Mathematical Representations of Electrical Power: Vector or Complex Number? Neither!

The paper examines mathematical representations of electrical magnitudes in a.c. Circuit theory. It gives an historical and technical perspective of the development of the power concept and its geometrical and algebraic interpretations. The paper criticises the existing mathematical model of electrical power for being an entanglement of two mutually inconsistent, algebras: 1) standard vector algebra (Gibbs-Heaviside) and 2) complex algebra. The paper examines the ubiquitous expressions for power: S = P + jQ Ṡ = V̇I*. The paper analyzes Steinmetz´s symbolic method and exposes its inconsistencies. The paper proves that Steinmetz hypothesis, of a new and noncommutative algebra for power theory, represents a rediscovery of Grassmann-Clifford Algebra. The paper proposes a new didactic of power theory that should include Geometric Algebra.