The instantaneous power quaternion of the three-phase electric circuit with linear load

The report deals with the study of a scalar (real) and a vector (imaginary) parts of instantaneous power quaternion in frame of algebraic approach applied to the different types of three-phase resistance-reactance and nonlinear loads. The target is to determine the inactive components of the total AC electrical energy flows per time unit for current compensation by means of active power filters. Based on made quantitative analysis, the different compensation objectives in the terms of hyper-complex numbers are have been formulated in the report. The compensation objectives permit to provide balanced or/ and sinusoidal source currents in the three-phase systems with the desired phase shift relative to the corresponding voltage.