IEEE Power Electronics Magazine - June 2021 - 51

where idf
and iqf
currents, respectively. Let vdf
q-axis voltages:
df
represents post fault d-axis and q-axis
and vqf
be the d-axis and
Tik vk TL^^=hh6 df ss
/
Tik vk TLff ssqq
^^=hh6
The cost function Cf
f 11 ik ik11 1
Ck hh hh h@2
(14)
^^ ^^ ^
+= +- ++ +- +
6ik ik
d
r
df
of NMPC for post-fault is
2
@
6
q
r
and the minimum cost function value is
,, ,
Min 11
s.t.
CT Tk kk
v VV V
f=- ++ -+
! "
e
r
sn
k
^^
bn__ _bn cn
1 zzs
s
r
f
cn
bn cn
i 12 6f=
and V .cn6
qf
e hh
11 22 66,
@
@
/
Table 3. Comparison of existing fault-tolerant
methods with the proposed NMPC.
Method
Current Residual
Vector method [13]
Allelic point function
method [14]
Non-Linear P-I
Observer [15]
Normalized Line-toLine
Current [16]
(15)
where Vbn _icni (, ,, ) represents two stator phase
voltages Vbn
Torque Estimation
The electromagnetic torque equation is
Tk pk ik
LL ik ik
em q
dq dq
^ hh
+= z ++
+- ++
1
Flux Estimation
Flux linkage expression is
<< 
TL z
pzm
e
r
2
3
qd
H
2
6iLdm@2
d
r
is assumed to be zero
Hence,
z
s
r
=+z
>
TL
2
e
r
3
qd
z
pzm
H
2
2
m
(21)
Figure 8 (a) and (b) shows phase A current waveform
after the occurrence of a single-phase open-circuit fault
(20)
Conclusion
This article shows the effectiveness of the LNSD system,
where the models created in MATLAB/Simulink software
can be tested in real-world situations, and successful results
can be received in just a few minutes. Two case studies
were performed to hypothesize the effects of the LNSD
drive. The first study tested automatic control of variable
speed synchronous servo motor, and the second study
tested the novel model predictive control for fault-tolerant
synchronous servo motor. This LNSD drive, along with the
MATLAB/Simulink software, can be beneficial in testing
real-life applications such as clearing faults in milliseconds
that occur in satellites, high-speed trains, and electric vehicles.
This set-up is an excellent tool for power electronics
engineers, students, researchers, and professors.
About the Authors
Yogita P. Akhare (yakhare@pvamu.edu) received her
Bachelor of Engineering (B.E.) in Electronics & Power
(Electrical) from Nagpur University, Nagpur, Maharashtra,
India, and Master of Engineering (M.E.) in Electrical (Power
Systems) from Pune University, Maharashtra, India. She is
currently working towards a Ph.D. degree in Electrical Engineering
at Prairie View A&M University, Prairie View, Texas,
USA. Her current research interests include electrical
machine drives, control systems, and renewable energy.
June 2021 z IEEE POWER ELECTRONICS MAGAZINE 51
2
3
6 ^^ h
^
11
h ^^
11 (16)hh@
at different speeds. From the figure, it can be clear that a
single-phase open-circuit fault that occurs in the drive gets
cleared within five milliseconds of that of the fault occurrence,
i.e., the fault clearance time is 1/6 that of the fundamental
period of the phase current (Tc), which is very small
as compared to the existing fault-tolerant control methods.
Figure 8 (c) shows the speed response for 1000 rpm reference
speed, and Figure 8 (d) shows the speed response
at a decrease of 50% of the reference speed. The responses
indicate that the machine runs continuously without any
disturbance in spite of the occurrence of the fault.
Comparison of existing fault-tolerant methods with the
proposed NMPC is summarized in Table 3.
Proposed NMPC
Fault Clearance
Time
< 1/4 Tc
About 1/4 Tc
< 1.5 Tc
< Tc
1/6 Tc
Computational
Burden
High
Medium
Low
Low
Low
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