Decoupled Transform (Six-Phase, Dual-Star)

R2026b

Implement abc and xyz to dqz1z2o1o2 transform with variable angular displacement

Renamed from Decoupled Transform (Six-Phase) in R2026b

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  • Decoupled Transform (Six-Phase, Dual-Star)

Libraries:
Simscape / Electrical / Control / Mathematical Transforms

Description

The Decoupled Transform (Six-Phase, Dual-Star) 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 β 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 equal to 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=0,     d−axis alignment−π2,    q−axis alignment

Equations

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

[dqz1z2o1o2]=13[cosθcos(θ−2π3)cos(θ+2π3)cos(θ−β)cos(θ−2π3−β)cos(θ+2π3−β)−sinθ−sin(θ−2π3)−sin(θ+2π3)−sin(θ−β)−sin(θ−2π3−β)−sin(θ+2π3−β)cosθcos(θ−2π3)cos(θ+2π3)−cos(θ−β)−cos(θ−2π3−β)−cos(θ+2π3−β)−sinθ−sin(θ−2π3)−sin(θ+2π3)sin(θ−β)sin(θ−2π3−β)sin(θ+2π3−β)111000000111][abcxyz].

Ports

Input

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

Data Types: single | double

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

Data Types: single | double

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

Data Types: single | double

Output

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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

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Since R2026b

Angular displacement between the abc and xyz three-phase systems, in degrees.

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

References

[1] Amy, John. "Six Phase Synchronous Machine Model in Machine Variables and “Dq” Variables". 2019 IEEE Electric Ship Technologies Symposium (ESTS), Washington, DC, USA, 2019, pp. 421-429. DOI.org (Crossref), https://doi.org/10.1109/ESTS.2019.8847819.

Extended Capabilities

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

Version History

Introduced in R2021a

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See Also

Simscape Blocks

Blocks