Ieee 14 Bus System Load Flow Using n

8/16/2019 Ieee 14 Bus System Load Flow Using n

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IEEE 14 BUS SYSTEM LOAD FLOW USING N-R METHOD

% Program for Newton-Raphson Load Flow Analysis..



nbus = 1! % "###-1$ = ybusppgnbus&! % 'alling ybusppg.m to get $-(us )atri*..busd = busdatasnbus&! % 'alling busdatas..()+a = 1,,! % (ase )A..bus = busd/1&! % (us Number..type = busd/0&! % ype of (us 1-2la34/ 0-P/ 5-P6.. = busd/5&! % 2pe3ified oltage..del = busd/&! % oltage Angle..Pg = busd/7&8()+a! % P9i..

6g = busd/:&8()+a! % 69i..Pl = busd/;&8()+a! % PLi..6l = busd/<&8()+a! % 6Li..6min = busd/&8()+a! % )inimum Rea3ti+e Power Limit..6ma* = busd/1,&8()+a! % )a*imum Rea3ti+e Power Limit..P = Pg - Pl! % Pi = P9i - PLi..6 = 6g - 6l! % 6i = 69i - 6Li..Psp = P! % P 2pe3ified..6sp = 6! % 6 2pe3ified..9 = real$&! % 'ondu3tan3e matri*..( = imag$&! % 2us3eptan3e matri*..

p+ = findtype == 0 > type == 1&! % P (uses..

p? = findtype == 5&! % P6 (uses..np+ = lengthp+&! % No. of P buses..np? = lengthp?&! % No. of P6 buses..

ol = 1!"ter = 1!while ol @ 1e-7& % "teration starting..

P = erosnbus/1&!

6 = erosnbus/1&! % 'al3ulate P and 6 for i = 1nbus for 4 = 1nbus Pi& = Pi& B i&C 4&C9i/4&C3osdeli&-del4&& B(i/4&Csindeli&-del4&&&! 6i& = 6i& B i&C 4&C9i/4&Csindeli&-del4&& -(i/4&C3osdeli&-del4&&&! end end

% 'he34ing 6-limit +iolations..

if "ter D= ; EE "ter @ 0 % nly 3he34ed up to ;th iterations.. for n = 0nbus if typen& == 0 69 = 6n&B6ln&! if 69 D 6minn& n& = n& B ,.,1!

elseif 69 @ 6ma*n& n& = n& - ,.,1! end end end end

% 'al3ulate 3hange from spe3ified +alue

dPa = Psp-P! d6a = 6sp-6! 4 = 1! d6 = erosnp?/1&! for i = 1nbus



if typei& == 5 d64/1& = d6ai&! 4 = 4B1! end end dP = dPa0nbus&! ) = GdP! d6H! % )ismat3h e3tor

% Ia3obian

% I1 - Jeri+ati+e of Real Power "nKe3tions with Angles..

I1 = erosnbus-1/nbus-1&! for i = 1nbus-1& m = iB1! for 4 = 1nbus-1& n = 4B1! if n == m for n = 1nbus I1i/4& = I1i/4& B m&C n&C-9m/n&Csindelm&-deln&&B (m/n&C3osdelm&-deln&&&! end I1i/4& = I1i/4& - m&0C(m/m&! else I1i/4& = m&C n&C9m/n&Csindelm&-deln&& -(m/n&C3osdelm&-deln&&&! end end end

% I0 - Jeri+ati+e of Real Power "nKe3tions with ..

I0 = erosnbus-1/np?&! for i = 1nbus-1& m = iB1! for 4 = 1np? n = p?4&! if n == m for n = 1nbus I0i/4& = I0i/4& B n&C9m/n&C3osdelm&-deln&& B

(m/n&Csindelm&-deln&&&! end I0i/4& = I0i/4& B m&C9m/m&! else I0i/4& = m&C9m/n&C3osdelm&-deln&& B (m/n&Csindelm&-deln&&&! end end end

% I5 - Jeri+ati+e of Rea3ti+e Power "nKe3tions with Angles..

I5 = erosnp?/nbus-1&! for i = 1np?

m = p?i&! for 4 = 1nbus-1& n = 4B1! if n == m for n = 1nbus I5i/4& = I5i/4& B m&C n&C9m/n&C3osdelm&-deln&&B (m/n&Csindelm&-deln&&&! end I5i/4& = I5i/4& - m&0C9m/m&! else I5i/4& = m&C n&C-9m/n&C3osdelm&-deln&& -(m/n&Csindelm&-deln&&&! end



end end

% I - Jeri+ati+e of Rea3ti+e Power "nKe3tions with ..

