Question

Consider the system shown in the single-line diagram of Figure (3). All reactances are shown in per unit to the same base. Assume that the voltage at both sources is \(1 \mathrm{p}\).u.

a- Find the fault current due to a bolted- three-phase short circuit at bus \(3 .[10\) points \(]\)

b- Find the fault current supplied by each generator and the voltage at each of the buses 1 and 2 under fault conditions. \([10\) points \(]\)

Answer 1

In order to find the short cirant fault Current and voltage at each bus, we have to find the Bus impedence matrix for the Given Bus diagram. Bus diagram The reactance diagram of the of the Given is as follows - 0.06 oot to om om 20.25 m uh um nu m d o to reference The following are the steps involved in Calculation of bus : Ly stepi: Adding Bus unten Ort [a] = Eos] [0.204] 0.28

Adding But 6 to Bus : 6.204 0.204 Cool 10.204 6 Bus Adding to Bus 6: hy Steps & 10.20t 3- 8,404 0.204 1 12 13ez lorot stot orotalot & Loot out (6.204 10-2) I 10.2 + 10.204 oot (0.2 to Bus • stapt & Adding 0204 0.204 0.204 0.204 Co.wt aloA) loot otot 0.204 (o. Aod no.wt) o not 0.204 on (0.20 A .O.dort) 0 0.2 -0.2 (0.404 to. Aot 2*0.204 +0.2 (0.6)

Coiners rule : U 24-214741 24A Z122 Zi2- Zia Z42 & soon. АА 71 2 0.264 0.204 0.337 0.204 0.27 0.264 0.204 0. 27 0-337 1313 4 stages : - Adding en om te vertence s 0.204 0.204 9.204 0.204 0.337 BWA 0.334 3.27 10.204 0.27 0.337 0.27 Toirot 0346 0.6 47 by Cornets sale :- 0.337 0.27 0.337+ 0.31 Tarsa 0.097 [6.139 0.097 0.118] 10.097 0.161 0.129 10.118 0.129 0.224 383 (Z) =

4 stopper Adding Band on the regione Adding Bus to referencer NA 8.204 cond 0.18 0.139 0.139 0.097 4X4 0.097 0.129 8.097 0.161 0129 0.22 4 0.118 0.139431 O-02 20.139 0.449 Byn Corneliu Bule- 16.95 0.066 0.081] ont 0.103 873 - 10.066 34 0.103 10.081 0.193 - 313 y step7 - Adding Bus @ to around. Ал мл сол O-104 0.31

o.oar 0.066 0.066 0.081 0.14 0.103 0.103 0.13 0.103 0.14 0.103 (+3140.14) 0.066 0.14 4. . 10.085 0.045 0.065 Z Bus = i 10.045 0.096 0.07 10.065 0.07 0.079 313 Nowo, Froom 36 Symmetrical fault analysis using (Elburg faut bus Voltage prefault Elang mation fault Corrent mation matern Voltage maturn o fault occurs at Bus ; Eh, o) & If to

Uz - o - Ct213 Up 2 = ush. Plgtes 0 Given that Prefaut voltages to a Eq③ Vg3 vs 3 - Itz zuz faut voltages vo' a Vo² = 10²-16 Bu ② } 130 {bca, fault ocurs at Vo? - Efyzza a Ff = 163 Z33 =!18 -312.658 yo.a79 4 [[f= -312.658 | Lault Current at Bus - Vfa - Pfz tez -- (-812,654)(60.065) Up = 0.17723 | fault Voltage at Bus 0 Up ² Vo? Ifz Zas Loon (-; 12:658) (10.07) [Ng? = 0.1139 4 1 fault voltage at Bus® &

0-17723 o.11 394 (7) 0-204 Tell 10.2 ruer 02 30.31 - 90.004 &= 120.17923 J j 4033 l supplied by a ha !~ 012223 - [3 2.654] supplered by 2 83 21-0113941-12.858 Supplied by @ jo.31 j 0.31 294 1-12.858 . I supplied by 84 1- 011394 30.31