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TRANSIENT ANALYSIS OF PARALLELY OPERATED SELF-EXCITED INDUCTION
GENERATORS
L.B. SHILPAKAR.
BHIM SINGH
and
K.S.P. RAO
Department of Electrical Engineering, IIU Delhi New
Delhi-lXO 016, INDIA, FAX 91-11-6862037
generation because of its advantages like
ruggedness, reduced cost, absence of DC
excitation, reduced maintenance and ar
appropriate level of performance durinc
transients[1-8J.
ABSTRACT
The objective of this paper is to predict
transient behavior of Self Excited
Induction Generator(SEIG). A system of
parallely operated SEIGa is subjected to
various transient conditions such as initial
excitation, load perturbation, switching of
another machine for parallel operation,
switch-in/out of capacitor in the system.
Mathematical model of this system is
developed which is based on d-q theory of
machine variables and it is represented in the
state space form. The developed model is
simulated to carry out performance analysis of
the
system
during
dynamic
conditions.
Experimental verification of the simulated
results examines the feasibility of the
proposed
system
and
validates
the
mathematical model. The feasibility^ of the
system is also examined for the purpose of
switching one induction generator in
parallel to another one with a view to
maintain the quality of power supply.
Usefulness of the results obtained in this
investigation is described.
Installation and parallel operation of i
number of SEIGs of different ratings is
often required to harness the full potential of
hydro energy available at the site. Parallel
operation of the SEIGs is commonly used in wind
power generation where the siz« of the machine
becomes one of the constraints. In remote
areas, diese! generator can be operated to
create lqca! grid and the power generation
from micr< hydro using grid connected
inductioi generator can be used to supply the
lighting and other loads of the area.
Identifyin< these applications, a need is felt
to stud; the transient behaviour of SEIGs
operatim in parallel.
Steady state and transient analysis o
single SEIG have been well investigated [ I1 9].
The initiation of the self excitatio: process
is a transient phenomenon and i better
understood if analysed usin< instantaneous
values of current and voltage Gratham et al
[5,6] used d-q axis model t-investigate the
process of current an voltage build up during
self excitation an load perturbations. But
effect of cros saturation is not included in
the model.
1. INTR0DUCTIOH
Increasing
depletion
of
reserve
of
conventional
source
of
energy
and
environmental concerns have necessitated the
tapping of clean and renewable energy
resources like hydro, wind, biomass etc.
Techno-economic difficulties in extending
the existing power line to remote areas and the
inherent advantages of induction machines
have called for their use as capacitor
excited induction generator in isolated
application. In the recent years, the
induction generators are preferred over an
alternator in micro hydro and wind power
Change in the level of saturation in on axis
causes a corresponding change of flu level in
the other perpendicular axis an this is
usually named as a cross-saturation The
transient behaviour of SEIG incorporating
the cross magnetization effec in the machine
model have been studied i
470
[7,8], Levi{9] has discussed different
applications of the model in analysis of
saturated induction machines. However, the
scope of these attempts is limited to
operation of single SEIG. In [10,11] an
analytical model is proposed to predict the
performance of a group of induction
generators operating in parallel, however,
p-the results were restricted to steady state
behaviour
only.
The
knowledge
of
instantaneous values of voltage, currents,
torque etc. in parallely operated SEIGs
during dynamic conditions are also of
interest and this helps in proper design of the
system.
2.
MODELING
Fig. 1 shows the schematic of the proposed
system. It consists of two delta connected
induction machines acting as generators and
excited by a common capacitor bank and
supplying a resistive load. The bank may
consists
of
fixed
and
variable
capacitors.
P
1
Generator
bus
SEIG
rime
The main thrust of this attempt is to predict
transient behavior of a system of SEIGs
operating in parallel and subjected to various
transient conditions such as voltage build up,
load perturbation, switching in another
induction generator in the system and
switch-in/out of capacitor to adjust the
excitation requirement as per the load
perturbation. The cross coupling effect of
main flux path saturation is ' also
incorporated in the model in order to make it
more realistic. Saturation in the magnetic
circuit of the machine is included in the
model. For the same, inductance (Lm) is
expressed as a function of magnetizing
current(im) by a fourth order polynomial. For
this, the data obtained in synchronous speed
test are used. Simulated results of SEIGs
operating
in
parallel
are
verified
experimentally in a laboratory test rig.
mOVer
T7T
Capacitor
Fig.l.
