Analysis of Synchronous Machines, 2nd Edition

Chapter 10

Linearization of the Synchronous Machine Equations

10.1  Introduction

Many problems exist in which the rotor speed can no longer be assumed as constant. The presence of the rotor speed dependant voltage term in Park’s equations and the torque equations results in a non-linear set of differential equation to be solved. In many problems, however, the change in speed can be considered as sufficiently small that the equations can be shown to remain essentially linear. The resulting set of equations is generally termed the small signal equations and is particularly important for the design of controllers.

10.2  Park’s Equations in Physical Units

Repeating here for convenience, Park’s equations in physical units are,

$v_{qs}=r_s{i}_{qs}+\frac{p}{{\text{ω}}_b}{\text{ψ}}_{qs}$