Bounded fuzzy logic control for optimal scheduling of green hydrogen production and revenue maximisation

Jens Jakob S{\o}rensen; Kary Fr\"amling; Matej Simurda; Sleiman Farah

REVIEW 4 major objections 6 minor 52 references

Bounded fuzzy logic control for optimal scheduling of green hydrogen production and revenue maximisation

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A bounded fuzzy logic controller using day-ahead forecasts recovers over 92% of perfect-foresight green hydrogen revenue.

desk verdict A competent, clearly written fuzzy-control application for daily HPA targets that plausibly beats steady control inside its model, but the 9% claim should be read as perfect-information, not realistic-forecast, performance. read the letter →

arxiv 2508.01468 v1 pith:VJEMXCCL submitted 2025-08-02 eess.SY cs.SY

Sleiman Farah , Jens Jakob S{o}rensen , Kary Främling , Matej Simurda This is my paper · ORCID

classification eess.SYcs.SY

keywords greenhydrogenfuzzylogiccontrolpurchaseagreementrenewableenergyschedulingrevenuemaximisationday-aheadforecastingwind-poweredelectrolysisbounded

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

This paper argues that long-term hydrogen purchase agreement obligations can be scheduled almost as well with a simple interpretable controller as with an all-knowing year-ahead optimizer. It introduces a Bounded Fuzzy Logic Control (BFLC) that reads day-ahead forecasts of electricity price, hydrogen price, and wind capacity, sets a daily HPA delivery target, and lets an hourly dispatch optimization allocate energy and hydrogen. Across several years of Danish wind and price data, the BFLC recovers 92.8% or more of the benchmark revenue in every year, including the volatile 2022 market, and always beats a steady daily delivery policy. The practical point is that realistic, bankable revenue estimates for green hydrogen projects need not assume perfect foresight; a rule-based controller using only day-ahead information is enough to stay within striking distance of the theoretical optimum.

What carries the argument

The central object is the Bounded Fuzzy Logic Controller, a three-input, one-output fuzzy system with triangular membership functions and centroid defuzzification, optimised against perfect-foresight benchmark trajectories. The load-bearing addition is the optimal-space bound: the convex hull of six benchmark cumulative-HPA-export curves, which clips the fuzzy output whenever cumulative deliveries would leave the hull. The daily target then enters a dispatch optimisation that maximises revenue from hourly electricity and hydrogen sales subject to meeting that target, with the fixed HPA target $M_2^*$ set at 48 tonnes.

What would settle it

Take a year, real or synthetic, whose optimal cumulative HPA-export path leaves the convex hull built from the 2017-2022 benchmark trajectories, run the BFLC on day-ahead data alone, and compare its normalised revenue against the perfect-foresight benchmark; if it falls below 92% or below steady control, the central claim is falsified. A cheaper check is to test whether any year-optimal path from a different site or market regime crosses the hull boundary.

Watch

Extended reading notes

Core claim

If the paper's results are right, the optimal sequencing of hydrogen deliveries under an HPA can be approximated by a transparent three-input fuzzy rule base plus a safety envelope. The envelope is the convex hull of the cumulative HPA-delivery paths produced by perfect-foresight optimization over six historical years; whenever the fuzzy controller's cumulative exports try to leave that hull, the target is clipped back inside. With that clipping, total market revenue (electricity plus hydrogen spot sales, excluding the fixed HPA value) stays within 9% of the perfect-foresight benchmark every year tested, with the worst case 92.8% in 2022, and consistently exceeds steady control. The largest gains over steady control occur exactly when electricity prices are high and volatile.

Load-bearing premise

The assumption that the convex hull of six historical optimal delivery paths covers the optimal paths of future years is load-bearing; if an unusual wind-price year makes the true optimal path leave that hull, the controller's bounds force it off the trained behavior and the 9% claim could fail.

