Clarke to Park Angle Transform
Implement αβ0 to dq0 transform
Simscape / Electrical / Control / Mathematical Transforms
The Clarke to Park Angle Transform block converts the alpha, beta, and zero components in a stationary reference frame to direct, quadrature, and zero components in a rotating reference frame. For balanced three-phase systems, the zero components are equal to zero.
You can configure the block to align the phase a-axis of the three-phase system to either the q- or d-axis of the rotating reference frame at time, t = 0. The figures show the direction of the magnetic axes of the stator windings in the three-phase system, a stationary αβ0 reference frame, and a rotating dq0 reference frame where:
The a-axis and the q-axis are initially aligned.
The a-axis and the d-axis are initially aligned.
In both cases, the angle θ = ωt, where
θ is the angle between the a and q axes for the q-axis alignment or the angle between the a and d axes for the d-axis alignment.
ω is the rotational speed of the d-q reference frame.
t is the time, in s, from the initial alignment.
The figures show the time-response of the individual components of equivalent balanced αβ0 and dq0 for an:
Alignment of the a-phase vector to the q-axis
Alignment of the a-phase vector to the d-axis
The Clarke to Park Angle Transform block implements the transform for an a-phase to q-axis alignment as
α and β are the alpha-axis and beta-axis components of the two-phase system in the stationary reference frame.
0 is the zero component.
d and q are the direct-axis and quadrature-axis components of the two-axis system in the rotating reference frame.
For an a-phase to d-axis alignment, the block implements the transform using this equation:
αβ0 — α-β axis and zero
Alpha-axis, α, beta-axis, β, and zero components of the two-phase system in the stationary reference frame.
θabc — Rotational angle
scalar | in radians
Angular position of the rotating reference frame. The value of this parameter is equal to the polar distance from the vector of the a-phase in the abc reference frame to the initially aligned axis of the dq0 reference frame.
dq0 — d-q axis and zero
Direct-axis and quadrature-axis components and the zero component of the system in the rotating reference frame.
Phase-a axis alignment — dq0 reference frame alignment
Q-axis (default) |
Align the a-phase vector of the abc reference frame to the d- or q-axis of the rotating reference frame.
 Krause, P., O. Wasynczuk, S. D. Sudhoff, and S. Pekarek. Analysis of Electric Machinery and Drive Systems. Piscatawy, NJ: Wiley-IEEE Press, 2013.