A Multi-Objective Approach for Designing Passive Harmonic Filters in Unbalanced Distribution Systems

This study addresses the challenge of determining the optimal placement and sizing of passive harmonic filters (PHFs) in unbalanced distribution systems with distributed generators (DGs). The problem is formulated as a nonlinear multi-objective optimization task and solved using the Genetic Algorithm (GA). The methodology is demonstrated on the IEEE 13-bus system. Optimal solutions are derived by optimizing the following objectives: (1) minimization of total harmonic distortion in voltage (THD<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</inf>), (2) minimization of PHFs costs, (3) minimization of power losses, (4) minimization of voltage deviation, (5) minimization of voltage unbalance, and (6) simultaneous minimization of THD<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</inf>, PHFs costs, power losses, voltage deviation, and unbalance. Furthermore, a sensitivity analysis investigates the impact of uncertainties in load and DG powers, variations in line parameters and frequency, and deviations in PHFs parameters on their performance and efficiency.