Ieee 14 Bus System Load Flow Using N-R Method

IEEE 14 BUS SYSTEM LOAD FLOW USING N-R METHOD

% Program for Newton-Raphson Load Flow Analysis..

nbus = 1! $ = ybusppgnbus&! busd = busdatasnbus&! ()+a = 1,,! bus = busd/1&! type = busd/0&!  = busd/5&! del = busd/&! Pg = busd/7&8()+a! 6g = busd/:&8()+a! Pl = busd/;&8()+a! 6l = busd/<&8()+a! 6min = busd/&8()+a! 6ma* = busd/1,&8()+a! P = Pg - Pl! 6 = 6g - 6l! Psp = P! 6sp = 6! 9 = real$&! ( = imag$&!

% % % % % % % % % % % % % % % % % % % %

"###-1 'alling ybusppg.m to get $-(us )atri*.. 'alling busdatas.. (ase )A.. (us Number.. ype of (us 1-2la34/ 0-P/ 5-P6.. 2pe3ified oltage.. oltage Angle.. P9i.. 69i.. PLi.. 6Li.. )inimum Rea3ti+e Power Limit.. )a*imum Rea3ti+e Power Limit.. Pi = P9i - PLi.. 6i = 69i - 6Li.. P 2pe3ified.. 6 2pe3ified.. 'ondu3tan3e matri*.. 2us3eptan3e matri*..

p+ = findtype == 0 > type == 1&! p? = findtype == 5&! np+ = lengthp+&! np? = lengthp?&! ol = 1! "ter = 1! while ol @ 1e-7&

% % % %

P (uses.. P6 (uses.. No. of P buses.. No. of P6 buses..

% "teration starting..

P = erosnbus/1&! 6 = erosnbus/1&! % 'al3ulate P and 6 for i = 1nbus for 4 = 1nbus Pi& = Pi& B i&C 4&C9i/4&C3osdeli&-del4&& B (i/4&Csindeli&-del4&&&! 6i& = 6i& B i&C 4&C9i/4&Csindeli&-del4&& (i/4&C3osdeli&-del4&&&! end end % 'he34ing 6-limit +iolations.. if "ter D= ; EE "ter @ 0 % nly 3he34ed up to ;th iterations.. for n = 0nbus if typen& == 0 69 = 6n&B6ln&! if 69 D 6minn& 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 = erosnp?/1&! for i = 1nbus

if typei& == 5 d64/1& = d6ai&! 4 = 4B1! end end dP = dPa0nbus&! ) = GdP! d6H!

% )ismat3h e3tor

% Ia3obian % I1 - Jeri+ati+e of Real Power "nKe3tions with Angles.. I1 = erosnbus-1/nbus-1&! for i = 1nbus-1& m = iB1! for 4 = 1nbus-1& n = 4B1! if n == m for n = 1nbus I1i/4& = I1i/4& B m&C n&C-9m/n&Csindelm&-deln&& B (m/n&C3osdelm&-deln&&&! end I1i/4& = I1i/4& - m&0C(m/m&! else I1i/4& = m&C n&C9m/n&Csindelm&-deln&& (m/n&C3osdelm&-deln&&&! end end end % I0 - Jeri+ati+e of Real Power "nKe3tions with .. I0 = erosnbus-1/np?&! for i = 1nbus-1& m = iB1! for 4 = 1np? n = p?4&! if n == m for n = 1nbus I0i/4& = I0i/4& B n&C9m/n&C3osdelm&-deln&& B (m/n&Csindelm&-deln&&&! end I0i/4& = I0i/4& B m&C9m/m&! else I0i/4& = m&C9m/n&C3osdelm&-deln&& B (m/n&Csindelm&deln&&&! end end end % I5 - Jeri+ati+e of Rea3ti+e Power "nKe3tions with Angles.. I5 = erosnp?/nbus-1&! for i = 1np? m = p?i&! for 4 = 1nbus-1& n = 4B1! if n == m for n = 1nbus I5i/4& = I5i/4& B m&C n&C9m/n&C3osdelm&-deln&& B (m/n&Csindelm&-deln&&&! end I5i/4& = I5i/4& - m&0C9m/m&! else I5i/4& = m&C n&C-9m/n&C3osdelm&-deln&& (m/n&Csindelm&-deln&&&! end

end end % I - Jeri+ati+e of Rea3ti+e Power "nKe3tions with .. I = erosnp?/np?&! for i = 1np? m = p?i&! for 4 = 1np? n = p?4&! if n == m for n = 1nbus Ii/4& = Ii/4& B n&C9m/n&Csindelm&-deln&& (m/n&C3osdelm&-deln&&&! end Ii/4& = Ii/4& - m&C(m/m&! else Ii/4& = m&C9m/n&Csindelm&-deln&& - (m/n&C3osdelm&deln&&&! end end end I = GI1 I0! I5 IH!

