Waveform distortions are one of the most diffused Power Quality disturbances and are nowadays gaining a growing interest by the researchers of modern smart grids where a massive presence of new technologies in distributed energy resources and in advanced smart metering systems is expected. Shunt active power filters are considered a high performing solution to limit the impact of this disturbance on the smart grid equipment, but their location and size in a multi-converter smart grid requires an optimization approach that should contemporaneously consider different and, sometimes, conflicting objectives. In this paper, a multi-objective optimization model is formulated to solve the problem and a new simplified approach is proposed to solve the model under non-certainty. The proposed approach applies the Rank-order centroid weights method and a criterion of the Decision Theory under non-certainty, assuming a complete knowledge of the future probabilities. Numerical applications to a test network permit to highlight the ease of application of the proposed method and the interest in the obtained results.
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