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REVIEW 3 major objections 4 minor 32 references

The Economic Dispatch of Power-to-Gas Systems with Deep Reinforcement Learning:Tackling the Challenge of Delayed Rewards with Long-Term Energy Storage

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Reward shaping lets deep reinforcement learning dispatch power-to-gas plants over a full year, nearly matching the ideal optimizer.

desk verdict A useful, incremental DRL-for-P2G dispatch study with a solid MIQP benchmark; the headline gains are real on the data shown, but the lack of any held-out evaluation means the 'significantly improve' claim is not yet proven. read the letter →

arxiv 2506.06484 v1 pith:MHXPOFUB submitted 2025-06-06 eess.SY cs.AIcs.LGcs.SY

Manuel Sage , Khalil Al Handawi , Yaoyao Fiona Zhao This is my paper
classification eess.SYcs.AIcs.LGcs.SY
keywords power-to-gasdeepreinforcementlearningeconomicdispatchrewardshapinglong-termenergystoragedelayedrewardsDQNPPO
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that deep reinforcement learning can handle the economic dispatch of a power-to-gas plant over a full year, despite the long delay between spending money to make synthetic natural gas and earning money by burning it later. Off-the-shelf DQN and PPO agents barely use the gas system; with reward modifications—penalties for low gas-storage state, penalties for leaving the plant idle in cheap-wind hours, delayed attribution of P2G operating costs, and perfect price forecasts—their year-2022 profits rise from roughly 19.9 and 18.7 million Canadian dollars to 22.3 and 22.4 million, against a mixed-integer quadratic programming optimum of 26.1 million. The point of showing this is that long-term gas storage, the main economic advantage of P2G over batteries, is exactly what prior DRL studies ignored by limiting themselves to 24-hour horizons.

What carries the argument

The central mechanism is reward shaping. Three additive modifications reshape the immediate reward so that the future value of stored gas is partially moved forward in time: a low-state-of-charge penalty $p_t=\omega \max((SOC_{P2G}^{p,\max}-SOC_{P2G,t})/SOC_{P2G}^{p,\max},0)$ that pushes the agent to keep about 0.01 of the gas tank (enough for roughly 22 MWh) available for price spikes; an inactivity penalty that subtracts $\omega$ when the wholesale price falls below $\tau=0.7$ times its running mean and the plant stays off despite enough wind; and a cost-attribution algorithm that zeroes the P2G operating cost and the lost-sales compensation at the charging step, banks them in two running sums, and charges them to the later fuel-burning steps through a deduction ratio $\rho$. Perfect price forecasts for 1 to 24 hours are added to the state but contribute little. The shaping works because the discounted-return objective makes delayed rewards nearly invisible; these terms make part of the gas-storage value visible immediately.

What would settle it

Run the identical comparison on a different year of the same market (for instance 2023 prices and wind) without retuning or re-selecting variants; if the combined reward designs do not beat the base agents by a comparable margin on that out-of-sample year, the reported improvement is at least partly an artifact of tuning on the evaluation data.

Watch

Extended reading notes

Core claim

On its own terms, the paper's claim is that P2G dispatch fails for DRL not because of uncertainty or model complexity but because the reward signal arrives too slowly: buying electricity, paying for CO2, and running an inefficient conversion chain produces no revenue until the gas is burned, possibly many hours later. The paper demonstrates this by building a wind-plus-battery, electrolyzer-methanation, gas-turbine plant and testing DQN and PPO on three horizons. In the hardest setting, a full year of real market data, the base agents barely operate the P2G system and score below the battery-only benchmark, while the combined reward design produces policies that run the P2G system for over 2,500 hours and the gas turbine for about 400 hours, recovering most of the gap to the MIQP optimum. The paper interprets this as unlocking long-term storage: a 12% gain for DQN and 20% for PPO come specifically from getting the agents to fill and later empty the gas storage.

Load-bearing premise

The evaluation assumes that training and tuning on the same full year that is also used for the reported scores gives a fair performance measure; there is no held-out year to test on.

