dq0 to Alpha-Beta-Zero

Table of Contents

The “dq0 to Alpha-Beta-Zero” converts a space vector from a rotating (dq0) to a stationary (αβ0) reference frame. The angle of the rotating reference frame is given by the second input $\theta=\omega t$.

The transformation is performed using the following rotation:

$$ \begin{bmatrix} V_\alpha\\V_\beta\\V_0\end{bmatrix}
= \begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1\end{bmatrix}\cdot
\begin{bmatrix} V_d\\V_q\\V_0\end{bmatrix}$$

Simulink block

Signal specification

The first input is a vector of dimension 3, containing the dq0 components of the space vector in the rotating reference frame.
The second input is the angle $\theta$ of the rotating reference frame, in radians.
The output is a vector of dimension 3, containing the αβ0 components of the space vector in the stationary reference frame.

Parameters

None.

PLECS block

None. The PLECS block Transformation RRF->SRF can be used instead.

C++ functions

The user template located in the installation folder of CPP SDK contains an API folder with implementations of the coordinate transformation functions. The dq0 to αβ0 function is the following:

void DQ02ABG(SpaceVector *fixed, const SpaceVector *rotating, const float theta);
Code language: C++ (cpp)

Parameters

fixed: pointer on the αβ0 space vector that will be updated. The SpaceVector structure is defined below.
rotating: pointer on the dq0 space vector that will be transformed. The SpaceVector structure is defined below.
theta: the angle of the rotating reference frame, in radians.

typedef struct{
	float real;       // d- or alpha-axis component
	float imaginary;  // q- or beta-axis component
	float offset;     // homopolar component
} SpaceVector;Code language: C++ (cpp)