Clarke to Park Angle Transform

Implementαβ0todq0transform

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Simscape / Electrical / Control / Mathematical Transforms

Description

TheClarke to Park Angle Transformblock 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 phasea-axis of the three-phase system to either theq- ord-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 stationaryαβ0reference frame, and a rotatingdq0reference frame where:

Thea-axis and theq-axis are initially aligned.
Thea-axis and thed-axis are initially aligned.

In both cases, the angleθ=ωt, where

θis the angle between theaandqaxes for theq-axis alignment or the angle between theaanddaxes for thed-axis alignment.
ωis the rotational speed of thed-qreference frame.
tis the time, in s, from the initial alignment.

The figures show the time-response of the individual components of equivalent balancedαβ0anddq0for an:

Alignment of thea-phase vector to theq-axis
Alignment of thea-phase vector to thed-axis

Equations

TheClarke to Park Angle Transformblock implements the transform for ana-phase toq-axis alignment as

$[\begin{matrix} d \\ q \\ 0 \end{matrix}] = [\begin{matrix} sin (θ) & - cos (θ) & 0 \\ cos (θ) & sin (θ) & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} α \\ β \\ 0 \end{matrix}]$

where:

αandβare the alpha-axis and beta-axis components of the two-phase system in the stationary reference frame.
0is the zero component.
dandqare the direct-axis and quadrature-axis components of the two-axis system in the rotating reference frame.

For ana-phase tod-axis alignment, the block implements the transform using this equation:

$[\begin{matrix} d \\ q \\ 0 \end{matrix}] = [\begin{matrix} cos (θ) & sin (θ) & 0 \\ - sin (θ) & cos (θ) & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} α \\ β \\ 0 \end{matrix}]$

Ports

Input

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`αβ0`—α-βaxis and zero components
vector

Alpha-axis,α, beta-axis,β, and zero components of the two-phase system in the stationary reference frame.

Data Types:single|double

`θ_abc`— 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 thea-phase in theabcreference frame to the initially aligned axis of thedq0reference frame.

Data Types:single|double

Output

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`dq0`—d-qaxis and zero components
vector

Direct-axis and quadrature-axis components and the zero component of the system in the rotating reference frame.

Data Types:single|double

Parameters

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`Phase-a axis alignment`—dq0reference frame alignment
`Q-axis`(default) |`D-axis`

Align thea-phase vector of theabcreference frame to thed- orq-axis of the rotating reference frame.

References

[1] Krause, P o . Wasynczuk S·d·Sudhoff和年代. Pekarek.Analysis of Electric Machinery and Drive Systems.Piscatawy, NJ: Wiley-IEEE Press, 2013.

Clarke to Park Angle Transform