Derivation of Park transformation formula for motor control

Motor control park Derivation of transformation formula

Clarke The transformation is to change the three-phase plane coordinate system to the two-phase plane coordinate system , Map it to the motor ,clarke The result of the transformation is static αβ Coordinate system , This corresponds to the stator of the motor . And what we are going to deduce today park Is rotating dq Coordinate system , This corresponds to the rotor of the motor . Let's start with . At rest αβ In coordinate system , Draw qd Coordinate system , add , In motor control ：（1）Q Shaft control torque ;（2）D The axis controls the magnetic field .

from Figure we can deduce ：

This side is park Transformation , Combine the preceding Clarke change , You can get Id、Iq And Ia、Ib、Ic The relationship between .