Third-Order Polar-Coordinate Model of Induction Motor Load

Induction motors are one of the major load components in power systems. To accurately predict the system's dynamic performance, a mathematical model of induction motors is necessary. The conventional third-order model, based on the orthogonal system (direct- and quadrature-axes,
${d-}$
and
$q$
-axes), is often used in large- and small-signal stability analysis. Since bus voltage magnitude and angle are commonly used as state variables in power-system analysis, a polar coordinate system can be a meaningful way to model induction motor loads. Hence, in this paper, the
${d-}$
and
$q$
-axis components of transient emf, found in the traditional third-order model of an induction motor, are converted into magnitude and phase angle using the polar coordinate frame of reference. Validation and discussion are fully provided.