I = erosnp?/np?&! for i = 1np? m = p?i&! for 4 = 1np? n = p?4&! if n == m

for n = 1nbus Ii/4& = Ii/4& B n&C9m/n&Csindelm&-deln&& -(m/n&C3osdelm&-deln&&&! end Ii/4& = Ii/4& - m&C(m/m&! else Ii/4& = m&C9m/n&Csindelm&-deln&& - (m/n&C3osdelm&-deln&&&! end end end

I = GI1 I0! I5 IH! % Ia3obian )atri*..

M = in+I&C)! % 'orre3tion e3tor dh = M1nbus-1&! % 'hange in oltage Angle.. d = Mnbusend&! % 'hange in oltage )agnitude..

% pdating 2tate e3tors..

del0nbus& = dh B del0nbus&! % oltage Angle.. 4 = 1! for i = 0nbus if typei& == 5 i& = d4& B i&! % oltage )agnitude.. 4 = 4B1! end end

"ter = "ter B 1!

ol = ma*abs)&&! % oleran3e..

endloadflownbus//del/()+a&! % 'alling Loadflow.m..

% Returns "nitial (us datas of the system...fun3tion busdt = busdatasnum&% ype.... % 1 - 2la34 (us..% 0 - P (us..% 5 - P6 (us.. % >(us > ype > sp > theta > P9i > 69i > PLi > 6Li > 6min > 6ma* >busdat1 = G1 1 1.,:, , , , , , , ,! 0 0 1.,7 , , 0. 01.; 10.; -, 7,! 5 0 1.,1, , , 05. .0 1., , ,! 5 1., , , , ;.< -5. , ,! 7 5 1., , , , ;.: 1.: , ,! : 0 1.,;, , , 10.0 11.0 ;.7 -: 0! ; 5 1., , , , ,., ,., , ,! < 0 1.,, , , 1;. ,., ,., -: 0! 5 1., , , , 0.7 1:.: , ,! 1, 5 1., , , , ., 7.< , ,! 11 5 1., , , , 5.7 1.< , ,! 10 5 1., , , , :.1 1.: , ,! 15 5 1., , , , 15.7 7.< , ,!



1 5 1., , , , 1. 7., , ,!H!

% Returns Line datas of the system...

fun3tion linedt = linedatasnum&

% > From > o > R > M > (80 > MOmer >

% > (us > (us > pu > pu > pu > AP a& >linedat1 = G1 0 ,.,15< ,.,71; ,.,0: 1 1 7 ,.,7,5 ,.005, ,.,0: 1 0 5 ,.,: ,.1;; ,.,01 1 0 ,.,7<11 ,.1;:50 ,.,1;, 1 0 7 ,.,7:7 ,.1;5<< ,.,1;5 1 5 ,.,:;,1 ,.1;1,5 ,.,,: 1 7 ,.,1557 ,.,011 ,., 1 ; ,., ,.0,10 ,., ,.;< ,., ,.77:1< ,., ,.: 7 : ,., ,.070,0 ,., ,.50 : 11 ,.,< ,.1<, ,., 1 : 10 ,.1001 ,.077<1 ,., 1 : 15 ,.,::17 ,.15,0; ,., 1

; < ,., ,.1;:17 ,., 1 ; ,., ,.11,,1 ,., 1 1, ,.,51<1 ,.,<7, ,., 1 1 ,.10;11 ,.0;,5< ,., 1 1, 11 ,.,<0,7 ,.10,; ,., 1 10 15 ,.00,0 ,.1<< ,., 1 15 1 ,.1;,5 ,.5<,0 ,., 1 H!

%%%% Program for (us Power "nKe3tions/ Line E Power flows p.u&...fun3tion GPi 6i Pg 6g Pl 6lH = loadflownb//del/()+a&

$ = ybusppgnb&! % 'alling $bus program..lined = linedatasnb&! % 9et linedats..

busd = busdatasnb&! % 9et busdatas..m = pol0re3t/del&! % 'on+erting polar to re3tangular..Jel = 1<,8piCdel! % (us oltage Angles in Jegree...fb = lined/1&! % From bus number...tb = lined/0&! % o bus number...nl = lengthfb&! % No. of (ran3hes..Pl = busd/;&! % PLi..6l = busd/<&! % 6Li..

"iK = erosnb/nb&!2iK = erosnb/nb&!2i = erosnb/1&!

% (us 'urrent "nKe3tions.. " = $Cm! "m = abs"&! "a = angle"&!

