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M.Tech, PS Power System Simulation Lab-1
FORMATION OF BUS ADMITTANCE MATRICES
Exp.No: 1 ate :
AIM:
To !etermine the a!mittance matrices "or the #i$en power system networ%.
SOFTWARE REQUIRED: M&TL&'
THEORY:
'us a!mittance is o"ten use! in power system stu!ies. (n most o" the power
system stu!ies it is re)uire! to "orm y- bus matrix o" the system by consi!erin# certain
power system parameters !epen!in# upon the type o" analysis. *-bus may be "orme!
by inspection metho! only i" there is no mutual couplin# between the lines. E$ery
transmission line shoul! be represente! by +- e)ui$alent. Shunt impe!ances are a!!e!
to !ia#onal element correspon!in# to the buses at which these are connecte!. The o""
!ia#onal elements are una""ecte!. The e)ui$alent circuit o" Tap chan#in# trans"ormers is
inclu!e! while "ormin# *-bus matrix.
Formation of Y-Bus Matri
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new M "ile by selectin# /ile - New M /ile
0. Type an! sa$e the pro#ram in the e!itor win!ow.
. Execute the pro#ram by either pressin# Tools 2un.
3. 4iew the results.
ept. o" EEE, S4E Pa#e 1
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M.Tech, PS Power System Simulation Lab-1
!RO"RAM
5M&TL&' pro#ram "or the "ormation bus a!mittance6*bus7 matrix
clc8
clear all8
n9
ybus9eros6n,n78y9eros6n,n78
"ori91:n
"or;9i
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M.Tech, PS Power System Simulation Lab-1
FORMATION OF $-BUS MATRI% USIN" MAT#AB
Expt.No: ate :
AIM : To !etermine the bus impe!ance matrices "or the #i$en power system networ%.
SOFTWARE REQUIRED: M&TL&'
THEORY:
Formation of $-Bus Matri
(n bus impe!ance matrix the elements on the main !ia#onal are calle! !ri$in#
point impe!ance an! the o""-!ia#onal elements are calle! the trans"er impe!ance o" the
buses or no!es. The bus impe!ance matrixes are $ery use"ul in "ault analysis. The bus
impe!ance matrix can be !etermine! by two metho!s. (n one metho! we can "orm the
bus a!mittance matrix an! than ta%in# its in$erse to #et the bus impe!ance matrix. (n
another metho! the bus impe!ance matrix can be !irectly "orme! "rom the reactance
!ia#ram an! this metho! re)uires the %nowle!#e o" the mo!i"ications o" existin# bus
impe!ance matrix !ue to a!!ition o" new bus or a!!ition o" a new line 6or impe!ance7
between existin# buses.
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new M "ile by selectin# /ile - New M /ile
0. Type an! sa$e the pro#ram in the e!itor Cin!ow
. Execute the pro#ram by either pressin# Tools 2un.
3. 4iew the results.
!RO"RAM
5M&TL&' pro#ram "or the "ormation bus impe!ance 6Dbus7 matrix
primary91 1 ? ?.3
1 ?.1
0 0 1 ?.1
? ?.3
3 0 ?.1 F8
elements,columnsF9sie6primary78
bus9F8
currentbusno9?8
"orcount91:elements8
rows,colsF9sie6bus78
ept. o" EEE, S4E Pa#e 0
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M.Tech, PS Power System Simulation Lab-1
"rom9primary6count,78
to9primary6count,078
$alue9primary6count,78
newbus9max6"rom,to78
re"9min6"rom,to78
i"newbus G currentbusno H re"99? bus 9bus eros6rows,17
eros61,cols7 $alue F8
currentbusno9newbus8
continue
en!
i"newbus Gcurrentbusno H re">9?8
bus9bus bus6:,re"7
bus6re",:7 $alue
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M.Tech, PS Power System Simulation Lab-1
SO#UTION OF !OWER F#OW USIN" "AUSS-SEIDE# METHOD
Expt.No: 0 ate :
AIM:
To un!erstan!, in particular, the mathematical "ormulation o" power "low mo!el in
complex "orm an! a simple metho! o" sol$in# power "low problems o" small sie!
system usin# auss-Sei!el iterati$e al#orithm
SOFTWARE REQUIRED: M&TL&'
THEORY:
The aussSei!el metho! is an iterati$e al#orithm "or sol$in# a set o" non-linear loa!
"low e)uations.
The non-linear loa! "low e)uation is #i$en by
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new M "ile by selectin# /ile - New M /ile
0. Type an! sa$e the pro#ram in the e!itor Cin!ow
. Execute the pro#ram by either pressin# Tools 2un.
3. 4iew the results.
!RO"RAM
5matlab pro#ramm "or loa!"low analysis usin# #auss sie!al metho!
clearn9
$91.? 1.? 1 1F*90-AiJ -
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M.Tech, PS Power System Simulation Lab-1
)limitmax9eros6n,17)limitmin9eros6n,17
$ma#"ixe!9eros6n,17type679
)limitmax6791.?)limitmin679?.