System
of
n
Induction G e n e r a t o r s
Self
bank
Excited
The
equivalent
circuit
of
the
system
in
d-q axis
stationary
reference
frame[13J
is
shown in
Fig.
2.
The
equations
of
the
induction generator
can
be
expressed
as
follows;
Voltage-Current
Equation: The
voltage-current
relationship
of
the
sn
(a)
D-axis
(b)
Q-axis
Fig.2.
D- and Q-axes
SEIGs coneected
equivalent circuit
in
parallel
471
of
n
(3)
T
system is expressed as[13];
[v]j=tR)j[iJj+[L]jp[i]j+tG]jti]jwrj
shaft
j = T
e
j
Capacitor
j
Equation:
I n i t ia t i o n o f s e l f e x c i t a t io n is b a s e d o n
residual magnetism in the rotor circuit and
voltage build up with the support of
reactive current supplied by the capacitor
bank connected to the common bus. When load
is connected to the bus, the equations which
describe the capacitor bank are:
(I)'
W h e r e , s u b s c r i p t j d e n o t e s t h e j machine(j
= l,2 ...n) and n is number of induction
generators, p(-d/dt) is a del operator,
[v],[i],[R],[L]
and
[GJ
are
voltage,
current, resistance, transformer inductance
and rotational
- inductance matrices
defined as follows and other notations have
their usual meaning[7,8,13].
P[Q]=[isT]-[iL]
(4
Where,
)
(5)
isqj irdj
R8j Rrj
Sndj
[L].
Jdqj
bmdj
[Q]=[Q
.
"T
i«J
i«sd
sqJ
*Mqj
Ldqj
b
mqj
mqj
Mqj dqj
dqj
L
L
lrj+Lmqj
dqj
00
[G].
Load
o0
For
for
0
0
-I
0
mdj
mqj
'
|v
l
1 = [V
sJ
l
,
V
sd
Equation:
resistive
load current
load
can
the
equation
be
written
as;
(6)
Owing
to
the
nonlinearity
in
the
magnetic circuit
of
the
machine,
the
magnetizing inductance
is dependent
on the
instantaneous value
of
the
magnetizing
current.
The magnetizing
current can be calculated
of
(7)
as;
L_,+L,
.+L
The effect of cross saturation is ensured
wit h t he pr es en ce of L, jqi t e r m s i n t n e
elements of matrix [L] . ana second term in
the expression of Lmd. and L . [7].
J
Where,
dqj
sqJ
,
and
0
lrj
1
Heife, [i sT] and [i Ll represents total stator
current matrix and load current matrix
respectively and [ Q ] is the charge matrix
for
capacitor
C.
Llrj+Lmdj
umdj
w
Q
The d-q axis components current
magnetization
are given by,
sdj^rdj
<dLmj/d'
and
i mqj- l Bqj +i rqj
The above model equations (1),(3) and (4)
describing the transient performance of the
system can be written as follows;
Lmj
dqj
When the machines are connected in
parallel the d-q axes voltages are;
sdj
sd
and
(8)
sq
pwrj=(P./2J.)<Tshaft P[Q]=[i8T]-[iL]
Developed
Electromaanetic
The set of Equations (8),(9)and (10) (10)
describes the dynamic model of the
SEIG system in terms of electrical and
mechanical variables.
The developed electromagnetic torque and the
mechanical motion of the SEIGs can be written
as;
Tej=(3/2)(Pj/2)Lraj(irdjisqj-irgjisdj)
(9)
3
472
3.
SYSTEM DATA, SOLUTION
EXPERIMENTAL VERIFICATION
stator
terminals
are
connected
in
parallel to
a
common
bus.
