Miona Andrejević Stošović, Marko Dimitrijević, Slobodan Bojanić, Octavio Nieto-Taladriz, Vančo Litovski

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Electronic devices are complex circuits, consisting of analog, switching, and digital subsystems that require direct current (DC) for polarization. Since they are connected to the mains delivering alternating current (AC), however, AC-to-DC converters are to be introduced between the mains and the electronics to be fed. A converter is an electric circuit containing several subsystems, the most important being the switch-mode power supply, drawing power from the mains in pulses hence it is highly nonlinear. That happens, in reduced amplitude, even when the electronics to be fed is switched off. The process of AC-to-DC conversion is not restricted to feeding electronic equipment only. It is more and more frequently encountered in modern smart-grid facilities giving rise to the importance of the studies referred hereafter. The converter can be studied (theoretically or by measurements) as two-port network with reactive and nonlinear port-impedances. Characterization is performed after determining the port electrical quantities which are voltages and currents. Based on these data power and power quality parameters – power factor and total harmonic distortion- may be extracted. When nonlinear loads are present, one should introduce new ways of thinking into the considerations due to the existence of harmonics and related power components. In that way the power factor can be generalized to total or true power factor where the apparent power, involved in its calculations, includes all harmonic components. After introducing a wide range of definitions used in contemporary literature, here we describe our measurement set-up both as hardware and a software solution. The results reported unequivocally confirm the importance of the subject of characterization of small nonlinear loads to the grid having in mind their number which is rising without saturation seen in the near and even far future.


smart grid, nonlinear loads, load characterization, power factor, harmonic distortions

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L. Freeman, “The Changing Nature of Loads and the Impact on Electric Utilities”, Tech Advantage Expo - Electronics Exhibition and Conference 2009, New Orleans, USA, Feb. 2009, 2009ConferenceHandouts/2E_Freeman.pdf.

V. Terzija, V. Stanojević, “STLS Algorithm for Power-Quality Indices Estimation”, IEEE Transactions on Power Delivery, vol. 24, no. 2, pp. 544-552, April 2008.

G. Goertzel, “An Algorithm for the Evaluation of Finite Trigonometric Series”, The American Mathematical Monthly, no. 1, vol. 65, pp. 34-35, January 1958.

S. Vukosavić, “Detection and Suppression of Parasitic DC Voltages in 400 V AC Grids”, Facta Universitatis, Series: Electronics and Energetics, vol. 28, no 4, pp. 527-540, December 2015.

L. Korunović, M. Rašić, N. Floranović, V. Aleksić, “Load Modelling at Low Voltage Using Continuous Measurements”, Facta Universitatis, Series: Electronics and Energetics, vol. 27, no. 3, pp. 455-465, September 2014.

M. Dimitrijević, V. Litovski, “Power Factor and Distortion Measuring for Small Loads Using USB Acquisition Module”, Journal of Circuits, Systems, and Computers, vol. 20, no. 5, pp. 867-880, August 2011.

M. Dimitrijević, “Electronic System for Polyphase Nonlinear Load Analysis Based on FPGA“, PhD thesis, Niš, 2012 (in Serbian).

M. Dimitrijević, and V. Litovski, “Quantitative Analysis of Reactive Power Definitions for Small Nonlinear Loads”, In Proc. of the 4th Small Systems Simulation Symposium, Niš, Serbia, 2012, pp. 150-154.

M. Dimitrijević, and V. Litovski, “Real-time virtual instrument for polyphase nonlinear loads analysis“, In Proc. of the IX Int. Symp. on Industrial Electronics, INDEL 2012, Banja Luka, B&H, November 2012, pp. 136-141.

M. Andrejević Stošović, M. Dimitrijević, and V. Litovski, “Computer Security Vulnerability as Concerns the Electricity Distribution Grid”, Applied Artificial Intelligence, vol. 28, pp. 323–336, 2014.

M. Dimitrijević, M. Andrejević Stošović, J. Milojković, V. Litovski, “Implementation of Artificial Neural Networks Based AI Concepts to theSmart Grid”, Facta Universitatis, Series: Electronics and Energetics, vol. 27, no. 3, pp. 411-424, September 2014.