$ma#"ixe!6791.?!i""91?8noo"iter91
$pre$9$8while6!i""G?.????1 noo"iter99178
abs6$7 abs6$pre$7
5pause $pre$9$8
p9in" ?.3 -1 ?.0F8 )9in" ? ?.3 -?.1F8
s9in"91, $6i79polartorect6$ma#"ixe!6i7,an#le6$6i7J1?@pi778
en!
!i""9max6abs6abs6$6:n77-abs6$pre$6:n77778
noo"iter9noo"iter
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M.Tech, PS Power System Simulation Lab-1
SO#UTION OF !OWER F#OW USIN" NEWTON-RA!HSON METHODExpt. No: ate:
AIM :
To !etermine the power "low analysis usin# Newton 2aphson metho!
SOFTWARE REQUIRED: M&TL&'
THEORY:
The Newton 2aphson metho! o" loa! "low analysis is an iterati$e metho! which
approximates the set o" non-linear simultaneous e)uations to a set o" linear
simultaneous e)uations usin# TaylorOs series expansion an! the terms are limite! to "irst
or!er approximation. The loa! "low e)uations "or Newton 2aphson metho! are non-
linear e)uations in terms o" real an! ima#inary part o" bus $olta#es.
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new M "ile by selectin# /ile - New M /ile
0. Type an! sa$e the pro#ram in the e!itor Cin!ow
. Execute the pro#ram by either pressin# Tools 2un.
3. 4iew the results.
ept. o" EEE, S4E Pa#e K
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M.Tech, PS Power System Simulation Lab-1
!RO"RAM
5 M&TL&' pro#ram "or Newton-2aphson metho!54 9 1.?38 1.?8 1.?F8
! 9 ?8 ?8 ?F8Ps9-8 .?F8
s9 -.38*' 9 ?-;J3? -1?R61,179467J4617J*6,17Jsin6t6,17-!67
R61,79-467J4607J*6,07Jsin6t6,07-!67
4607J*6,07Jcos6t6,07-!67
R6,794607J4617J*60,17Jsin6t60,17-!607
R6,0794607J*6,07Jcos6t60,7-!607
467J4607J*6,07Jcos6t6,07-!67
R60,079-4617J*6,17Jsin6t6,17-!67
P 9 Ps - P8 9 s - 8
9 P8 FR
9 R!67 9!67
ept. o" EEE, S4E Pa#e
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M.Tech, PS Power System Simulation Lab-1
OUT!UTiter 9 1
9
-.B?? 1.0
-?.??
R 9 3.?? -00.?? .B??
-00.?? BB.??? -1B.B?? -K.1?? 1B.B?? A.K??
9
-?.?30 -?.??KK
-?.?B3
4 9
1.?3?? ?.AK03 1.???
! 9
? -?.?30
-?.??KK
iter 9
9
-?.?AA ?.?1K -?.?3?A
R 9
31.KK -01.KB3B 1.0?B -0.A1B B3.B3B -13.0KA1
-.30B 1K.? .1?0B
9 -?.??1
-?.??1?
-?.??1
4 9
1.?3?? ?.AK1K
1.???! 9
? -?.?K1
-?.??K
ept. o" EEE, S4E Pa#e A
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M.Tech, PS Power System Simulation Lab-1
iter 9 0
9
1.?e-??0 J
-?.1BB ?.?0
-?.10?
R 9 31.3ABK -01.BA0A 1.1K
-0.A00A B3.3AKB -13.031B -.3 1K.0ABA K.A3A
9
1.?e-??3 J
-?.03B
-?.0B -?.1
4 9 1.?3??
?.AK1K 1.???
! 9
? -?.?K1
-?.??K
P1 9 .1
1 9 1.?3
0 9 1.B1
RESU#T:
ept. o" EEE, S4E Pa#e 1?
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M.Tech, PS Power System Simulation Lab-1
FAST DECOU!#ED #OAD F#OW ANA#YSIS USIN" MAT#AB SOFTWARE
Expt. No: 3 ate:
AIM:
To become pro"icient in the usa#e o" so"tware in sol$in# loa! "low problems usin# /ast
!ecouple! loa! "low metho!.
SOFTWARE REQUIRED: M&TL&'
THEORY:
Loa! "low stu!y is use"ul in plannin# the expansion o" power system as well as
!eterminin# best operation o" the system. The principle obtaine! "rom loa! "low stu!y is
the ma#nitu!e an! phase an#le o" the $olta#e at each bus an! real an! reacti$e power
"lowin# in each line. Loa! "low analysis may be per"orme! usin# &.. networ% analyer
an! also by !i#ital computer. 'ut now a-!ays !i#ital computer oriente! loa! "low analysis
is a stan!ar! practice. The "ast !ecouple! loa! "low metho! is a $ery "ast metho! o"
obtainin# loa! "low solutions.
