Polynomial Chaos-Based Stochastic Dispatch with Adaptive Setpoint Control for Renewable-Integrated Electric Arc Furnace Steelmaking

Scrap-based electric arc furnace (EAF) steelmaking powered by on-site variable renewable energy is a key decarbonisation route, but the heteroscedastic, non-Gaussian nature of joint wind–photovoltaic forecast errors makes the EAF—a large, metallurgically constrained load—hard to coordinate with on-site generation under feeder limits. We develop a unified stochastic dispatch and adaptive setpoint-control framework. A chance-constrained dispatch over a zone-wise Beta uncertainty model is propagated through a degree-two polynomial chaos expansion (PCE) and reformulated as a second-order cone programme via the Cantelli inequality, with EAF-specific metallurgical constraints (electrode slew, short-circuit-ratio-tied flicker, stage-dependent melt-power floor, multi-stage tap-to-tap profile) embedded by the same procedure. The EAF setpoint gain is then extracted in closed form—without Jacobian inversion—as a ratio of first-order PCE coefficients, so it inherits the dispatch’s 95% feeder-security guarantee. Calibrated on 24 months of real wind/PV data for a Qingdao site (ERA5 reanalysis vs. archived ECMWF-IFS forecast), which confirms the heteroscedastic premise and a measured wind–PV error correlation of 0.015, the extracted gain scales across the Low–Mid–High zones (medians 6.07, 11.91, 17.22 p.u.) following the operating regime rather than the disturbance magnitude. The scheme bounds worst-case tracking below 1.18 MW per zone (vs. up to 3.34 MW for no droop), satisfies the feeder limit in 100% of realisations, matches model-predictive control without online optimisation, and lowers within-EAF specific CO2 emissions by 4.4% versus no droop. An out-of-sample test on real records confirms a decisive advantage in the data-rich zones and, candidly, a shortfall in the data-limited high-wind zone.