during the simulations. The first
one is the normal operation mode without any open-circuit
phase. During the second stage, phase A1 became opencircuit.
Torque (Nm)
to compensate the torque-producing current loss during
open-circuit fault, namely set the q1-axis component of
armature current invariant before and after the fault, hence
the electromagnetic torque of the TSW-FSPM motor can
be maintained.
Fig. 6: Phase currents and output torque under: (a) Normal condition
and (b) phase A1 in open-circuit fault.
The remedial BLAC operation (method 1) is shown in
Fig. 7 (a). To reduce these oscillations, the phase currents
of the faulty star-winding set connected to the inverter are
forced to zero by opening all its switches at 720 deg.
While the outputs of the other two VSIs are increased to
support the portion of the faulty inverter. That is, before
the fault, each VSI delivers one-third of the motor power,
but after the fault, each non-faulty VSI delivers one half of
the motor power. Indeed, the TSW-FSPM motor operates
as a dual star-winding FSPM motor in this case. The motor
torque is non-oscillating, but the motor losses increase
compared to the healthy case. In fact, the current
magnitude of the active phases is 1.5 times greater with
the one in the healthy case, making 1.5 times of the total
copper losses.
The remedial BLAC with harmonic current injection
operation (method 2) is shown in Fig. 7 (b). The proposed
fault-tolerant control strategy is activated at 720 deg. It can
be observed that the motor drive can online switch to the
fault-tolerant mode. The torque oscillations are efficiently
reduced, and the system can operate continuously and
steadily after the open-circuit fault occurrence, slightly
less oscillating than in Fig. 7 (a) because of higher phase
number working. By using the proposed remedial strategy,
the locus of the αβ stator currents has been observed in
Fig. 8, verifying that the fifth and seventh harmonic
currents injected in the stator windings are used to coproduce circular rotating fundamental MMF during faulttolerant operation.
5
First star-winding
-5
0
Torque (Nm)
60
720
1440
Rotor position (deg)
50
40
0
Current (A)
0
Transient
torque
Torque (Nm)
Current (A)
5
720
1440
Rotor position (deg)
(a)
0
First star-winding
-5
0
60
720
1440
Rotor position (deg)
50
40
0
720
1440
Rotor position (deg)
(b)
β7 (A)
β5 (A)
β1 (A)
Fig. 7: Phase currents and output torque under: (a) Remedial BLAC
and (b) remedial BLAC with harmonic current injection.
Fig. 9: Copper losses at two remedial operations.
B. Experiment
In order to validate the theoretical study described in
the previous sections, a prototype of the proposed TSWFSPM motor drive system has been designed and built, as
shown in Fig. 10, and its parameters are given in Table 1.
The drive is controlled by a dSPACE digital control card
(DS1005) whose sampling period is 100 μs. It sends PWM
commands to three VSIs supplied by a 500 V dc-source.
The load is a DC motor controlled by a Buck chopper
circuit supplying a variable resistance. In the experiment,
the currents of the motor are sensed by nine Hall-effect
current sensors, and an optical encoder with an accuracy of
2048 counts per revolution is used to obtain position
information.
Firstly, the TSW-FSPM motor drive operates steadily
in the nine-phase BLAC mode. The measured phase
currents in the first star-winding and the output torque are
shown in Fig. 11 (a). It can be found that the phase current
waveform is ideal sinusoidal, which agrees with the
theoretical one shown in Fig. 6.
Secondly, the operation under open-circuit fault
condition is evaluated. It can be seen that the residual two
phase currents in the first star-winding are distorted, and
become equal and opposite to each other, as shown in Fig.
11 (b). Due to the high phase number, the TSW-FSPM
motor can also operate steadily under such faulty condition
with a torque ripple of 40% (which is higher than the
simulated value).
DC motor
Torque transducer
Fig. 8: Locus of currents in: (a) α1-β1, (b) α5-β5 and (c) α7-β7.
Although non-oscillating torque operation of the TSWFSPM motor can be achieved in both remedial methods,
the copper losses are different as shown in Fig. 9. It can be
noted that the copper losses average value in normal
operating mode is equal to 12.5W. When an open-circuit
fault occurs, the copper losses become 1.5 times greater
with the method 1, while they increase only 25% with the
method 2. This is due to the fact that the remedial BLAC
operation employs higher current amplitudes.
Fig. 10: Experimental bench.
TSW-FSPM motor
iA1
iB1
iC1
(a)
iB1
waveform have a significant discrepancy with those
simulated ones shown in Fig. 7. This discrepancy is due to
the fact that the predicted torque waveforms take into
account the cogging torque ripple only, whereas the
measured torque waveforms consist of all torque ripples,
such as operating torque ripple, and torque ripples caused
by imperfection in manufacture. Nevertheless, for the
normal and remedial operations, the measured torque
performances (average torque and torque ripple) are
equivalent to simulated results, verifying the effectiveness
of the proposed remedial operations.
In conclusion, the remedial BLAC with harmonic
current injection strategy is an effective way to minimize
both torque ripple and copper losses during open-circuit
fault.
iC1
(b)
Fig. 11: Measured (left traces) phase currents in the first star-winding
and (right trace) output torque. (a) Normal condition (20 ms/div; 1
A/div; 5 N·m/div). (b) Open-circuit fault condition (20 ms/div; 1
A/div; 10 N·m/div).
iA1
iB1
iC1
(a)
iB1
VI.
CONCLUSION
In this paper, two remedial control strategies have been
proposed and implemented for fault-tolerant operation of a
TSW-FSPM motor drive. By disconnecting the faulty starwinding set, the remedial BLAC operation is proposed to
provide no-control generated-torque-ripple operation. A
constraint setting the summation of the phase currents
equal to zero has been incorporated in derivation of the
remedial BLAC with harmonic current injection operation.
By injecting fifth and seventh harmonic currents, the
currents are calculated to satisfy the minimum stator
copper loss and minimum output torque ripple. Both the
simulated and measured results show fault-tolerant
characteristics of the TSW-FSPM motor. The proposed
fault-tolerant motor drive can be expected to have a bright
future in a wide variety of drive applications with the
requirements of high reliability and high power density.
ACKNOWLEDGMENT
This work was supported in part by the 973 Program
of China under Project 2013CB035603.
iC1
(b)
Fig. 12: Experimental responses of (left traces) phase currents and
(right trace) output torque (20 ms/div; 1 A/div; 10 N·m/div). (a)
Remedial BLAC. (b) Remedial BLAC with harmonic current
injection.
Finally, the dynamic performance of the proposed
TSW-FSPM motor drive is evaluated. Fig. 12 shows the
responses of torque and current before and after the
remedial BLAC and remedial BLAC with harmonic
current injection operations. It can be found that the motor
drive can online switch to the fault-tolerant mode. As
expected, theses current waveforms agree with the
simulated ones shown in Fig. 7, verifying that the
proposed remedial operations can maintain the torque
performance. It should be noted that the measured torque
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