I
ADVANCED EiiECTRIC DRIVES
Assignment-4
ETE SYLLABUS
I
QUESTION
..\ 7.~ k\\7, 3-phase, 415 l\ 3300 rpni, 4-pole, l"-connected, Pl\lSAI ,,ith a synchronous
inductance of 3.5 mH obtains the rated inducNI open circuit ,·olfage at 2500 rpm. H
this n1otor is operated at 3000 rpm and at 75% of ra.ted torque in field oriented control
mode, calculate t_he resultant arm.ature nu:1 linkage (in ,,b) llith dirett axis current
zero (id=O).
QUESTION
A 7.5 k\\', 3-phase, 415 \-·, ~0 112, _4-pole, Y-rounertNI. s)11cbronous 1·elurtanr• motor
bas !ollowlna pa1·1.1nete1·s: Xsct ::J()!t X14 ~n, 111ted po,vt't" tactol' =0.80 (laggia&). •~d
Rr=IO. Negjtt,. ftirttou. u-iodage and toi•e loss. Tilt sJ>fftl or the moto1· 1, c-O11trollftt
fa vttro.. ('OotroJ oslna three-phase P\\'M voltage somTr 1u,-.~11er with almost 11wty
• po,,·er fartor at AC: mafias and ,vttll nc· bus ,·olfage of 100,r. Tht' motor is controlled
,vtth constant, ff us b.tlow bast speed and roustant 1-attd l"0ltaae abo,"e bas~ spet<t
C"alr11Jate 1notor rms r1u·a-e11f (lu ..\) at· startl11g It tbe·sta1·ting to1-que is t"N)uirNI equal
to-the
rated f01·que.
,
QUESTION
Q. A 15 kVA, 3-phase, 415 v, 2-pole. Y-connected,
pen11a~ent magnet synchrono11s n1otor . has the
followmg parameters: maximum speed .of 10000
rpm: synchronous inductance of 2.5 mH The
maxun~un torque. which it can produce without
exceedmg rated armature current is 20 Nm.
.
~alc~late the speed at which produces rated open
etrc.u1t voltage
.
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;.
!.
QUESTION
'
¥-connected,·
le,
po
2V,
5
41
e,
as
ph
3A,
kV
IO
A
Q.
has following
or
ot
m
s
ou
on
hr
nc
sy
t
ne
ag
n1
t
en
an
nn
pe
~10000 • (Pm,
of
d
ee
sp
.
tim
im
ax
m
·
s:
ter
e
111
ra
pa
ted induced
ra
d
an
H
m
2.5
of
e
nc
cta
du
in
tlS
lo
oi
synthr
th e
~
at
ul
lc
·ca
.·
m
rp
00
75
at
ge
open circuit volta
oduce without
pr
n
ca
it
ich
wh
,
ue
rq
to
n
o1
iin
1nax
exceedi11g rated an11atl1re ct1rre11t.
~-
QUESTION·
catiops: 7.S k\ l: 3ifi
ec
sp
ng
,vi
flo
e
-th
-.
ha~
e
i1·
,ir
\ri
.