Editorial extensions

If this is right

  • Reward shaping that punishes empty gas tanks and idle conversion lets DRL agents use long-term gas storage, whereas off-the-shelf agents leave the P2G plant almost unused.
  • The low-SOC penalty is the most influential single modification; its best setting keeps about 22 MWh of fuel in reserve, which the agent can burn during one price spike.
  • With all modifications combined, DRL reaches roughly 85% of the ideal mixed-integer quadratic programming profit on a full year of real market data.
  • Perfect short-term price forecasts are not the answer: they improve results only slightly, suggesting the core difficulty is credit assignment over long storage cycles, not near-term price uncertainty.
  • The same modifications transfer from 24-hour and weekly episodes to a 8760-step year-long episode, indicating the reward-shaping effect is not specific to one horizon.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: because the 'Combined' variant was chosen as the best of many after experiments on the same year, the reported 12% and 20% gains are likely optimistic; a holdout-year evaluation is the natural check.
  • Editorial extension: the inactivity penalty is essentially a hand-coded 'buy cheap, store' heuristic, so a reasonable next step is replacing it with a learned opportunity-cost baseline that adapts to seasonal price patterns.
  • Editorial extension: the cost-attribution scheme leaves total episode reward unchanged and barely helps, which suggests the bottleneck is not accounting timing but the agent's inability to propagate value through hundreds of steps; methods like hindsight relabeling or option-based temporal abstraction may be more effective.
  • Editorial extension: the SOC-penalty result implies a practical design rule—if a DRL controller cannot see the value of stored gas, add a minimum-reserve constraint as a safety layer; the penalty is essentially a soft version of that constraint.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies economic dispatch of a hybrid power-to-gas (P2G) system with battery storage, wind generation, and a gas turbine, using deep reinforcement learning (DQN and PPO). The main contribution is a set of reward-function modifications—future price forecasts, low-SOC penalties, inactivity penalties, and delayed cost attribution—designed to help DRL agents exploit long-term gas storage. The authors evaluate these modifications on three case studies of increasing horizon (24 hours, 168 hours, and one full year, 2022, for a plant in Southern Alberta) and compare against a mixed-integer quadratic programming (MIQP) optimum. The headline result is that the combined modifications raise CS3 episodic rewards from roughly 19,900 to 22,300 kC$ for DQN and from 18,700 to 22,400 kC$ for PPO, narrowing the gap to the MIQP value of 26,087 kC$.

Significance. If the reported improvements generalize to unseen conditions, the paper is a useful step toward making DRL practical for long-horizon energy storage dispatch, where delayed rewards are a recognized difficulty. The evaluation has notable strengths: the MIQP benchmark is a genuine external optimum, all DRL results are averaged over five seeds with standard deviations, and the reward-shaping modifications are disabled during evaluation so that reported rewards are computed on the original objective. The three case studies with increasing episode length also make the delayed-reward challenge concrete. The main weakness is that the evaluation is entirely in-sample: training, hyperparameter tuning, and final scoring all happen on the same data, and the 'Combined' configuration is selected as the best of many variants on that same data. A held-out evaluation is therefore needed before the central claim of 'significantly improved' long-horizon dispatch can be considered established.

major comments (3)
  1. [Section 4 and Section 5, Table 2] The evaluation protocol does not separate training from test data. For CS3, the full year 2022 is used for training, for the approximately 1,000 Optuna trials per case study, and for the final scoring reported in Table 2; CS1 and CS2 similarly reuse the same generated synthetic episodes for both training and evaluation. Because the penalty parameters (omega=1000, SOC_p,max=0.01, tau=0.7, alpha=0.02) and the DRL hyperparameters are tuned on the exact trajectories used to compute the reported rewards, the 12% and 20% improvements for the 'Combined' rows in CS3 are in-sample upper bounds. A temporal holdout (for example, training on earlier years and scoring on 2022, or a cross-year validation scheme) is needed to support the claim that the proposed modifications 'significantly improve' long-horizon P2G dispatch.
  2. [Section 5, Table 2 and accompanying text] The 'Combined' variant is selected as 'the best combination found out of all modifications' after inspecting the results of all variants on the same data. This selection-of-best-on-the-evaluation-set introduces a multiple-comparison bias that is material here: for PPO on CS3, the individual variant rewards range from 18,554 to 22,411 kC$, so choosing the maximum as the headline result inflates the expected performance. The authors should either pre-specify the combined configuration before seeing the test results, use a validation split for model selection, or report all combinations with an appropriate correction for multiple comparisons.
  3. [Section 3.2.4, Algorithm 2] The cost-attribution scheme preserves total episode reward only if all produced fuel is burned by the end of the episode. The paper does not state whether the CS3 episodes end with nonzero remaining SOC in the P2G storage; if fuel remains, the training-time reward signal differs from the evaluation-time objective, which could bias the learned policy. The authors should either verify that fuel is fully consumed at episode end or qualify the conservation claim in Algorithm 2.
minor comments (4)
  1. [References [16] and [18]] There are small typographical errors in the reference list: 'visisted' should be 'visited' in both entries, and the arXiv entry for PPO would benefit from a proper DOI or URL formatting.
  2. [Figure 3] The time-series plots in Figure 3 are dense and hard to read at the printed size; enlarging them or splitting the wind and price panels would improve readability.
  3. [Section 5] The text notes that 'one of the five independent runs failed' for PPO on CS1, but the seed-level breakdown is not shown anywhere; reporting all five runs in a supplementary table would make the variability more transparent.
  4. [Algorithm 2, line 11] The computation of rho divides by SOC_{P2G,t-1}; this is safe under feasible states because the GT can only operate when fuel is available, but adding an explicit guard or note would avoid any ambiguity for readers implementing the algorithm.

