SOPF-Based Adaptive Droop Control for Hybrid AC--HVDC Grids Under Offshore Wind Uncertainty

Conventional fixed-gain droop controllers in hybrid AC-HVDC grids struggle with the stochastic volatility of offshore wind integration. To address this, Du and Lekić introduce a Stochastic Optimal Power Flow (SOPF)-based adaptive droop framework that bridges system-level economic dispatch and converter-level control. Rather than heuristic tuning, they model wind forecast uncertainty with a zone-wise Beta distribution, capturing heteroscedastic error patterns across low, mid, and high power regimes. Using Polynomial Chaos Expansion (PCE) within a chance-constrained SOPF, the system's stochastic states are analytically formulated, and optimal adaptive droop gains are directly extracted from first-order PCE coefficients via a Jacobian-free sensitivity analysis. This embeds statistical voltage-security guarantees into local converter control.

Validation on a 4-terminal AC-HVDC system demonstrates that scenario-adaptive gains outperform standard fixed-coefficient approaches, effectively minimizing active-power tracking errors during extreme wind disturbances. The method reduces reliance on reactive or heuristic tuning, offering a robust, analytically grounded solution for DC voltage regulation in grids with massive offshore wind penetration. This work provides a scalable path for integrating high levels of renewable uncertainty while maintaining grid stability.