# C2000 Clarke Transformation

Convert balanced three-phase quantities to balanced two-phase quadrature quantities

## Library

Embedded Coder® Support Package for Texas Instruments™ C2000™ Processors/ Optimization/ C28x DMC

Embedded Coder Support Package for Texas Instruments C2000 F28M3x Concerto™ Processors Processors/ Optimization/ C28x DMC

• ## Description

This block converts balanced three-phase quantities into balanced two-phase quadrature quantities. The transformation implements these equations

`$\begin{array}{l}Id=Ia\\ Iq=\left(2Ib+Ia\right)/\sqrt{3}\end{array}$`

and is illustrated in the following figure. The inputs to this block are the phase a (`As`) and phase b (`Bs`) components of the balanced three-phase quantities and the outputs are the direct axis (`Alpha`) component and the quadrature axis (`Beta`) of the transformed signal.

The instantaneous outputs are defined by the following equations and are shown in the following figure:

`$\begin{array}{l}ia=I*\mathrm{sin}\left(\omega t\right)\\ ib=I*\mathrm{sin}\left(\omega t+2\pi /3\right)\\ ic=I*\mathrm{sin}\left(\omega t-2\pi /3\right)\\ id=I*\mathrm{sin}\left(\omega t\right)\\ iq=I*\mathrm{sin}\left(\omega t+\pi /2\right)\end{array}$` The variables used in the preceding equations and figures correspond to the variables on the block as shown in the following table:

Equation VariablesBlock Variables
InputsiaAs
ibBs
OutputsidAlpha
iqBeta

Note

• To generate optimized code from this block, enable the ```TI C28x``` or `TI C28x (ISO)` CRL.

• The implementation of this block does not call the corresponding Texas Instruments library function during code generation. The TI function uses a global Q setting and the MathWorks® code used by this block dynamically adjusts the Q format based on the block input. See Using the IQmath Library for more information.

## References

For detailed information on the DMC library, see C/F 28xx Digital Motor Control Library, Literature Number SPRC080, available at the Texas Instruments Web site.