-,”IEEE Trial-Use Standard Definitions for the Measurement of Electric Power Quantities under Sinusoidal, Non-sinusoidal, Balanced, or Unbalanced Conditions”, IEEE Power Engineering Society, IEEE Std. 1459-2000, 30. January 2000.

IEEE Power Engineering Society: IEEE Trial-Use Standard Definitions for the Measurement of Electric Power Quantities under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. IEEE Std. 1459-2010, 2. February 2010.

L. S. Czarnecki, “Harmonics and Power Phenomena”, Encyclopedia of Electrical and Electronics Engineering, J. Wiley and Sons, 1999.

A. E. Emanuel, “Power Definitions and the Physical Mechanism of Power Flow”, J. Wiley and Sons, 2010.

C. I. Budeanu, “Reactive and Fictitious Powers.” Rumanian National Institute, no. 2.,1927.

E. W. Kimbark, “Direct Current Transmission” J. Wiley and Sons, 1971.

D. Sharon, “Reactive Power Definition and Power-factor Improvement in Nonlinear Systems.” 1973. In Proc. of Ins Vol. Electric Engineers, vol. 120, pp. 704-706.

S. Fryze, et al., “Elektrischen Stromkreisen Mit Nichtsinusoidalformingem Verfauf von Strom und Spannung.” Elektrotechnische Zeitschriji, no. 53, vol. 25, pp. 596-599, 1932. [20] N. L. Kusters, W. J. M. Moore, “On the Definition of Reactive Power under Nonsinusoidal Conditions.” IEEE Trans. Power Apparatus Systems, no. 99, vol. 5, pp. 1845-1854, 1980.

W. Shepard, P. Zakikhani, “Power Factor Correction in Nonsinusoidal Systems by the Use of Capacitance”, Journal of Physics D: Applied Physics, no. 6, pp. 1850–1861, 1973.

M. W. Depenbrock, E. T. G. Blindleistung, Fachtagung Blindleistung. Aachen, 1979.

L. S. Czarnecki, “Powers in Nonsinusoidal Networks: Their Interpretation, Analysis and Measurement”, IEEE Trans. Instrumental Measurements, no. 39, vol. 2, pp. 340-345, 1990. [24] L. S. Czarnecki, “Physical Reasons of Currents RMS Value Increase in Power Systems with Nonsinusoidal Voltage”, IEEE Trans. in Power Delivery, no. 8, vol. 1, pp. 437-447, 1993.

M. E. Balci, M. H. Hocaoglu, “Quantitative comparison of power decompositions”, Electric Power Systems Research, no. 78, pp. 318-329, 2008.

-,“NI PXI-7813R R Series Digital RIO with Virtex-II 3M Gate FPGA.” National Instruments.

-, “NI 9225 Operating Instructions and Specifications.” National Instruments.

-, “NI 9227 Operating Instructions and Specifications”, National Instruments.

C. Jarvis, C., K. Kinsella, P. Timpanaro, “Phar Lap ETS™ – An Industrial-Strength RTOS White Paper.”

National Instruments: “LabVIEW Real-Time.” National Instruments WEB Page. [URL] nips/cds/view/p/lang/en/nid/2381.

National Instruments, “LabVIEW System Design Software.” [32] D. Stevanović, P. Petković, “Smarter Power Meters Reduce Economic Losses at Utility Grid”, Facta Universitatis, Series: Electronics and Energetics, vol. 28, no 3, pp. 407-421, September 2015.

S. Puzović, B. M. Koprivica, A. Milovanović, M. Đekić, “Analysis of Measurement Error in Direct and Transformer-Operated Measurement Systems for Electric Energy and Maximum Power Measurement”, Facta Universitatis, Series: Electronics and Energetics, vol. 27, no. 3, pp. 389-398, September 2014.

M. Etezadi-Amoli, T. Sr. Florence, “Power factor and harmonic distortion characteristics of energy efficient lamps”, IEEE Transactions on Power Delivery, no. 4, pp. 1965–1969, 1989.


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