Question

An alternator is operating at rated capacity has per unit reactance represented by x. If capacity is tripled for the same alternator and voltage is halved, the per unit reactance will become

• A. 6 x
• B. 8 x
• C. 12 x
• D. 18 x

Answer 1

The correct option is C 12 x

We know $,Z_{pu}=\frac{Z_{act}}{Z_{base}}$

also$Z_{base}=\frac{k{V}_{base}^2}{MV{A}_{base}}$

$\therefore Z_{pu}=Z_{act}\times \frac{MV{A}_{base}}{k{V}_{base}^2}=x$ ...(1)

After capacity is tripled and voltage is halved,

$Z_{pu}^{\prime }=\left(Z_{act}\right)\times \frac{3MV{A}_{base}}{{\left(\frac{k{V}_{base}}{2}\right)}^2}=Z_{act}\times \frac{12MV{A}_{base}}{k{V}_{base}^2}$ ...(2)

Dividing equation (1) and (2)

$\frac{x}{Z_{pu}^{\prime }}=\frac{1}{12}or{Z}_{pu}^{\prime }=12x$