For the stator voltage vector components in the [d, q] rotor rotating coordinate system, there are valid the following voltage equations:
where: [i.sub.Sd], [i.sub.Sq]--stator current vector components in [d, q] rotating coordinate system; [U.sub.Sd], [U.sub.Sq]--stator voltage vector components in [d, q] rotating coordinate system; [[PHI].sub.F] magnetic flux of permanent magnets; [L.sub.Sd]--stator inductance in d-axis; [L.sub.Sq]--stator inductance in q-axis; [R.sub.S]--stator phase resistance; [omega]--electrical angular speed of the rotor; [THETA] rotor angle.
The vector rotation and the reverse vector rotation of the complex space vector components from the [[alpha], [beta]] stationary coordinate system to the [d,q] rotor rotating coordinate system respectively, are performed using the rotor angle [THETA].
The positive and negative sequence vector orientation of stator voltage is used respectively in the positive synchronous rotating coordinate system
([d.sup.p] [q.sup.p]) and the negative synchronous rotating coordinate system
([d.sup.n] [q.sup.n]), expressed as follows:
The mathematical model of a variable speed constant frequency generator under a dq synchronous rotating coordinate system is shown as follows:
If the stator flux linkage is defined in the same direction as the d axis of rotating coordinate system, that is [[psi].sub.sd]=0, the following expression can be obtained:
The topics include coordinate systems, rotating coordinate systems
, inertial accelerations, equations of motion, flying qualities, and trends in automatic flight control.
Appendices cover three-dimensional rigid-body motion in rotating coordinate systems
, moments of inertia for some common body shapes, and the parallel axis theorem.