Multivariate Scenario-Based Optimization Framework for Wind Power Bidding Curves with Heavy-Tailed Forecast Uncertainty

Wind power producers face severe financial risks from intermittent generation and volatile prices. In this paper, we develop a multivariate scenario-based optimization framework that integrates heavy-tailed Laplace forecast-error path generation, principal component (PC) score matching, and Frequency-Concentrated Projection (FCP) to determine day-ahead bidding curves that maximize expected settlements. To model uncertainty, 24-h scenarios are generated by sequentially accumulating heavy-tailed Laplace forecast-error increments. Trajectories of specific variables are integrated via PC-score matching to construct joint scenarios preserving inter-variable dependencies. A dense optimal response derived from these scenarios is compressed into a market-compatible 11-point bidding curve using FCP, which strategically allocates submission points to highly probable clearing intervals. Evaluation on 2021 NYISO West data demonstrates substantial improvements in both feasibility of scenarios and financial performance. The Laplace specification captures extreme price spikes, so it significantly reduces downside risk compared to a Gaussian baseline. PC-score matching ensures feasibility of structure by preserving daily trajectory shapes. Leveraging these robust scenarios, the FCP curve yields substantially higher realized settlements than the Uniform Support Baseline (USB), which uniformly places the limited submission points across the price range, recovering approximately 90% of the settlement gap between USB and the Dense Optimal Response (DOR), which serves as a non-submittable dense-grid upper-bound benchmark. Ultimately, this framework translates complex uncertainty models into actionable strategies, enabling producers to systematically maximize economic returns under rigid market constraints.