Output LC Filter#

An LC filter may be used between the voltage-source converter and the electric machine in some applications [1]. The subscripts c and s refer to the converter-side and stator-side quantities, respectively. The superscript s refers to the stationary coordinates.

A dynamic model of the filter is

(1)#\[\begin{split}L_\mathrm{f} \frac{\mathrm{d}\boldsymbol{i}_\mathrm{c}^\mathrm{s}}{\mathrm{d} t} &= \boldsymbol{u}_\mathrm{c}^\mathrm{s} - \boldsymbol{u}_\mathrm{s}^\mathrm{s} - R_\mathrm{f} \boldsymbol{i}_\mathrm{c}^\mathrm{s} \\ C_\mathrm{f} \frac{\mathrm{d}\boldsymbol{u}_\mathrm{s}^\mathrm{s}}{\mathrm{d} t} &= \boldsymbol{i}_\mathrm{c}^\mathrm{s} - \boldsymbol{i}_\mathrm{s}^\mathrm{s}\end{split}\]

where \(L_\mathrm{f}\) is the filter inductance, \(R_\mathrm{f}\) is the series resistance of the filter inductor, and \(C_\mathrm{f}\) the filter capacitance. Furthermore, \(\boldsymbol{i}_\mathrm{c}^\mathrm{s}\) is the converter current, \(\boldsymbol{i}_\mathrm{s}^\mathrm{s}\) is the stator current, \(\boldsymbol{u}_\mathrm{c}^\mathrm{s}\) is the converter voltage, and \(\boldsymbol{u}_\mathrm{s}^\mathrm{s}\) is the capacitor voltage (corresponding to the stator voltage).

The filter model is implemented in the class motulator.drive.model.LCFilter. For its usage, see the example 2.2-kW induction motor, LC filter.

References