Harmonic Distortion Reduction of Transformer-Less Grid-Connected Converters by Ellipsoidal-Based Robust Control

Hisham M. Soliman, Ashraf Saleem, Ehab H. E. Bayoumi and Michele De Santis ()
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Hisham M. Soliman: Department of Electrical Power Engineering, Faculty of Engineering, Cairo University, Cairo 12613, Egypt
Ashraf Saleem: Department of Applied Computing, College of Computing, Michigan Technological University, Houghton, MI 12613, USA
Ehab H. E. Bayoumi: Department of Mechanical Engineering, Faculty of Engineering, The British University in Egypt, Cairo 11837, Egypt
Michele De Santis: Department of Engineering, Niccolò Cusano University, 00166 Roma, Italy

Energies, 2023, vol. 16, issue 3, 1-18

Abstract: A photovoltaic generator connected to a large network and supplying a nonlinear load (source of harmonics) injects distorted current into the grid. This manuscript presents an invariant-ellipsoid set design of a robust controlled active power filter to inject current into the large grid with minimum total harmonic distortion (THD). The nonlinear load current is considered an external disturbance to minimize its effect on the injected grid current. Moreover, the large grid is modeled as a fixed voltage source in a series with a Thevenin impedance whose value changes within an interval. Using the invariant-ellipsoid technique, the problem is cast as a robust disturbance-rejection tracking control. The volume of the ellipsoid is minimized, which results in minimizing the effect of disturbance on system performance and keeping the trajectories as close as possible to the origin. The design is cast into a set of nonlinear matrix inequalities that are linearized by fixing a scalar. The resulting convex optimization is solved iteratively by linear matrix inequalities (LMIs). The simulation and experimental findings show that the proposed design is successful in reducing THD injected into the grid when grid impedance is uncertain and variable loads are applied (balanced and unbalanced cases).

Keywords: active power filter; invariant ellipsoid; linear matrix inequalities; robust control (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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