This metho! re)uires less number o" arithmetic operations to complete iteration
conse)uently. This metho! re)uires less time per iterations. (n N-2 metho!, the
elements o"Racobian are to be compute! in each iteration .So the time per iteration is
consi!erably more in N-2 metho! than in /L/. The rate o" con$er#ence in /L/ metho!
is slow re)uirin# consi!erably more number o" iterations to obtain a solution than in the
case o" N-2 metho!. Uowe$er accuracy is same in both the cases. (n this metho! both
the spee!s as well as the sparsity are exploite!.
This is an extension o" N-2 metho! "ormulate! in polar co-or!inates with certain
approximation which results into a "ast al#orithm "or loa! "low solution. (n practice,
transmission system operatin# un!er stea!y state possesses stron# inter!epen!ence
between acti$e powers an! bus $olta#es, an#les, similarly there is stron#inter!epen!ence between bus $olta#e an! reacti$e power
ept. o" EEE, S4E Pa#e 11
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M.Tech, PS Power System Simulation Lab-1
The e)uation "or power "low are a#ain expresse! below "or calculatin# elements o"
Racobian 6ie U H L7
There"ore the elements o" Racobian 6ie U H L7 can be calculate! as "rom the e)uations
abo$e o" power. V// !ia#onal element o" U is
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new M "ile by selectin# /ile - New M /ile
0. Type an! sa$e the pro#ram in the e!itor Cin!ow
. Execute the pro#ram by either pressin# Tools 2un.
3. 4iew the results.
!RO"RAM
5M&TL&' pro#ram "or /ast ecouple! Metho!5
clc8
clear all8
5bus!ata
5bus!ata9'us No bus co!e 4olta#e &n#le p! )! p# )#F
bus!ata91 1 1.?B ? ? ? ? ?8 ? 1 ? ?.3 ?. ? ?80 ? 1 ? ?. ?.0 ? ?8 ? 1 ? ?.0 ?.1 ?
? 8F
5line!ata
5line!ata9start bus en! bus rxshunt-*F
line!ata91 ?81 0 1 ?8 0 ?.BBB .BB ?8 1 ?80 ?8F
5uass-Sei!al &l#orithm
ept. o" EEE, S4E Pa#e 1
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M.Tech, PS Power System Simulation Lab-1
nl9line!ata6:,178
nr9line!ata6:,78
nbr9len#th6nl78
nbus9max6max6nl7,max6nr778
r9line!ata6:,0785line resistance
x9line!ata6:,785line resistancebc9line!ata6:,378
y9complex6r,-x78
epsilon9?.??18
r9epsilon 9%7 sum9sum
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M.Tech, PS Power System Simulation Lab-1
p8
$8
en!
$
!$9abs6$oi!-$78
r9max6!$78 $oi!9$8
iter9iter9ba7
line"low6ab,ba796$6ab7Jcon;6ibus6ab,ba7778
en!
en!
en!
line"lowislac%9?8
"orab91:nbus
"orba91:nbus
i"6ab9917
islac%9islac%
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M.Tech, PS Power System Simulation Lab-1
en!
en!
en!
pw
OUT!UTbus!ata 9
1.???? 1.???? 1.?B?? ? ? ? ? ?
.???? ? 1.???? ? ?.3??? ?.??? ? ?
0.???? ? 1.???? ? ?.??? ?.0??? ? ?
.???? ? 1.???? ? ?.0??? ?.1??? ? ?
line!ata 9
1.???? .???? .???? .???? ?
1.???? 0.???? 1.???? .???? ?
.???? 0.???? ?.BBB? .BB? ?
.???? .???? 1.???? .???? ? 0.???? .???? .???? .???? ?
ybus 9
0.???? -1.????i -.???? < .????i -1.???? < .????i ?
-.???? < .????i 0.BBB? -1.BB?i -?.BBB? < .BB?i -1.???? < .????i
-1.???? < .????i -?.BBB? < .BB?i 0.BBB? -1.BB?i -.???? < .????i
? -1.???? < .????i -.???? < .????i 0.???? -1.????i
ibus 9
? ?.K31 - ?.KAi ?.A? - ?.11Bi ?
-?.K31 < ?.KAi ? ?.?K1 - ?.??i ?.1KA? - ?.?BAi -?.A? < ?.11Bi -?.?K1 < ?.??i ? ?.103B < ?.??3i
? - ?.1KA? < ?.?BAi -?.103B - ?.??3i ?
line "low 9
? ?.?03 < ?.AB?i ?.31AB < ?.0i ?
-?.K0 - ?.1Ai ? ?.?K0 < ?.?i ?.133 < ?.?330i
-?.3?A - ?.13K0i ?.?KKB - ?.?0A3i ? ?.10B - ?.?1A?i
? -?.100 - ?.?BBi -?.10? < ?.?1i ?
islac% 9 1.0 - ?.A?Ai
slac%power 9 1.00 - ?.3?0ipw 9 3.?1e-??
