# Calculate the per-unit synchronous reactance on the base value of 200 MVA and 20 kV when a 100 MVA with 20 kV synchronous generator has 1pu synchronou

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Calculate the per-unit synchronous reactance on the base value of 200 MVA and 20 kV when a 100 MVA with 20 kV synchronous generator has 1pu synchronous reactance.
1. 2 pu
2. 4 pu
3. 6 pu
4. 8 pu

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Correct Answer - Option 1 : 2 pu

Concept:

The relation between new per-unit value & old per unit value of reactance

${({X_{pu}})_{new}}\; = {({X_{pu}})_{old}} \times {\left( {\frac{{k{V_{base}}}}{{k{V_{new}}}}} \right)^2} \times \;\left( {\frac{{MV{A_{new}}}}{{MV{A_{old}}}}} \right)$

Also ${X_{pu}} = \frac{{{X_{Actual}}}}{{{X_{base}}}}$

${X_{base}} = \frac{{kV_{base}^2}}{{MV{A_{base}}}}$

Where,

(Xpu)new = New per unit value of reactance

(Xpu)old = Old per unit value of reactance

kVbase = Old base value of voltage

kVnew = New base value of voltage

MVAnew = New base value of power

MVAold = Old base value of power

Calculation:

Given that,

Xd(old) = 1 pu

MVA(new) = 200

MVA(old) = 100

kV(old) = 20

kV(new) = 20

∴ ${X_{d\left( {new} \right)}} = 1 \times \frac{{200}}{{100}} \times {\left( {\frac{{20}}{{20}}} \right)^2} = 2\;pu$