Circularity Check

1 steps flagged · score 3.0 of 10

Headline gains are partly in-sample: the 'Combined' variant is selected by Optuna on the same full-year 2022 trajectory that is then scored, so the reported 12% and 20% improvements are in-sample maxima rather than independent predictions.

  1. fitted input called prediction [Section 4 (Case Study, hyperparameter tuning paragraph) and Section 5, Table 2 caption.]
    "We first tune both DRL models without the introduced methods for improved P2G control and then conduct another round of tuning including these methods and their respective parameters for around 1,000 trials on each case study. Then, based on the best parameters found, we conduct a sensitivity analysis for the proposed methods. For a fair comparison, all methods that manipulate the reward function are only applied during training and deactivated for evaluation. Table 2: 'Combined' for the best combination found out of all modifications."

    The penalty hyperparameters (omega=1000, SOC_p,max=0.01, tau=0.7, alpha=0.02) and the choice of the 'Combined' modification set were selected on the same CS3 2022 trajectory that is later reported as the evaluation result. The 'Combined' row is, by definition, the best-scoring variant on that exact data. Therefore the headline improvements over Base (12% for DQN, 20% for PPO) are maxima of an in-sample selection process, not out-of-sample predictions; the result is statistically forced by the tuning/evaluation protocol even though the shaped penalties are deactivated when the rewards are measured.

full rationale

The paper's central comparison against MIQP is external and non-circular: Gurobi solves the same environment with full lookahead and provides a genuine upper bound, and the reported DRL rewards use the original reward function because the reward modifications are deactivated at evaluation. Thus the reward-shaping terms do not directly enter the scored numbers. The main circularity concern is limited to the selection of hyperparameters and the 'Combined' variant. Section 4 states that roughly 1,000 Optuna trials per case study were used to tune the models, and Section 5/Table 2 reports the best combination found on the same full-year 2022 data used for training and scoring. Consequently, the 12% and 20% headline gains are in-sample maxima over the tuned variants rather than held-out performance estimates; this is a selection-based circularity in the quantitative claim. The self-citations (Refs [1,2,11,12]) introduce modeling choices such as the GT cost allocation scheme, time encodings, and forecasts, but they are not the proof of the reward-modification result, so they do not materially add circularity. Overall, the derivation is not definitionally circular, but the headline improvement is partly forced by in-sample tuning.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim depends on five tuned penalty and discretization parameters, plus a full set of DRL hyperparameters that are not reported. The system model itself uses literature values for efficiencies and costs, which are plausible but unverified. No new physical entities are introduced.