%Line 'urrent Flows..for m = 1nl p = fbm&! ? = tbm&! "iKp/?& = -mp& - m?&&C$p/?&! % $m/n& = -ym/n&.. "iK?/p& = -"iKp/?&!end"iK = sparse"iK&!"iKm = abs"iK&!



"iKa = angle"iK&!

% Line Power Flows..for m = 1nb for n = 1nb if m = n 2iKm/n& = mm&C3onK"iKm/n&&C()+a! end endend

2iK = sparse2iK&!PiK = real2iK&!6iK = imag2iK&!

% Line Losses..LiK = erosnl/1&!for m = 1nl p = fbm&! ? = tbm&! LiKm& = 2iKp/?& B 2iK?/p&!endLpiK = realLiK&!L?iK = imagLiK&!

% (us Power "nKe3tions..for i = 1nb for 4 = 1nb 2ii& = 2ii& B 3onKmi&&C m4&C$i/4&C()+a! endendPi = real2i&!6i = -imag2i&!Pg = PiBPl!6g = 6iB6l!

dispOQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQO&!dispO-----------------------------------------------------------------------------------------O&!dispO Newton Raphson Loadflow Analysis O&!dispO-----------------------------------------------------------------------------------------O&!dispO> (us > > Angle > "nKe3tion > 9eneration >Load >O&!dispO> No > pu > Jegree > ) > )ar > ) > )+ar >) > )ar > O&!for m = 1nb

dispO-----------------------------------------------------------------------------------------O&! fprintfO%5gO/ m&! fprintfO %<.fO/ m&&! fprintfO %<.fO/ Jelm&&!

fprintfO %<.5fO/ Pim&&! fprintfO %<.5fO/ 6im&&!fprintfO %<.5fO/ Pgm&&! fprintfO %<.5fO/ 6gm&&!fprintfO %<.5fO/ Plm&&! fprintfO %<.5fO/ 6lm&&! fprintfOSnO&!

enddispO-----------------------------------------------------------------------------------------O&!fprintfO otal O&!fprintfO %<.5fO/ sumPi&&! fprintfO%<.5fO/ sum6i&&!fprintfO %<.5fO/ sumPiBPl&&! fprintfO %<.5fO/ sum6iB6l&&!fprintfO %<.5fO/ sumPl&&! fprintfO %<.5fO/ sum6l&&! fprintfOSnO&!dispO-----------------------------------------------------------------------------------------O&!



dispOQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQO&!

dispO-------------------------------------------------------------------------------------O&!dispO Line FLow and Losses O&!dispO-------------------------------------------------------------------------------------O&!dispO>From>o > P > 6 > From> o > P > 6 >Line Loss >O&!

dispO>(us >(us> ) > )ar > (us > (us> ) > )ar > )> )ar >O&!for m = 1nl p = fbm&! ? = tbm&!

dispO-------------------------------------------------------------------------------------O&! fprintfO%gO/ p&! fprintfO%gO/ ?&! fprintfO %<.5fO/ PiKp/?&&!fprintfO %<.5fO/ 6iKp/?&&!

fprintfO %gO/ ?&! fprintfO%gO/ p&! fprintfO %<.5fO/ PiK?/p&&!fprintfO %<.5fO/ 6iK?/p&&! fprintfO %<.5fO/ LpiKm&&! fprintfO %<.5fO/ L?iKm&&! fprintfOSnO&!

enddispO-------------------------------------------------------------------------------------O&!fprintfO otal Loss O&!fprintfO %<.5fO/ sumLpiK&&! fprintfO %<.5fO/ sumL?iK&&! fprintfOSnO&!dispO-------------------------------------------------------------------------------------O&!dispOQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQO&!

% Program to for Admittan3e And "mpedan3e (us Formation....

fun3tion $ = ybusppgnum& % Returns $

linedata = linedatasnum&! % 'alling Linedatas...fb = linedata/1&! % From bus number...tb = linedata/0&! % o bus number...r = linedata/5&! % Resistan3e/ R...* = linedata/&! % Rea3tan3e/ M...b = linedata/7&! % 9round Admittan3e/ (80...a = linedata/:&! % ap setting +alue.. = r B iC*! % matri*...y = 1.8! % o get in+erse of ea3h element...b = iCb! % )a4e ( imaginary...

nb = ma*ma*fb&/ma*tb&&! % No. of buses...nl = lengthfb&! % No. of bran3hes...

$ = erosnb/nb&! % "nitialise $(us...

