Power Delivered in AC Networks as an Algebraic Sum, P + Q not Phasor Sum, P + jQ when power is expressed as VmIm sin(ωt) sin(ωt − θ)

This paper discusses measurement techniques for the total amount of power injected in an alternating current (AC) power system. It is shown that the power network consisting of reactances and resistances will have covariance elements of voltage and current. A demodulator is used to reduce correlated current and voltage waveforms into singular waveforms and the amount of power is accurately estimated from an analysis of 3-dimensional (3D) complex sinusoids. A validation framework is also presented to show that the total power injected, PT in an AC power network is an algebraic sum function of both the sine and cosine of the power factor (PF) angle, when power is written as VmIm sin(ωt) sin(ωt − θ), so PT = f(cos θ + sin θ). The proposed technique will find use in smart power meters to determine accurate amount of power generation needed, amount of power stored, and amount of power consumed, power system quality and billing rates for different classes of loads.