Summary Varied control applications in electrical engineering find the utility of the theory of transformation of three‐phase quantities from abc to αβ0 and dq0 reference frames. These transformations are vital in simplifying the control equations and their implementation. However, for different applications, different orientations of the abc‐, αβ‐, and dq‐axes are used. This results in a different transformation matrix for each such orientation. In this paper, a generalized abc to αβ0 and dq0 transformation matrix is proposed which can be utilized for any possible orientation and thus effectuates faster derivation of the transformation matrix. This is achieved by defining two parameters l and m whose values are obtained by observing the orientation of the axes. The transformation equation can therefore be obtained without having to undergo the steps of resolving abc quantities into their components along the αβ‐ or dq‐axes. Furthermore, this paper discusses the visual understanding of transformed electrical quantities. It is shown that the complex plots of real versus imaginary parts of instantaneous positive and negative symmetrical components have shapes which exhibit specific characteristics of electrical quantities and give a direct understanding about unbalance and presence of harmonics in the system.

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