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A Behavior-Guided Online Probabilistic Forecasting Method for Electric vehicle Charging Loads

Chenghan Li, Qingxiang Liu, Yinliang Xu, Yuxuan Liang

arXiv:2608.24441v1cs.AI

TL;DR

EV charging loads vary across stations and evolve over time, challenging online probabilistic forecasting based on fixed historical patterns. The paper introduces behavior-guided adaptation using dual-timescale behavior representations, semantic encoding, and delayed feedback, and reports consistent gains across ten heterogeneous stations and two horizons.

  • Problem

    Heterogeneous and evolving charging behaviors create a gap between EV behavior analysis and online probabilistic load forecasting.

  • Method

    The framework models persistent station-specific patterns and recent behavioral deviations, semantically encodes them for drift-aware adaptation, and uses delayed feedback for temporally consistent online updates.

  • Results

    The method consistently outperformed conventional and concept-drift-aware baselines on ten heterogeneous stations in 1-h- and 4-h-ahead forecasting.

  • Takeaways & Limitations

    The results show improved probabilistic accuracy, interval sharpness, and calibration under evolving charging behaviors and extended forecasting horizons.

Abstract

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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.

I. INTRODUCTION

EV charging loads are heterogeneous across users and stations, while evolving behaviors make fixed-pattern forecasting difficult. The paper addresses this gap with behavior-guided online probabilistic forecasting.

  • EV charging demand varies across users and stations in timing, duration, energy demand, and charging frequency.
  • Behavioral changes can cause future charging loads to deviate from historical patterns, motivating probabilistic forecasts that represent predictive uncertainty.
  • Existing forecasting studies improve temporal, spatial, or uncertainty representations but generally rely on historically learned patterns without explicitly modeling heterogeneous charging behavior.
  • Online concept-drift methods adapt to new patterns, but their adaptation is driven primarily by temporal representation changes rather than explicit behavioral information.
  • The proposed framework models persistent station-specific patterns and recent behavioral deviations, then translates those changes into online probabilistic adaptation.
  • 15.3% and 17.8% reductions in MSE and Pinball loss occur for 1-h-ahead forecasting, increasing to 16.8% and 22.6% for 4-h-ahead forecasting.

II. PROBLEM FORMULATION

The paper formulates H-step-ahead EV load forecasting from recent load history and known target-time calendar information. Because future observations arrive after forecasts are issued, updates use delayed feedback and matured samples.

  • The H-step-ahead forecast uses station load history, the most recent L observations, target-time calendar covariates, and model parameters available at origin t.
  • Predictive distributions are represented through conditional quantiles rather than an explicitly specified parametric distribution.
  • Each forecast is retained until its target observation becomes available, because the observation is unavailable when the forecast is issued.
  • Only matured samples with available observations enter online adaptation, while stored predictions remain available for evaluating the forecasts originally issued.
  • At target time u = t + H, the current model evaluates pinball loss and computes gradients for matured samples before aggregating them into an online parameter update.
  • The 90% prediction interval is evaluated for nominal coverage, with empirical coverage expected to converge to 0.90 over the online stream.

III. METHOD

The framework combines persistent station-specific behavior with recent behavioral changes for drift-aware online probabilistic forecasting. Semantic encoding, behavior-guided adaptation, quantile forecasting, and online calibration operate together under evolving charging patterns.

  • Historical observations establish a long-term behavioral representation, while a rolling window captures recent dynamics and deviations from that representation.
  • Behavioral changes are semantically encoded to guide drift-aware model adaptation.
  • Quantile-based forecasting and online calibration produce probabilistic predictions under evolving charging behaviors.

A. Dual-Timescale Behavior Modeling

The dual-timescale representation separates persistent station charging preferences from short-term behavioral changes. Their deviation provides an explicit behavioral signal for subsequent online adaptation.

  • A behavior operator extracts charging characteristics from load windows to represent complementary temporal aspects of charging behavior.
  • The behavior features include mean activity, load volatility, zero-load ratio, peak-hour index, ramping intensity, high-load fraction, and day-to-day variability.
  • The long-term behavior anchor is computed from initial historical observations and remains fixed during online forecasting.
  • A recent behavior state is continuously extracted from a rolling window to capture short-term changes.
  • The deviation between recent behavior and the station-specific baseline explicitly characterizes current behavioral change and guides online adaptation.
  • Historical load sequences and target-time calendar covariates are encoded separately as temporal information for forecasting.

B. Behavior-Semantic Prompt Encoding

The framework semantically encodes long-term and recent charging behaviors, then uses their deviations to guide drift-aware probabilistic forecasting adaptation. It integrates behavior-aware corrections into temporal representations before producing quantile forecasts and online updates.

