αβ transformation part [abc-αβ Transformer]

Appearance

---

Description

αβ transformation part [abc-αβ Transformer] is a part that applies an αβ transformation to three-phase voltages.
The calculation expressions are as follows

Condition	Expression
Absolute transformation	$$\begin{bmatrix} Vα \ Vβ \ V0 \end{bmatrix} = \sqrt{\frac{2}{3}} \begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2} \ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \end{bmatrix} \begin{bmatrix} Va \ Vb \ Vc \end{bmatrix}$$
Relative transformation	$$\begin{bmatrix} Vα \ Vβ \ V0 \end{bmatrix} = \frac{2}{3}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2} \ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \ \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} \end{bmatrix} \begin{bmatrix} Va \ Vb \ Vc \end{bmatrix}$$

Note

This part is a discrete model. A discrete model performs a sample-and-hold operation.
The voltage is sampled at the beginning of each main period, and within that period the voltage is held and remains constant.

---

Terminals

Terminal	Name	Description
A,B,C	Three-phase input terminals	Input the voltage [V] of each phase between them and the ground terminal described below.
α,β,0	αβ0 terminals	Output the converted α, β, and 0 voltages [V] between them and the ground terminal described below.
G	Ground terminal	This is the terminal that serves as the ground for the terminals described above.

---

Spec

Parameter	Description	Parameter name
Power Invariant	Flag for calculating with the absolute transformation	-

---

Output variables

Parameter	Description	Output argument
0 Voltage	0 axis voltage	V0
A Voltage	a phase voltage	Va
Alpha Voltage	α axis voltage	Val
B Voltage	b phase voltage	Vb
Beta Voltage	β axis voltage	Vbe
C Voltage	c phase voltage	Vc

---