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M.Tech, PS Power System Simulation Lab-1
SIMU#ATION OF SIN"#E AREA !OWER SYSTEMS
Expt . No: B ate:
AIM:
To become "amiliar with mo!ellin# an! analysis o" the "re)uency an! tie-line "low
!ynamics o" a power system without an! with loa! "re)uency controllers 6L/7 an! to
!esi#n better controllers "or #ettin# better responses.
THEORY:
&cti$e power control is one o" the important control actions to be per"orm to be
normal operation o" the system to match the system #eneration with the continuously
chan#in# system loa! in or!er to maintain the constancy o" system "re)uency to a "ine
tolerance le$el. This is one o" the "oremost re)uirements in pro$in# )uality power supply.
& chan#e in system loa! cases a chan#e in the spee! o" all rotatin# masses 6Turbine
#enerator rotor systems7 o" the system lea!in# to chan#e in system "re)uency. The
spee! chan#e "orm synchronous spee! initiates the #o$ernor control 6primary control7
action result in the entire participatin# #enerator turbine units ta%in# up the chan#e in
loa!, stabiliin# system "re)uency.
2estoration o" "re)uency to nominal $alue re)uires secon!ary control action which
a!;usts the loa! - re"erence set points o" selecte! 6re#ulatin#7 #enerator turbine units.
The primary ob;ecti$es o" automatic #eneration control 6&7 are to re#ulate system
"re)uency to the set nominal $alue an! also to re#ulate the net interchan#e o" each areato the sche!ule! $alue by a!;ustin# the outputs o" the re#ulatin# units. This "unction is
re"erre! to as loa! "re)uency control 6L/7.
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new Mo!el by selectin# /ile - New Mo!el
0. Pic% up the bloc%s "rom the simulin% library browser an! "orm a bloc% !ia#ram.
. &"ter "ormin# the bloc% !ia#ram, sa$e the bloc% !ia#ram.
3. ouble clic% the scope an! $iew the result.
ept. o" EEE, S4E Pa#e 1B
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M.Tech, PS Power System Simulation Lab-1
SIMU#IN& B#OC& DIA"RAM
OUT!UT
RESU#T
ept. o" EEE, S4E Pa#e 1K
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M.Tech, PS Power System Simulation Lab-1
SIMU#ATION OF TWO AREA !OWER SYSTEM
Expt . No: K ate :
AIM:
To become "amiliar with mo!ellin# an! analysis o" the "re)uency an! tie-line "low
!ynamics o" a two area power system without an! with loa! "re)uency controllers 6L/7
an! to !esi#n better controllers "or #ettin# better responses.
THEORY:
&cti$e power control is one o" the important control actions to be per"ormin# to
be normal operation o" the system to match the system #eneration with the continuously
chan#in# system loa! in or!er to maintain the constancy o" system "re)uency to a "ine
tolerance le$el. This is one o" the "oremost re)uirements in pro$in# )uality power supply.
& chan#e in system loa! cases a chan#e in the spee! o" all rotatin# masses 6Turbine
#enerator rotor systems7 o" the system lea!in# to chan#e in system "re)uency. The
spee! chan#e "orm synchronous spee! initiates the #o$ernor control 6primary control7
action result in the entire participatin# #enerator turbine units ta%in# up the chan#e in
loa!, stabiliin# system "re)uency.
2estoration o" "re)uency to nominal $alue re)uires secon!ary control action which
a!;usts the loa! re"erence set points o" selecte! 6re#ulatin#7 #enerator turbine units.
The primary ob;ecti$es o" automatic #eneration control 6&7 are to re#ulate system
"re)uency to the set nominal $alue an! also to re#ulate the net interchan#e o" each area
to the sche!ule! $alue by a!;ustin# the outputs o" the re#ulatin# units. This "unction is
re"erre! to as loa! "re)uency control 6L/7.
!ROCEDURE:
1. Enter the comman! win!ow o" the M&TL&'.
. reate a new mo!el by selectin# /ile New Mo!el
0. Pic% up the bloc%s "rom the simulin% library browser an! "orm a bloc% !ia#ram.
. &"ter "ormin# the bloc% !ia#ram, sa$e the bloc% !ia#ram.
3. ouble clic% the scope an! $iew the result.
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M.Tech, PS Power System Simulation Lab-1
SIMU#ATION OF AUTOMATIC "ENERATION USIN" MAT#AB
Expt . No: ate:
AIM:
To obtain automatic #eneration control usin# Matlab
THEORY:
(" a loa! on the system is increase! thr turbine spee! !rops be"ore the #o$ernor
can a!;ust the input o" the steam to a new loa!. &s the $alue o" spee! !iminishes, error
si#nal becomes smaller an! position o" "ly ball #o$ernor #ets closer to point re)uire! to
maintain a constant spee!. Uowe$er the spee! will not be set to a constant point. Vne
way to restore spee! or "re)uency to its nominal $alue is by use o" inte#rator. This unit
monitors the a$era#e error o$er a perio! o" time an! because o" its ability to return a
system to its set point, the inte#ral action is also %nown as rest action.
