@article{Sirotin_Ierusalimova_2016, title={INSTANTANEOUS AND INTEGRAL POWER EQUATIONS OF NONSINUSOIDAL 3-PHASE PROCESSES}, url={http://eie.khpi.edu.ua/article/view/2074-272X.2016.1.13}, DOI={10.20998/2074-272X.2016.1.13}, abstractNote={<strong><em>Purpose.</em></strong><em> To identify the mathematical relationship between the instantaneous powers (classical and vectorial) and integral powers in non-sinusoidal mode and to get complex form of instantaneous powers in 3-phase 4-wire power supply in terms of the spectral approach. <strong>Methodology.</strong> We have applied the vector approach with one voice allows you to analyze the energy characteristics of 3-phase power supply circuits (for 4-wire and 3-wire circuits) in sinusoidal and nonâ€“sinusoidal mode, both the time domain and frequency domain. We have used 3-dimensional representation of the energy waveforms with the complex multi-dimensional Fourier series. <strong>Results.</strong> For 4-wire network with a non-sinusoidal (regardless of their symmetry) processes, we have developed the mathematical model one-dimensional representations of the complex form for the active (scalar) instantaneous power (IP) and 3-dimensional form (inactive) vectorial IP. It is possible to obtain two dual integral power equations for complex scalar and vector integrated power of non-sinusoidal modes. The power equations generalize generalizes the equations of sinusoidal modes for 4-wire network. <strong>Originality</strong><strong>.</strong> In addition to the classification of energy local regimes in the time domain for the first time we spent the classification of non-sinusoidal modes in the spectral region and showed the value and importance of the classification of regimes based on the instantaneous powers. <strong>Practical value.</strong> The practical value the obtained equations is the possibility of their use for improving the quality of electricity supply and the quality electricity consumption. </em>}, number={1}, journal={Electrical Engineering & Electromechanics}, author={Sirotin, Iu. A. and Ierusalimova, T. S.}, year={2016}, month={Mar.}, pages={69â€“73} }