Probability-Layer Clustering for Bound-and-Budget Calibration in Multi-Bound Robust Bidding of Renewable-Based Virtual Power Plants

Abstract

RVPPs that aggregate dispatchable and non-dispatchable renewable energy sources, storage, and flexible demand that bid in the day-ahead and secondary reserve markets must cope with uncertainties in market prices, renewable generation, and demand. MBRO is well suited to this setting because it hedges adverse realizations through several deviation layers while keeping the final bidding problem as a tractable, scenario-free MILP. Its performance, however, depends on how the deviation bounds and uncertainty budgets are calibrated. Existing MBRO implementations commonly rely on fixed percentile-based bounds and externally specified budget vectors, usually examined through sensitivity analysis. This paper proposes PL-MBRO, that constructs parameter-specific deviation bounds from historical data conditional on selected risk-attitude quantiles and automatically derives the corresponding uncertainty budgets from empirical cluster probabilities. For each uncertain parameter, k-medians clustering partitions the historical daily profiles into representative probability layers; the cluster median defines the balanced representative, while favorable and adverse within-cluster percentiles define the optimistic and pessimistic representatives. The empirical cluster probabilities are mapped to integer full-horizon uncertainty budgets over the 96 quarter-hourly periods, while the robust inner problem determines the periods in which the corresponding deviation layers are most adverse to the schedule. Compared with a percentilebased MBRO benchmark, in-sample and out-of-sample tests on an RVPP bidding in both markets show that PL-MBRO consistently achieves better realized economic outcomes across the optimistic, balanced, and pessimistic strategies, with improvements of up to 92.7% in-sample and 57.3% out-of-sample, measured relative to the absolute value of the corresponding benchmark realized profit.