MATLAB: Are the equations implemented by the SimPowerSystems 5.7 (R2012b) “abc_to_dq0” block defined differently than what I have observed in a textbook

Question

Comparing the textbook definition of the "abc-to-dq0" transformation to the SimPowerSystems documentation it appears that the first and second rows of the transformation matrix are swapped. Why is this?

Answer 1

The convention used in the SimPowerSystems block is likely different than that observed in the textbook. The "abc_to_dq0" block implements the Park Transformation using Krause's convention. This is specific to the following reference:

[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994, p.135.