Interactive visualization demonstrating alpha-beta and the rotating reference frame transformations for advanced power systems analysis
I would like to express my sincere gratitude to Professor Eduardo Prieto Araujo for helping me understand these complex topics with clear explanations, and for encouraging me to explore them as deeply as I wished.
If you wish to discover 3D Clarke transformation, follow this link.
The Clarke transformation is the first step in the Park transformation process. It converts three-phase quantities into stationary two-phase orthogonal components plus a zero component:
This transformation preserves power between the reference frames when using the power invariant form.
The Park transformation takes the stationary αβ0 components and applies a rotation to align with a rotating reference frame:
When the electrical angle θ = ωt is synchronized with the system frequency, balanced sinusoidal three-phase quantities become DC values in the dq reference frame, greatly simplifying control system design.
The current three-phase system is represented as a Fourier series with fundamental, third, and fifth harmonic components:
Note how harmonics of different orders transform differently in the dq reference frame:
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