CoCopula

Conformal Calibration and Copula Aggregation for Reliable Renewable Energy Forecasting

Alireza Moradi · Mathieu Tanneau · Reza Zandehshahvar · Pascal Van Hentenryck

NSF AI Institute for Advances in Optimization (AI4OPT), Georgia Institute of Technology

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This repo includes the codes and data for our recent paper CoCopula: Conformal Calibration and Copula Aggregation for Reliable Renewable Energy Forecasting. A BibTeX entry for citation is provided at the end of this page.

Overview

System operators often receive probabilistic forecasts for individual sites (solar or wind farms) but have no forecasting model for the fleet as a whole. CoCopula builds a reliable fleet-level forecast from the site-level forecasts alone, in two stages:

1. Aggregation. A Gaussian copula captures the dependence between the forecast errors of the sites. Monte Carlo samples from the copula are mapped through each site's predictive distribution and summed, giving a predictive distribution for the total fleet generation.
2. Calibration. Context-Aware Conformal Prediction (CACP) corrects the aggregated intervals using past forecast errors, weighting each past hour by how similar its context (solar position, time of day/year, previous-day generation) is to the hour being forecast.

Repository structure

CoCopula/
├── cocopula/                 the method
│   ├── data.py               loading the arrays and the context features
│   ├── copula.py             PIT values, Gaussian-copula fit, Monte Carlo aggregation
│   ├── conformal.py          CQR and CACP calibration
│   ├── metrics.py            PICP, AIW and Winkler score
│   └── pipeline.py           the two stages over a year of data
├── scripts/
│   ├── download_data.py      download the PERFORM data and build the arrays
│   └── run.py                run one method: aggregation -> calibration -> metrics
├── covariates/               context features of CACP (not part of the NREL data)
├── sites/                    site order used in the paper, one list per ISO
├── figures/                  overview animation of the README
├── requirements.txt
└── LICENSE

Installation

git clone https://github.com/AI4OPT/CoCopula.git
cd CoCopula
pip install -r requirements.txt        # numpy, scipy, pandas, scikit-learn, h5py

Data

Source. NREL / ARPA-E PERFORM dataset (documentation, AWS Open Data): day-ahead solar forecasts and actuals for MISO and SPP (2019) and ERCOT (2018). The data is public; no account is needed.

Download. One command per ISO downloads the raw files and builds the arrays used by the code:

python scripts/download_data.py --iso MISO  --data_dir DATA_DIR   # ~6 GB
python scripts/download_data.py --iso SPP   --data_dir DATA_DIR   # ~1.5 GB
python scripts/download_data.py --iso ERCOT --data_dir DATA_DIR   # ~1.9 GB

This writes DATA_DIR/<ISO>/{site_actuals, site_quantiles, fleet_actuals, fleet_quantiles_nrel, fleet_capacity}.npy (raw files are cached in DATA_DIR/raw/). Running MISO needs about 6 GB of memory (its site forecasts are 5.2 GB).

Included in this repository. covariates/ holds the CACP context features (not part of PERFORM) and sites/ the site order used in the paper.

Usage

One command runs a method on one ISO: it aggregates the site forecasts (if the method needs it), calibrates the fleet forecast (if --calibration is given), and reports the metrics.

python scripts/run.py --data_dir DATA_DIR --iso MISO --aggregation copula --calibration cacp --out_dir out/

Method	--aggregation	--calibration
NREL †	nrel	–
NREL+CQR †	nrel	cqr
NREL+CACP †	nrel	cacp
Ind	independent	–
Copula	copula	–
Copula+CQR	copula	cqr
CoCopula	copula	cacp

– : leave the argument out. † NREL's own fleet-level forecast, a reference that is not available in the setting studied. --iso is MISO, SPP or ERCOT.

The command prints PICP, AIW and Winkler score at the 90%, 80%, 70% and 60% levels and saves out/<iso>_<aggregation>[_<calibration>]_{quantiles,times,metrics} (calibrated quantiles of every test hour, their time stamps, and the metrics). The aggregated fleet forecast is saved as out/<iso>_<aggregation>.npy and reused by later runs, so the copula is fitted only once per ISO.

Experimental protocol

• Normalization. Generation and forecasts are divided by the fleet capacity; hours with zero generation (night) are excluded.
• Aggregation. Σ is first fitted on January–June (used for January–July) and refitted at the start of every later month on all earlier data. PIT values use piecewise-linear CDFs through the 99 quantiles, clipped to [10⁻⁴, 0.999]; 1000 Monte Carlo samples.
• Calibration. July–December is split into consecutive 7-day test windows. For each window, the preceding 7 days form the validation set and all earlier hours the calibration set. CACP selects its kernel (RBF or Laplacian) and bandwidth γ ∈ {0.5, 1, 2} on the validation week by the lowest mean Winkler score. Both CQR and CACP use finite-sample conformal quantiles: CQR takes the ⌈(n+1)(1−α)⌉-th smallest calibration score, and CACP the weighted quantile in which the test hour keeps its own weight ψ(c_t, c_t) = 1 as a point mass at +∞ (the correction is +∞ when the weights of the calibration hours never reach 1−α). The calibrator is then refitted on calibration + validation data and applied to the test window.
• Metrics. PICP, AIW and Winkler score are computed within each test window and averaged over the windows.

Citation

If you use this code, please cite:

@article{moradi2026copula,
  title={Copula-based aggregation and context-aware conformal prediction for reliable renewable energy forecasting},
  author={Moradi, Alireza and Tanneau, Mathieu and Zandehshahvar, Reza and Van Hentenryck, Pascal},
  journal={arXiv preprint arXiv:2602.02583},
  year={2026}
}

License

Released under the MIT License.