abc to Alpha-Beta-Zero

The “adc to Alpha-Beta-Zero” block computes the coordinates of a three-phase (abc) signal in a stationary reference frame (αβ0).

The transformation is performed using the following equation:

$$ \begin{bmatrix} V_\alpha\\V_\beta\\V_0\end{bmatrix}
= \frac{2}{3}\cdot
\begin{bmatrix} 1 & -1/2 & -1/2\\0 & \sqrt{3}/2 & -\sqrt{3}/2\\ 1/2 & 1/2 & 1/2\end{bmatrix}\cdot
\begin{bmatrix} V_a\\V_b\\V_c\end{bmatrix}$$

Simulink block

Signal specification

Parameters

None.

PLECS block

None. The PLECS block Transformation 3ph->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 abc to αβ0 function is the following:

void abc2ABG(SpaceVector *fixed, const TimeDomain *physical);
Code language: C++ (cpp)

Parameters

• fixed: pointer on the αβ0 space vector that will be updated. The SpaceVector structure is defined below.
• physical: pointer on the time domain abc data that will be transformed. The TimeDomain structure is defined below.

typedef struct{
	float real;       // alpha-axis component
	float imaginary;  // beta-axis component
	float offset;     // homopolar component
} SpaceVector;

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