An Augmented Lagrangian Lyrebird Optimization for UPQC-based optimal power flow in wind-integrated power systems

The large-scale integration of wind energy into modern power systems introduces operational uncertainties, voltage instability, and power quality degradation due to the intermittent nature of wind speed variations. This paper proposes a Power Quality-Constrained Optimal Power Flow (PQ-OPF) framework for wind-integrated power systems using the Augmented Lagrangian Lyrebird Optimization Algorithm (AL-LOA). A probabilistic wind generation model based on the Weibull distribution is employed to capture stochastic wind behavior, and the wind turbine output is modeled using a piecewise nonlinear power curve. The formulated PQ-OPF problem incorporates voltage deviation, reactive power limits, line flow constraints, and total harmonic distortion (THD) as power quality constraints. The Augmented Lagrangian method effectively handles equality and inequality constraints, while the Lyrebird Optimization algorithm enhances global search capability and convergence robustness in nonlinear and non-convex solution spaces. To further improve system performance, a Unified Power Quality Conditioner (UPQC) is optimally installed at a critical bus identified based on voltage and harmonic analysis. The proposed method is validated on the IEEE 57-bus test system under varying wind penetration levels (20%–50%). Simulation results show that the proposed AL-LOA-based PQ-OPF achieves up to 14.6% reduction in real power losses, 6.8% improvement in minimum bus voltage, and 30% reduction in THD compared to conventional OPF and existing metaheuristic techniques. In addition, improved convergence characteristics and constraint satisfaction demonstrate the effectiveness of the proposed framework for reliable, efficient, and high-quality operation of wind-integrated power systems.