A geometric algebra reformulation and interpretation of Steinmetz’s symbolic method and his power expression in alternating current electrical circuits

摘要

Developed more than a century ago, Steinmetz’s symbolic method is still puzzling us. It puzzles us because, in spite of its theoretical inconsistencies, it is heuristically efficient. However, it remains the dominant method in design, analysis, and operation of electrical power networks. The paper shows that Steinmetz’s mathematical expression for electrical power is based on assumptions inconsistent with the algebra of complex numbers. The paper argues that, although the numbers are correct, the mathematical interpretation of these numbers is not. Steinmetz got empirical right results for wrong conceptual reasons; the success of the symbolic method is based on the fact that, unwittingly, Steinmetz rediscovered Grassmann–Clifford geometric algebra. The paper challenges the dominant paradigm in power theory which represents voltage, current, active, reactive and apparent power as complex numbers and/or vectors (phasors). The author proposes a new paradigm in which these entities are represented as an algebraic group; the group is composed of a scalar, two vectors and a bivector which are residing in a four-dimensional algebraic space and in a two-dimensional Euclidean geometric space. The paper claims that Steinmetz’s symbolic method is the oldest engineering application of Clifford Algebra. The paper provides a strong motivation for a new didactic of power theory based on Geometric Algebra as Physics’ unifying language.