Figure 0.5 : Simulation of coordinates transformations
Simulation comments :
Theta is positive.
Voltage is placed on the d axis.
Beta signal is delay (lag).
We verify a direct three phase system (A first[0 rad], B in second[ 2 /3 rad], C third[ 4 /3 rad]).
5 Impedance in synchronous coordinates We assume in the report (current controller design) that the impedance is : . We can prove this relation with the following. is a general space vector, its transformation in synchronous coordinates is
and its time derivative is transformed as
Then, using the derivative operation
In the Laplace domain, the following substitution is made : complex impedance of an inductor in synchronous coordinates is
. This implies that the