Clarke and Park Transforms

Implement Clarke and Park transforms for motor control

Clarke and Park transforms are commonly used in field-oriented control of three-phase AC machines. The Clarke transform converts the time domain components of a three-phase system (in abc frame) to two components in an orthogonal stationary frame (αβ). The Park transform converts the two components in the αβ frame to an orthogonal rotating reference frame (dq). Implementing these two transforms in a consecutive manner simplifies computations by converting AC current and voltage waveform into DC signals.

The time domain components of a three-phase system (in abc frame).

Resulting signals for the Clarke transform (αβ).

Resulting signals for the Park transform (dq).

An efficient process for developing and implementing field-oriented control involves designing and testing control algorithms in a simulation environment, and generating C or HDL code for real-time testing and implementation.

Motor control engineers can use Simulink® to:

  • Model and simulate inverter power electronics and various types of motors, including synchronous and asynchronous three-phase machines.
  • Design and simulate motor control algorithms, including computationally efficient implementations of Clarke and Park transforms.
  • Run closed-loop simulations of the motor, inverter, and controller to test system performance under normal and abnormal operating scenarios.
  • Automatically generate ANSI, ISO, or processor-optimized C code and HDL for rapid prototyping, hardware-in-the-loop testing, and production implementation.

Model of PMSM current controller implemented with Park and Clarke transform.

Software Reference

See also: Simscape Power Systems, Simscape Electronics, Embedded Coder, pulse-width modulation, motor control design with Simulink, motor and power control design with Simulink, motor control development, boost converter simulation, buck converter simulation

Field-Oriented Control with Simulink