Reference frames for simulation of electric motors and drives

Simulations of AC electric machines are usually performed in a coordinate system, or reference frame, with two axes (often denoted by d and q, or represented as a complex space vector). A third axis, the zero-sequence axis, is a homopolar axis that is necessary for handling certain unbalanced conditions. Historically, the transformation was essential to getting reasonable results, since computations were expensive and the transformation results in great simplification of the electrical and mechanical differential equations. Today, however, computation has become so incredibly cheap that the computing power of imbedded controllers in many appliances exceeds that of the early mainframe computers. Consequently, this paper revisits the issue of transformation of coordinate frames for performing simulations.