.J•. A P~AIS
, Xs d= 20 . Xsq=lO
ed
eet
nn
co
Ye,
Ol
4-p
,
Hz
50
\;
.s
phase, 41
1·manent .,magnet
pe
,
ng
_gi
Jag
6
0.9
r=
~to
faer
1v
po
n, rate-<J
gible R~ .! NegJe~t (1-,ictioa,
flux Jinkages=i.015 l's anti negli
e.d of motor is conh~olled
,,·indin.g, an,l co1·e l'oss. The spe
usin·g P\\~'1 \"SI. The
ie
en
sch
·0J
o·t1
co·
1·
cto
.,rre
t
·e-c
di1
in:
using
.-Ou::t helo,,· b,as,e speed [.•
t
tan
ns
'(-o
th
,,,~J
d
lle
ro
nt
eo
is
r
moto
.ba-se ·speed. c:atcuJate
and ~anit1t1Jf J:-a.ted ,·oltage abo.,~e
nts -()f 1he sJatc)r
~t. retereoce· d-<J C<l111p<>1te·
cu rr~ nt at sta1.1•i11g i_f
tJ1-c rat~tl tt"1rc1t1,c,,
srarr·ing r,,.rque is tt·(1-uircd ct}lJ,.11 rt)
i sta h) r
t'>f th,~ -~Utf<.lr ClU"fe.1·11. anc
nts
n,c
po
lil1
c<
J
,1-<
e
tJc
ere
•b. ref
sp~.:cl iU lJ 11:._lf,tll~ l'Ul\.~, l(lf(.ltl\.~~
fi·t:(JIICJ)(.'"}t a.r l1i 1lf tll~ rtllcc.l
.,
•
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'
QUESTION
A thNe-Pha!e VSI fed three-phase, 415 V (line), 50 Hz, 4pote, star connttted, synchronous reluctance motor has an Xd=45
obmstpha.,e, X"=lO ohms and negligible Jl.. Thi., motor is driving a fan
load, Which torque is propordonal to speed square and is 10 Nm at
lSOO rpm. The speed ot the motor is controlled using indirect vector
control scheme through- PW~I VSJ. The motor is controlled with
constant flux below base speed and constant rated ,·oltage above base
speed. Calculate (a) reference d-q components of stator current at
starting if starting torque is required rated torque, (b) reference d-q
components of stat~r current and stator frequenc)' at half the rated
speed ·and one fourth the rated torque for maximum transient
performance (c) If rotor speed is required to raise 0. 75 times the rated
speed then, calculate reference tl-q components of stator current~
QUESTION
The three-phase, 2Jo..,·, 60-Hz, ll-k\\·, four-pole Induction motor ls to be driven by
a field-oriented sprefl.con1rol systen1 at• $peed of 1740 rpm. A~~umln1 the controller
is programmed to s-et the rotor· ftu·s linkages ;.., to the -mach.lne rated ~•k ,talue, nn·d
th~ rms amplitude of the armature tUfftnt (in Amps), if the tltttroinagnttfc power
is 9.7 k\\: and the n1oto-r Is operati·ng at a speed of 1680 rpm. The parameter$ or the
induction n1otor are:
RI= 0.09~obm Rl =0.2ohm Lr= ~J.J9mH Ls= ~l.41mH
Lm 49.6mH
=
(Q no: 1) The modnlating waves for the VSC shown in the Fig.1 are given by Va(t), Vb(t)
and vc(t), as per the following expressions
v.(t) = 0..75 sm{tot) + 0.JS sm(3mt)
Vb(t) = 0.75 sin(mt-lff/3) + 0.15 sin(3mt)
vc:(t) = 0.75 sin(mt+2ffl3) + 0.15 sin(3mt)
where m==2n*S0 rad/s is the fundamental frequency. The DC bus voltage is 500V. Neglect
switching frequency harmonics.
The RMS vaine ofload phase voltage is
I
.
The RMS valne of fnndamental component ofVSC pole voltage is
Ds
Di
Aj
I
I
B.
Vdc
j
I
Dz
•
I
04
,
,
o.
Fig.I
(Q No:2) A three phase VSC having a DC bus voltage of 1000v f~eds a star connected load
of impedance 5 ohm. The modulating waves for three phases of the VSC are given by Va(t),
Vb(t) and Vc(t), given by the foUowing expressions
Va(t)
V6 (t)
=0. 4 sln(rut) + 0. 1 sin(rut)
2,r
=0.4sln(tAJ t-3) + 0.1sin(rut)
4,r
Vc(t) = 0.4sin(ld t-3) + 0.1sln(ldt)
Where
"'= 314.15rad/s,. They are compared with high frequency carrier spanning
between 1.3 and-1.3 for switching purpose. What is the RMS magnitude of the 'a' phase load
current in ampere?
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Q3
The magnitude of the load phase voltage space vector VR is 0. 49Vde as shown in the space
vector diagram in Fig.4. H the DC bus voltage is 600V, then what is the magnitude of the
fundamental RMS load phase voltage (in V)?
I
I
2/3Vdc
Fig.4
Q4
.
f
A three-phase converter shown in the Fig.S(a) is used to drive an R-L load. The de bus voltage
is 1573V. The modulating wave for leg A is shown below in Fig.S(b) which contains a
fundamental and third harmonic component. The modulating wave is given by the expression
f (t) m.sin(tdt) + kstn(3tdt). High frequency carrier is between +1 and -1 and is not
shown.