Editorial extensions

If this is right

A hydrogen project can be operated in real time with only day-ahead market data while keeping annual market revenue within 9% of the perfect-foresight optimum.
The controller's guaranteed delivery bounds make it possible to quote a bankable HPA volume without either over-committing or stranding market upside.
The advantage over steady delivery grows when electricity prices are high and volatile, so the method is most valuable in the market regimes that are hardest to plan.
Because the HPA contract value is fixed, the same framework can separate scheduling skill from contract terms when evaluating project economics.

Reading between the lines

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

A natural extension is to re-derive the convex-hull bounds for other plant sizes, storage additions, or hybrid wind-solar sites; the paper only demonstrates the method on the six-year Danish and UK cases, so the transfer is plausible but unproven.
Because the hydrogen price series are synthetic, derived by scaling electricity prices and adding noise, part of the claimed performance may depend on the correlation between the two price series; an independent real hydrogen-price series would test that.
The same controller logic could be applied at shorter time scales, such as weekly or intraday targets, if the benchmark paths were recomputed at that resolution; the paper does not test this.
The worst-case year 2022 is inside the training hull because 2022 is a training year, so out-of-sample performance in a similarly extreme but structurally different year would be the stricter test.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this is a solid, clearly written application of established fuzzy logic and PSO to a real operational problem—setting daily hydrogen delivery targets under an HPA—and the central simulation claim is plausible within the stated model. What is genuinely new: no one in the cited sequential-planning line ([21]–[23]) uses a fuzzy controller or benchmark-derived convex-hull bounds for daily HPA targets, and the bounding idea is a reasonable safeguard against the controller drifting too fast or too slow. The authors also did the right thing by testing on out-of-sample years (2015, 2016, 2023) and a UK site, and the BFLC consistently beats a steady controller in their simulations. I give them credit for that design.

The soft spots are real but not fatal. First, Appendix A shows that the "day-ahead forecasts" are actually historical day-ahead electricity prices and bias-corrected reanalysis wind actuals, with no forecast error introduced anywhere. The dispatch also has no recourse or imbalance penalty if wind falls short. So the comparison is internally consistent—benchmark and BFLC both see perfect information—but the abstract's phrase "realistic revenue quantification" oversells it. The 92.8% floor could erode under realistic day-ahead errors, exactly as the stress-test note says. This is the load-bearing weakness.

Second, hydrogen prices are synthetic: scaled electricity prices with ±25% noise, clipped to 1–5 €/kg. That is fine for a method demonstration but limits the economic realism of the revenue numbers. Third, the convex-hull bounds are built from only six yearly benchmark trajectories, and the paper itself concedes unusual years could leave the hull; the out-of-sample results help, but the generalization is borrowed confidence. Fourth, 2017–2022 results partly evaluate a controller fitted to the benchmark, so the in-sample revenue ratios measure fit quality as much as control quality. No code or data are released, so independent reruns are impossible.

Who is this for? People working on operational hydrogen scheduling and HPA contract structures, not control theorists. The paper deserves a serious referee: the method is clearly explained, the comparison is coherent, and the flaws are addressable rather than structural. A good referee should ask for a forecast-error stress test, a clearer distinction between actuals and forecasts in the text, and ideally code/data release.

Referee Report

4 major / 6 minor

Summary. The paper proposes a Bounded Fuzzy Logic Control (BFLC) for scheduling hydrogen production under a long-term Hydrogen Purchase Agreement. The controller maps daily mean electricity price, hydrogen price, and wind capacity factor to a daily HPA delivery target; the target is capped by producibility and bounded by a convex hull of cumulative benchmark export paths, and is then imposed as a minimum production constraint in an hourly dispatch optimisation. The BFLC is trained with particle swarm optimisation against benchmark results obtained from a year-ahead perfect-foresight optimisation over 2017-2022, and revenue comparisons are reported for Denmark 2015-2023 and for a UK site. The central claim is that BFLC total revenue is within 9% of the perfect-foresight benchmark and consistently exceeds steady control, with the lowest normalised revenue of 92.8% in 2022.

