| \(J\) | rotor moment of inertia in \(kg-m^{2}\) |
|---|---|
| \(\omega_{sm}\) | synchronous speed in \(rad~(mech)/s\) |
| \(\omega_{s}=\left(\dfrac{P}{2}\right)\omega_{sm}\) | rotor speed in \(rad~(elect)/s\) |
| \(P\) | number of machine poles |
| \(M\) | moment of inertia in \(MJ-s/elec~rad\) |
| \(G\) | machine rating (base) in MVA (3-phase) |
| \(H\) | intertia constant in \(MJ/MVA\) |
The kinetic energy of the synchronous machine rotor is given as \[\begin{aligned} KE & =\dfrac{1}{2}J\omega_{sm}^{2}\times10^{-6}~\mbox{MJ}\\ & =\dfrac{1}{2}\left[J\left(\dfrac{2}{P}\right)^{2}\omega_{s}\times10^{-6}\right]\omega_{s}\\ & =\dfrac{1}{2}M\omega_{s} \end{aligned}\]
where \[M=J\left(\dfrac{2}{P}\right)^{2}\omega_{s}\times10^{-6}\]
Also \[KE = G\cdot H = \dfrac{1}{2}M\omega_{s}\]
\[\begin{aligned} M & =\dfrac{2GH}{\omega_{s}}=\dfrac{GH}{\pi f}~\mbox{MJ-s/elect rad}\\ & =\dfrac{GH}{180f}~\mbox{MJ-s/elect degree} \end{aligned}\] Taking \(G\) as base \[\begin{aligned} M~(p.u) & =\dfrac{H}{\pi f}~\mbox{MJ-s/elect rad}\\ & =\dfrac{H}{180f}~\mbox{MJ-s/elect degree} \end{aligned}\]