m.tech lab manual - pss

7/26/2019 M.tech Lab Manual - PSS

1/33

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


2/33


!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


3/33


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%.


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:



0. Type an! sa$e the pro#ram in the e!itor Cin!ow



!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



4/33


"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


5/33


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


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:






!RO"RAM

5matlab pro#ramm "or loa!"low analysis usin# #auss sie!al metho!

clearn9

$91.? 1.? 1 1F*90-AiJ -


6/33


)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


7/33


SO#UTION OF !OWER F#OW USIN" NEWTON-RA!HSON METHODExpt. No: ate:

AIM :

To !etermine the power "low analysis usin# Newton 2aphson metho!


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:






ept. o" EEE, S4E Pa#e K


8/33


!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


9/33


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


10/33


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?


11/33


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!.


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



12/33


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:






!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



13/33


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


14/33


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%


15/33


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-??


16/33


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:


. 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


17/33


SIMU#IN& B#OC& DIA"RAM

OUT!UT

RESU#T

ept. o" EEE, S4E Pa#e 1K


18/33


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:


. 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.



19/33


20/33


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 ?


21/33


OUT!UT

RESU#T:



22/33


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


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



23/33


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 ?


24/33


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


25/33


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 - [email protected] 5 an#le o" max swin#

c1 9 66!elm-!elo7-61.?3Jcos6!elo77


26/33


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


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&'.


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


27/33


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

"[email protected]

tan91@6DJCn78

th9acos6D78

!o91?J0.1@1?8

t9?:?.?1:08

!9!o@s)rt61-DQ7Jexp6-DJCnJt7.Jsin6C!Jt


28/33


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:



29/33


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

ept. o" EEE, S4E Pa#e A


30/33


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?


31/33


/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.



32/33


!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


33/33


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

m.tech lab manual - pss

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