Significance. If the claims held in realistic operation, the paper would make a useful practical contribution: an interpretable fuzzy controller running on daily information would capture most of the variable-market revenue available to a perfect-foresight scheduler while maintaining HPA deliverability. The use of out-of-sample years (2015, 2016, 2023) and a second country is a genuine strength, as is the explicit comparison against a steady controller and the use of established open-source tools (PyPSA, scikit-fuzzy). The main limitations are that the inputs are effectively perfect-information realisations rather than forecasts, the hydrogen price series is synthetic, and the in-sample years partly evaluate a controller fitted to the benchmark. These limitations do not invalidate the relative comparison, but they do mean the quantitative floor of 92.8% should be treated as a simulation result under idealised information rather than a realistic revenue guarantee.

major comments (4)

[Section V.A, Figure 3, Appendix A] The paper presents BFLC as using 'only 24 h of forecast inputs', but the implementation uses realised historical data: electricity prices are historical ENTSO-E day-ahead prices and wind capacity factors are bias-corrected reanalysis actuals (Appendix A). No forecast error is introduced anywhere, while the daily dispatch optimisation in Section V.A imposes the daily HPA target as a minimum production constraint and Section II prohibits grid imports. Under a realistic day-ahead wind forecast error, the electrolyser may be unable to meet the daily HPA target, and the model contains no imbalance settlement, storage recourse, or penalty mechanism. The benchmark in Section IV also uses perfect foresight, so the revenue comparison is internally consistent, but the abstract's claim that the BFLC enables 'realistic revenue quantification' is not supported by the simulation design; a sensitivity analysis with additive forecast error is needed before the 92.8% floor can be regarded as robust.
[Section V.B, Section VI, Figure 8] The membership functions and rule base are optimised by PSO to reproduce benchmark HPA supply over 2017-2022 (Section V.B), and Figure 8 reports the resulting in-sample BFLC revenues for the same years, including 2022, the year of the 92.8% floor. These in-sample results partly quantify fit quality rather than control performance. The out-of-sample years (2015, 2016, 2023) and the UK case in Appendix D provide genuine independent evidence and should be the primary support for the revenue claim, but the paper should state explicitly that the 92.8% floor occurs in a training year and should separate in-sample and out-of-sample results in the headline claims.
[Section V.C, Figure 6] The 'optimal space' is the convex hull of exactly six benchmark cumulative HPA-export trajectories (2017-2022; Figure 6). Whenever the cumulative export would leave this hull, the bounding logic overrides the trained fuzzy output, and Section V.C concedes that optimal paths for some unusual years may cross outside the hull. Since the 92.8% floor and the beats-steady-control claim depend on the hull containing the tested years, the paper should provide a concrete robustness test, such as leave-one-year-out construction of the hull, before generalising from six yearly paths.
[Appendix A] Revenues from the hydrogen market are computed with a synthetic price series generated by scaling electricity prices to a 3 EUR/kg mean, adding uniform +/-25% random variation, and capping to 1-5 EUR/kg (Appendix A). Because hydrogen sales are one of the two revenue streams being optimised, every quantitative revenue ratio in Section VI is conditional on this constructed series. The relative comparison between controllers remains informative because all controllers face the same prices, but the absolute claim of 'realistic revenue quantification' is not supported; the authors should either use a published hydrogen price series or report sensitivity of the 92.8% figure to the hydrogen price model.

minor comments (6)

