active and inactive Fryze current, asymmetrical voltage and load, reactive compensator, symmetrical components


Purpose. Investigation of the optimal current distribution between source, shunt active filter and reactive compensator of a three-phase three-wire system that provides consumption of a sinusoidal symmetric current under asymmetric source voltages with minimal power losses was provided. Methodology. The tasks were solved by conducting theoretical and experimental studies. The main provisions of the theory of electrical circuits, the apparatus of mathematical analysis, methods for solving linear differential and algebraic equations, elements of matrix and complex calculus and vector algebra are used. During the development, modern methods and software of computer simulation of electrical engineering complexes and dynamic systems were applied: Matlab-Simulink, MATHCAD. Originality. The principle of compensating current distribution between PAF and reactive compensator of a three-phase three-wire power system with asymmetric sinusoidal voltage was proposed at which the input current is equal to the positive-sequence active current and rms value of PAF current is minimal. The feasibility to compensate the inactive sinusoidal Fryze current by reactive elements under arbitrary combination of load and source parameters was proved and expression for direct calculation of the reactive compensator parameters for generation of inactive Fryze current in the source unbalanced mode was obtained. Practical value. The simulative example for transmission line load showed that combined application of PAF and reactive compensator with the specified distribution of compensating currents ensured a reduction of power losses in 3.273 times and rms value of the SAF current is 12.9 % of rms value total compensation current.


1. Fryze S. Active, reactive and apparent power in circuits with nonsinusoidal voltage and current. Przegląd Elektrotechniczny, 1931, no.7, 8, pp. 193-203.

2. Shidlovskii A.K., Kuznetsov V.G. Povysheniye kachestva elektroenergii v elektricheskikh setyakh [Improving of the power quality in electrical networks]. Kiev: Naukova Dumka Publ., 1985. 268 p.(Rus).

3. Hanzelka Z. Mitigation of voltage unbalance. Available at: http://www.leonardo-energy.org/chapter-5-mitigation-voltage-unbalance (accessed 22 May 2016).

4. Czarnecki L.S., Haley P.M. Unbalanced Power in Four-Wire Systems and Its Reactive Compensation. IEEE Transactions on Power Delivery, 2015, vol.30, no.1, pp. 53-63. doi: 10.1109/TPWRD.2014.2314599.

5. Sirotin Iu.A. Fryze’s compensator and Fortescue transformation. Przegląd Elektrotechniczny, 2011, no.1, pp. 101-106.

6. Sirotin Iu.A. Non-pulsed mode of supply in a three-phase system at asymmetrical voltage. Przegląd Elektrotechniczny, 2013, no.7, pp. 54-58.

7. IEEE Std. 1459-2010. Definitions for the measurement of electric power quantities under sinusoidal non-sinusoidal, balanced or unbalanced conditions. doi: 10.1109/IEEESTD.2010.5439063.

8. Salmerón Revuelta P., Pérez Litrán S., Prieto Thomas J. Active power line conditioners design, simulation and implementation for improving power quality. Elsevier Inc.: Academic Press, 2016. 436 p.

9. Artemenko M.Y., Batrak L.M., Polishchuk S.Y., Mykhalskyi V.M., Shapoval I.A. Reactive compensation of non-active power in hybrid shunt filter of three-phase four-wire system at random load. Proceedings of 2016 2nd International Conference on Intelligent Energy and Power Systems (IEPS). Кiev, 2016. doi: 10.1109/IEPS.2016.7521863.

10. Artemenko M.Y., Polishchuk S.Y., Mykhalskyi V.M., Shapoval I.A. Apparent power decompositions of the three-phase power supply system to develop control algorithms of shunt active filter. Proceedings of the IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2017, pp. 495-499. doi: 10.1109/UKRCON.2017.8100537.



How to Cite

Artemenko, M. Y., Batrak, L. M., & Polishchuk, S. Y. (2018). СURRENT FILTERING IN A THREE-PHASE THREE-WIRE POWER SYSTEM AT ASYMMETRIC SINUSOIDAL VOLTAGES. Electrical Engineering & Electromechanics, (2), 63–68. https://doi.org/10.20998/2074-272X.2018.2.11



Power Stations, Grids and Systems