  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.