[Section V.C] In the paragraph after Figure 6, 'convex full' should be 'convex hull'.
[Section II] The text contains the typo 'disptach optimisation'; it should read 'dispatch optimisation'.
[Nomenclature and Appendix B] The notation for the daily HPA target is inconsistent: Section II uses Mbar^d_2, Section V.A uses M^d_2, and Appendix B uses fM^d_2 and M^d_2; please unify the symbols and define the capped target before first use.
[Figure 2 caption] The caption lists the colour coding for the electrical-energy panel but not for the hydrogen panel; make the caption self-contained.
[Section III] The statement that 40% of mean maximum production is 'assumed' to be a suitable contract volume is not justified; a sensitivity analysis over this fraction would clarify how the 92.8% result depends on the contract volume.
[Reproducibility] No code or data availability statement is included; given that the model is built on PyPSA and Gurobi, a reproducibility statement or repository link would materially strengthen the paper.

Circularity Check

1 steps flagged · score 4.0 of 10

In-sample revenue floor (92.8% in 2022) partly reflects PSO fitting to the benchmark HPA schedule; out-of-sample and UK results provide independent support.

fitted input called prediction [Section V.B, optimisation step 7; Section VI, revenue analysis]
"Calculate the optimisation objective function as the sum of two components: the first is the sum of squared difference between the benchmark hydrogen supply to the HPA and the output (emd2) of the fuzzy logic controller. ... The normalised total revenues achieved with the BFLC are consistently higher than 92%; the lowest normalised total revenue is 92.8% achieved in 2022."

The PSO objective directly trains the BFLC to reproduce the benchmark HPA delivery schedule for 2017-2022, including 2022, which is then the year giving the lowest reported normalized revenue of 92.8%. Because the benchmark's total revenue is generated from that same yearly HPA schedule, an in-sample controller that is fitted to match that schedule is expected, by construction, to earn close to the benchmark revenue when the fitted daily target is imposed in the dispatch optimisation. Thus the headline in-sample revenue floor is partly a measure of training fit rather than an independent prediction.

full rationale

The paper's central derivation chain is mostly self-contained. The BFLC membership functions and rule base are fitted with PSO to the perfect-foresight benchmark HPA export series for 2017-2022, and the convex-hull bounds are derived from those same benchmark trajectories. Consequently, the in-sample revenue ratios, including the 92.8% minimum in 2022, partly quantify how well the fitted controller reproduces the benchmark schedule rather than testing an independent prediction. This is a genuine but limited circular step. The out-of-sample years (2015, 2016, 2023), explicitly marked in Figure 8, and the separate UK case study are not used in training, so the paper does provide independent evidence that the BFLC stays within 9% of the benchmark. No load-bearing self-citation chain or imported uniqueness theorem is present; references to the authors' prior work are background comparisons. The forecast-error realism issue (using historical day-ahead prices and bias-corrected reanalysis actuals without adding forecast error) is a validity limitation, not a circularity, and therefore does not by itself raise the circularity score.

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

The central result depends on 20 fitted membership parameters, a 27-rule base, a hand-chosen 40% contract volume, and synthetic hydrogen prices with +/-25% noise. The benchmark-derived convex hull is an additional ad hoc assumption about future optimal paths. No new physical entities are introduced.

free parameters (7)

Fuzzy membership parameters for wind capacity factor (p1-p5) = 0.22, 0.57, 0.60, 0.60, 0.87
Fitted by PSO in Section V.B to match benchmark HPA supply; they define the low, medium, and high fuzzy sets for wind input.
Fuzzy membership parameters for electricity price (p1-p5) = 118.85, 413.26, 417.15, 519.96, 569.89
Fitted by PSO in Section V.B to match benchmark HPA supply; they define the low, medium, and high fuzzy sets for electricity price input.
Fuzzy membership parameters for hydrogen price (p1-p5) = 1.65, 3.04, 3.24, 3.71, 4.36
Fitted by PSO in Section V.B to match benchmark HPA supply; they define the fuzzy sets for hydrogen price input.
Fuzzy membership parameters for HPA supply output (p1-p5) = 4.90, 4.90, 10.34, 11.52, 13.14
Fitted by PSO in Section V.B to match benchmark HPA supply; they define the fuzzy sets for the daily HPA delivery target.
Fuzzy rule base selection = 27 rules selected from 81 as shown in Table IV
Selected by highest cumulative activation against benchmark time series in Section V.B step 5; this is a discrete fitted structure.
HPA contract volume fraction = 40% of mean maximum production, 48 t
Hand-chosen in Section III as suitable for financial and risk mitigation; not optimized, but it affects all revenue levels and delivery paths.
Hydrogen price noise amplitude = +/-25%
Chosen in Appendix A to generate synthetic hydrogen prices from electricity prices; no real market data and no random seed are provided.

