Stationary and Rotary Frames

[dzt]

Hi,

I have been searching for an explanation for some time online and in books about this, but none offered a clear explanation. Maybe someone here can help me. What does a stationary or a rotary frame mean when applied to Park and Clarke Transformations, please?

Thanks

 

[xnuke]

A phasor is a vector that rotates with respect to a stationary frame of reference. The typical abc phasor representation consists of three vectors that are rotating in reference to a stationary reference frame. The Clarke transformation converts three balanced phasors abc separated by 120° into two orthogonal phasors α and β. If abc are unbalanced, a third phasor γ is required. Since αβγ are phasors, they are still rotating in reference to a stationary reference frame. However, motion is relative, so one can think of either rotating vectors in a stationary reference frame, or stationary vectors in a rotating reference frame. In order to create the latter, the Park transformation is applied. The Park transformation converts three balanced phasors abc separated by 120° into two orthogonal vectors d and q. If abc are unbalanced, a third vector 0 is required. The dq0 vectors are are stationary in reference to a rotating reference frame.

I like to think of the rotor of a machine when I think of these representations. If I'm observing the rotor from outside, I see the αβγ representation. If I'm sitting on the rotor and spinning with it, what appeared to be rotating phasors are now stationary vectors from my point of view, and I see the dq0 representation.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[dzt]

Thanks for the answer, xnuke.

So if I understood correctly in the case of the Clarke Transformation when it is stated that the transformation converts time domain signals from a stationary 3-phase phase coordinate system (ABC) to a stationary 2-phase coordinate system (αβγ), what is meant is that the frame (ABC) is stationary while the voltages (or currents) Va, Vb, Vc are rotating and the frame (αβγ) is also stationary while voltages (or currents) Vα, Vβγ, Vγ are rotating.

Again, if I understood correctly for the Park Transformation, it converts time domain signals from a stationary phase coordinate system (ABC) to a rotating coordinate system (dq0), where the frame (ABC) is stationary while the voltages (or currents) Va, Vb, Vc are rotating and the frame (dq0) is rotating while voltages (or currents) Vd, Vq, V0 are stationary.
So this is what makes the 3-phase voltages (or currents) after the (dq0) transformation appear as a constant (like a DC value) representing the magnitude?

 

[xnuke]

That's correct.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[dzt]

Great
Thanks for the great help, xnuke, I really appreciate it.