  • B. Behavior-Semantic Prompt Encoding: Descriptor-specific prompts encode each recent behavioral state and its change relative to the corresponding long-term behavior.The prompts are constructed for each of J behavior descriptors.
  • B. Behavior-Semantic Prompt Encoding: A frozen language model encodes behavior prompts, and a shared trainable projection maps them into a compact semantic space.The resulting semantic feature characterizes behavioral changes for subsequent behavior-guided adaptation.
  • C. Behavior-Guided Online Probabilistic Forecasting: The integrated behavior representation combines behavior information, its deviation from the long-term pattern, and semantic features to construct a behavior-aware residual correction.The residual is produced through trainable adapter matrices.
  • C. Behavior-Guided Online Probabilistic Forecasting: Figure 3 presents the framework of the proposed behavior-guided online probabilistic forecasting method.
  • B. Behavior-Semantic Prompt Encoding: Figure 4 presents semantic prompts for long-term and recent charging behaviors.
  • C. Behavior-Guided Online Probabilistic Forecasting: Drift intensity controls both the residual contribution and the station-specific online learning rate, enabling adaptive responses to evolving charging patterns.The learning rate uses a base rate with lower and upper scaling factors.
  • C. Behavior-Guided Online Probabilistic Forecasting: The behavior-aware residual is incorporated into the temporal representation, while the temporal encoder remains the primary forecasting representation.The behavior branch supplies an adaptive correction according to observed charging-pattern changes.
  • C. Behavior-Guided Online Probabilistic Forecasting: The adapted representation is mapped through a monotonic quantile decoder to produce probabilistic forecasts.The resulting quantiles provide the median forecast and corresponding 90% prediction interval.

A. Setting

The evaluation uses a ten-station heterogeneous EV charging dataset and processes observations sequentially after an initial historical period. Algorithm 1 generates probabilistic forecasts and updates the model using matured observations.

  • A. Setting: Algorithm 1 requires a charging stream, forecast horizon, look-back length, long-term and recent behavior windows, and a forecasting model.
  • A. Setting: At each forecast origin, the algorithm initializes long-term behavior, encodes temporal and semantic behavior representations, computes drift-aware adaptation, and generates quantile forecasts.
  • A. Setting: Online updates retrieve matured observation sets and evaluate gradients using observations whose feedback has become available.
  • A. Setting: The dataset contains ten heterogeneous charging stations with diverse charging behaviors and operating characteristics.The proposed method is compared with TCN, PatchTST, LSTM, FSNet, and OneNet.
  • A. Setting: The first 60 days initialize the historical period, after which remaining observations are processed sequentially in a rolling online manner.

B. Dataset

The ten selected stations exhibit substantial cross-station heterogeneity and evolving behavioral drift. Experiments show that behavior-guided forecasting improves accuracy, probabilistic quality, and online practicality across heterogeneous stations.

  • Dataset: Ten stations differ in mean activity, volatility, zero-load ratio, ramping intensity, day-to-day variability, and daily charging profiles.Their peak timing, peak magnitude, and within-day variability also vary substantially.
  • Dataset: Seven-day drift trajectories vary across stations and time, with several stations showing pronounced deviations from historical behavior.These observations motivate behavior modeling and online adaptation.
  • Result Analysis: The proposed method maintains accuracy, interval sharpness, and probabilistic calibration across 1-h and 4-h horizons.For 4-h forecasting, it reports MSE 0.412, Pinball loss 0.106, PINAW@90 0.223, CD@90 0.003, and PICP@90 0.897.
  • Result Analysis: The full model generally outperforms TS-only, long-term, and 7-day-prompt variants, while jointly using long-term and recent behavior benefits most stations.Individual components can provide limited or negative gains at some stations.
  • Result Analysis: Behavior-guided forecasting remains computationally efficient, with 1.85 ms/sample inference, 8.67 ms/step updates, 20.62 ms P95 latency, and 17.4 MB memory.Its inference latency is lower than PatchTST and comparable to other online baselines.
  • Result Analysis: Forecasting gains generally increase with behavior-drift intensity, and semantic encoding outperforms direct numerical encoding at most stations.Semantic information is particularly beneficial when complex temporal variation exceeds numerical descriptors alone.

V. CONCLUSION

The paper concludes that explicitly modeling evolving charging behaviors improves online EV load forecasting under heterogeneous conditions. It also identifies broader behavioral environments as a direction for future work.

  • V. CONCLUSION: The framework consistently outperforms conventional and concept-drift-aware online baselines for 1-h and 4-h forecasting across ten heterogeneous stations.It improves probabilistic accuracy, interval sharpness, and calibration, while ablations confirm complementary long-term and recent behavioral information.
  • V. CONCLUSION: Future work will incorporate external behavioral factors and investigate generalizability across broader charging environments.

APPENDIX

The evaluation uses complementary metrics for point accuracy, probabilistic accuracy, interval coverage, and calibration, including pinball loss and 90% interval measures.

  • Forecasting performance is evaluated across point accuracy, probabilistic accuracy, interval coverage, and calibration.
  • The average pinball loss evaluates probabilistic forecasting accuracy, with lower values indicating better performance.
  • A 90% prediction interval should achieve PICP close to 0.90 for good calibration.
  • PINAW measures 90% prediction-interval sharpness, with lower values indicating narrower intervals relative to observed-load range.
  • Coverage deviation at 90% quantifies the difference between empirical and nominal interval coverage.

B. Baselines

The baselines cover convolutional, Transformer-based, recurrent, fast–slow adaptive, and online ensemble forecasting approaches. Their training and online adaptation settings are summarized in Table III.

  • TCN uses temporal convolutions to capture local and long-range dependencies in charging-load sequences and provides an online convolutional baseline.
  • PatchTST divides observations into patches and uses a Transformer to model temporal dependencies as a representative Transformer-based baseline.
  • LSTM models sequential dependencies through recurrent hidden states and gated memory mechanisms as a representative recurrent baseline.
  • FSNet combines fast and slow learning mechanisms to adapt forecasting models to evolving time-series distributions and temporal shifts.
  • OneNet dynamically combines forecasting models through online ensembling to adapt to concept drift and non-stationary charging-load patterns.
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