Inverse Decoupled Transform (Six-Phase)

Implementdqz₁z₂o₁o₂toabcandxyztransform

expand all in page

Library:
Simscape / Electrical / Control / Mathematical Transforms

Description

TheInverse Decoupled Transform (Six-Phase)block converts the direct, quadrature,z₁,z₂,o₁, ando₂components in a rotating reference frame to the components of a six-phase system in theabcandxyzreference frame. The three-phase systemsabcandxyz由30电度空间转移。

You can configure the block to align the phasea-axis of the five-phase system to either thed-axis orq-axis of the rotating reference frame at timet= 0.

θ = ωt + Offsetis the angle between theaandqaxes for theq-axis alignment or the angle between theaanddaxes for thed-axis alignment, where:

ωis the rotational speed of the rotational reference frame.
tis the time, in s, from the initial alignment.
$O f f s e t = \begin{matrix} 0, d - a x i s a l i g n m e n t \\ - \frac{π}{2}, q - a x i s a l i g n m e n t \end{matrix}$

Equations

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

$[\begin{matrix} a \\ b \\ c \\ x \\ y \\ z \end{matrix}] = [\begin{matrix} \cos θ & - \sin θ & 1 & 0 & 1 & 0 \\ \cos (θ - \frac{2 π}{3}) & - \sin (θ - \frac{2 π}{3}) & - \frac{1}{2} & - \frac{\sqrt{3}}{2} & 1 & 0 \\ \cos (θ + \frac{2 π}{3}) & - \sin (θ + \frac{2 π}{3}) & - \frac{1}{2} & \frac{\sqrt{3}}{2} & 1 & 0 \\ \cos (θ - \frac{π}{6}) & - \sin (θ - \frac{π}{6}) & - \frac{\sqrt{3}}{2} & \frac{1}{2} & 0 & 1 \\ \cos (θ - \frac{5 π}{6}) & - \sin (θ - \frac{5 π}{6}) & \frac{\sqrt{3}}{2} & \frac{1}{2} & 0 & 1 \\ \cos (θ + \frac{π}{2}) & - \sin (θ + \frac{π}{2}) & 0 & - 1 & 0 & 1 \end{matrix}] [\begin{matrix} d \\ q \\ z_{1} \\ z_{2} \\ o_{1} \\ o_{2} \end{matrix}]$

Thez₁–z₂ando₁–o₂pairs do not form a rotating magnetic potential. They are generalized zero-sequence components.

Ports

Input

expand all

`dqz1z2o1o2`— Direct, Quadrature,z₁,z₂,o₁, ando₂components
vector

Direct, quadrature,z₁-axis,z₂-axis,o₁-axis, ando₂-axis 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

expand all

`abc`—a-,b-, andc-phase components
vector

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

Data Types:single|double

`xyz`—x-,y-, andz-phase components
vector

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

Data Types:single|double

Parameters

expand all

`Phase-a axis alignment`—dqz₁z₂o₁o₂reference frame alignment
`Q-axis`(default) |`D-axis`

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

Inverse Decoupled Transform (Six-Phase)