Magnetically Nonlinear Dynamic Models of Synchronous Machines: Their Derivation, Parameters and Applications

Nonlinear Three-Phase Reluctance Synchronous Machine Modeling With Extended Torque Equation

“…A lot of research has already been conducted to accurately model three-phase RSMs. In [11][12][13][14][15][16][17][18][19][20], nonlinear RSM models are provided in the (d, q)-reference frame. However, all of these papers assume a symmetric (balanced) system and, therefore, neglect the γ-component, which is generally obtained by the Clarke transformation in an unbalanced system and corresponds to a scaled 0-component.…”

“…In most publications, the magnetic behavior is described by nonlinear (apparent) inductances that depend on the stator currents or rotor position [11,12,14,15,17,18,20], while cross-coupling is mostly neglected (although present if not adequately considered during apparent inductance derivation). Other authors use flux linkage maps for modeling and, therefore, allow to include cross-coupling effects [12,13,16,19]. Most papers utilize the (average) torque equation which does not allow to reflect the intrinsic torque ripple (angle dependency) to its full extent.…”

Nonlinear Three-Phase Reluctance Synchronous Machine Modeling With Extended Torque Equation

“…A lot of research has already been conducted to accurately model three-phase RSMs. In [11][12][13][14][15][16][17][18][19][20], nonlinear RSM models are provided in the (d, q)-reference frame. However, all of these papers assume a symmetric (balanced) system and, therefore, neglect the γ-component, which is generally obtained by the Clarke transformation in an unbalanced system and corresponds to a scaled 0-component.…”

“…In most publications, the magnetic behavior is described by nonlinear (apparent) inductances that depend on the stator currents or rotor position [11,12,14,15,17,18,20], while cross-coupling is mostly neglected (although present if not adequately considered during apparent inductance derivation). Other authors use flux linkage maps for modeling and, therefore, allow to include cross-coupling effects [12,13,16,19]. Most papers utilize the (average) torque equation which does not allow to reflect the intrinsic torque ripple (angle dependency) to its full extent.…”

“…Most papers utilize the (average) torque equation which does not allow to reflect the intrinsic torque ripple (angle dependency) to its full extent. Only the authors of [13,16] use a fitting function, which takes the position (angle) dependency of the torque into account; while the angle dependency of the magnetic flux linkages and inductances are completely ignored in all the publications mentioned above. While iron losses are considered in the electromagnetic models in [15,17], their effect on torque production and torque ripples are neglected.…”