I have been attempting to find the differential equation describing the dynamic of the dc link voltage of the induction machine based electric drive in braking mode.
I have started with the energy balance with the assumption that there are no losses i.e. the energy absorbed by the dc link capacitor equals the kinetic energy reduction i.e.
$$ \begin{eqnarray} \frac{\mathrm{d}E_{v_{dc}}}{\mathrm{d}t} &=& \frac{\mathrm{d}E_{k}}{\mathrm{d}t} \nonumber\\ \frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{1}{2}\cdot C\cdot v^2_{dc}\right) &=& \frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{1}{2}\cdot J\cdot \omega^2\right)\nonumber \end{eqnarray} $$
I have evaluated the derivatives and I have got following non-linear differential equation
$$ C\cdot v_{dc}\cdot\frac{\mathrm{d}v_{dc}}{\mathrm{d}t} = J\cdot\omega\cdot \frac{\mathrm{d}\omega}{\mathrm{d}t} $$
Can anybody tell me whether my considerations I have used in derivation are correct?
