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ElectricalPower System
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Four alternators,┬аeach rated at 5 MVA, 11 kV, with 20% reactance are working in parallel. The short circuit level at bus is

A

25 MVA

B

20 MVA

C

25 MVA

D

100 MVA

Correct Answer

тЪЩя╕П TE тАв Technical Direct FormulaElectricalPower System
Option D

100 MVA

Quick Summary:

Given: Four alternators, each rated at 5 MVA with 20% reactance, are connected in parallel.

ЁЯУРMAMath SolutionDirect Formula
ЁЯУЛ Given

Four alternators, each rated at 5 MVA with 20% reactance, are connected in parallel.

ЁЯФв Formula Used

MVAsc=TotalтАЙMVAp.u.тАЙReactanceMVA_{sc} = \frac{Total \, MVA}{p.u. \, Reactance}MVAscтАЛ=p.u.ReactanceTotalMVAтАЛ

ЁЯФв Step-by-Step Solution
1

Identify Total MVA

Since there are 4 alternators in parallel, each rated at 5 MVA, the total capacity is 4├Ч5=20┬аMVA4 \times 5 = 20 \text{ MVA}4├Ч5=20┬аMVA.

MVAtotal=4├Ч5=20┬аMVAMVA_{total} = 4 \times 5 = 20 \text{ MVA}MVAtotalтАЛ=4├Ч5=20┬аMVA

2

Determine Per Unit Reactance

The reactance given is 20%, which in per-unit (p.u.) form is 0.20.

Xpu=20100=0.2X_{pu} = \frac{20}{100} = 0.2XpuтАЛ=10020тАЛ=0.2

3

Calculate Short Circuit Level

Using the formula for short circuit capacity, divide the total MVA by the per-unit reactance.

MVAsc=200.2=100┬аMVAMVA_{sc} = \frac{20}{0.2} = 100 \text{ MVA}MVAscтАЛ=0.220тАЛ=100┬аMVA

тЬЕ

D is correct because the short circuit MVA is calculated by dividing the total MVA (20 MVA) by the per-unit reactance (0.2), resulting in 100 MVA.

Core Concepts Used
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Short Circuit Capacity Per-unit System Alternator Impedance
ЁЯТб EXAM TIP

In power system analysis, remember that adding more parallel generators increases the short circuit level, which directly influences the selection of circuit breaker ratings.

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