Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption

TL;DR

DER adoption forecasting must confront strong uncertainty and spatial heterogeneity while providing trustworthy decisions at multiple grid scales. The paper introduces Hierarchical Probabilistic Conformal Prediction (HPCP), a framework that combines multivariate Hawkes process forecasting with a topology-aware split conformal predictor to deliver valid circuit- and substation-level prediction intervals. A novel sibling-circuit nonconformity score and thinning-based simulations enable accurate calibration and sharp intervals, with finite-sample validity under mild mixing assumptions and improved efficiency relative to baselines. Empirical results on synthetic data and real Indianapolis data demonstrate calibrated, tight uncertainty bounds and superior predictive performance compared with standard baselines such as VAR, RNN, LSTM, GP, and QR, supporting HPCP's value for topology-conscious DER planning.

Abstract

The rapid growth of distributed energy resources (DERs) presents both opportunities and operational challenges for electric grid management. Accurately predicting DER adoption is critical for proactive infrastructure planning, but the inherent uncertainty and spatial disparity of DER growth complicate traditional forecasting approaches. Moreover, the hierarchical structure of distribution grids demands that predictions satisfy statistical guarantees at both the circuit and substation levels, a non-trivial requirement for reliable decision-making. In this paper, we propose a novel uncertainty quantification framework for DER adoption predictions that ensures validity across hierarchical grid structures. Leveraging a multivariate Hawkes process to model DER adoption dynamics and a tailored split conformal prediction algorithm, we introduce a new nonconformity score that preserves statistical guarantees under aggregation while maintaining prediction efficiency. We establish theoretical validity under mild conditions and demonstrate through empirical evaluation on customer-level solar panel installation data from Indianapolis, Indiana that our method consistently outperforms existing baselines in both predictive accuracy and uncertainty calibration.

Figures (9)

• Figure 1: Geographical distribution of incremental photovoltaic (PV) unit installations collected from a real-world dataset. The most recent five-year interval (2019–2024) shows significantly higher growth and greater spatial disparity compared to the preceding interval (2014–2019), highlighting the need for reliable prediction and uncertainty quantification to support future planning and infrastructure development.
• Figure 2: Example illustration of the network topology structure considered in the problem setup. Left: Affiliated Circuits and DERs (PV Units) of a representative substation. Right: Adoption event sequences (hollow dots) for eight circuits associated with the substation.
• Figure 3: Simulation of counterexample provided in Example \ref{['ex']} with 10,000 samples. The density of $Y_1 + Y_2$ is a point mass at the origin in the third plot.
• Figure 4: Illustration of our proposed algorithm. The training phase splits the dataset ($\mathcal{D}$), where the training data ($\mathcal{D}_{\rm tr}$) is used to fit the model ($\lambda$), and then used with the calibration data ($\mathcal{D}_{\rm cal}$) to calculate the set of neighbor-aware nonconformity scores ($\mathcal{E}$). Finally, Quantile regression ($\mathcal{Q}$) is fitted over $\mathcal{E}$ to predict the magnitude of the uncertainty and augment the base predictions of $\lambda$ to produce the prediction intervals.
• Figure 5: Coverage rate under four different configurations of data generation mechanisms. The gray dashed line represents the reference for the nominal significance level ($\hat{\alpha} = 70\%$).

Theorems & Definitions (15)

• Example 1: Toy Example with Two Circuits
• Theorem 5.1: Validity
• Remark 1
• Proposition 1: Efficiency
• Definition C.1: Topology Matrix
• Lemma C.2: Properties of $\mathbf{S}$
• proof
• Lemma C.3
• proof
• proof : Proof of Theorem \ref{['thm:val']}