At
instant
t = 0,
■ capacitor
of
50 uf
is
switched
into the bus. Fig.3
shows the
line voltage build up of th« bus
with
simultaneous
excitation
of
both
TECHNIQUE AND
Two induction generators with ratings 7.5 kW
and 3.7 kW, respectively are selected for the
purpose of studying the dynamic behavior of the
proposed system. The parameters of b o t h t h e
m a c h i n e s a l o n g w i t h t h e r mathematical
relationship pertaining to the
saturation in the magnetic circuit are given in
Appendix. The
model
described
in
the
foregoing section is general one, where, n
r e p re s en ts
th e
n um b e r
of
in du c ti on
generators in the system. The number of
equations representing the model increases in
proportion to the number of generators put for
parallel
operation.
In
present
investigation n is equal to 2(i.e. two
genera tors
oper ati ng
in
p aral lel).
Therefore, the model consists of only twelve
differential equations (five equations for
each induction generator and two equations for
capacitor excitation) . These first order
nonlinear differential equations are solved,
using the fourth-order Runga-Kutta method of
numerical integration. The validity of the
developed mathematical model have been verified
experimentally on a test rig. The test rig
mainly consists of above mentioned two
induction generators, two dc machines acting
as prime mover and a load resistor.
(b)
1I
RESULTS
1
Self
im
p
1
u.iuitniullllillllf
uUiiiu(tnnyH||HiW
-t
m
HttBfflMBiaiai
a
I
1
|l"M
1
1
1
1
i
t
i
M
l
1
i
1
i
i
i
i
ii
1S2
■»■
—f
t
>">
**
Fig.3
M
M*
i
i
.
i
LiiwrBlHMIWiHIIH
""^wMnnanm
M
Voltage and current build-up in
parallel
connected
SEIGs
during
simultaneous excitation
X-axis :200 ms/div Y-axix
:(vs) 0.85 pu/div
s2 > 1-23
the
machines.
The
value
of
capacitance is a d e q u a t e l y c h o s e n s o a s t o
o b t a i n t h e n o load steady state rms voltage
of
bus
at
1.06
pu.
This
value
of
c a p a c i t a n c e m a y b e considered as fixed
.one. It is observed that the b us v o ltage
c o ntinu es to b u ild u p u n til the magnetic
circuits of both the machines g e t s a t u r a t e d
and thereafter, it stabilises t o a s t e a d y
s t a t e v a l u e w h i c h i s proportional to the
shunt capacitor.
AND DISCUSSION
of
'
|
InHlflm
1
1
i
1
1
ComputedHHIBBBB
I
(a)
The simulated results are compared with
experimental ones. Following observations
are
mad e
fr om
th e se
resu lts.
Whil e
discussing the results, 7.5 kW machine is
numbered as first one and the machine with 3.7
kW rating is referred as second one.
4.1 Initiation
1
1
11
The following dynamic conditions have been
investigated here.
i)
Simultaneous excitation of both the
machines ii) Sequential excitation
of both the
machines, one after
another, with
sufficient
time
gap
required
for
voltage build up iii) Resistive load
switching and load
perturbation iv)
Switching of capacitor
4.0
Measured
Excitation
In
some
practical
cases,
sequential
excitation of induction generators is
r e q u ir e d th a t i s e x c i ta t i o n o f o n e m a c h in e
is followed by another one. In order to
investigate this case, a capacitor of
reduced
value
(31
uf
per
phase)
is
switched-i n , w h e n th e - s p e e d o f f i r s t
m a c h i n e i s br o ug h t to a re qu ire d lev el. On
c omp letion o f s e l f e x c i t a t i o n o f t h i s
m a c h i n e , t h e second machine which
is
driven by a separate
B o th th e in d uc tio n mac h in es are dr iv en a t
same speeds of 1.01 pufbase speed 1500 rpm)
by
two
independent
prime
movers
and
their
473
t- -rT
■nw
w
WNM
Mft
1
t
1 1
1
1
M
M
1
1
1
to
■H
• ■--<H
3
ft
-
..,...», - - ..i.,
M
"
■
m
m
"^ffMHf^flRtf^
i
i
-
1
1
1 1
1
1
i
t
ii
i
(
—I
200 ms/div
(a) measured
•D
a
PliWi
i
liilflliil
i
■ffiiiiri
f
it
200 ms/div
(b) computed
"*■
Fig.4. Voltage and current build-up in 7.5 kW
induction generator
3
to
"0
rO
rH
ft
ft
3
3
zuu ms/aiv
200 ms/div
(a) Measured
(b) Computed
3
■ft
Fig.5 Bus voltage and line current of 7.5 kW
induction generator during switching
o"f 3.7 kW induction generator.
