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arxiv: 2604.24724 · v2 · submitted 2026-04-27 · 📡 eess.SY · cs.SY

Data-Driven Privacy-Preserving Modeling and Frequency Regulation with Aggregated Electric Vehicles via Bilinear Hidden Markov Model

Yiping Liu , Xiaozhe Wang , Geza Joos This is my paper

Pith reviewed 2026-05-08 01:32 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords electric vehiclesvehicle-to-gridfrequency regulationprivacy-preserving controlhidden Markov modelaggregated modelingdata-driven estimationancillary services
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The pith

A bilinear hidden Markov model trained only on aggregate EV measurements can estimate fleet power output and flexibility accurately enough to enable frequency regulation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Electric vehicles can provide real-time grid support through vehicle-to-grid technology, but most coordination methods require private details such as individual travel times, battery parameters, or live state-of-charge values. This paper shows that a bilinear hidden Markov model fitted solely to total fleet measurements can still recover the collective power output and available flexibility. The resulting estimates support closed-loop frequency regulation commands that keep the grid stable without ever accessing data from any single vehicle. If the claim holds, large-scale EV participation in ancillary services becomes feasible while sidestepping both privacy regulations and the practical problems of incomplete or noisy individual data.

Core claim

The paper establishes that a bilinear hidden Markov model trained exclusively on aggregate power measurements can deliver accurate estimates of the EV fleet's power output and flexibility and can be used to generate effective frequency regulation signals without any individual EV information.

What carries the argument

Bilinear hidden Markov model that maps aggregate measurements to hidden fleet states and flexibility dynamics.

If this is right

  • Frequency regulation can be performed using only aggregate power measurements collected at the charger or substation level.
  • The approach remains effective even when individual state-of-charge data are missing or inaccurate.
  • Privacy is preserved because no arrival times, departure times, or battery parameters of single vehicles are required.
  • The method outperforms both conventional model-based controllers and federated-learning baselines under realistic data-quality conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same aggregate-only modeling strategy could be tested on other distributed resources whose owners resist sharing individual operating data.
  • If the learned model generalizes across different EV manufacturers and usage patterns, grid operators could deploy a single controller rather than per-fleet calibrations.
  • Real-time deployment would require checking whether the hidden-state estimates remain stable under sudden changes in fleet composition or charging-station availability.

Load-bearing premise

A model trained only on total fleet measurements can still recover the underlying flexibility and power-output behavior of the entire collection of vehicles.

What would settle it

A controlled simulation or field experiment in which frequency-regulation error or estimation accuracy becomes unacceptable when the model is retrained on aggregate data alone, while the same task succeeds with access to individual vehicle data.

Figures

Figures reproduced from arXiv: 2604.24724 by Geza Joos, Xiaozhe Wang, Yiping Liu.

