Output LC Filter#

This document describes a continuous-time model of an LC filter, which may be used between the converter and the electric machine in some applications [1]. Space vectors are used to represent the three-phase quantities. The subscript c and s refer to the converter-side and the stator-side quantities, respectively. The superscript s refers to the stationary coordinates.

A dynamic model of the filter is

(1)#\[\begin{split}L \frac{\mathrm{d}\boldsymbol{i}_\mathrm{c}^\mathrm{s}}{\mathrm{d} t} &= \boldsymbol{u}_\mathrm{c}^\mathrm{s} - \boldsymbol{u}_\mathrm{s}^\mathrm{s} - R \boldsymbol{i}_\mathrm{c}^\mathrm{s} \\ C \frac{\mathrm{d}\boldsymbol{u}_\mathrm{s}^\mathrm{s}}{\mathrm{d} t} &= \boldsymbol{i}_\mathrm{c}^\mathrm{s} - \boldsymbol{i}_\mathrm{s}^\mathrm{s}\end{split}\]

where \(L\) and \(R\) are the inductance and the series resistance of the inductor, respectively, and \(C\) is the 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