% Ia3obian )atri*..

M = in+I&C)! dh = M1nbus-1&! d = Mnbusend&!

% 'orre3tion e3tor % 'hange in oltage Angle.. % 'hange in oltage )agnitude..

% pdating 2tate e3tors.. del0nbus& = dh B del0nbus&! 4 = 1! for i = 0nbus if typei& == 5 i& = d4& B i&! 4 = 4B1! end end "ter = "ter B 1! ol = ma*abs)&&! end loadflownbus//del/()+a&!

% oltage Angle..

% oltage )agnitude..

% oleran3e..

% 'alling Loadflow.m..

% Returns "nitial (us datas of the system... fun3tion busdt = busdatasnum& % ype.... % 1 - 2la34 (us..% 0 - P (us..% 5 - P6 (us.. % >(us > ype > sp > theta > P9i > 69i > PLi > 6Li > busdat1 = G1 1 1.,:, , , , , , 0 0 1.,7 , , 0. 01.; 10.; 5 0 1.,1, , , 05. .0 1.,  5 1., , , , ;.< -5. 7 5 1., , , , ;.: 1.: : 0 1.,;, , , 10.0 11.0 ;.7 ; 5 1., , , , ,., ,., < 0 1.,, , , 1;. ,., ,.,  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.<

6min > 6ma* > , ,! -, 7,! , ,! , ,! , ,! -: 0! , ,! -: 0! , ,! , ,! , ,! , ,! , ,!

1

5

1.,

,

,

,

1.

7.,

,

(80 pu ,.,0: ,.,0: ,.,01 ,.,1;, ,.,1;5 ,.,,: ,., ,., ,., ,., ,., ,., ,., ,., ,., ,., ,., ,., ,., ,.,

> MOmer > > AP a& > 1 1 1 1 1 1 1 ,.;< ,.: ,.50 1 1 1 1 1 1 1 1 1 1 H!

% Returns Line datas of the system... fun3tion linedt = linedatasnum& % > From > o % > (us > (us linedat1 = G1 0 1 7 0 5 0  0 7 5   7  ;   7 : : 11 : 10 : 15 ; < ;   1,  1 1, 11 10 15 15 1

> >

R > M > pu > pu > ,.,15< ,.,71; ,.,7,5 ,.005, ,.,: ,.1;; ,.,7<11 ,.1;:50 ,.,7:7 ,.1;5<< ,.,:;,1 ,.1;1,5 ,.,1557 ,.,011 ,., ,.0,10 ,., ,.77:1< ,., ,.070,0 ,.,< ,.1<, ,.1001 ,.077<1 ,.,::17 ,.15,0; ,., ,.1;:17 ,., ,.11,,1 ,.,51<1 ,.,<7, ,.10;11 ,.0;,5< ,.,<0,7 ,.10,; ,.00,0 ,.1<< ,.1;,5 ,.5<,0

%%%% Program for (us Power "nKe3tions/ Line E Power flows p.u&... fun3tion GPi 6i Pg 6g Pl 6lH = loadflownb//del/()+a& $ = ybusppgnb&! lined = linedatasnb&! busd = busdatasnb&! m = pol0re3t/del&! Jel = 1<,8piCdel! fb = lined/1&! tb = lined/0&! nl = lengthfb&! Pl = busd/;&! 6l = busd/<&!

% % % % % % % % % %

'alling $bus program.. 9et linedats.. 9et busdatas.. 'on+erting polar to re3tangular.. (us oltage Angles in Jegree... From bus number... o bus number... No. of (ran3hes.. PLi.. 6Li..

"iK = erosnb/nb&! 2iK = erosnb/nb&! 2i = erosnb/1&! % (us 'urrent "nKe3tions..  " = $Cm!  "m = abs"&!  "a = angle"&! %Line 'urrent Flows.. for m = 1nl p = fbm&! ? = tbm&! "iKp/?& = -mp& - m?&&C$p/?&! % $m/n& = -ym/n&.. "iK?/p& = -"iKp/?&! end "iK = sparse"iK&! "iKm = abs"iK&!

