Question

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

Answer 1

Correct Answer - Option 1 : 60, 0.67

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

Inertia: M_old = 10 pu

Reactance: X_old = 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

⇒ Pu_old × Base old = Pu_new × Base_new

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