Abstract
The main goal of this work is the proposal of an optimization algorithm based on linear matrix inequalities (LMI) used to selectively compensate the unbalance, the harmonic distortion, and the phase shift introduced by the load currents in a three phase four-wire system. The use of the IEEE Std.1459 allows determining each of the power terms associated to these non-efficient phenomena. Once these power terms are defined, a quadratically constrained quadratic program is set and solved by LMIs. The algorithm uses three weighting coefficients associated to each non-efficient term in order to assign them a relative importance depending on a user determined criterion. Moreover, the paper presents the design of the DC bus capacitor as well as the regulators used to control its voltage. Furthermore, three different regulators are introduced and designed to control the SAPC currents. A comparison among them is also introduced. Finally, simulation results for different selective compensation cases are presented, analyzed and various conclusions are extracted.
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