Perform transformation from αβ0 stationary reference frame to dq0 rotating reference frame or the inverse
Control and Measurements/Transformations
The Alpha-Beta-Zero to dq0 block performs a transformation of αβ0 Clarke components in a fixed reference frame to dq0 Park components in a rotating reference frame.
The dq0 to Alpha-Beta-Zero block performs a transformation of dq0 Park components in a rotating reference frame to αβ0 Clarke components in a fixed reference frame.
The block supports the two conventions used in the literature for Park transformation:
Rotating frame aligned with A axis at t = 0. This type of Park transformation is also known as the cosine-based Park transformation.
Rotating frame aligned 90 degrees behind A axis. This type of Park transformation is also known as the sine-based Park transformation. Use it in Simscape™ Power Systems™ models of three-phase synchronous and asynchronous machines.
Knowing that the position of the rotating frame is given by ω.t (where ω represents the frame rotation speed), the αβ0 to dq0 transformation performs a −(ω.t) rotation on the space vector Us = uα + j· uβ. The homopolar or zero-sequence component remains unchanged.
Depending on the frame alignment at t = 0, the dq0 components are deduced from αβ0 components as follows:
When the rotating frame is aligned with A axis, the following relations are obtained:
When the rotating frame is aligned 90 degrees behind A axis, the following relations are obtained:
The abc-to-Alpha-Beta-Zero transformation applied to a set of balanced three-phase sinusoidal quantities ua, ub, uc produces a space vector Us whose uα and uβ coordinates in a fixed reference frame vary sinusoidally with time. In contrast, the abc-to-dq0 transformation (Park transformation) applied to a set of balanced three-phase sinusoidal quantities ua, ub, uc produces a space vector Us whose ud and uq coordinates in a dq rotating reference frame stay constant.
Select the alignment of rotating frame, when wt = 0, of the dq0 components of a three-phase balanced signal:
(positive-sequence magnitude = 1.0 pu; phase angle = 0 degree)
When you select
Aligned with phase A axis,
the dq0 components are d = 0, q = −1, and zero = 0.
When you select
90 degrees behind phase A axis,
the default option, the dq0 components are d = 1, q = 0, and zero
The vectorized αβ0 signal.
The vectorized dq0 signal.
The angular position, in radians, of the dq rotating frame relative to the stationary frame.
shows various uses of blocks performing Clarke and Park transformations.