Output LC Filter

An LC filter may be used between the voltage-source converter and the electric machine in some applications [Salomäki et al., 2006]. Figure 1 shows its space-vector model in stator coordinates. The subscripts c and s refer to the converter-side and stator-side quantities, respectively. The LC filter model is implemented in the motulator.drive.model.LCFilter class.

Figure 1: LC filter in stator coordinates.

Figure 1: LC filter in stator coordinates.

In general coordinates rotating at the angular speed \(\omegac\), the dynamic model of the filter is

(1)\[\begin{split} \Lf \frac{\D\ic}{\D t} &= \uc - \us - \Rf \ic - \jj\omegac \Lf\ic \\ \Cf \frac{\D\us}{\D t} &= \ic - \is - \jj\omegac \Cf\us\end{split}\]

where \(\Lf\) is the filter inductance, \(\Rf\) is the series resistance of the filter inductor, and \(\Cf\) the filter capacitance. Furthermore, \(\ic\) is the converter current, \(\is\) is the stator current, \(\uc\) is the converter voltage, and \(\us\) is the capacitor voltage (corresponding to the stator voltage).

See also the 2.2-kW IM, LC filter, V/Hz control example.