Question

Assume a voltampere-base S3b = 100 MVA and a line-to-neutral voltage base Vb = 7.5 kV. Find the current base Ib. Also, by using this information per-unitize the phasors V˜ as and ˜Ias, e.g., V˜ as,u = V˜ as/Vb.

Answer 1

Explanation:

Let the frequency of the operation "W"ras/s

$\begin{aligned}V(t) &=7.5 \cos (\omega t+\varnothing v) k V \\&=7.5 \cos w t \quad k V \\I(t) &=\cos \left(\omega t+\phi_{i}\right) \quad k A \\&=\cos (\omega t-\pi / 6) \quad k A\end{aligned}$

$\(\therefore\) Power, \(P(t)=v(t) I(t)\) \begin{array}{l}=[7.5 \cos \omega t][\cos (\cot -\pi / 6)] \times 10^{6} w \\=7.5 \cos ^{2}(2 \omega t-\pi / 6)+7.5 \cos \left(\pi_{6}\right) MW \\=3.75+7.5 \cos (2 \omega t-\pi / 6) \quad MW\end{array}$

$Real powel, \(P=\left(7.5 \times 10^{3}\right)\left(10^{3}\right) \cos \left(\varnothing_{v}-\varnothing_{I}\right)\) \begin{array}{l}=7.5 \cos (-\pi / 6) MW \\=3.75 MW\end{array}$