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

Abstract

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 twodimensional 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.

Quadrature Current Compensation in Non-Sinusoidal Circuits Using Geometric Algebra and Evolutionary Algorithms

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Geometric Objects: A Quality Index to Electromagnetic Energy Transfer Performance in Sustainable Smart Buildings

“…Despite the application of GA to circuit analysis and power theory has a very short history some relevant advances have been made in this area from different perspectives [27][28][29][30][31][32][33][34][35].…”

Multivectorial strategy to interpret a resistive behaviour of loads in smart buildings

“…Both approaches were criticized much later by Czarnecki [6], who suggested reject the Budeanu reactive power component [7]. Triggered by these papers many investigations appeared consequently [8][9][10][11][12][13], each shedding more light on power factor improvement. In [7] a "reactive power" was defined that permits the derivation of the value of passive linear devices to achieve a relative optimum power factor.…”

“…Significant progress in the analysis of power equations has been made recently through the use of vector spaces [12]. Reference [14] introduces a new mathematical structure for a clear definition of vector-space applied to the power multivector concept.…”