o -a
3
>
3
ft
>
O
>
T3
(N
H
-^4
H
•
m
ft
fl
^~-
3
CM CD
•rH
50 ms/div (a) Measured
Fig. 6;. Bus voltage and line current of 3.7 kW
induction generator during its
switching
prime-mover is connected in parallel to it.
For the same, proper matching of phase
sequence of both the machines must be
ensured. To meet the excitation requirement of
both
the
machines
an
additional
capacitor^16 uf per phase) is switched-in to
the bus prior to, the ■„ switching of second
machine. The transient performance of the
system during this dynamic condition are
50 ms/div
(b) Computed
shown in Figs.4, 5 and 6. Pig. 4 pertains to the
excitation
of
first
generator,
and
quantities of interest(current and voltage)
are shown. It is observed from Fig. 5 that
switching of second machine causes a small dip
in the bus voltage, however, it smoothly
recovers to a steady state value within 0.3
seconds. The current surge experienced in
first and second generators during the
474
■
■
►4
switching of second generator are shown in
Figs.5 and 6, respectively. The current surge
in the first generator remains below 2 pu while
it shoots up to 5 pu in the second generator.
The per unit,value of current of each generator
is calculated with reference to its rated
current as base. However, the current surges in
both the generators are settled down only in 30
ms, and thereby, the ■^system is able to sustain
its excitation.
j --- j -- 1
--- j —
1
■I PHHI||ml|lfl
f illf
1
1
i
t
—-j—- j—-i—
4.2 Load Switching and Perturbation
(a) Measured
i
!
A balanced resistive load of 0.15 pu(base power
11 kW) is suddenly switched into the system bus.
Apart from this an additional load of 0.15 pu
is switched-in/out in order to demonstrate
the effect of load perturbation. The bus
voltage and load current during the load
switching and the load perturbation are
portrayed in Figs. 7 and 8. During the load
application, the steady state voltage of the
bus is observed to be reduced. This is
indicative of poor regulation of the system.
Therefore, a suitable voltage regulator must
be provided to make the system useful for
practical application.
i i
Fig.8.
i
i
i
i
t
|lvWraywvWWvi)
--i—+—j-—-j—
v
100 ms/div
i
lluiflftAISlillll&aftMAAAA
(b) Computed
i
; ulin
Load
terminal voltage and load
current during load perturbation
r- "O
3
O.
3
a.
O 3
•a
•a
100 ms/div
(b) Computed
a
r- «-i c T3
(a) Measured
j p i
! ! !
Fig.9. Bus
voltag
3 ft
■0
i-
3
v
e
o ^
and
0
•H
■o
3
04
capac
itor
curre
100 m s/div (b)
>
compute d
terminal voltage
and
load
Fig.7, L o a d
current during
load switching
■A
•a
o 3
nt
during
a step
change
of
ft
capaci
tor
bank
475
4.3 Capacitor switching
In this study, switching-in/out of capacitor
i n d i s c re t e s t e p s i s a p p l i e d i n o rd e r t o
supply the excitation current. Fig.9 shows
the bus voltage and the capacitor current
when a capacitor of 10 uf is switched in the
system. Since no abnormal transient are
fac ed in the bus vol tage and capac itor
current, the switching of discrete steps of
capacitor bank can be used for the purpose
of improving the bus voltage under varying
load condition.
5.0
CONCLUSION
It has
been
demonstrated
that
the
developed
model
is capable
of analyzing
the
excitation
phenomenon
of
a
group
of
induction
generators, it has been found that
there is
close
agreement
between
simulated
and
measured
results,
hence
validity
of
the
developed
model
is
confirmed.
