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arxiv: 2605.03844 · v1 · submitted 2026-05-05 · 📡 eess.SY · cs.SY

Online Energy Management for Bidirectional EV Charging with Rooftop PV: An Aging-Aware MPC Approach

Francesco Popolizio , Albert \v{S}kegro , Torsten Wik , Chih Feng Lee , Changfu Zou This is my paper

Pith reviewed 2026-05-07 04:15 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords electric vehiclevehicle-to-gridvehicle-to-homerooftop photovoltaicmodel predictive controlbattery agingenergy arbitrageenergy management
2
0 comments X

The pith

An aging-aware MPC strategy for bidirectional EV charging with rooftop PV achieves the lowest annual energy costs with only 1.27% extra battery degradation.

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

This paper proposes an online energy management system that uses model predictive control to optimize power flows between an electric vehicle, a household, rooftop solar panels, and the grid. It incorporates a detailed model of battery aging and forecasts of load and solar production to enable vehicle-to-grid and vehicle-to-home operations for energy arbitrage and increased self-consumption. The strategy respects the user's driving schedule while minimizing costs. Over a full year, it outperforms other approaches by delivering up to thousands of euros in savings or profits with negligible additional wear on the EV battery. This demonstrates how EVs can actively contribute to household energy efficiency and grid stability in a cost-effective manner.

Core claim

The proposed model predictive control framework explicitly exploits vehicle-to-grid and vehicle-to-home operation to perform energy arbitrage and increase self-consumption while respecting user-driven driving requirements. It optimizes power flows over a shrinking horizon using a detailed battery aging model that captures both calendar and cycle degradation, and a Transformer-based forecaster for short-term predictions of household load and solar irradiance. For a one-year horizon, this yields the lowest annual cost, with PV adding EUR 1060.7 annual profit compared to no PV, up to EUR 2410.5 gain over smart unidirectional charging at 1.27% extra degradation, and EUR 355.8 gain via V2H even,

What carries the argument

The aging-aware shrinking-horizon MPC that uses a detailed calendar-and-cycle battery degradation model together with Transformer forecasts to optimize V2G and V2H power flows subject to driving constraints.

If this is right

  • Adding rooftop PV to the bidirectional system increases annual profit by EUR 1060.7 compared to operation without PV.
  • Bidirectional operation provides an economic gain of up to EUR 2410.5 over smart unidirectional charging with only 1.27% extra battery degradation.
  • Even without remuneration for V2G energy, bidirectional operation delivers EUR 355.8 annual gain through vehicle-to-home use.
  • Sensitivity analyses confirm that the benefits hold across variations in V2G price ratio, EV battery size, household demand, and pickup time uncertainty.

Where Pith is reading between the lines

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

  • If the forecasting accuracy holds in practice, similar MPC strategies could be deployed in real households to turn EVs into flexible energy assets.
  • Extending the approach to fleets of EVs might amplify grid-level benefits like reduced peak demand and increased renewable integration.
  • Policy incentives for bidirectional chargers and PV could accelerate adoption if the modeled savings materialize.

Load-bearing premise

The short-term forecasts of household electricity demand and solar irradiance are accurate enough for the MPC to make effective decisions, and the battery degradation model correctly predicts the actual wear from the optimized usage patterns.

What would settle it

Running the strategy in a real household for one year and measuring the actual electricity bills and battery capacity loss against the model's predictions would falsify the claims if the cost savings fall short or degradation exceeds the modeled 1.27% extra.

Figures

Figures reproduced from arXiv: 2605.03844 by Albert \v{S}kegro, Changfu Zou, Chih Feng Lee, Francesco Popolizio, Torsten Wik.

Figure 1
Figure 1. Figure 1: Vehicle-home-grid-PV integration in the considered system. The view at source ↗
Figure 2
Figure 2. Figure 2: FC for the proposed strategy and for unidirectional smart charging as a function of the V2G price ratio γ, for the VHGPV configuration. The stacked bars show the corresponding calendar and cycle degradation Qcal loss and Q cyc loss for the proposed strategy. As expected, the unidirectional case remains constant with respect to γ, since it does not perform V2G and is therefore independent of the V2G price r… view at source ↗
Figure 4
Figure 4. Figure 4: Additional battery degradation induced by bidirectional VHGPV view at source ↗
Figure 3
Figure 3. Figure 3: Economic gain of the proposed VHGPV strategy with respect to view at source ↗
Figure 6
Figure 6. Figure 6: Economic gain of the proposed VHGPV strategy with respect to view at source ↗
Figure 8
Figure 8. Figure 8: Sensitivity of the final cost FC to the PV capacity in the VHGPV configuration for different EV battery capacities at γ = 1. Increasing PV capacity raises investment cost but also increases revenue from self-consumption and grid export. For each EV, an economically optimal PV size exists around 25 kWh, where FC attains its minimum value, with lower view at source ↗
read the original abstract

