Decoupled Transform (Six-Phase, Symmetrical)

R2026b

Implement abcdef to d_sq_sxyo₁o₂ transform

Since R2026b

Libraries:
Simscape / Electrical / Control / Mathematical Transforms

Description

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

You can configure the block to align the phase a-axis of the six-phase system to either the d-axis or the 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.
$O f f s e t = \begin{matrix} 0, d - a x i s a l i g n m e n t \\ - \frac{π}{2}, q - a x i s a l i g n m e n t \end{matrix}$

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

$[\begin{matrix} d_{s} \\ q_{s} \\ x \\ y \\ o_{1} \\ o_{2} \end{matrix}] = \frac{1}{3} [\begin{matrix} \cos θ & \cos (θ - \frac{π}{3}) & \cos (θ - \frac{2 π}{3}) & \cos (θ - π) & \cos (θ + \frac{2 π}{3}) & \cos (θ + \frac{π}{3}) \\ - \sin θ & - \sin (θ - \frac{π}{3}) & - \sin (θ - \frac{2 π}{3}) & - \sin (θ - π) & - \sin (θ + \frac{2 π}{3}) & - \sin (θ + \frac{π}{3}) \\ 1 & - 0.5 & - 0.5 & 1 & - 0.5 & - 0.5 \\ 0 & \frac{\sqrt{3}}{2} & - \frac{\sqrt{3}}{2} & 0 & \frac{\sqrt{3}}{2} & - \frac{\sqrt{3}}{2} \\ 0.5 & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\ 0.5 & - 0.5 & 0.5 & - 0.5 & 0.5 & - 0.5 \end{matrix}] [\begin{matrix} a \\ b \\ c \\ d \\ e \\ f \end{matrix}] .$

Ports

Input

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

Components of the six-phase system in an abcdef 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

expand all

dsqsxyo1o2 — Direct, quadrature, x, y, and zero components
vector

Direct, quadrature, x-axis, y-axis, and zero components of the system in the rotating reference frame, returned as a vector.

Data Types: single | double

Parameters

expand all

Phase-a axis alignment — d_sq_sxyo₁o₂ 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.

Decoupled Transform (Six-Phase, Symmetrical)

Description

Equations

Ports

Input

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

θ_elec — Rotational angle
scalar

Output

dsqsxyo1o2 — Direct, quadrature, x, y, and zero components
vector

Parameters

Phase-a axis alignment — d_sq_sxyo₁o₂ reference frame alignment
`Q-axis` (default) | `D-axis`

References

Extended Capabilities

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

Version History

See Also

Decoupled Transform (Six-Phase, Symmetrical)

Description

Equations

Ports

Input

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

θelec — Rotational angle scalar

Output

dsqsxyo1o2 — Direct, quadrature, x, y, and zero components vector

Parameters

Phase-a axis alignment — dsqsxyo1o2 reference frame alignment Q-axis (default) | D-axis

References

Extended Capabilities

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

Version History

See Also

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

θ_elec — Rotational angle
scalar

dsqsxyo1o2 — Direct, quadrature, x, y, and zero components
vector

Phase-a axis alignment — d_sq_sxyo₁o₂ reference frame alignment
`Q-axis` (default) | `D-axis`

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