Power Flow S + Buses with either or both Generator Load S G1 S G2 S G3 S D3 S D1 S D4 S D5. S Dk. Injection S G1
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1 ower Flow uses wth ether or both Geerator Load G G G D D 4 5 D4 D5 ecto G Net Comple ower ecto - D D ecto s egatve sg at load bus = _ G D mlarl Curret ecto = G _ D At each bus coservato of comple power curret holds: 5 G = D G D
2 ower Flow Equatos Geerators Load L Node = = bus = = = comple power ecto = = = = Let = = = = = + - =
3 Eample: Use = equvalet crcuts for trasmsso les 00 all capactors c Z = 0 L 0 L bus = Comple ower ectos: = uadratc fucto wth respect to voltages Nolear equatos that ca ot be easl solved closed form Now cosder the power flow equatos
4 = = cos s = cos F s Full load Flow equatos Aother Formulato: Let G { cos G s } [cos cos s s ] = G cos = = s F [s cos cos s ] = cos G s = = t 4
5 mplfed Forms: Al Neglect resstaces trasmsso les G 0 Trasmsso losses represet about % of the power geerated s = F cos = reactace b / susceptace z b b b z b s s cos cos mall A le agles 0 less tha 0 0 s rada cos The J = become does ot deped o δ ad δ F 5
6 & decoupled A A A or costat for all buses the DC load flow Lear equatos uows gve = = Zero f ot coected b a le dag : off dag : f coected b a le 6
7 7 DC load flow soluto Fd the verse of The do the multplcato - Fast: ormall for o-le computato ad plag purpose accurac ma suffer Ca be used to redspatch geerato for cogesto maagemet F
8 ower Flow roblem - For bus there are 4 etwor varables comple power comple voltage Ge pecfed uattes Load Uow arables Load bus Ge bus lac bus Ref bus swg bus all scalars tead-state etwor relatoshp -bus cl Ref Real power balace F 0 Reactve power balace G 0 4 varables { specfed { uows 8
9 - equatos olear wat comple voltages ca be solved to fd the uows - The soluto ma ot est Eve f a soluto ests t ma ot be uque - For ormal operato codtos of a power sstem a soluto ests the eghborhood of = =0 zero flow for all les rated voltages at all buses - Closed form soluto mpossble - Numercal methods - Gauss-edel - Fast Decoupled Load Flow - Newto-Raphso - DC load Flow Eample: F e relato of F Real power flow relatoshp ol assume all voltage magtudes = p set 0 Gve wat to fd les are assumed lossless hece 0 9
10 0 s / s / s / s / s / s / + 0 = 0 equatos are depedet o eed ol equatos from fd to wat gve s s s s
11 E eqs doe load eqs for geerator slac bus bus gve Noe for slac 0 load ge 0 swg slac bus -bus wat ad comple voltages wll be ow ca fd ad all le flows Form bus = Ge: equato Load: & equatos F cos cos s s cos s cos cos s eqs wth uows
12 g of r bus elemets z r z r r0 0 r r r r pos real part 0 0 r r r eg real part 0 0 A ver log but complete eample: Le Wat bus & power flow formulato Le Le Le : 90 m : 95 m : 5 m Les: R= 0075 /m ωl= 05 /m = 0 /m c slac
13 semes semes semes z z z huts: / 0 c m M c Le : semes half le legth Le : semes Le : semes
14 ] [ ] [ ] [48 semes semes bus shuts F s cos = Total of 6 eqs tep comple voltages Fd Wrte
15 tep ar ect of ge ecto of slac bus Oce are foud teratve method ca calculate s s s ad cos cos cos s s s TE : Le Flows R X R X 5
16 6 currets short b dffer ower Flow tep 4 c ' R X ' c ' ' ' ' geeral c c c c
17 7 f 0 G For all les the bus reduces to bus F s 5 s 0 s s cos s ad Tr
18 8 F for smlarl F5 DC load Flow: bus
19 9 lac 0 Has to be true for loseless sstem Needs ol F5 too 0 referece fromst row of bus Note the matr for F5 s dfferet from the bus for F4! huts have o real power flow 0 5 = 0
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