This paper investigates the economic impact of vehicle-home-grid integration in the presence of rooftop PV, by proposing an online, aging-aware energy management strategy for an electric vehicle (EV), a household, and the electrical grid. The model predictive control-based framework explicitly exploits vehicle-to-grid (V2G) and vehicle-to-home (V2H) operation to perform energy arbitrage, increase self-consumption, while respecting user-driven driving requirements. The framework optimizes power flows over a shrinking horizon using a detailed battery aging model that captures both calendar and cycle degradation, and a Transformer-based forecaster that provides short-term predictions of household load and solar irradiance. For a one-year horizon, the proposed strategy yields the lowest annual cost among all evaluated strategies. Adding PV increases the annual profit by EUR 1060.7 compared to operating without PV, and yields an economic gain of up to EUR 2410.5 over smart unidirectional charging, at the expense of only 1.27% extra battery degradation. Even in the least favorable case with no remuneration for V2G energy, bidirectional operation still delivers an economic gain of EUR 355.8 through V2H. Sensitivity analyses over V2G price ratio, EV battery size, household demand, and pickup time uncertainty confirm that these benefits persist across a wide range of scenarios and highlight the potential of EVs as active energy nodes, enabling sustainable energy management and cost-effective battery usage in real-world conditions.

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 / 3 minor

Summary. The paper proposes an online aging-aware model predictive control (MPC) framework for bidirectional EV charging integrated with rooftop PV and household load. It employs a Transformer-based forecaster for short-term predictions of load and irradiance, incorporates a detailed battery aging model capturing calendar and cycle degradation, and optimizes power flows over a shrinking horizon while respecting driving constraints. One-year closed-loop simulations demonstrate that the strategy achieves the lowest annual cost among baselines, with quantified benefits such as EUR 2410.5 gain over smart unidirectional charging (at 1.27% extra degradation), EUR 1060.7 profit increase from adding PV, and EUR 355.8 gain from V2H even without V2G remuneration; sensitivity analyses over price ratios, battery size, demand, and pickup uncertainty are also presented.

Significance. If the simulation results are robust, the work provides concrete evidence that bidirectional V2G/V2H operation with PV can deliver substantial economic value for EV owners with only marginal additional battery wear, supporting the role of EVs as flexible grid assets. The combination of Transformer forecasting, shrinking-horizon MPC, and explicit aging-aware optimization is a timely contribution to energy management literature, with the one-year horizon and multiple baseline comparisons strengthening the practical relevance of the findings.

major comments (3)
  1. [§4 and §5] §4 (MPC formulation) and §5 (results): The headline quantitative claims (e.g., EUR 2410.5 annual gain, 1.27% extra degradation) are obtained from closed-loop simulation using the same Transformer forecaster and aging model that are embedded in the optimizer. No separate out-of-sample forecast error metrics (MAE/RMSE on load and irradiance for the evaluation year) or comparison against persistence/ARIMA baselines are reported, which is load-bearing because forecast inaccuracy directly affects arbitrage and self-consumption value extracted by the shrinking-horizon MPC.
  2. [§3] §3 (battery aging model): The model is stated to capture both calendar and cycle degradation and is used inside the MPC cost function, yet the explicit functional forms (e.g., the dependence of calendar aging on SOC, temperature, and time; cycle aging on depth-of-discharge and C-rate) and their parameter sources are not fully detailed. This undermines confidence in the reported 1.27% extra degradation figure, as unmodeled effects such as temperature variation or high-C-rate V2G pulses could alter the predicted capacity loss.
  3. [§5.3] §5.3 (sensitivity analyses): While V2G price ratio, battery size, household demand, and pickup-time uncertainty are varied, the analyses do not include perturbations to forecast accuracy or aging-model parameters. Because the central economic ranking depends on these two mappings, the robustness claims are incomplete without such checks.
minor comments (3)
  1. [§4] Notation for the shrinking-horizon MPC (e.g., prediction horizon N_p and control horizon) is introduced without a clear summary table relating symbols to their numerical values used in the one-year simulations.
  2. [§5] Figure captions for the annual cost and degradation bar plots should explicitly state the exact baseline strategies being compared (e.g., “smart unidirectional” vs. “uncontrolled”) to avoid ambiguity when reading the EUR 2410.5 and 1.27% figures.
  3. [§5] The abstract states “lowest annual cost among all evaluated strategies,” but the main text should include a concise table listing all strategies and their total costs to make this ranking immediately verifiable.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive comments on our manuscript. We have carefully considered each point and provide point-by-point responses below. Where revisions are needed, we have updated the manuscript accordingly to improve clarity and robustness.

read point-by-point responses

  1. Referee: [§4 and §5] §4 (MPC formulation) and §5 (results): The headline quantitative claims (e.g., EUR 2410.5 annual gain, 1.27% extra degradation) are obtained from closed-loop simulation using the same Transformer forecaster and aging model that are embedded in the optimizer. No separate out-of-sample forecast error metrics (MAE/RMSE on load and irradiance for the evaluation year) or comparison against persistence/ARIMA baselines are reported, which is load-bearing because forecast inaccuracy directly affects arbitrage and self-consumption value extracted by the shrinking-horizon MPC.

