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Fault at load end of overhead line

Short answer

On 15 MVA base, Thevenin reactance is 0.4255 pu. Fault level is 35.3 MVA, fault current 617 A at 33 kV. On the 11 kV side, total fault current is 1850 A; G1 supplies 1110 A, G2 supplies 740 A.

Figure below shows a three-phase system. Calculate the short circuit MVA and the fault current when 3-phase balanced short-circuit fault occurs at the load end of the transmission line. Also, determine the fault current supplied by each generator. [Figure: G1 10 MVA, 11 kV, X1'' = 10% and G2 5 MVA, 11 kV, X2'' = 7.5% on a common bus; transformer T1 15 MVA, 11/33 kV, XT = 6%; overhead line XTL = 20 Ω to the load, where the fault occurs]

Base: 15 MVA (transformer rating), 11 kV on the generator side and 33 kV on the line side. Pre-fault voltage is taken as 1.0 pu and pre-fault load current is neglected (usual assumption for fault level calculation).

Per-unit reactances (15 MVA)

ElementCalculationpu
G10.10×15/100.10 \times 15/100.150
G20.075×15/50.075 \times 15/50.225
T16% on 15 MVA0.06
Line20/(332/15)=20/72.620/(33^2/15) = 20/72.60.2755
 G1 j0.150--+
               +--T1 j0.06--line j0.275--F (load end)
 G2 j0.225--+

Thevenin reactance

XG=0.150×0.2250.150+0.225=0.090Xth=0.090+0.06+0.2755=0.4255 pu\begin{aligned} X_G &= \frac{0.150 \times 0.225}{0.150 + 0.225} = 0.090 \\ X_{th} &= 0.090 + 0.06 + 0.2755 = 0.4255\ \text{pu} \end{aligned}

Short-circuit MVA and fault current

SC MVA=150.4255=35.25 MVAIf=10.4255=2.3503 puIbase,33=15×1063×33×103=262.43 A⇒If=616.8 A at 33 kV\begin{aligned} \text{SC MVA} &= \frac{15}{0.4255} = 35.25\ \text{MVA} \\ I_f &= \frac{1}{0.4255} = 2.3503\ \text{pu} \\ I_{base,33} &= \frac{15 \times 10^6}{\sqrt{3} \times 33 \times 10^3} = 262.43\ \text{A} \Rightarrow I_f = 616.8\ \text{A at 33 kV} \end{aligned}

Current supplied by each generator

On the 11 kV side, Ibase,11=15×1063×11×103=787.30I_{base,11} = \dfrac{15 \times 10^6}{\sqrt{3} \times 11 \times 10^3} = 787.30 A, so the fault current there is 2.3503×787.30=1850.42.3503 \times 787.30 = 1850.4 A. It divides inversely as the generator reactances:

IG1=1850.4×0.2250.150+0.225=1110.2 AIG2=1850.4×0.1500.150+0.225=740.1 A\begin{aligned} I_{G1} &= 1850.4 \times \frac{0.225}{0.150 + 0.225} = 1110.2\ \text{A} \\ I_{G2} &= 1850.4 \times \frac{0.150}{0.150 + 0.225} = 740.1\ \text{A} \end{aligned}

Answer: SC MVA ≈35.25\approx 35.25 MVA; fault current ≈617\approx 617 A at 33 kV; G1 supplies ≈1110\approx 1110 A and G2 ≈740\approx 740 A (at 11 kV).

✓ Answer checked by Claude Sonnet 5.5

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