% Formation of the ff Jiagonal #lements... for 4 = 1nl $fb4&/tb4&& = $fb4&/tb4&& - y4&8a4&! $tb4&/fb4&& = $fb4&/tb4&&! end

% Formation of Jiagonal #lements.... for m = 1nb for n = 1nl if fbn& == m



$m/m& = $m/m& B yn&8an&0& B bn&! elseif tbn& == m $m/m& = $m/m& B yn& B bn&! end end end %$! % (us Admittan3e )atri* %T = in+$&! % (us "mpedan3e )atri*

% Polar to Re3tangular 'on+ersion

% GR#'H = R#'0PLRU/ U#A&% R#' - 'omple* matri* or number/ R#' = A B K(/ A = Real/ ( = "maginary% RU - )agnitude% U#A - Angle in radians

fun3tion re3t = pol0re3trho/theta&re3t = rho.C3ostheta& B KCrho.Csintheta&!

OUTPUT:-

QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ----------------------------------------------------------------------------------------- Newton Raphson Loadflow Analysis-----------------------------------------------------------------------------------------> (us > > Angle > "nKe3tion > 9eneration> Load >> No > pu > Jegree > ) > )ar > ) > )+ar

> ) > )ar >----------------------------------------------------------------------------------------- 1 1.,:,, ,.,,,, 050.75 -17.055 050.75-17.055 ,.,,, ,.,,,----------------------------------------------------------------------------------------- 0 1.,7, -.<1 1<.5,, 57.00< ,.,,,;.0< 01.;,, 10.;,,----------------------------------------------------------------------------------------- 5 1.,1,, -10.;0 -.0,, <.;7< ,.,,,0;.;7< .0,, 1.,,,----------------------------------------------------------------------------------------- 1.,150 -1,.00, -;.<,, 5.,, ,.,,,-,.,,, ;.<,, -5.,,----------------------------------------------------------------------------------------- 7 1.,1:: -<.;:,1 -;.:,, -1.:,, -,.,,,-,.,,, ;.:,, 1.:,,



----------------------------------------------------------------------------------------- : 1.,;,, -1.: -11.0,, 17.70: -,.,,,05.,0: 11.0,, ;.7,,----------------------------------------------------------------------------------------- ; 1.,7; -15.05:< -,.,,, ,.,,, -,.,,,,.,,, ,.,,, ,.,,,

----------------------------------------------------------------------------------------- < 1.,<,, -15.05:< ,.,,, 01.,5, ,.,,,01.,5, ,.,,, ,.,,,----------------------------------------------------------------------------------------- 1.,5,7 -1.<0,1 -0.7,, -1:.:,, ,.,,,-,.,,, 0.7,, 1:.:,,----------------------------------------------------------------------------------------- 1, 1.,0 -17.,5:, -.,,, -7.<,, -,.,,,,.,,, .,,, 7.<,,----------------------------------------------------------------------------------------- 11 1.,:1 -1.<7<1 -5.7,, -1.<,, ,.,,,,.,,, 5.7,, 1.<,,----------------------------------------------------------------------------------------- 10 1.,755 -17.0;5 -:.1,, -1.:,, ,.,,,,.,,, :.1,, 1.:,,----------------------------------------------------------------------------------------- 15 1.,:: -17.5515 -15.7,, -7.<,, ,.,,,

,.,,, 15.7,, 7.<,,----------------------------------------------------------------------------------------- 1 1.,15 -1:.,;1; -1.,, -7.,,, -,.,,,,.,,, 1.,, 7.,,,----------------------------------------------------------------------------------------- otal 15.75 51.,, 0;0.751,.7, 07.,,, ;5.7,,-----------------------------------------------------------------------------------------

QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ



------------------------------------------------------------------------------------- Line FLow and Losses------------------------------------------------------------------------------------->From>o > P > 6 > From> o > P > 6 >Line Loss >>(us >(us> ) > )ar > (us > (us> ) > )ar >

) > )ar >------------------------------------------------------------------------------------- 1 0 17;.,<, -1;.< 0 1 -170.;;0 5,.:5.5, 15.177------------------------------------------------------------------------------------- 1 7 ;7.715 ;.<1 7 1 -;0.;, 5.:0.;;5 11.7------------------------------------------------------------------------------------- 0 5 ;5.5: 7.5: 5 0 -;1.,:5 5.<0.555 .<5,------------------------------------------------------------------------------------- 0 77.5 0.57 0 -7.0;5 0.1501.:;, 7.,:;------------------------------------------------------------------------------------- 0 7 1.;55 .;5< 7 0 -,.<15 -1.0,.0, 0.<,-------------------------------------------------------------------------------------