, '
,. '
1·. , '
=
1
What is the per phase RMS voltage across the load in volt?
I
. I
Ds
Di
R
a•.
Dz
I
D,
Fig.5 (a)
1111
D,
L
1t
Q)
r
r
!:: , I
r
::.:_ r
r
T
r
,
,
M~ul~tin~ sign~I
i
0.5
-0
:J
0.
0 •
E
<C -0.5
0.005
0
0.01
0.015
0.02
Time(s)
QS
Fig.5 {b)
Consider a 3-phase voltage source converter with 3-phase periodic pole voltage
waveforms having 3-phase symmetry, half wave symmetry, and odd symmetry. The de
bus voltage magnitude is Vde. The instantaneous pole voltage magnitudes (measured with
respect to midpoint of DC bus) in phases A, Band Cat 9=mt=15 degrees are -Vdc/2, Vdc/2, Vdc/2 respectively. Consider phase sequence A-B-C.
The instantaneous pole voltage magnitude in phase A at O=cot=-105 degrees is - - The instantaneous pole voltage magnitude in phase Bat D=mt=-105 degrees is - - The instantaneous pole voltage magnitude in phase Cat D=mt=-105 degrees· is-----
..
Q6
For realizing the reference vector VR using space vector PWM, the following information
is provided: Sampling time period TS= 100 ps, VD=700 V and Tl=T2=TO = (l/3)TS. The
switching states (000),(001), (101), (111) are switched to realize the reference vector VR
in the sampling period.
What is the angle of the reference vector (VR) in degrees?
Iii
Q7
In the space vector diagram shown, the reference vector VR touches the boundary of t he
hexagon. Given, sampling time period Ts = 200 JlSec and VD=571 V. What is the
combined duration of time for the zero vectors, in 11sec, to realize the reference vector ?
.
Vl. ___.__~---... __ _yl
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f
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•
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\\
"\
\
- ,v,
.;·
/
l;
v,. \
~\.
...
\
\\
\•
........._.._... i
V\
:s
t
/
I
v,
Q8
The modulating waveform for a 3-phase VSC switched using SVPWM-is shown in the
figure. The high frequency carrier spanning between + 1 and -1 is not shown. H the DC
" bus voltage is 486 V, then what is the fundamental RMS AC line voltage obtained in
Volts?
0 • 8 1 z:::.::::
::::.:=
0.4 I- I
\.. -
OJ
'-
;,a ' zu:::.::::::::: :;,,,.a
z:.;:: JI :,;;P-
• - !
¥\. f
I
{
'
u.....:::: i' :;,.;z
'
z::::...::::
•
z::::....:::::
'
-....:::::J:-,.a
•\
yW
cc...:::::
\
•
'
:--4
_j.
:J. ·\
.. ,
+-J .. \
\
,.
:;,,,,,,a ftIs z::w..;;;:: :,,s--
"k
1
-04
• L
-0.8
0
-,.,,,
:::r"·
o.oos
<
i
"'> II _,. :
_..,... " ' _..,... :,-, I -
0.01
0.015
0.02
-- 0
()
times
.... j .....,, ...-:::::::1.
0. 03
0..02S
Q9
A 3-phase VSC is having a DC bus voltage of 600V and feeds a star connected load of
impedance 10 ohm. The modulating waves for three phases of the VSC are given by va(t),
vb(t) and vc(t), given by the following expressions:
va(t) = 0.66sin (mt) + 0.2sin (3mt)+o. lsin (9mt)
r
0~
I.
f\
'IJ
vb(t) = 0.66sin (mt-2,r/3) + 0.2sin (3mt)+O. lsin (9mt)
)
''\
,(I
vc(t) = 0.66sin (mt+2n/3) + 0.2sin (3mt)+o.lsin (9rot)
where m=314.1S rad/s. They are used for switching the three switches of the converter
using a high frequency carrier spanning between + 1 and -1.
What is the RMS magnitude of the 'a' phase load current in Amperes?
and carrier is as shown in the
The timing diagram of a three-phase modulating signal
QlO diagram.
Identify the sector in which the space vector lies?
Vb
-v r
VJ
··~·
-.-,
~::
i
/
•~~•.:::.."'::,..I ....... _
Time (t)