A Newton–Raphson-Based Optimizer for PI and Feedforward Gain Tuning of Grid-Forming Converter Control in Low-Inertia Wind Energy Systems

The increasing penetration of wind energy has led to reduced system inertia and heightened sensitivity to dynamic disturbances in modern power systems. This paper proposes a Newton–Raphson-Based Optimizer (NRBO) for tuning proportional, integral, and feedforward gains of a grid-forming converter applied to a wind energy conversion system operating in a low-inertia environment. The study considers an aggregated wind farm modeled as a single equivalent DFIG-based wind turbine connected to an infinite bus, with detailed dynamic representations of the converter control loops, synchronous generator dynamics, and network interactions formulated in the dq reference frame. The grid-forming converter operates in a grid-connected mode, regulating voltage and active–reactive power exchange. The NRBO algorithm is employed to optimize a composite objective function defined in terms of voltage deviation and active–reactive power mismatches. Performance is evaluated under two representative scenarios: small-signal disturbances induced by wind torque variations and short-duration symmetrical voltage disturbances of 20 ms. Comparative results demonstrate that NRBO achieves lower objective values, faster transient recovery, and reduced oscillatory behavior compared with Differential Evolution, Particle Swarm Optimization, Philosophical Proposition Optimizer, and Exponential Distribution Optimization. Statistical analyses over multiple independent runs confirm the robustness and consistency of NRBO through significantly reduced performance dispersion. The findings indicate that the proposed optimization framework provides an effective simulation-based approach for enhancing the transient performance of grid-forming wind energy converters in low-inertia systems, with potential relevance for supporting stable operation under increased renewable penetration. Improving the reliability and controllability of wind-dominated power grids enhances the delivery of cost-effective, cleaner, and more resilient energy systems, aiding in expanding sustainable electricity access in alignment with SDG7.