Thus as system loa! chan#es continuously the #eneration is a!;uste!
automatically to restore the "re)uency to its nominal $alue. This is %nown as #eneration
control.
The main role o" & is an interconnecte! system is to !i$i!e the loa!s amon#
system stations an! #enerators to achie$e maximum economy besi!es maintainin#
uni"orm "re)uency
SIMU#IN& B#OC& DIA"RAM:
ept. o" EEE, S4E Pa#e ?
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M.Tech, PS Power System Simulation Lab-1
OUT!UT
RESU#T:
ept. o" EEE, S4E Pa#e 1
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M.Tech, PS Power System Simulation Lab-1
DE'E#O! A !RO"RAM TO SO#'E SWIN" EQUATION
Exp. No.: A ate:
Aim: To e$elop a pro#ram to sol$e swin# e)uation
SOFTWARE REQUIRED: M&TL&'
THEORY:
Stability:
Stability problem is concerne! with the beha$ior o" power system when it is
sub;ecte! to !isturbance an! is classi"ie! into small si#nal stability problem i" the
!isturbances are small an! transient stability problem when the !isturbances are lar#e.
Transient stability:
Chen a power system is un!er stea!y state, the loa! plus transmission loss
e)uals to the #eneration in the system. The #eneratin# units run at synchronous spee!
an! system "re)uency, $olta#e, current an! power "lows are stea!y. Chen a lar#e
!isturbance such as three phase "ault, loss o" loa!, loss o" #eneration etc., occurs the
power balance is upset an! the #eneratin# units rotors experience either acceleration or
!eceleration. The system may come bac% to a stea!y state con!ition maintainin#
synchronism or it may brea% into subsystems or one or more machines may pull out o"
synchronism. (n the "ormer case the system is sai! to be stable an! in the later case it is
sai! to be unstable.
Small Signal Stability:
Chen a power system is un!er stea!y state, normal operatin# con!ition, the
system may be sub;ecte! to small !isturbances such as $ariation in loa! an! #eneration,
chan#e in "iel! $olta#e, chan#e in mechanical to)ue etc., the nature o" system response
to small !isturbance !epen!s on the operatin# con!itions, the transmission system
stren#th, types o" controllers etc. (nstability that may result "rom small !isturbance may
be o" two "orms,6i7 Stea!y increase in rotor an#le !ue to lac% o" synchroniin# tor)ue.6ii7
2otor oscillations o" increasin# ma#nitu!e !ue to lac% o" su""icient !ampin# tor)ue.
!RO"RAM
5 Point by Point Solution o" Swin# E)uation
5 JJJJJJJJJJJJJJJJJJJWWJJJJJJJJJJJJJJJJJJJJ5 Swin# e)uation bein# a non linear e)uation, numerical metho!s are use to
5 sol$e it. Point by Point metho! is one o" the classical solution to sol$e5 swin# e)uation
5
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M.Tech, PS Power System Simulation Lab-1
5 'elow is a solution o" swin# e)uation "or a machine connecte! to in"inite bus5 throu#h two parallel lines. Swin# e)uation is !rawn "or a persistin# "ault in
5 one o" the parallel line an! also a"ter "ault is cleare!. stability5 o" system is conclu!e! a"ter analysin# the swin# cur$e.
5 clearin# an#le is calculate! "or system stability55 M4& base 9 3?
5 #i$enE 9 3?8 4 918 ! 9 ?.8 1 9?.8 9 ?.8U 9 .K8
5 pre"ault con!ition!el 9 ?:pi@1?:pi8
!el1 9!el8!el 9 !el8
M 9 .K@61?J3?78 5 an#ular momentum 9 U@1?J"Peo 9 61.?3@?.7Jsin6!el78 5 (nitial power cur$e
Po 9 1 8 5 power output in pu 9 3? MC@3? M4&!elo 9 asin!6?.@1.?378 5 initial loa! an#le in !e#rees @@Pe 9 6EJ4@7 sin6!elo7
5 urin# "ault
Pe 9 1.?3Jsin6!el178 5 Power cur$e !urin# "ault5Post "ault con!ition
Pe0 9 61.?3@?.B7Jsin6!el78 5 Power cur$e a"ter clearin# "ault55 Primary Power cur$e plot /i#ure-1plot6!el,Peo78
set6#ca,=Tic%=,?:pi@1?:pi78set6#ca,=Tic%Label=,X=?=,==,==,==,==,=pi@=,==,==,==,==,=pi=Y78
title6=Power ur$e=78xlabel6=Loa! an#le=78
ylabel6=enpower=78text66@07Jpi,61.?3@?.7Jsin66@07Jpi7,=le"tarrow intial
cur$e=,=Uoriontal&li#nment=,=le"t=78text6pi@,.K3,=.B3Jsin!elta=,=Uoriontal&li#nment=,=center=78
hol! all
plot6!el1,Pe78text66@07Jpi,1.?3Jsin66@07Jpi7,=le"tarrow !urin# "ault=,=Uoriontal&li#nment=,=le"t=78text6pi@,1.?,=1.?3Jsin!elta=,=Uoriontal&li#nment=,=center=78
plot6!el,Pe078text66@07Jpi,61.?3@?.B7Jsin66@07Jpi7,=le"tarrow "ault
cleare!=,=Uoriontal&li#nment=,=le"t=78text6pi@,1.1,=1.K3Jsin!elta=,=Uoriontal&li#nment=,=center=78
hol! o""55 ------------
t 9 ?.?38 5 time step pre"erably ?.?3 secon!st1 9 ?:t:?.38
55 6a7 sustaine! "ault at t 9 ?