,!H!

"iKa = angle"iK&! % Line Power Flows.. for m = 1nb for n = 1nb if m = n 2iKm/n& = mm&C3onK"iKm/n&&C()+a! end end end 2iK = sparse2iK&! PiK = real2iK&! 6iK = imag2iK&! % Line Losses.. LiK = erosnl/1&! for m = 1nl p = fbm&! ? = tbm&! LiKm& = 2iKp/?& B 2iK?/p&! end LpiK = realLiK&! L?iK = imagLiK&! % (us Power "nKe3tions.. for i = 1nb for 4 = 1nb 2ii& = 2ii& B 3onKmi&&C m4&C$i/4&C()+a! end end Pi = real2i&! 6i = -imag2i&! Pg = PiBPl! 6g = 6iB6l! dispOQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQO &! dispO----------------------------------------------------------------------------------------O &! dispO Newton Raphson Loadflow Analysis O &! dispO----------------------------------------------------------------------------------------O &! dispO> (us >  > Angle > "nKe3tion > 9eneration > Load >O&! dispO> No > pu > Jegree > ) > )ar > ) > )+ar > ) > )ar > O&! for m = 1nb dispO----------------------------------------------------------------------------------------O &!   fprintfO%5gO/ m&! fprintfO %<.fO/ m&&! fprintfO %<.fO/ Jelm&&!   fprintfO %<.5fO/ Pim&&! fprintfO %<.5fO/ 6im&&! fprintfO %<.5fO/ Pgm&&! fprintfO %<.5fO/ 6gm&&! fprintfO %<.5fO/ Plm&&! fprintfO %<.5fO/ 6lm&&! fprintfOSnO&! end dispO----------------------------------------------------------------------------------------O &! fprintfO otal O&!fprintfO %<.5fO/ sumPi&&! fprintfO %<.5fO/ sum6i&&! fprintfO %<.5fO/ sumPiBPl&&! fprintf O %<.5fO/ sum6iB6l&&! fprintfO %<.5fO/ sumPl&&! fprintfO %<.5fO/ sum6l&&! fprintfOSnO&! dispO----------------------------------------------------------------------------------------O &!

dispOQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQO &! dispO------------------------------------------------------------------------------------O&! dispO Line FLow and Losses O&! dispO------------------------------------------------------------------------------------O&! dispO>From>o > P > 6 > From> o > P > 6 > Line Loss >O&! dispO>(us >(us> ) > )ar > (us > (us> ) > )ar > ) > )ar >O&! for m = 1nl p = fbm&! ? = tbm&! dispO------------------------------------------------------------------------------------O&!   fprintfO%gO/ p&! fprintfO%gO/ ?&! fprintfO %<.5fO/ PiKp/?&&! fprintfO %<.5fO/ 6iKp/?&&! fprintfO %gO/ ?&! fprintfO%gO/ p&! fprintfO %<.5fO/ PiK?/p&&! fprintfO %<.5fO/ 6iK?/p&&!   fprintfO %<.5fO/ LpiKm&&! fprintfO %<.5fO/ L?iKm&&!   fprintfOSnO&! end dispO------------------------------------------------------------------------------------O&! fprintfO otal Loss O&! fprintfO %<.5fO/ sumLpiK&&! fprintf O %<.5fO/ sumL?iK&&! fprintfOSnO&! dispO------------------------------------------------------------------------------------O&! dispOQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQO&! % Program to for Admittan3e And "mpedan3e (us Formation.... fun3tion $ = ybusppgnum&

% Returns $

linedata = linedatasnum&! fb = linedata/1&! tb = linedata/0&! r = linedata/5&! * = linedata/&! b = linedata/7&! a = linedata/:&!  = r B iC*! y = 1.8! b = iCb!

% % % % % % % % % %

nb = ma*ma*fb&/ma*tb&&! nl = lengthfb&! $ = erosnb/nb&!

% No. of buses... % No. of bran3hes... % "nitialise $(us...

'alling Linedatas... From bus number... o bus number... Resistan3e/ R... Rea3tan3e/ M... 9round Admittan3e/ (80... ap setting +alue..  matri*... o get in+erse of ea3h element... )a4e ( imaginary...

