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

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.

💡 Research Summary

The paper tackles a pressing problem in modern power systems: how to obtain reliable, calibrated probabilistic forecasts at the fleet (system) level when only site‑level predictive distributions are available from heterogeneous third‑party providers. Directly aggregating marginal forecasts ignores spatial dependencies and often yields mis‑calibrated intervals. To address both dependence modeling and calibration, the authors propose a two‑stage framework that first builds a joint predictive distribution using a Gaussian copula and then post‑processes the resulting fleet‑level quantiles with Context‑Aware Conformal Prediction (CACP).

Stage 1 – Copula‑based aggregation.
For each site i and historical time t, the observed output x_{i,t} is transformed through its marginal predictive CDF \hat F_{i,t} to a uniform variable \hat y_{i,t}. Applying the inverse standard normal CDF yields a Gaussian‑distributed variable \hat z_{i,t}. Stacking these across sites produces a matrix \hat Z, from which the empirical correlation matrix \hat Σ is estimated. This matrix parametrizes a Gaussian copula C_{\hat Σ}. For a future horizon τ, the site‑level marginal CDFs \hat F_{i,τ} are combined with the copula to define a joint distribution \hat F_τ. Because a closed‑form aggregate CDF is unavailable, Monte‑Carlo sampling is used: draw S samples from MVN(0,\hat Σ), transform them to uniforms via Φ, and map each uniform through the inverse marginal CDFs to obtain site‑level forecasts. Summing the N site samples for each Monte‑Carlo draw yields S fleet‑level samples, which empirically approximate the fleet‑level predictive distribution \hat F_{0,τ}. This step captures cross‑site correlations that would be missed by naïve independent aggregation.

Stage 2 – Context‑Aware Conformal Calibration.
Even with a well‑specified copula, the derived fleet quantiles may not satisfy the desired coverage 1−α due to model misspecification, sampling error, or systematic bias in the site forecasts. The authors therefore apply a conformal calibration at the aggregated level. They adopt the Conformalized Quantile Regression (CQR) framework, which adjusts the lower and upper quantiles by a data‑driven correction \hat s derived from conformity scores s_t = max{ \hat q_{α/2}(x_t)−y_t, y_t−\hat q_{1−α/2}(x_t) }. Standard CQR treats all calibration points equally, an assumption that is unrealistic for renewable generation where errors depend heavily on weather regimes, time of day, and season.

To make the calibration locally adaptive, the authors introduce weighted conformal prediction. Each calibration point τ receives a similarity weight w_τ = ψ(c_t, c_τ), where c_t is a context vector for the test instance and c_τ for the calibration point. The similarity function ψ is chosen as an RBF kernel exp(−γ‖c_t−c_τ‖²). The context vector comprises physically meaningful features: lagged historical generation values, periodic time embeddings (hour‑of‑day, day‑of‑week, month), and a normalized solar‑day indicator. Normalized weights p_τ are used to compute a weighted (1−α)‑quantile of the conformity scores, yielding a locally tuned correction \hat s. The final calibrated interval is