Clarke transformation, A method for three-phase/two-phase conversion

　・In Japanese

■Clarke transformation, 3-phase/2-phase transformation

Clarke transformation is also called 3-phase/2-phase conversion, and is a method of converting 3-phase AC to 2-phase (2-axis) to make it easier to calculate. It is used when performing vector control of motors, etc.

■How to derive 3-phase/2-phase conversion

The three-phase AC currents are u, v, and w. The relationship between u, v, and w is as follows:



Next, calculate α for the X-axis component. The X-axis component is the cosine component of u, v, and w. Therefore:



Next, we calculate the β of the Y-axis component. The Y-axis component is the sine component of u, v, and w. Therefore:



From (2) and (3),

■2-phase to 3-phase conversion formula

To convert from 2 phase to 3 phase:

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