The
steady
state voltage of the bus is observed
to be
proportional
to
shunt
capacitor.
The
feasibility of parallel operation of
induction generators has been examined,
therefore it may be implemented in the
practical field. The transient study carried
out in this investigation may be useful in
design of
a practical
system.
6.0
REFERENCES
[1] E.D. Bassett and F.M. Potter, "Capacitive
E x cita tion fo r in du c tion g en er a tor", AI E E
Trans., Vol.54, pp.540-545, May 1935.
[2] J.M. Elder, J.T. Boys and J.L. Woodward,"The
process of self excitation in induction
generators", IEE Proc, Pt.B, Vol.130, pp.103
-107, March 1983.
[3] A.K. Tandon, S.S. Murthy and G.J. Berg,
"Steady state analysis of capacitor excited
induction generators", IEEE Trans, on Power
App. and Sys., Vol. PAS-103, No.3,
pp.612-618, March 1984.
[4] L. Shridhar, Bhim Singh and C.S. Jha,"A step
towards improvement in the characteristics
of the self excited induction generator",
IEEE Trans, on Energy Conversion Vol.8,
No.l, pp.40-46, March 1993.
[5] D.
Sutanto,
B.
Mismail,
H.R.
Outhred,
C. Grantham,
P.
Bryce and
K.C. Daly,"Transient simulation
of
capacitively
self-excited induction
generators",
Electric
Energy
Conference, Adelaide, 6^-9 October 1987.
[6] C.Grantham, D.Sutanto and B. Mismail,"Steady
state and transient analysis of self-excited
induction generator", IEE Proc, Pt.B,
Vol.136, No.2, pp.61-68, March 1989.
[7] K.E. Hallenius, P. Vas and J.E. Brown,
"The analysis
of
a
saturated
self-excited, asynchronous generator",
IEEE Trans,
on Energy Conversion,
Vol.6, No.2, pp.336-345, June 1991.
[8] L.Sridhar, Bhim Singh and C.S.Jha,"Transient
Performance of series regulated short shunt
self excited induction generator", IEEE
Trans, on Energy Conversion, Vol.10, No.2,
pp.261-267, June 1995.
[ 9 ] E. Levi, "Applications of the current state
space model in analysis of saturated
induction machine", Electric Power Systems
Research, Vol.31, pp.203-216, 1994.
[10] A.H. Al-Bahrani and N.H. Malik, "Steady
state analysis of parallel -operated self
excited induction generators", IEE Proc,
Pt.C,
Vol.140, No.l, pp.49-55,
January
1993.
[11] A.H. Al-Bahrani and N.H. Malik, "Voltage
control of parallel operated self excited
induction generators", IEEE Trans, on Energy
Conversion, Vol.8, No.2, June 1993.
[12] JiM. Elder, J.T. Boys and J.L.Woodward,"Self
-excited induction machine as a small
low-cost generator", IEE Proc, Pt.C,
Vol.131, No.2, pp.33-41, March 1984.
[13] Paul C. Krause, "Analysis of electric
machinery",
McGraw-Hill
International
Edition, Singapore, 1987.
APPENDIX
Machine - I
7.5
kW,
3-phase,
4 Pole,
50Hz,
415 V,
14
Delta
Connected,
1450
rpm,J=0.1384
Kg-nT,
pu,
R =0.0409
pu,X, =X, =0.1013
pu
R =0.0493 r_.
Base Voltage/Base Current=415/8.
Relation between Lm and im is as follows;
m
0.44
0.43-0.04Im-0.0351'
-0.00028I4m 0.2
•n+0.0056l'm
4
1.27
1.27—7.21
57.21
Machine - II
3.7 kW, 3-phase, 4 Pole, 50 Hz 415 V, 77.6 A,
delta connected, 1420 rpm, J=0.0842 Kg-m '
R =0.053 pu, R =0.061 pu, X , = X , =0.087 pu
Base Voltage/base Current=415/4.39
i is follows;
m
0.84
0.89-0.Q039Im-0.107I2m+0.0245I3m
-0.00121 m
0.43
£0.77
0.77--4.0
A,
476