Clifford Theory: A Geometrical Interpretation of Multivectorial Apparent Power

In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in n-sinusoidal/nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions result in a novel representation of the apparent power, similar to the Steinmetz´s phasor model, based on complex numbers, but limited to the purely sinusoidal case. The multivectorial approach presented is based on the frequency-domain decomposition of the apparent power into three components: the real part and the imaginary part of the complex-scalar associated to active and reactive power respectively, and distortion power, associated to the complex-bivector. A geometrical interpretation of the multivectorial components of apparent power is discussed. Numerical examples illustrate the clear advantages of the suggested approach.