2 Principles of Electrical Power Control Zbigniew Hanzelka 1 and Jovica V. Milanović 2 1 Department of Electrical Drive and Industrial Equipment, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland. Email: Hanzel@agh.edu.pl 2 School of Electrical and Electronic Engineering The University of Manchester, B11 P.O. Box 88, Sackville Street, Manchester M60 1QD, UK. Email: Milanovic@manchester.ac.uk 2.1 Power Theory The term power theory of circuits can be understood as the state of knowledge on their power properties. In that sense it is a set of true statements, interpretations, definitions and equations describing these properties [1]. The theory of power, understood that way, is a collective product of those who seek an answer to the question why a load with the active power P usually demands a power source with an apparent power S greater than its active power [2]. This question is closely related to the need for interpretation of power phenomena in electric circuits. Another factor is of a practical nature – power theory attempts to answer the question how the apparent power of the source can be reduced without the reduction in the load active power. 2.1.1 Critical Review of Classical Power Theory In the 1920s two major trends in power theory had developed. The first uses Fourier series expansion to describe power properties of a circuit. Since electric quantities are regarded as sums of components with different frequencies, the electric circuit properties are defined in the frequency domain. Budeanu’s power theory [3] is the most widespread theory in the frequency domain. Almost simultaneously, another trend has emerged which does not employ Fourier series and emphasizes defining the circuit power properties in the time domain. Since its conception the power theory in time domain is associated with Fryze’s name [4]. The existence of these two trends has been evident in power theory development in the past as well as the present.