Alpha-Beta-Zero to abc
SD032Table of Contents
The “Alpha-Beta-Zero to abc” block computes a three-phase (abc) signal from a space vector in a stationary reference frame (αβ0).
The transformation is performed using the following equation:
$$ \begin{bmatrix} V_a\\V_b\\V_c\end{bmatrix}
= \begin{bmatrix} 1 & 0 & 1\\-1/2 & \sqrt{3}/2 & 1\\ -1/2 & -\sqrt{3}/2 & 1\end{bmatrix}\cdot
\begin{bmatrix} V_\alpha\\V_\beta\\V_0\end{bmatrix}$$
Simulink block
Signal specification
- The input is a vector of dimension 3, containing the αβ0 components of the three-phase signal in the stationary reference frame.
- 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 SRF->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 αβ0 to abc function is the following:
void ABG2abc(TimeDomain *physical, const SpaceVector *fixed);
Code language: C++ (cpp)Parameters
physical: pointer on the time domain abc data that will be updated. TheTimeDomainstructure is defined below.fixed: pointer on the αβ0 space vector that will be transformed. TheSpaceVectorstructure 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)