5 "or !iscontinuity at t 9 ? , we ta%e the a$era#e o" acceleratin# power
5 be"ore an! a"ter the "ault5 at t 9 ?-, Pa1 9 ?
5 at t 9 ?
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M.Tech, PS Power System Simulation Lab-1
i"i 99 1
!6i7 9 !1JPa6i78 !el6i7 9 !elo8
else
c!el6i7 9 c!el6i-17
!el6i7 9 !el6i-17
!el"6i7 9 !el"6i-17
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M.Tech, PS Power System Simulation Lab-1
5 a"ter clearin# "ault, power cur$e shi"t to Pe0"ori 9 0:11
i"i 99 0 c!el"6i7 9 c!el"6i-17
Pa"6i7 9 1 - Pe"6i78 a1 9 Pa"6i78
!"6i7 9 !1JPa"6i78 a 9 !"6i78
Pe"6i7 9 1.K3Jsin!6!el"6i778 Pa"6i7 9 1 - Pe"6i78
!"6i7 9 !1JPa"6i78 Pa"6i7 9 6Pa"6i7< a17@8
!"6i7 9 6!"6i7 < a7@8 else
c!el"6i7 9 c!el"6i-17
Pe"6i7 9 1.K3Jsin!6!el"6i778
Pa"6i7 9 1 - Pe"6i78
!"6i7 9 !1JPa"6i78
en!en!
55 ------"i#ure 6078
plot6t1,!el"78
set6#ca,=tic%=,?:?.?3:?.378set6#ca,=tic%Label=,X=?=,=?.?3=,=?.1?=,=?.13=,=?.?=,=?.3=,=?.0?=,=?.03=,=?.?=,=?.3=,=?.3?=Y78
title6=Swin# ur$e=78xlabel6=secon!s=78
ylabel6=!e#rees=78text6?.3,3K,= /ault leare! in ?.1? sec=,=Uoriontal&li#nment=,=ri#ht=78
text6?.13,0?,= loa! an#le !ecreases with time -- Stablestate=,=Uoriontal&li#nment=,=le"t=78
55 6c7 critical clearin# an#le!elo 9 !e#tora!6!elo78 5 initial loa! an#le in ra!
!elm 9 pi - asin61@1.K378 5 an#le o" max swin#
c1 9 66!elm-!elo7-61.?3Jcos6!elo77
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M.Tech, PS Power System Simulation Lab-1
STABI#ITY ANA#YSIS: SIN"#E MACHINE CONNECTED TO AN INFINITE
BUS SYSTEMExp. No: 1? ate:
AIM :
To become "amiliar with $arious aspects o" the transient an! small si#nal stability
analysis o" Sin#le-Machine-(n"inite 'us 6SM('7 system
SOFTWARE REQUIRED: M&TL&'
THEORY:
Stability:
Stability problem is concerne! with the beha$ior o" power system when it issub;ecte! to !isturbance an! is classi"ie! into small si#nal stability problem i" the
!isturbances are small an! transient stability problem when the !isturbances are lar#e.
Transient stability:
Chen a power system is un!er stea!y state, the loa! plus transmission loss
e)uals to the #eneration in the system. The #eneratin# units run a synchronous spee!an! system "re)uency, $olta#e, current an! power "lows are stea!y. Chen a lar#e
!isturbance such as three phase "ault, loss o" loa!, loss o" #eneration etc., occurs the
power balance is upset an! the #eneratin# units rotors experience either acceleration or!eceleration. The system may come bac% to a stea!y state con!ition maintainin#
synchronism or it may brea% into subsystems or one or more machines may pull out o"
synchronism. (n the "ormer case the system is sai! to be stable an! in the later case it issai! to be unstable.
Small Signal Stability:
Chen a power system is un!er stea!y state, normal operatin# con!ition, the systemmay be sub;ecte! to small !isturbances such as $ariation in loa! an! #eneration, chan#e
in "iel! $olta#e, chan#e in mechanical to)ue etc., the nature o" system response to small!isturbance !epen!s on the operatin# con!itions, the transmission system stren#th,
types o" controllers etc. (nstability that may result "rom small !isturbance may be o" two"orms,
6i7 Stea!y increase in rotor an#le !ue to lac% o" synchroniin# tor)ue.6ii7 2otor oscillations o" increasin# ma#nitu!e !ue to lac% o" su""icient !ampin#
tor)ue.
