Deduction of coordinate transform for instantaneous reactive power theory and analysis on relationship between α — β and dq0 transformation

Instantaneous reactive power theory (IRPT) proposed by H. Akagi is shortage of detail explanation on the matrix coefficient of alpha - beta transformation. Based on power conservation, the matrix coefficient is deduced in-plane. As the transformation was given out in plane domain, the matrix coefficient is deduced in-plane by rigorous mathematical deduction based on power conservation. Consequently, the coefficient deduction for IRPT is solved. In the view of there being two kinds of instantaneous reactive theories widely used in harmonic current detection, the alpha - beta transformation and dp0 transformation, which one is better or is same is a problem. In order to find this, the relationship between the alpha - beta transformation and dp0 transformation is discovered through theoretical deduction, pointing out that the currents containing harmonic and fundamental got through the two methods are of the relationship of a proportion difference in size, and one´s phase lagging behind the other´s. The analysis in this paper is available for understanding and application of this harmonic current detection method.