T fqs fds fabs T fas fbs Ks cos sin sin cos 116 REFERE

T
= fqs fds
(fabs ) [ ]
T
= fas fbs
Ks =





cos sin
sin cos


116 REFERENCE-FRAME THEORY
where is defi ned by (3.3-5) .
(a) Determine ( K s ) 1 .
(b) Depict the transformation similar to that shown in Figure 3.3-1 .

Solution

Reference Frame Theory is classified into many categories

Park\'s Transformation : Synchronous Machine, Rotor reference frame

Stanley\'s Transformation: Induction machine

Power of Reference Frame Theory:
Eliminates Rotor Position Dependence Inductances and Capacitances .
Transforms Nonlinear Systems to Linear Systems for Certain Cases
Fundamental Tool For Rigorous Development of Equivalent Circuits
Can Be Used to Make AC Quantities Become DC Quantities
Framework of Most Controllers

Park’s Transformation ¾Synchronous Machine; Rotor Reference Frame

Stanley ¾Induction Machine; Stationary Reference Frame

Kron ¾Induction Machine; Synchronous Reference Frame

Brereton Induction Machine; Rotor Reference Frame

Krause ¾Arbitrary Reference Frame

Please provide data for wich type of transformation required