Analysis and Compensation of Power Systems with Harmonics and Unbalance

Conventional active and reactive power definitions are premised on balanced sinusoidal currents and voltages. In modern power systems with increased converter-driven generation, non-linear loads, harmonics, and source unbalance, inconsistencies in the calculation of reactive power arise. In this paper, we go through the definitions of conventional reactive power, pq theory and the general power theory. A new analytical method based on the hysteresis characteristics of the system is proposed to calculate reactive power (Q) in the presence of unbalance and harmonics. The results showed that under balanced and unbalanced conditions, the proposed method derived from first principles in physics is consistent with pq theory. When harmonics are introduced, however, results for Q differ greatly. This paper shows that the orthogonality assumed by the power triangle may not be valid in practical power systems. The results have implications on the correct compensation in modern power systems with the increasing presence of non-ideal conditions such as those brought about by unbalance and harmonic distortion.