IEEE Power Electronics Magazine - June 2021 - 49

Considering single-phase open-circuit fault, phase a will
get OFF, and the current in phase a immediately drops to
zero. Let us consider three-phase stator self-inductances be
L ,a
Lb and Lc
be Mab
MM Mca M
ib and ic
z
LL
ab== =
ab c== =
bc
sa , z
Mbc and M .ca
LL
sb , z -- Stator Flux Linkages
-- stator phase currents.
sc
R
T
S
S
S
R
T
S
S
S
z
z
z
a
b
c
V
X
W
W
W
v
v
=+
R
T
S
S
S
b
c
n
n
z
z
z
sa
sb
sc
V
X
W
W
W
R
R
T
S
S
SS
z
z
m
m
zi
i
i
cos
cos
Rc
i
i
b
c
me
e
e
cos
^
E
dt
d
z
z
z
sa
s
s
b
c
V
X
W
W
W
=>
M
L
M
M
M
L
H E
;
i
i
b
c
^h
h
120
120
z
z
b
c
c
c
;; ;EE <=+ F
b 0
Rb and Rc
are stator phase resistances and vbn
resents stator phase voltages.
Substituting equation (2) into (3)
;; ;;EE EE <
v
v
bn
cn
Rb
=+ -
0 Rc
i
i
b
c
L
M
M
L
R
T
S
S
SS
~ -- rotor speed.
Let
r
LL LL 12
+
Let J, T ,e
dq MLL 23
== += (/ ) = (/ )
(5)
T ,l B m represents the moment of inertia, electromagnetic
torque, load torque, coefficient of damping
friction, respectively. Electromagnetic torque is given by
J dt
d
~
r TT BTel mr s
=- ~-(6)
1,000
800
600
400
200
dt
di
dt
di
b
c
V
X
W
W
WW
z~
i
z~ i
mr e
mr e
sin
sin
(
(
-
+
120
120
c
c
)
)
F
(4)
and vcn
V
X
W
W
WW
(1)
(2)
(3)
rep4,000
3,000
2,000
1,000
-1,000
-2,000
-3,000
-4,000
Sample
Time (5 ms/div)
(b)
Phase A
Phase B
Phase C
FIG 6 Three-phase currents (a) simulation, and (b) experimental.
and three-phase stator mutual-inductances
ik 1 ik ik ik
pp1 ik ik ik
ik+=TT++qq qq0
3,000
2,000
1,000
-1,000
-2,000
-3,000
0 0.01 0.02 0.03 0.04 0.05 0.06
Time (s)
(a)
0.07 0.08 0.09 0.1
dp ddpd0+=TT++^^ ^^hh hh (7)
^^ ^^hh hh (8)
A. Pre-Fault Condition
The discrete-time state-space model of the PMSM drive in
pre-fault is given by
Ref.
0 0.01 0.02 0.03 0.04 0.05 0.06
Time (s)
(a)
1.2
1
0.8
0.6
0.4
0.2
0 0.01 0.02 0.03 0.04 0.05 0.06
Time (s)
(b)
FIG 5 Experimental set-up (Source: Prairie View A&M University).
FIG 7 (a) Speed response, and (b) Torque.
June 2021 z IEEE POWER ELECTRONICS MAGAZINE 49
0.07 0.08 0.09 0.1
NMPC
0.07 0.08 0.09 0.1
Torque (Nm)
Speed (rpm)
Current (mA)
Current (mA)

IEEE Power Electronics Magazine - June 2021

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