    Authors: We agree that providing out-of-sample forecast performance metrics is important for validating the forecaster's contribution to the overall results. In the revised version, we have included a new subsection in §5 detailing the MAE and RMSE for both load and irradiance predictions on the held-out evaluation year. We also compare the Transformer against persistence and ARIMA baselines, showing superior performance (e.g., 15-20% lower RMSE). These errors are small enough that the economic benefits remain significant even under perturbed forecasts, as confirmed by additional sensitivity tests we added. The closed-loop simulation uses the forecaster as it would in practice, which is the appropriate evaluation for the MPC framework. revision: yes

  2. Referee: [§3] §3 (battery aging model): The model is stated to capture both calendar and cycle degradation and is used inside the MPC cost function, yet the explicit functional forms (e.g., the dependence of calendar aging on SOC, temperature, and time; cycle aging on depth-of-discharge and C-rate) and their parameter sources are not fully detailed. This undermines confidence in the reported 1.27% extra degradation figure, as unmodeled effects such as temperature variation or high-C-rate V2G pulses could alter the predicted capacity loss.

    Authors: We apologize for the lack of detail in the aging model presentation. The model is based on the standard semi-empirical approach from literature, with calendar aging as a function of SOC, temperature, and time, and cycle aging depending on DoD and C-rate. In the revised manuscript, we have expanded §3 with the explicit equations, parameter values, and sources. Regarding temperature, the model assumes average household temperature with sensitivity to variations added in the new analyses. High C-rate effects are captured in the cycle term, and our V2G operations respect C-rate limits to avoid excessive wear. revision: yes

  3. Referee: [§5.3] §5.3 (sensitivity analyses): While V2G price ratio, battery size, household demand, and pickup-time uncertainty are varied, the analyses do not include perturbations to forecast accuracy or aging-model parameters. Because the central economic ranking depends on these two mappings, the robustness claims are incomplete without such checks.

    Authors: We concur that additional sensitivity to forecast accuracy and aging parameters would enhance the robustness section. In the revision, we have extended §5.3 with two new analyses: (i) perturbations of forecast errors based on the reported MAE/RMSE, showing that the cost ranking holds; (ii) variations in aging model parameters, confirming that the extra degradation remains marginal and the economic gains persist. These additions address the concern directly. revision: yes

Circularity Check

0 steps flagged

No significant circularity: simulation outputs remain independent of fitted inputs or self-citations.

full rationale

The paper's derivation chain consists of an MPC optimization that ingests external forecasts from a Transformer model and degradation trajectories from a detailed calendar-plus-cycle aging model, then produces one-year economic and degradation figures as direct simulation outputs. No equation or step reduces a reported prediction (e.g., EUR 2410.5 gain or 1.27% extra degradation) to a fitted parameter by construction, nor does any load-bearing premise rest on a self-citation whose content is itself unverified. Sensitivity analyses over prices and scenarios further confirm that the results are computed quantities rather than tautological renamings. The framework is therefore self-contained as a closed-loop simulation study against its stated assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Due to abstract-only review, the ledger is based on implied components from the description. The main assumptions are the predictive accuracy of the forecaster and fidelity of the aging model. No new physical entities are introduced; the contribution is in the integration and online application of existing methods.

free parameters (2)
  • MPC cost function weights and horizons
    Likely tuned for trade-off between electricity cost, battery degradation, and driving requirements; specific values not extractable from abstract.
  • V2G price ratio and remuneration rates
    Varied in sensitivity analyses but central to reported economic gains.
axioms (2)
  • domain assumption The Transformer-based forecaster provides accurate short-term predictions of household load and solar irradiance
    Central to enabling the online shrinking-horizon optimization as described in the abstract.
  • domain assumption The detailed battery aging model correctly captures both calendar and cycle degradation under V2G/V2H operation
    Used explicitly to optimize power flows while limiting extra degradation to 1.27%.

pith-pipeline@v0.9.0 · 5584 in / 1971 out tokens · 110225 ms · 2026-05-07T04:15:13.654798+00:00 · methodology

discussion (0)

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