Linear quadratic regulator-based coordinated optimization for harmonic compensation in multifunctional grid-connected inverters

• A system-level harmonic mitigation method for distribution systems is presented. • A novel measurement-point selection approach based on complementarity is presented. • An optimal harmonic compensation method with analytical solutions is presented. The increasing penetration of distributed energy resources (DERs) and electric vehicles (EVs) introduces widespread power electronic devices that significantly challenge harmonic mitigation in distribution systems. This study proposes a linear quadratic regulator (LQR)-based coordinated optimization method for harmonic compensation using multifunctional grid-connected inverters (MFGCIs) to minimize voltage distortion across all system buses. A measurement-point selection method based on harmonic mitigation complementarity evaluation is proposed to conserve measurement resources while maximizing system-wide voltage distortion improvement. System buses are comprehensively evaluated in three dimensions: control complementarity, coverage complementarity, and sensing complementarity. Multi-harmonic weighting calculations ensure that the selected measurement bus combination provides the maximum harmonic information. A quadratic objective function minimizes harmonic voltages at selected buses, incorporating Lagrange multipliers to handle combinatorial constraints when partial MFGCIs participate in the harmonic compensation. An analytical solution is derived to obtain the optimal harmonic compensation currents for arbitrary MFGCI combinations, considering the MFGCI capacity constraints on individual harmonic compensation current levels. Simulation results on a modified IEEE 25-bus distribution system demonstrate that the proposed method effectively reduces system-wide voltage distortion with fewer measurement points and achieves balanced MFGCI participation under capacity constraints, offering an effective solution for harmonic mitigation in power electronics-dominated distribution systems at the system-level.