Inverse Decoupled Transform (Six-Phase, Symmetrical)

R2026b

Implement d_sq_sxyo₁o₂ to abcdef transform

Since R2026b

• 

Inverse Decoupled Transform (Six-Phase, Symmetrical) block

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Libraries:
Simscape / Electrical / Control / Mathematical Transforms

Description

The Inverse Decoupled Transform (Six-Phase, Symmetrical) block converts the time-domain direct, quadrature, x, y, and zero components in a rotating reference frame to the components of a six-phase system in an abcdef reference frame.

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 where time t is 0.

Equations

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.

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

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

$$\left[\begin{array}{c}a\\ b\\ c\\ d\\ e\\ f\end{array}\right]=\left[\begin{array}{cccccc}\cos \theta & -\sin \theta & 1& 0& 0.5& 0.5\\ \cos \left(\theta -\frac{\pi }{3}\right)& -\sin \left(\theta -\frac{\pi }{3}\right)& -0.5& \frac{\sqrt{3}}{2}& 0.5& -0.5\\ \cos \left(\theta -\frac{2\pi }{3}\right)& -\sin \left(\theta -\frac{2\pi }{3}\right)& -0.5& -\frac{\sqrt{3}}{2}& 0.5& 0.5\\ \cos \left(\theta -\pi \right)& -\sin \left(\theta -\pi \right)& 1& 0& 0.5& -0.5\\ \cos \left(\theta +\frac{2\pi }{3}\right)& -\sin \left(\theta +\frac{2\pi }{3}\right)& -0.5& \frac{\sqrt{3}}{2}& 0.5& 0.5\\ \cos \left(\theta +\frac{\pi }{3}\right)& -\sin \left(\theta +\frac{\pi }{3}\right)& -0.5& -\frac{\sqrt{3}}{2}& 0.5& -0.5\end{array}\right]\left[\begin{array}{c}{d}_s\\ q_s\\ x\\ y\\ o_1\\ o_2\end{array}\right].$$

Ports

Input

dsqsxyo1o2 — Direct, quadrature, x, y, o₁, and o₂ components

vector

Direct, quadrature, x-axis, y-axis, and zero components of the system in the rotating 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

abcdef — a-, b-, c-, d-, e-, and f-phase components

vector

Components of the six-phase system in an abcdef reference frame, returned as a vector.

Data Types: single | double

Parameters

Phase-a axis alignment — dqxyo₁o₂ reference frame alignment

Q-axis (default) | D-axis

Option to align the a-phase vector of the abcdef reference frame to either the d-axis or the q-axis of the rotating reference frame.

References

[1] Yepes, Alejandro G., et al. "Comparison of Stator Winding Connections in Multiphase Drives under Healthy Operation and with One Open Converter Leg". IET Electric Power Applications, vol. 14, no. 4, Apr. 2020, pp. 584–96. DOI.org (Crossref), https://doi.org/10.1049/iet-epa.2019.0467.

Extended Capabilities

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

Version History

Introduced in R2026b