General PMSM d,q-model using optimized interpolated absolute and differential inductance surfaces

Abstract

Widely used permanent magnet synchronous machines (PMSMs) often show a significant inductance variation near and above the rated current values due to saturation. When the inductances are no longer constant, the model equations have to be modified. This paper proposes new, extended equations, which are as similar as possible to the linearized equations, to make the conversion of existing control schemes to the new approach as easy as possible. In addition, methods to measure the inductances needed for the new PMSM equations are explained together with an efficient implementation of the inductances.

Bivariate polynomial approximation of cross-saturated flux curves in synchronous machine models

“…Note that on the contrary to other works (e.g. [6]), there are no additional parameters or measurements necessary for determining the differential inductances.…”

“…By differentiating the approximation functions, the differential inductances were obtained in order to describe the transient behavior of the currents mathematically. In [6], absolute and differential inductances are independently measured and plotted as two-dimensional functions of the direct and quadrature stator current components. For practical use, the look-up data is applied for linear or bi-cubic spline interpolation.…”