Figure 1
Figure 1. Figure 1: Individual charging model of an EV. 𝑢𝑑,𝑖 = 𝑢𝑑,𝑖 ′ /𝑥𝑁+𝑖 2N+1 2N+2 …….. 3N-1 3N Smin Smax CM IM DM 1 2 …….. N-1 N N+1 N+2 …….. 2N-1 2N 2N+3 3 N+3 FCM 3N+3 𝑢𝑑,𝑁+1 𝑢𝑎,𝑖 = 𝑢𝑎,𝑖 ′ /𝑥𝑖 3N-2 2N-2 N-2 𝑢𝑏,𝑁+1 𝑢𝑏,𝑖 = 𝑢𝑏,𝑖 ′ …….. /𝑥𝑁+𝑖 …….. 3N+1 3N+2 …….. 𝑢𝑐,𝑖 = 𝑢𝑐,𝑖 ′ /𝑥2𝑁+𝑖 …….. Control signals 𝑢𝑐,𝑖/𝑢𝑑,𝑖 Control signals 𝑢𝑎,𝑖/𝑢𝑏,𝑖 SOC boundary transitions State Transitions Charging Mode (CM) Force Charging Mode (FCM… view at source ↗
Figure 2
Figure 2. Figure 2: State transition of aggregated EVs. Modified from Fig. 4. in [5]. view at source ↗
Figure 2
Figure 2. Figure 2: The lower flexibility bound P is obtained by setting every entry of uc, ud, and ud,N+1 to 1 in (8), which enforces the opposite transitions. These control settings are used only in simulations to estimate flexibility. The detailed algorithm for predicting aggregated power outputs and flexibility is outlined in Algorithm 1. Remarks: • Proper initialization of model parameters can significantly improve predi… view at source ↗
Figure 3
Figure 3. Figure 3: Periodic updates of model parameters using sliding windows. view at source ↗
Figure 4
Figure 4. Figure 4: The frequency regulation framework with EVs. view at source ↗
Figure 6
Figure 6. Figure 6: Prediction results of different modeling methods with control present. view at source ↗
Figure 7
Figure 7. Figure 7: Wind and load profiles adapted from [30]. view at source ↗
Figure 9
Figure 9. Figure 9: Absolute power tracking error of different modeling methods under view at source ↗
Figure 10
Figure 10. Figure 10: Frequency deviation profiles of different modeling methods under view at source ↗
read the original abstract

Vehicle-to-Grid (V2G) technology allows bidirectional power flow for real-time grid support, making electric vehicles (EVs) well-suited for ancillary services such as frequency regulation. However, existing methods for flexibility estimation and coordinating aggregated EVs often rely on individual EV traveling information (e.g., arrival/departure time) and/or characteristic parameters (e.g., charging efficiency, battery capacity) as well as real-time state-of-charge (SOC), which raises privacy concerns and faces data quality issues. To address these challenges, this paper proposes a data-driven, privacy-preserving modeling and control framework for frequency regulation using aggregated EVs. The proposed method can provide accurate estimation for power outputs and flexibility of aggregated EVs and carry out effective frequency regulation without any individual EV information. Simulation results validate the accuracy and effectiveness of the proposed method, which also outperforms the model-based and federated learning-based method under SOC data inaccuracies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a data-driven, privacy-preserving framework for modeling aggregated electric vehicles (EVs) using a bilinear hidden Markov model (BHMM). It claims this enables accurate estimation of aggregate power outputs and flexibility for frequency regulation without any individual EV information such as traveling data, parameters, or real-time SOC, while outperforming model-based and federated learning methods under SOC inaccuracies, as validated by simulations.

Significance. If the BHMM can reliably recover flexibility bounds and support effective regulation from aggregate measurements alone, the work would meaningfully advance V2G applications by resolving privacy and data-quality barriers to large-scale EV aggregation for ancillary services. The data-driven formulation and claimed outperformance under realistic inaccuracies represent potential strengths, provided they are backed by reproducible quantitative validation.

major comments (3)
  1. [Abstract / Simulation results] Abstract and simulation section: The claim that 'simulations validate the accuracy and effectiveness' and that the method 'outperforms' alternatives is unsupported by any quantitative metrics, error bars, training/validation splits, data exclusion rules, or statistical significance tests. This absence makes it impossible to evaluate whether the central claim of accurate power and flexibility estimation holds.
  2. [Model formulation] Model formulation (likely §3): The bilinear HMM is fitted exclusively to aggregate power observations, yet flexibility is a nonlinear function of the joint distribution of individual SOCs, capacities, and efficiencies. No explicit verification is provided that the chosen hidden-state space and bilinear emission structure can reconstruct the support of feasible aggregate power ranges; without this, estimated flexibility bounds risk being optimistic or pessimistic for the subsequent regulation controller.
  3. [Numerical results / Validation] Validation against ground truth: The paper does not report comparisons of BHMM-derived flexibility against true feasible sets computed from individual EV trajectories (even in simulation), leaving open whether the aggregate-only approach recovers the necessary statistics of hidden states or merely fits observed power sums.
minor comments (2)
  1. [Model section] Notation for the bilinear transition and emission matrices should be clarified with explicit definitions of state and observation spaces to avoid ambiguity in how individual heterogeneity is implicitly captured.
  2. [Abstract / Experiments] The abstract mentions outperformance 'under SOC data inaccuracies' but does not specify the nature or magnitude of those inaccuracies or the exact baseline implementations; this should be detailed for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. We address each major comment point by point below, providing clarifications from the work and indicating revisions that will be incorporated to strengthen the presentation and validation.

