A geometric algebra reformulation and interpretati

Authors: Alexander I Petroianu

Publish Date: 2014/12/13

Volume: 97, Issue: 3, Pages: 175-180

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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 fourdimensional 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

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