!ROCEDURE:1. Enter the comman! win!ow o" the M&TL&'.
. reate a new M "ile by selectin# /ile - New M /ile
0. Type an! sa$e the pro#ram.. Execute the pro#ram by either pressin# Tools 2un3. 4iew the results.
ept. o" EEE, S4E Pa#e B
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M.Tech, PS Power System Simulation Lab-1
A#"ORITHM:
!RO"RAM5transient small si#nal stability5
5clc
5clear all
E91.038
491.?8
U9A.A8
9?.B38
Pm9?.B8
9?.108
"o9B?8
Pmax9EJ4@8
!o96asin6Pm@Pmax778
Ps9PmaxJcos6!o78
Cn9s)rt60.1JB?@6UJPs778
D9@Js)rt60.1JB?@6UJPs778
C!9CnJs)rt61-DQ78
"!9C!@6J0.178
tan91@6DJCn78
th9acos6D78
!o91?J0.1@1?8
t9?:?.?1:08
!9!o@s)rt61-DQ7Jexp6-DJCnJt7.Jsin6C!Jt
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M.Tech, PS Power System Simulation Lab-1
xlabel6=tsec=7
ylabel6=!elta !e#ree=7
subplot6,1,7
plot6t,"7
#ri!
xlabel6=tsec=7ylabel6="re)uency as hert=7
title6=$ariation o" #enerator "re)uency=7
OUT!UT:
RESU#T:
ept. o" EEE, S4E Pa#e
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M.Tech, PS Power System Simulation Lab-1
SO#UTION OF ECONOMIC DIS!ATCH !ROB#EM IN !OWER SYSTEMS
Exp. No.: 11 ate:
!ROB#EM:The "uel cost "unctions "or three thermal plants is W@h are #i$en by,
1 9 3?? < 3.0P1 < ?.??P1
9 ?? < 3.3P < ?.??BP
0 9 ?? < 3.P0 < ?.??AP0
where P1,P an! P0 are in MC. The total loa! P is ??MC. Ne#lectin# line losses an!#enerator limits, "in! the optimal !ispatch an! the total cost in W@h.
AIM:To !e$elop a pro#ram "or sol$in# economic !ispatch problem without
transmission losses "or a #i$en loa! con!ition usin# !irect metho! an! Lamb!a-iterationmetho!.
TOO# BAR:M&TL&'
THEORY:
& mo!ern power system is in$ariably "e! "rom a number o" power plants.2esearch an! !e$elopment has le! to e""icient power plant e)uipment. & #eneratin# unit
a!!e! to the system to!ay is li%ely to be more e""icient than the one a!!e! some timebac%. Cith a $ery lar#e number o" #eneratin# units at han!, it is the ;ob o" the operatin#
en#ineers to allocate the loa!s between the units such that the operatin# costs are to beminimum. The optimal loa! allocation is by consi!erin# a system with any number o"
units. The loa!s shoul! be so allocate! amon# the !i""erent units that e$ery unitoperates at the same incremental cost. This criterion can be !e$elope! mathematically
by the metho! o" La#ran#ian multiplier.
Statement of Economic Dispatch Problem (EDP)(n a power system, with ne#li#ible transmission loss an! with N number o"
spinnin# thermal #eneratin# units the total system loa! P at a particular inter$al can bemet by !i""erent sets o" #eneration sche!ules.
XP16%7, P
6%7, ..................PN6[7Y8 % 9 1,,........NS
Vut o" these NS set o" #eneration sche!ules, the system operator has to choose the seto" sche!ules, which minimie the system operatin# cost, which is essentially the sum o"
the pro!uction cost o" all the #eneratin# units. This economic !ispatch problem is
mathematically state! as an optimiation problem.
The number o" a$ailable #eneratin# units N, their pro!uction cost "unctions, theiroperatin# limits an! the system loa! P.
To !etermine the set o" #eneration sche!ules P,
N
Min /T9\/i 6Pi7 ]].617i91
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M.Tech, PS Power System Simulation Lab-1
N
9 \ Pi P 9 ? .]].67
i91
Pimin ^ Pi^ Pimax ]]..607
The units pro!uction cost "unction is usually approximate! by )ua!ratic "unction/i 6Pi7 9 ai Pi
< bi Pi< ci 8 i9 1,,.......N ]..67
where ai, bi an! ci are constants
Necessary conditions for the existence of solution to EDP
The E problem #i$en by the e)uations 617 to 67. 'y omittin# the ine)uality constraints,the re!uce! E problem may be restate! as an unconstraine! optimiation problem by
au#mentin# the ob;ecti$e "unction with the constraint _ multiplie! by La#ran#emultiplier, to obtaine! the La#ran#e "unction, L as
N NMin L 6P1........PN, `7 9 \/i6Pi7 - `\Pi PF ]]637
i91 i91
The necessary con!itions "or the existence o" solution to 6B7 are #i$en by
L @ Pi9 ? 9 !/i6Pi7 @ !Pi- `8 i 9 1, ,........N ..]..6B7
NL @ `9 ? 9 \Pi P ]].6K7
i91
The solution to E problem can be obtaine! by sol$in# simultaneously the necessary
con!itions 6B7 an! 6K7 which state that the economic #eneration sche!ules not only
satis"y the system power balance e)uation 67 but also !eman! that the incremental
cost rates o" all the units be e)ual be e)ual to ` which can be interprete! as incrementalcost o" recei$e! power.