5 -05.15; ;.;70 5 05.70< -:.;75,.51 ,.<------------------------------------------------------------------------------------- 7 -7.7<7 11.7; 7 :,.,: -1,.,:5,.; 1.711------------------------------------------------------------------------------------- ; 0;.,:: -17.5: ; -0;.,:: 1;.50;,.,,, 1.50-----------------------------------------------------------------

-------------------- 17.: -0.:, -17.: 5.50-,.,,, 1.00------------------------------------------------------------------------------------- 7 : 7.<< -0,.<5 : 7 -7.<< 0:.:1;,.,,, 7.;;------------------------------------------------------------------------------------- : 11 <.0<; <.<< 11 : -<.1:7 -<.:1,.105 ,.07;



------------------------------------------------------------------------------------- : 10 <.,: 5.1;: 10 : -;.< -5.,,<,.,<1 ,.1:<------------------------------------------------------------------------------------- : 15 1<.55; .<1 15 : -1<.,<7 -.<7,.070 ,.:

------------------------------------------------------------------------------------- ; < -,.,,, -0,.5:0 < ; ,.,,, 01.,5,,.,,, ,.::<------------------------------------------------------------------------------------- ; 0;.,:: 1.;< ; -0;.,:: -15.<,-,.,,, ,.7;------------------------------------------------------------------------------------- 1, .55 -,., 1, -.5<; ,.0,,.,,: ,.,1:------------------------------------------------------------------------------------- 1 <.:5; ,.501 1 -<.7; -,.151,.,< ,.1,------------------------------------------------------------------------------------- 1, 11 -.:15 -:.;0, 11 1, .::7 :.<1,.,71 ,.10,------------------------------------------------------------------------------------- 10 15 1.<< 1.,< 15 10 -1.<;5 -1.5<

,.,11 ,.,1,------------------------------------------------------------------------------------- 15 1 :.7< 7.,<5 1 15 -:.575 -.<:,.1,7 ,.017------------------------------------------------------------------------------------- otal Loss15.75 7:.1,-------------------------------------------------------------------------------------

QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ

DC LOAD FLOW SOLUTION:



For ea3h bus/

MATLAB CODE:

3lear all!3l3!tstart=3putime!dispGO OH&

dispGOCCCCCJ' Power Flow 2olution - 5 (us systemCCCCCOH& Nbus=5!Nele=5!%line data#data=G1 1 0 1,i! 0 0 5 7i! 5 1 5 1,iH!%bus data bus 5 as sla34(data=G1 , 0,,,! 0 , 1,,,! 5 5,,, ,H! % Formation of $bus matri*$bus = erosNbus/Nbus&!for 4 = 1Nele

p = #data4/0&! ? = #data4/5&! yele = 18#data4/&! $busp/p& = $busp/p& B yele ! $bus?/?& = $bus?/?& B yele! $busp/?& = $busp/?& - yele! $bus?/p& = $bus?/p& - yele! end

$bus%%basem+a=1,,!refVbus=5!



(1=imag$bus&(=(1!(refVbus/&=GH!(/refVbus&=GH!((=-(delPbus=(data/ 5&& - (data/ 0&&&!delPbusrefVbus/&=GH!delPbustheta=in+((&CdelPbusthetarefVbus/1&=,!

thetafor i=1Nbus for K=1Nbus Pi/K&=thetai&-thetaK&&C(1i/K&! endendPdispOLine FlowsO&!for i=1Nbus for K=1Nbus if i=K EE iDK& Pi/K&! M = sprintfOP%d%d %d.O/i/K/Pi/K&&! dispM&! end endend

OUTPUT:

CCCCCJ' Power Flow 2olution - 5 (us systemCCCCC

$bus =

, - ,.0,,,i , B ,.1,,,i , B ,.1,,,i , B ,.1,,,i , - ,.5,,,i , B ,.0,,,i , B ,.1,,,i , B ,.0,,,i , - ,.5,,,i

(1 =

-,.0,,, ,.1,,, ,.1,,, ,.1,,, -,.5,,, ,.0,,, ,.1,,, ,.0,,, -,.5,,,

(( =

,.0,,, -,.1,,, -,.1,,, ,.5,,,

delPbus =

0,,, 1,,,

theta =

1.,eB,, C



1.,,, ,.<,,,

theta =

1.,eB,, C

1.,,, ,.<,,,

,

P =

1.,eB,,5 C

, ,.:,,, 1.,,, -,.:,,, , 1.:,,, -1.,,, -1.:,,, ,

Line FlowsP10 :.,,,,,,eB,,0.P15 1,,.P05 1.:,,,,,eB,,5.

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Ieee 14 Bus System Load Flow Using n