Copula-Based Aggregation and Context-Aware Conformal Prediction for Reliable Renewable Energy Forecasting

TL;DR

This work addresses the challenge of producing reliable fleet-level probabilistic forecasts when only site-level forecasts are available. It combines a Gaussian copula-based aggregation to capture cross-site dependencies with context-aware conformal prediction (CACP) to calibrate the aggregated forecasts, ensuring valid coverage and sharp intervals. Empirical results on large-scale solar data from MISO, ERCOT, and SPP show near-nominal coverage with significantly sharper intervals than baselines, notably outperforming uncalibrated aggregation and system-level forecasts. The approach is practical for operational settings, requiring no retraining of site-level models or access to proprietary data, and demonstrates robust performance across diurnal and regime-changing conditions. Overall, Copula+CACP offers a scalable, calibration-guaranteed pathway to fleet-level probabilistic forecasting in renewable energy systems.

Abstract

The rapid growth of renewable energy penetration has intensified the need for reliable probabilistic forecasts to support grid operations at aggregated (fleet or system) levels. In practice, however, system operators often lack access to fleet-level probabilistic models and instead rely on site-level forecasts produced by heterogeneous third-party providers. Constructing coherent and calibrated fleet-level probabilistic forecasts from such inputs remains challenging due to complex cross-site dependencies and aggregation-induced miscalibration. This paper proposes a calibrated probabilistic aggregation framework that directly converts site-level probabilistic forecasts into reliable fleet-level forecasts in settings where system-level models cannot be trained or maintained. The framework integrates copula-based dependence modeling to capture cross-site correlations with Context-Aware Conformal Prediction (CACP) to correct miscalibration at the aggregated level. This combination enables dependence-aware aggregation while providing valid coverage and maintaining sharp prediction intervals. Experiments on large-scale solar generation datasets from MISO, ERCOT, and SPP demonstrate that the proposed Copula+CACP approach consistently achieves near-nominal coverage with significantly sharper intervals than uncalibrated aggregation baselines.

Figures (5)

• Figure 1: Conceptual overview of the proposed probabilistic aggregation framework. Site-level marginal forecasts are first combined using copula-based dependency modeling to construct an aggregated predictive distribution. A context-aware conformal calibration step (CACP) is then applied to obtain calibrated and sharp fleet-level probabilistic forecasts.
• Figure 2: Spatial distribution of solar generation sites across MISO, ERCOT, and SPP, illustrating the geographic diversity of the systems evaluated in this work.
• Figure 3: Coverage–sharpness trade-off for the MISO system. The figure shows the relationship between empirical coverage and average interval width for different aggregation and calibration strategies. Copula+CACP consistently achieves lower interval widths across a wide range of coverage levels.
• Figure 4: Example day-ahead probabilistic forecast for the MISO system. The figure compares prediction intervals produced by Copula and Copula+CACP at the 5%–95% level. The CACP calibration step notably reduces interval width during peak generation hours while maintaining coverage.
• Figure 5: Hourly conditional coverage for the MISO system at target coverage $c=80\%$. Solid lines denote system-level coverage for different methods, while the semi-transparent bars indicate the corresponding site-level coverage.

Theorems & Definitions (2)

• Definition 1: Copula
• Theorem 1: Sklar's Theoremsklar1959fonctions