# The pu parameters for a 300 MVA machine on its own base are inertia M = 10 pu and reactance X = 4 pu. The pu values of inertia and reactance on 50 MVA

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The pu parameters for a 300 MVA machine on its own base are inertia M = 10 pu and reactance X = 4 pu. The pu values of inertia and reactance on 50 MVA common base, respectively, will be:
1. 60, 0.67
2. 40, 0.67
3. 60, 0.4
4. 4, 10

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Correct Answer - Option 1 : 60, 0.67

Given that, pu parameters for a 300 MVA machine on its own base

Inertia: Mold = 10 pu

Reactance: Xold = 4 pu

New base = 50 MVA

New pu value of inertia,

${M_{Pu\;new}} = {M_{Pu\;old}} \times \frac{{{{\left( {MVA} \right)}_{old}}}}{{{{\left( {MVA} \right)}_{new}}}}$

$\Rightarrow \;{M_{Pu\;new}} = 10 \times \frac{{300}}{{50}} = 60\;Pu$

New pu value of reactance,

${X_{Pu\;new}} = {X_{Pu\;old}} \times \frac{{{z_{Base\;old}}}}{{{Z_{Base\;new}}}}$

$\Rightarrow {Z_{Base}} = \frac{{{{\left( {kV} \right)}^2}}}{{MVA}}$

$\Rightarrow {X_{Pu\;new}} = {X_{Pu\;old}} \times \frac{{{{\left( {MVA} \right)}_{new}}}}{{{{\left( {MVA} \right)}_{old}}}} \times \frac{{\left( {kV} \right)_{old}^2}}{{\left( {kV} \right)_{new}^2}}$

Now (kV)old = (kV)new­ [not given]

$\Rightarrow {X_{Pu\;new}} = 4 \times \frac{{50}}{{300}} = 0.67\;Pu$

Note:

We know that Pu value depends on the base value of that quantity hence the actual value of that quantity is always equal-

pu value old = actual/old base

Now, new pu value = actual/new base

⇒ Puold × Base old = Punew × Basenew

⇒ pu new = (pu old × old base)/(new base)