% Formation of the ff Jiagonal #lements... for 4 = 1nl $fb4&/tb4&& = $fb4&/tb4&& - y4&8a4&! $tb4&/fb4&& = $fb4&/tb4&&! end % Formation of Jiagonal #lements.... for m = 1nb for n = 1nl if fbn& == m

$m/m& = $m/m& B yn&8an&0& B bn&! elseif tbn& == m $m/m& = $m/m& B yn& B bn&! end end end %$! %T = in+$&! % % % % %

% (us Admittan3e )atri* % (us "mpedan3e )atri*

Polar to Re3tangular 'on+ersion GR#'H = R#'0PLRU/ U#A& R#' - 'omple* matri* or number/ R#' = A B K(/ A = Real/ ( = "maginary RU - )agnitude U#A - Angle in radians

fun3tion re3t = pol0re3trho/theta& re3t = rho.C3ostheta& B KCrho.Csintheta&!

OUTPUT:-

QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQQQ ---------------------------------------------------------------------------------------Newton Raphson Loadflow Analysis ---------------------------------------------------------------------------------------> (us >  > Angle > "nKe3tion > 9eneration > Load > > No > pu > Jegree > ) > )ar > ) > )+ar > ) > )ar > ---------------------------------------------------------------------------------------1 1.,:,, ,.,,,, 050.75 -17.055 050.75 -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,.00, -;.<,, 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.,15 -1:.,;1; -1.,, -7.,,, -,.,,, ,.,,, 1.,, 7.,,, ---------------------------------------------------------------------------------------otal 15.75 51.,, 0;0.75 1,.7, 07.,,, ;5.7,, ----------------------------------------------------------------------------------------

QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQQQQQ

-----------------------------------------------------------------------------------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 0.150 1.:;, 7.,:; -----------------------------------------------------------------------------------0 7 1.;55 .;5< 7 0 -,.<15 -1.0 ,.0, 0.<, -----------------------------------------------------------------------------------5  -05.15; ;.;70  5 05.70< -:.;75 ,.51 ,.< ----------------------------------------------------------------------------------- 7 -7.7<7 11.7; 7  :,.,: -1,.,:5 ,.; 1.711 ----------------------------------------------------------------------------------- ; 0;.,:: -17.5: ;  -0;.,:: 1;.50; ,.,,, 1.50 -----------------------------------------------------------------------------------  17.: -0.:,   -17.: 5.50 -,.,,, 1.00 -----------------------------------------------------------------------------------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, .55 -,., 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 Loss 15.75 7:.1, -----------------------------------------------------------------------------------QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQQQQQQQQQQQQQQQQQQ

DC LOAD FLOW SOLUTION:

For ea3h bus/

 MATLAB CODE:

3lear all! 3l3! tstart=3putime! dispGO OH& dispGOCCCCCJ' Power Flow 2olution - 5 (us systemCCCCCO H& 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 = erosNbus/Nbus&! for 4 = 1Nele p = #data4/0&! ? = #data4/5&! yele = 18#data4/&! $busp/p& = $busp/p& B $bus?/?& = $bus?/?& B $busp/?& = $busp/?& $bus?/p& = $bus?/p& end $bus %%basem+a=1,,! refVbus=5!

yele ! yele! yele! yele!

(1=imag$bus& (=(1! (refVbus/&=GH! (/refVbus&=GH! ((=-( delPbus=(data/ 5&& - (data/ 0&&&! delPbusrefVbus/&=GH! delPbus theta=in+((&CdelPbus thetarefVbus/1&=,! theta for i=1Nbus for K=1Nbus   Pi/K&=thetai&-thetaK&&C(1i/K&! end end P dispOLine FlowsO&! for i=1Nbus for K=1Nbus if i=K EE iDK&   Pi/K&! M = sprintfOP%d%d %d.O/i/K/Pi/K&&!   dispM&! end end end 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

(1 = -,.0,,, ,.1,,, ,.1,,,

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

(( = ,.0,,, -,.1,,,

delPbus =    

0,,, 1,,,

theta = 1.,eB,, C

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

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

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

   

1.,,, ,.<,,,

theta = 1.,eB,, C    

1.,,, ,.<,,, ,

P = 1.,eB,,5 C , -,.:,,, -1.,,,

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

Line Flows P10 :.,,,,,,eB,,0. P15 1,,. P05 1.:,,,,,eB,,5.

1.,,, 1.:,,, ,