Uncertainty quantification for electric vehicle (EV) charging demand is essential to turn the increasing pressure of EV adoption on power systems into a source of flexibility. We study a large-scale dataset of public charging stations in Scotland, where demand exhibits a hierarchical structure, organized across multiple aggregation levels, from individual charging points to regional and national scales. The charging infrastructure is continuously evolving, with new stations deployed and existing ones occasionally removed, which calls for forecasting and uncertainty quantification methods tailored to this evolving structure. To address these challenges, we combine hierarchical forecasting with recent advances in conformal prediction with missing data. The conformal procedures considered produce valid prediction intervals at every node of the hierarchy and the algorithm CP-MNR-Nested successfully accounts for the time-varying hierarchical structure of the data.
Figures & tables
Fig 1: Hierarchical structure of EV charging energy demand in Scotland.
Fig 2: The left panel represents the spatial repartition of the charging stations in Scotland (top) and in Glasgow (bottom). Stations are represented by blue dots, and the size of the dot is proportional to the number of charging points within each station. The right panel shows the corresponding time series of daily energy demand.
Indices
Domain
Description
t
Days
time index, on a daily basis
i
[m]
node index, i=1,…,m :
stations, i=1,…,n
local authorities aggregate, i=n+1,…,m−1
Scotland aggregate, i=m
Variables
Domain
Description
Table 1: Basic notations.
Fig 3: Time series of daily energy demand at four charging stations in Glasgow City. The figure illustrates three typical node behaviors: Station 410 is active throughout the entire period, Station 406 becomes inactive at the end of 2023, Stations 403 and 386 both exhibit the effect of predictable temporary closures.
Functions
Domain
Description
A
X×{0,1}m→Rm
base predictor
A
X×{0,1}m→Rm
reconciled predictor
R
Rm×{0,1}m→Rm
reconciliation function
Variables
Formula
Description
y(k)∈Rm
A(x(k),a(k))=R(A(x(k),a(k)),a(k))
reconciled forecasts at day k
s(k)∈Rm
y(k)−y(k)=s((x(k),a(k)),y(k);A)
vectorial non-conformity score at day k
Table 2: Advanced notations.
Fig 4: The CP procedure, adapted from conformal prediction for hierarchical data.
Fig 5: Rolling-window data partitioning. At the first block, the available data is split into a training set (80%) and a calibration set (20%) . The calibration set of indices is drawn once, combining the week preceding the test period and randomly sampled one-week historical blocks. The same partition is then shifted forward by two weeks across subsequent blocks.
Fig 6: Boxplots of the node-wise RMSEs of the base forecasts (a) and reconciled forecasts (b) across aggregation levels. The Global entry (c) corresponds to the square root of the average MSE over all nodes in the hierarchy.
Node type
Level
CP
CP-MNR
CP-MNR Nested ⋆
Adaptive CP-MNR
National
1−α
40.0% ± 16.3%
40.0% ± 16.3%
90.0% ± 10.0%
0.0% ± 0.0%
1−2α
100.0% ± 0.0%
100.0% ± 0.0%
100.0% ± 0.0%
100.0% ± 0.0%
Regional
1−α
51.9% ± 1.2%
51.9% ± 1.2%
71.2% ± 1.2%
47.8% ± 0.9%
1−2α
98.8% ± 0.5%
98.8% ± 0.5%
99.1% ± 0.5%
100.0% ± 0.0%
Station
1−α
38.1% ± 0.4%
56.2% ± 0.4%
73.6% ± 0.6%
57.6% ± 0.6%
1−2α
67.7% ± 0.3%
93.6% ± 0.3%
90.8% ± 0.4%
98.0% ± 0.1%
Table 3: Validity rates at two coverage levels: the nominal level 1−α=90% and a relaxed level 1−2α=80% . Results are grouped by aggregation level/conformal procedure, and reported as mean±1.96×standarderror .
Fig 7: Validity rates at the station-level, respectively marginally and conditionally on the activity regime (Low or High) within the region of the station under scrutiny.
Fig 8: Coverage and average length of the prediction intervals for Scotland (top left), Glasgow (top right), Station 406 (bottom left), and Station 386 (bottom right). The results are reported as mean±1.96×standarderror .
Fig 9: Prediction intervals for Scotland (top) and Glasgow (bottom).
Fig 10: Prediction intervals for Station 406.
Fig 11: Prediction intervals for Station 386.
Node type
Reconciliation
CP
CP-MNR
Adaptive CP-MNR
National
OLS
50.0% ± 16.7%
50.0% ± 16.7%
80.0% ± 13.3%
rOLS
60.0% ± 16.3%
60.0% ± 16.3%
90.0% ± 10.0%
Regional
OLS
55.9% ± 2.2%
55.9% ± 2.2%
46.9% ± 1.5%
rOLS
61.6% ± 2.4%
61.6% ± 2.4%
47.5% ± 1.5%
Station
OLS
48.0% ± 0.4%
42.4% ± 0.3%
37.7% ± 0.3%
rOLS
81.0% ± 0.2%
59.4% ± 0.3%
57.4% ± 0.2%
Table 4: Win rate of OLS and rOLS with respect to Direct in terms of prediction interval average lengths. Results are reported as mean±1.96×standarderror .
