Decoupled Transform (Six-Phase)

Implement abc and xyz to dqz₁z₂o₁o₂ transform

Since R2021a

• 

Libraries:
Simscape / Electrical / Control / Mathematical Transforms

Description

The Decoupled Transform (Six-Phase) block converts the time-domain components of a six-phase system in abc and xyz reference frames to direct, quadrature, z₁, z₂, o₁, and o₂ components in a rotating reference frame. The three-phase systems abc and xyz are spatially shifted by 30 electrical degrees.

You can configure the block to align the phase a-axis of the six-phase system to either the d-axis or q-axis of the rotating reference frame at time t = 0.

θ = ωt + Offset 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, where:

• ω is the rotational speed of the rotational reference frame.

• t is the time, in s, from the initial alignment.

• $$Offset=\begin{array}{c}0,d-axisalignment\\ -\frac{\pi }{2},q-axisalignment\end{array}$$

Equations

The Decoupled Transform (Six-Phase) block implements the transform as

$$\left[\begin{array}{c}d\\ q\\ z_1\\ z_2\\ o_1\\ o_2\end{array}\right]=\frac{1}{3}\left[\begin{array}{cccccc}\cos \theta & \cos \left(\theta -\frac{2\pi }{3}\right)& \cos \left(\theta +\frac{2\pi }{3}\right)& \cos \left(\theta -\frac{\pi }{6}\right)& \cos \left(\theta -\frac{5\pi }{6}\right)& \cos \left(\theta +\frac{\pi }{2}\right)\\ -\sin \theta & -\sin \left(\theta -\frac{2\pi }{3}\right)& -\sin \left(\theta +\frac{2\pi }{3}\right)& -\sin \left(\theta -\frac{\pi }{6}\right)& -\sin \left(\theta -\frac{5\pi }{6}\right)& -\sin \left(\theta +\frac{\pi }{2}\right)\\ 1& -\frac{1}{2}& -\frac{1}{2}& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& 0\\ 0& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& \frac{1}{2}& \frac{1}{2}& -1\\ 1& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1\end{array}\right]\left[\begin{array}{c}a\\ b\\ c\\ x\\ y\\ z\end{array}\right]$$

Ports

Input

abc — a-, b-, and c-phase components

vector

Components of the three-phase system in an abc reference frame, specified as a vector.

Data Types: single | double

xyz — x-, y-, and z-phase components

vector

Components of the three-phase system in an xyz reference frame, specified as a vector.

Data Types: single | double

θ_elec — Rotational angle

scalar

Angular position of the rotating reference frame, specified as a scalar.

Data Types: single | double

Output

dqz1z2o1o2 — Direct, Quadrature, z₁, z₂, o₁, and o₂ components

vector

Direct, quadrature, z₁-, z₂-, o₁-, and o₂-axis components of the system in the rotating reference frame, returned as a vector.

Data Types: single | double

Parameters

Phase-a axis alignment — dqz₁z₂o₁o₂ reference frame alignment

Q-axis (default) | D-axis

Whether to align the a-phase vector of the abc reference frame to the d-axis or q-axis of the rotating reference frame.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2021a