dq0 to abc

Table of Contents

The “dq0 to abc” block computes a three-phase (abc) signal from a space vector in a rotating reference frame (dq0). The angle of the rotating reference frame is given by the second input $\theta=\omega t$.

The transformation is performed by applying successively a dq0 to alpha-beta-0, and an alpha-beta-0 to abc transformation:

$$ \begin{bmatrix} V_a\\V_b\\V_c\end{bmatrix}
= \begin{bmatrix} 1 & 0 & 1\\-1/2 & \sqrt{3}/2 & 1\\ -1/2 & -\sqrt{3}/2 & 1\end{bmatrix}\cdot
\begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1\end{bmatrix}\cdot
\begin{bmatrix} V_d\\V_q\\V_0\end{bmatrix}$$

Simulink block

Signal specification

The first input is a vector of dimension 3, containing the dq0 components of the three-phase signal 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 abc components of the three-phase signal.

Parameters

None.

PLECS block

None. The PLECS block Transformation RRF->3ph 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 abc function is the following:

void DQ02abc(TimeDomain *physical, const SpaceVector *rotating, const float theta);
Code language: C++ (cpp)

Parameters

physical: pointer on the time domain abc data that will be updated. The TimeDomain 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-axis component
	float imaginary;  // q-axis component
	float offset;     // homopolar component
} SpaceVector;

typedef struct{
	float A;
	float B;
	float C;
} TimeDomain;Code language: C++ (cpp)