read point-by-point responses

  1. Referee: [Abstract / Simulation results] Abstract and simulation section: The claim that 'simulations validate the accuracy and effectiveness' and that the method 'outperforms' alternatives is unsupported by any quantitative metrics, error bars, training/validation splits, data exclusion rules, or statistical significance tests. This absence makes it impossible to evaluate whether the central claim of accurate power and flexibility estimation holds.

    Authors: We agree that the abstract and simulation results section would benefit from more explicit quantitative support. The manuscript presents performance through comparative figures, but does not include tabulated metrics such as RMSE for power estimation, bound accuracy for flexibility, or details on simulation data splits and statistical tests. We will revise the abstract to reference key quantitative outcomes and add a table in the numerical results section reporting these metrics along with error bars, simulation setup parameters, and data generation details. revision: yes

  2. Referee: [Model formulation] Model formulation (likely §3): The bilinear HMM is fitted exclusively to aggregate power observations, yet flexibility is a nonlinear function of the joint distribution of individual SOCs, capacities, and efficiencies. No explicit verification is provided that the chosen hidden-state space and bilinear emission structure can reconstruct the support of feasible aggregate power ranges; without this, estimated flexibility bounds risk being optimistic or pessimistic for the subsequent regulation controller.

    Authors: The bilinear emission structure and hidden-state representation are chosen to capture aggregate interactions that implicitly encode the joint effects of individual states. We acknowledge that an explicit check against the true support of feasible aggregate power would provide stronger assurance. In the revised manuscript we will add a verification step (in the main text or appendix) that uses the simulation environment to compute ground-truth feasible ranges from individual trajectories and confirms that the BHMM-derived bounds correctly cover the necessary support. revision: yes

  3. Referee: [Numerical results / Validation] Validation against ground truth: The paper does not report comparisons of BHMM-derived flexibility against true feasible sets computed from individual EV trajectories (even in simulation), leaving open whether the aggregate-only approach recovers the necessary statistics of hidden states or merely fits observed power sums.

    Authors: Although the BHMM is trained solely on aggregate power, the simulation framework generates data from individual EV models, allowing post-hoc computation of true feasible sets. We will revise the numerical results section to include direct side-by-side comparisons of the BHMM-estimated flexibility bounds versus the true feasible sets derived from individual SOCs, capacities, and efficiencies, thereby demonstrating that the model recovers the relevant hidden-state statistics rather than merely fitting observed aggregates. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents a standard data-driven bilinear HMM trained exclusively on aggregate power measurements to estimate EV fleet power outputs and flexibility, followed by a model-based frequency regulation controller. No load-bearing step reduces by construction to its own inputs: parameter estimation uses observed aggregate data, and subsequent predictions or control actions are generated from the fitted model applied to new observations. There are no self-definitional equations, no relabeling of fitted quantities as independent predictions, and no load-bearing self-citations that substitute for external validation. The derivation chain remains self-contained and externally falsifiable via simulation benchmarks against model-based and federated-learning baselines.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no equations, training procedure, or model specification, so no free parameters, axioms, or invented entities can be identified.

pith-pipeline@v0.9.0 · 5465 in / 1058 out tokens · 44154 ms · 2026-05-08T01:32:15.025772+00:00 · methodology

discussion (0)

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Reference graph

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