Node type
Reconciliation
CP
CP-MNR
Adaptive CP-MNR
National
Direct
10.0% ± 10.0%
10.0% ± 10.0%
0.0% ± 0.0%
OLS
30.0% ± 15.3%
30.0% ± 15.3%
0.0% ± 0.0%
rOLS
40.0% ± 16.3%
40.0% ± 16.3%
0.0% ± 0.0%
Regional
Direct
67.2% ± 0.8%
67.2% ± 0.8%
62.8% ± 1.4%
OLS
53.8% ± 1.7%
53.8% ± 1.7%
49.1% ± 1.6%
rOLS
51.9% ± 1.2%
51.9% ± 1.2%
47.8% ± 0.9%
Table 5: Validity rates at level 1−α=90% for the different reconciliation procedures. Results are reported as mean±1.96×standarderror . The best-performing reconciliation procedure is shown in bold.
Node type
Reconciliation
CP
CP-MNR
Adaptive CP-MNR
National
Direct
100.0% ± 0.0%
100.0% ± 0.0%
100.0% ± 0.0%
OLS
100.0% ± 0.0%
100.0% ± 0.0%
100.0% ± 0.0%
rOLS
100.0% ± 0.0%
100.0% ± 0.0%
100.0% ± 0.0%
Regional
Direct
97.2% ± 0.7%
97.2% ± 0.7%
100.0% ± 0.0%
OLS
98.8% ± 0.5%
98.8% ± 0.5%
100.0% ± 0.0%
rOLS
98.8% ± 0.5%
98.8% ± 0.5%
100.0% ± 0.0%
Table 6: Validity rates at the relaxed level 1−2α=80% for the different reconciliation procedures. Results are reported as mean±1.96×standarderror . The best-performing reconciliation procedure is shown in bold.
Accurate forecasting of electric vehicle (EV) charging demand is critical for grid management and infrastructure planning. Yet the field continues to rely on legacy benchmarks; such as the Palo Alto (2020) dataset; that fail to reflect the scale and behavioral diversity of modern charging networks. To address this, we introduce a novel large-scale longitudinal dataset collected across Scotland (2022 2025), which release it as an open benchmark for the community. Building on this dataset, we formulate EV charging demand as a spatio-temporal latent Gaussian field and perform approximate Bayesian inference via Integrated Nested Laplace Approximation (INLA). The resulting model jointly captures spatial dependence, temporal dynamics, and covariate effects within a unified proba bilistic framework. On station-level forecasting tasks, our approach achieves competitive predictive accuracy against machine learning baselines, while additionally providing principled uncertainty quan tification and interpretable spatial and temporal decompositions properties that are essential for risk-aware infrastructure planning.
Kaoutar Bouaachra, Yvenn Amara-Ouali, Yannig Goude +1
École Polytechnique de Paris · EDF Lab Paris-Saclay Palaiseau, France · INRIA Paris, DYOGENE/MATHNET Team
Electric vehicle (EV) charging loads exhibit strong behavioral heterogeneity and temporal variability, posing significant challenges for online probabilistic forecasting under evolving operating conditions. In particular, persistent charging patterns may differ substantially across stations, while recent behavioral changes can continuously alter the underlying load distributions. This paper proposes a behavior-guided online probabilistic forecasting framework that explicitly characterizes persistent station-specific patterns and recent behavioral changes. A dual-timescale behavior representation is constructed to distinguish long-term charging characteristics from recent behavioral states and quantify their deviations. These behavioral changes are further semantically encoded to guide drift-aware forecasting adaptation, while a delayed-feedback mechanism ensures temporally consistent online updates when observations become available across different forecasting horizons. Experiments on ten heterogeneous real-world charging stations demonstrate that the proposed method consistently outperforms conventional forecasting models and concept-drift-aware online baselines in forecasting accuracy and probabilistic reliability. For 1-h-ahead forecasting, the proposed method reduces MSE and Pinball loss by 15.3% and 17.8%, respectively, over the corresponding best baselines. For 4-h-ahead forecasting, the improvements further reach 16.8% and 22.6%, respectively, demonstrating consistent performance gains under evolving charging behaviors and extended forecasting horizons.
Chenghan Li, Qingxiang Liu, Yinliang Xu +1
Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China · Intelligent Transportation Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511458, China
Accurate forecasting of electric vehicle (EV) charging demand is critical for grid stability, infrastructure planning, and real-time charging optimization. In this work, we study the problem of early prediction of charging demand, where the total energy of a session is estimated using only information available at plug-in time and during the first minutes of charging. This enables actionable decisions while the session is still in progress, which is of direct importance for EV network operators. We construct a session-level dataset from the Adaptive Charging Network (ACN), combining session metadata with early-window charging measurements, and derive tabular features capturing user intent, temporal patterns, and initial charging behavior. We focus on a single operational depot, Caltech, and model intra-depot heterogeneity through station-level client partitions while evaluating multiple model families in a federated learning (FL) setting. Our results show that federated models can approach centralized predictive performance while keeping data in-depot, enabling privacy-enhanced training across distributed charging infrastructures. Overall, we demonstrate that reliable demand estimates can be obtained early in the session with minimal data, and that FL provides a practical pathway toward scalable and privacy-aware analytics for EV charging networks. Code is available at https://github.com/Indigma-Innovations/federated-learning-ev-charging-demand.