d-q(direct-quadrature) transformation, Park transformation



Electrical/electronic circuit

Release date:2025/3/19         

 ・In Japanese
Prerequisite knowledge
 ・3-phase/2-phase conversion


■What is d-q conversion, Park conversion?

The d-q(direct-quadrature) conversion is a method of converting the two-phase motor current expressed in the stationary coordinate system into a rotating coordinate system with d (field) and q (torque) components. It is also called the Park conversion.

As shown below, the motor current expressed in two axes, α and β (see: 3-phase/2-phase conversion) is an alternating current, so the phase and amplitude of the current change depending on the angle of the rotor. Here, if we consider the axis based on the rotor position, we can consider the current to be constant if the rotation speed is constant, making it easier to handle complex AC calculations.


■d-q conversion formula

The following is the case when converting the α-β axis to the d-q axis.



The following is the case when converting the d-q axis to the α-β axis.










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