Mitigation of Harmonic Distortions in Low Voltage Distribution Grids With Fair Utilization of Resources

Harmonic distortions have adverse effects on the operation of the power system. Harmonic sources in low voltage distribution grids (LVDG) are highly dispersed in nature. Therefore, managing the resulting voltage and current distortions through conventional measures, such as passive or active power filters, becomes challenging. This work coordinates the harmonic injection capabilities of enhanced photovoltaic inverters to form a distributed active power filter. The proposed method aims to reduce the voltage and current distortions of the LVDG with fair utilization of inverters. Towards this direction, a lexicographic optimization scheme is formulated to derive the inverters' harmonic current set-points by (i) minimizing the harmonic voltage limit violations, (ii) maximizing the inverter utilization fairness based on Jain's fairness index, and (iii) minimizing the compensating currents of the inverters to reduce their lifetime degradation. The resulting optimization model is non-convex, thus a convex second-order cone program (SOCP) is formulated by relaxing the non-convex constraints and reformulating the Jain's index as an SOCP constraint. Moreover, an iterative algorithm is developed to find the feasible operating point that maximizes the Jain's fairness value. Simulation results indicate the superiority of the proposed scheme compared to existing methodologies in mitigating harmonic distortions in three-phase four-wire LVDGs.