Identification of distribution features of the instantaneous power components of the electric energy of the circuit with polyharmonic current




electric energy power, power norm, active power, reactive power


Many researchers pay attention to the problem of the distortion electric power. The known theoretical results that are reflected in the acting standards are reasonably criticized in the part of the distortion power generation by current and voltage of different frequencies. The paper deals with the approach based on the order of generation of instantaneous electric power components depending on the combination (sum or difference) of current and voltage frequencies. The analytical expressions for the instantaneous electric power components of a harmonic current circuit consisting of a capacitor, an inductance coil and a resistor connected in series are obtained. With this purpose in view, two components – active and reactive – are singled out from the obtained four components of instantaneous power, as well as the orthogonal power components oscillating with double frequency. It is demonstrated that the sum of the squares of the active and reactive components and the sum of the squares of the mentioned orthogonal components coincide and are equal to the total (apparent) power. The used method is developed for the general case of polyharmonic current and voltage. In this case, it is observed that the active and reactive power components can be singled out from the instantaneous power components as orthogonal quadrature components of zero frequency. Though, it is impossible to single out the apparent power. Two numerical experiments with periodic current and voltage, containing three harmonics each, were carried out. The acting values of currents and voltages in each of the experiments were assumed equal. In this case, the amplitudes of the second and the third harmonics exchanged their positions. This example demonstrates that the integral indices of the apparent power and the distortion power, calculated by conventional methods, proved to be the same in both cases, which is incorrect. Under the same conditions, such instantaneous power components whose values turned out to be different for each of the experiments are found among the proposed instantaneous power components. As a result, it is proposed to use a root-mean-square value of the mentioned components for the assessment of the distortion degree in relation to the root-mean-square value of the instantaneous power

Author Biographies

Mohamed Zaidan Qawaqzeh, Ma’an University College Al-Balqa’ Applied University Maan, Jordan, P. O. Box 194, 19117

PhD, Associate Professor

Department of Technical Sciences

Olexii Bialobrzheskyi, Kremenchuk Mykhailo Ostrohradskyi National University Pershotravneva str., 20, Kremenchuk, Ukraine, 39600

PhD, Associate Professor

Department of Electricity Systems and Energy Management

Mykhaylo Zagirnyak, Kremenchuk Mykhailo Ostrohradskyi National University Pershotravneva str., 20, Kremenchuk, Ukraine, 39600

Doctor of Technical Sciences, Professor, Rector

Department of Electric Machines and Devices 


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How to Cite

Qawaqzeh, M. Z., Bialobrzheskyi, O., & Zagirnyak, M. (2019). Identification of distribution features of the instantaneous power components of the electric energy of the circuit with polyharmonic current. Eastern-European Journal of Enterprise Technologies, 2(8 (98), 6–13.



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