Three-Phase Voltage Source

A model for an ideal three-phase voltage source is implemented in the class motulator.grid.model.ThreePhaseVoltageSource. The voltage space vector is calculated as a combination of a positive-sequence and optional negative-sequence components as

(1)\[\begin{split}\frac{\mathrm{d}\vartheta_\mathrm{g}}{\mathrm{d} t} &= \omega_\mathrm{g} \\ \boldsymbol{e}_\mathrm{g}^\mathrm{s} &= e_\mathrm{g+}\mathrm{e}^{\mathrm{j}(\vartheta_\mathrm{g} + \phi_\mathrm{+})} + e_\mathrm{g-}\mathrm{e}^{-\mathrm{j}(\vartheta_\mathrm{g} + \phi_\mathrm{-})}\end{split}\]

where \(e_\mathrm{g+}\) and \(e_\mathrm{g-}\) are the magnitudes of the positive-sequence and negative-sequence components, respectively, and \(\phi_\mathrm{+}\) and \(\phi_\mathrm{-}\) are the positive-sequence and negative-sequence phase shifts, respectively. The angle \(\vartheta_\mathrm{g}\) is obtained by integrating the angular frequency \(\omega_\mathrm{g}\). All parameters can be given as time-varying functions to simulate various fault conditions.