free parameters (7)
  • SOC penalty weight omega = 1000
    Tuned via Optuna on each case study; best value 1000 used for both penalties in all experiments.
  • SOC penalty upper limit SOC_P2G^{p,max} = 0.01
    Tuned; best value 0.01, which corresponds to roughly 22 MWh of fuel for the GT.
  • Inactivity penalty weight omega = 1000
    Tuned; same best weight as SOC penalty.
  • Inactivity threshold tau = 0.7
    Tuned; price threshold as fraction of running mean.
  • Running mean learning rate alpha = 0.02
    Tuned; controls how fast the mean price is updated.
  • Action discretization levels = 2 for GT/P2G, 3 for BES
    Authors report both DRL models worked best with the coarsest discretization, which was tuned per dimension.
  • DQN and PPO hyperparameters = not fully reported
    Tuned with ~1,000 Optuna trials per case study, but final hyperparameter values are not listed in the paper.
assumptions (5)
  • domain assumption The plant is a price-taker that can only sell power to the grid (Eq. 4) and can run BES/P2G only on available renewable power (Eq. 5).
    Stated in Sec. 2.1; simplifies the market interaction and removes load-following, which affects optimal dispatch but is a modeling choice.
  • domain assumption The DRL implementations in stable-baselines3 behave as described and the tuning procedure via Optuna is sufficient to find near-optimal hyperparameters.
    Implicit in Sec. 4; the paper relies on standard library implementations without verifying their correctness beyond the reported results.
  • standard math The GT fuel consumption model, start-up correction, and the cost allocation scheme from Ref. [11] are accurate enough for dispatch decisions.
    Taken from prior work; these approximations (piecewise linear fuel curve, 20-minute startup) are applied to all methods equally.
  • domain assumption The synthetic data for CS1 and CS2 matches the magnitudes of CS3 so that the same plant configuration is valid.
    Stated in Sec. 4; the generation process is not specified in detail, so reproducibility and realism are limited.
  • domain assumption Reward shaping applied during training and deactivated during evaluation leaves the optimal policy unchanged in principle.
    The paper notes this deactivation, but does not prove that the shaped objective preserves the optimal policy under the true reward (potential-based shaping is not invoked).

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Cite this review

Pith. "Pith review of The Economic Dispatch of Power-to-Gas Systems with Deep Reinforcement Learning:Tackling the Challenge of Delayed Rewards with Long-Term Energy Storage." pith.science (2026). https://pith.science/paper/MHXPOFUB

@misc{pith2026250606484,
  author       = {Pith},
  title        = {Pith review of: The Economic Dispatch of Power-to-Gas Systems with Deep Reinforcement Learning:Tackling the Challenge of Delayed Rewards with Long-Term Energy Storage},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHXPOFUB}},
  note         = {Machine review of arXiv:2506.06484}
}
read the original abstract

Power-to-Gas (P2G) technologies gain recognition for enabling the integration of intermittent renewables, such as wind and solar, into electricity grids. However, determining the most cost-effective operation of these systems is complex due to the volatile nature of renewable energy, electricity prices, and loads. Additionally, P2G systems are less efficient in converting and storing energy compared to battery energy storage systems (BESs), and the benefits of converting electricity into gas are not immediately apparent. Deep Reinforcement Learning (DRL) has shown promise in managing the operation of energy systems amidst these uncertainties. Yet, DRL techniques face difficulties with the delayed reward characteristic of P2G system operation. Previous research has mostly focused on short-term studies that look at the energy conversion process, neglecting the long-term storage capabilities of P2G. This study presents a new method by thoroughly examining how DRL can be applied to the economic operation of P2G systems, in combination with BESs and gas turbines, over extended periods. Through three progressively more complex case studies, we assess the performance of DRL algorithms, specifically Deep Q-Networks and Proximal Policy Optimization, and introduce modifications to enhance their effectiveness. These modifications include integrating forecasts, implementing penalties on the reward function, and applying strategic cost calculations, all aimed at addressing the issue of delayed rewards. Our findings indicate that while DRL initially struggles with the complex decision-making required for P2G system operation, the adjustments we propose significantly improve its capability to devise cost-effective operation strategies, thereby unlocking the potential for long-term energy storage in P2G technologies.

Figures

Figures reproduced from arXiv: 2506.06484 by the authors.

Figure 1
Figure 1. FIGURE 1: Simplified plant layout [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. FIGURE 3: Time-series data for wind power generation and whole [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 2
Figure 2. FIGURE 2: A simplified visualization of the proposed reward attri [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIGURE 4: Training progress of tested models measured in accu [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIGURE 5: Best policy learned by PPO on CS2, using the combination of proposed modifications. (TOP) The dispatch decisions with P2G [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.