Currents’ Physical Components (CPC) in Three-Phase Systems with Asymmetrical Voltage

Energy flow related phenomena in three-phase unbalanced, linear, time-invariant (LTI) loads, supplied with asymmetrical, but sinusoidal voltage, in three-wire systems, are investigated in the paper. It is demonstrated that the load current can be decomposed into Currents’ Physical Components (CPC), associated with distinctive physical phenomena in the load. It is also shown how the CPC can be expressed in terms of the supply voltage and equivalent parameters of the load. An equivalent circuit of LTI loads at asymmetrical, but sinusoidal supply voltage is presented as well. This decomposition provides solid fundamentals for defining powers of such loads. Streszczenie. Artykuł przedstawia wyniki badań nad zjawiskami energetycznymi w liniowych, czasowo-niezmienniczych (LTI) odbiornikach niezrównoważonych, zasilanych niesymetrycznym, lecz sinusoidalnym napięciem w obwodach trójprzewodowych. Pokazano, że prąd takich odbiorników może być rozłożony na Składowe Fizyczne, jednoznacznie stowarzyszone z określonymi zjawiskami fizycznymi. Pokazano także, że prądy te mogą być określone poprzez napięcie zasilania i parametry równoważne odbiornika. Przedstawiono także obwód równoważny niezrównoważonych odbiorników LTI, zasilanych niesymmetrycznym, lecz sinusoidalnym napięciem. Rozkład ten tworzy solidne podstawy dla definicji mocy takich odbiorników. (Składowe Fizyczne Prądów w obwodach trójfazowych z niesymetrycznym napięciem zasilania).

[1]  Hirofumi Akagi,et al.  Instantaneous Reactive Power Compensators Comprising Switching Devices without Energy Storage Components , 1984, IEEE Transactions on Industry Applications.

[2]  Leszek S. Czarnecki.  Powers in three-phase systems with neutral conductor at sinusoidal voltages and currents , 2013 .

[3]  V. G. Smith.  Reactive and Fictitious Power , 1933, Transactions of the American Institute of Electrical Engineers.

[4]  L. S. Czarnecki.  Equivalent circuits of unbalanced loads supplied with symmetrical and asymmetrical voltage and their identification , 1995 .

[5]  F. B. Silsbee,et al.  Definitions of Power and Related Quantities , 2022, Transactions of the American Institute of Electrical Engineers.

[6]  C. Fortescue.  Method of Symmetrical Co-Ordinates Applied to the Solution of Polyphase Networks , 1918, Transactions of the American Institute of Electrical Engineers.

[7]  Leszek S. Czarnecki,et al.  Energy flow and power phenomena in electrical circuits: illusions and reality , 2000 .

[8]  M. Depenbrock.  The FBD-method, a generally applicable tool for analyzing power relations , 1993 .

[9]  J. Cohen,et al.  A practical approach to power factor definitions: transmission losses, reactive power compensation, and machine utilization , 2006, 2006 IEEE Power Engineering Society General Meeting.

[10]  L. Czarnecki.  Orthogonal decomposition of the currents in a 3-phase nonlinear asymmetrical circuit with a nonsinusoidal voltage source , 1988 .

[11]  C. L. Fortescue,et al.  Method of symmetrical co-ordinates applied to the solution of polyphase networks , 1918, Proceedings of the American Institute of Electrical Engineers.

[12]  M.E. El-Hawary,et al.  Defining Power Components in Nonsinusoidal Unbalanced Polyphase Systems: The Issues , 2008, IEEE Transactions on Power Delivery.

[13]  A. E. Emanuel,et al.  IEEE Std 1459–2010. IEEE Standard Definitions for the Measurement of Electric Power Quantities under Sinusoidal, Nonsinusoidal, Balanced or Unbalanced Conditions , 2010 .

[14]  Leszek S. Czarnecki,et al.  Unbalanced Power in Four-Wire Systems and Its Reactive Compensation , 2015, IEEE Transactions on Power Delivery.