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Fault at generator terminal feeding motor

Short answer

Base 50 MVA, 11 kV. Motor-side series reactance = 0.1967 pu; in parallel with generator 0.1 pu gives Thevenin reactance 0.0663 pu. Fault current = 1/0.0663 = 15.08 pu = 39.6 kA. Fault MVA = 50/0.0663 = 754 MVA.

An alternator is connected to a synchronous motor through a transmission line and two transformers as shown in the figure below. The rated MVA, voltage rating and percentage reactance of the components are depicted in the figure. The transmission line reactance is also shown in the figure in Ω. Compute the fault current, if a 3-phase bolted fault occurs at the terminal of the generator. Consider the pre fault voltage as 1 p.u. Also determine the fault MVA at the generator terminal. [Figure: generator 50 MVA, 11 kV, 10% - T1 100 MVA, 11/132 kV, 5% - line j25 Ω - T2 50 MVA, 132/6.6 kV, 4% - motor 50 MVA, 6.6 kV, 6%]

For a bolted fault at the generator terminal, both the generator and the synchronous motor (acting as a source) feed the fault. If=Vf/XthI_f = V_f / X_{th} with Vf=1V_f = 1 pu.

Per unit values

Base: 50 MVA, 11 kV at the generator, so 132 kV on the line and 6.6 kV at the motor (voltage bases follow the transformer ratios, so no voltage correction is needed). Zb,line=1322/50=348.48 ΩZ_{b,line} = 132^2/50 = 348.48\ \Omega.

ElementCalculationX (pu)
Generator (50 MVA, 10%)own base0.10
T1 (100 MVA, 5%)0.05×50/1000.05 \times 50/1000.025
Line (25 Ω)25/348.4825/348.480.0717
T2 (50 MVA, 4%)own base0.04
Motor (50 MVA, 6%)own base0.06
        F
 G      o   T1     Line     T2     M
(~)-0.1-+-0.025--0.0717--0.04--0.06-(~)
 |                                   |
 +====== reference (EMF = 1 pu) =====+

Fault current

Reactance on the motor side seen from F:

Xm=0.025+0.0717+0.04+0.06=0.1967 puX_m = 0.025 + 0.0717 + 0.04 + 0.06 = 0.1967\ \text{pu} Xth=0.10×0.19670.10+0.1967=0.0663 puIf=10.0663=15.08 puIb=50×1063×11×103=2624.3 AIf=15.08×2624.3=39 582 A≈39.6 kA\begin{aligned} X_{th} &= \frac{0.10 \times 0.1967}{0.10 + 0.1967} = 0.0663\ \text{pu} \\ I_f &= \frac{1}{0.0663} = 15.08\ \text{pu} \\ I_b &= \frac{50\times10^6}{\sqrt3 \times 11\times10^3} = 2624.3\ \text{A} \\ I_f &= 15.08 \times 2624.3 = 39\,582\ \text{A} \approx 39.6\ \text{kA} \end{aligned}

Contributions: generator 1/0.1=101/0.1 = 10 pu (26.24 kA); motor side 1/0.1967=5.081/0.1967 = 5.08 pu (13.34 kA).

Fault MVA at the generator terminal

Fault MVA=SbXth=500.0663=754.1 MVA\text{Fault MVA} = \frac{S_b}{X_{th}} = \frac{50}{0.0663} = 754.1\ \text{MVA}

Check: 3×11×39.58=754.1\sqrt3 \times 11 \times 39.58 = 754.1 MVA.

Answer: Fault current ≈ 15.08 pu ≈ 39.6 kA; fault MVA ≈ 754 MVA.

✓ Answer checked by Claude Sonnet 5.5

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