In this paper, we present two modulation schemes for generating unbalanced voltages by means of four-leg voltage-source inverters. The first modulation is an extended scheme of a digital-scalar pulsewidth modulation previously proposed for controlling three-leg inverters. The second one is based on the decomposition of the voltage reference signals into their symmetrical components. The schemes are compared theoretically by simulations and experimental results. As a consequence, we find out a total equivalence between the two modulations despite their different conceptions. The fundamentals of both techniques and a mathematical proof of their equivalence are unfolded. Also, the performances of the techniques with respect to the harmonic distortion and power switching loss are discussed. The results show that the techniques are effective.

This paper proposes the usage of a repetitive-based control to dynamically restore the voltage applied to sensitive and critical loads of power system. The control intrinsically is able to wipe off harmonic distortion and relies on simple transfer function. As a consequence, there is no need to apply harmonic selective filters. Furthermore, the control system is able to work out on sinusoid references and, thus, avoids the need of employing the dq transform. A recursive least-squares is also included to the control system in order to assure the synchronization of the voltages to be restored. The design of the control parameters along with the system stability is discussed. The experimental results are produced with a setup of a three-phase series compensator. The scenarios for emulating faulty voltages are the same for experimental and simulated results. The results corroborates the usage of the proposed method.