Chen the ine)uality constraints 607 are inclu!e! in the E problem the necessarycon!ition 6B7 #ets mo!i"ie! as
!/i 6Pi7 @ !Pi9 ` "or Pimin ^ Pi^ Pimax
^ ` "or Pi9 Pimax
` "or Pi9 Pimin ]]]..67
M(t)o*s of so+ution for ED! ,it)out transmission +oss(s:The solution to the E problem with the pro!uction cost "unction assume! to be a)ua!ratic "unction, e)uation 67, can be obtaine! by simultaneously sol$in# 6B7 an! 6K7
usin# a !irect metho! as #i$en below,
Economic Sche!ule
!/i 6Pi7 @ !Pi9 ai Pi < bi 9 ` 8 i 9 1,, ........ N ]]6A7
ept. o" EEE, S4E Pa#e 0?
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M.Tech, PS Power System Simulation Lab-1
/rom E)uation 6A7 we obtain
Pi9 6` bi 7 @ ai 8 i91,.........N .]]61?7
Substitutin# E)uation 61?7 in E)uation 6K7 we obtainN
6- bi7 @ ai 9 P
i91
N N
61@ai7 9 6b1@ai7
i91 i91
N N
` 9 P < \6 bi@ai 7F @ \61@ai7 F ]]]6117 i91 i91
A+orit)m for ED! ,it)out transmission +oss:
The metho! o" solution in$ol$es computin# La#ran#ian multiplier 6`7 usin# e)uation 6117an! then computin# the economic sche!ules Pi8 i91,,........N usin# e)uation 61?7. (n
or!er to satis"y the operatin# limits 607 the "ollowin# iterati$e al#orithm is to be use!.
Step 1: ompute ` usin# E)uation 6117.
Step 2: ompute usin# E)uation 61?7 the economic sche!ulesPi8 i 9 1,,........N
Step 3: (" the compute! Pi satis"y the operatin# limitsPimin Pi Pimax 8 i 9 1,,.........N
Then stop, the solution is reache!. Vtherwise procee! to Step
Step 4: /ix the sche!ule o" the N4 number o" $iolatin# units whose #eneration Pi$iolates the operatin# limits 617 at the respecti$e limit, either
Pimax or Pi min
Step 5: istribute the remainin# system loa! P minus the sum o" the "ixe!#eneration sche!ules to the remainin# units numberin# N2 69 N-N47 by
computin# ` usin# E)uation 6117 an! the Pi8 iN2 usin# e)uation 61?7
where N2 is the set o" remainin# units.
Step 6: hec% whether optimality con!ition 67 is satis"ie!. (" yes, stop the solution
Vtherwise, release the #eneration sche!ule "ixe! at Pi max or Pi min o"those #enerators not satis"yin# optimality con!ition 67, inclu!e these units
in the remainin# units, mo!i"y the sets N4, N2 an! the remainin# loa!.
o to Step 5.
ept. o" EEE, S4E Pa#e 01
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M.Tech, PS Power System Simulation Lab-1
!RO"RAM
clc
clear all
!isp96=input !ata=7
alpha9input6=enter the alpha $alue in cost "unction: =7
beta9input6=enter the beta $alue in cost "unction:=7
P!9input6=enter the total loa! in mw:=7
#amma9input6=enter the #amma $alue in cost "unction:=7
!elp91?8
lam!a9input6=enter the estimate! $alue o" lam!a:=7
!isp96=output=7
!isp96=lam!a p1 p p0 #ra! !el lam!a=F7
iter9?8
whileabs6!elp7G9?.??1
iter9iteren!
totalcost9sum6alpha
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M.Tech, PS Power System Simulation Lab-1
beta 9 3.0???
3.3??? 3.???
enter the total loa! in mw:??
P! 9 ??
enter the #amma $alue in cost "unction:?.??8?.??B8?.??AF
#amma 9
?.???
?.??B?
?.??A?
enter the setimate! $alue o" lam!a:3
lam!a 9 3
!isp 9
output
!isp 9
lam!a p1 p p0 #ra! !el lam!a
!isp 9
3.???? -0K.3??? -1.BBBK -. A0.B111 B0.A 0.3???
!isp 9
.3??? ??.???? 3?.???? 13?.???? ? B0.A ?
totalcost 9
B.B3e
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