# C2000 Park Transformation

Convert two-phase stationary system vectors to rotating system vectors

## Library

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

• ## Description

This block converts vectors in balanced two-phase orthogonal stationary systems into an orthogonal rotating reference frame. The transformation implements these equations

`$\begin{array}{l}ID=Id*\mathrm{cos}\theta +Iq*\mathrm{sin}\theta \\ IQ=-Id*\mathrm{sin}\theta +Iq*\mathrm{cos}\theta \end{array}$`

and is illustrated in the following figure. The variables used in the preceding figure and equations correspond to the block variables as shown in the following table:

Equation VariablesBlock Variables
InputsidAlpha
iqBeta
θAngle
OutputsIDDs
IQQs

The inputs to this block are the direct axis (`Alpha`) and the quadrature axis (`Beta`) components of the transformed signal and the phase angle (`Angle`) between the stationary and rotating frames.

The outputs are the direct axis (`Ds`) and quadrature axis (`Qs`) components of the transformed signal in the rotating frame.

The instantaneous inputs are defined by the following equations:

`$\begin{array}{l}id=I*\mathrm{sin}\left(\omega t\right)\\ iq=I*\mathrm{sin}\left(\omega t+\pi /2\right)\end{array}$`

Note

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

• 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.