Non-Classical computation of active-, apparent- and reactive powers and of the power- and distortion factors

Author(s):Harald Richter
 Clausthal University of Technology, Arnold-Sommerfeld-Str. 1, 38678 Clausthal, Germany
International Journal of Smart Grid and Clean Energy, vol. 5, no. 1, January 2016: pp. 56-71
ISSN: 2315-4462 (Print)
ISSN: 2373-3594 (Online)
Digital Object Identifier: 10.12720/sgce.5.1.56-71

Abstract:In this paper, new mathematical formulas for the computation of the apparent power, the active power, and the reactive power are given, together with equations for the power factor and the distortion factor. These formulas are applicable for all four operational states, in which electric power networks can be. The given results remain valid also in the difficult case of nonlinear AC generators and loads, which exhibit non-sinusoidal line voltages and currents. The results are obtained by means of a Thevenin equivalent voltage and resistance of the power grid for every load. The advantages of the formulas are that they can directly use Fourier coefficients and that approximations of them do not depend on the equivalent resistance. Applications are seen in photovoltaic energy systems and in industry 4.0, where nonlinear AC generators and nonlinear user loads exist, respectively, as well as in general power systems.

Keywords:Apparent power, active power, reactive power, power factor, distortion factor

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