assumptions (5)

domain assumption The year-ahead perfect-foresight optimization provides the maximum achievable revenue benchmark.
Used to train the BFLC and as the comparison baseline in Sections IV and VI; it assumes full knowledge of the year, which is an upper bound by construction.
ad hoc to paper The convex hull of six benchmark cumulative HPA paths (2017-2022) bounds optimal paths in all evaluated years.
Section V.C states the hull 'is likely to encompass most optimal paths' with no independent justification; out-of-sample performance depends on this assumption.
domain assumption Day-ahead forecasts available to the BFLC are the realized daily mean prices and wind capacity factors, with no forecast error model.
Section V.A and Figure 3 describe sequential operation with 24 h forecasts, but Appendix A uses historical prices and reanalysis wind, so within-day forecasts are effectively perfect.
ad hoc to paper Synthetic hydrogen prices (scaled electricity prices plus random +/-25% variation, capped at 1-5 EUR/kg) represent hydrogen spot market dynamics.
Appendix A generates the only hydrogen price data used in training and evaluation; no real hydrogen market time series are used.
domain assumption Hydrogen production is wind-only with no grid electricity import and no hydrogen storage.
Section II deliberately excludes grid imports for regulatory compliance and assumes no storage; results may not generalize to systems with storage or grid-backed electrolysis.

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Cite this review

Pith. "Pith review of Bounded fuzzy logic control for optimal scheduling of green hydrogen production and revenue maximisation." pith.science (2026). https://pith.science/paper/VJEMXCCL

@misc{pith2026250801468,
  author       = {Pith},
  title        = {Pith review of: Bounded fuzzy logic control for optimal scheduling of green hydrogen production and revenue maximisation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VJEMXCCL}},
  note         = {Machine review of arXiv:2508.01468}
}

read the original abstract

Hydrogen Purchase Agreements (HPAs) guarantee revenue streams that mitigate the financial risks inherent in the long-term production of green hydrogen from renewable energy sources. However, the intermittency of renewable electricity and the availability of parallel revenue opportunities in both the electricity and hydrogen markets complicate the scheduling of green hydrogen production. The scheduling should maximise the total revenue from short-term sales of electricity and hydrogen against the long-term HPA delivery obligations. This challenge is addressed by developing a Bounded Fuzzy Logic Control (BFLC) which determines the daily HPA delivery target based on day-ahead forecasts of electricity and hydrogen prices, as well as wind capacity factors. Subsequently, the daily target is imposed as a constraint in dispatch optimisation which allocates energy and hydrogen flows for each hour of the day. Revenue comparisons over several years demonstrate that the BFLC achieves total annual revenues within 9% of optimal revenues that are based on perfect foresight. The BFLC revenues consistently exceed those of steady control, with the largest differences observed under conditions of elevated price levels and variability. The BFLC provides an effective long-term scheduling of green hydrogen production, enabling realistic revenue quantification that mitigates economic risks without overlooking economically viable projects.

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Beyond short-duration energy storage

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A green hydrogen economy for a renewable en- ergy society

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[3] [1]

, p5), thereby defining the fuzzy mem- bership functions for both the inputs and the out- put

The PSO algorithm initialises/updates the param- eters (p1, . . . , p5), thereby defining the fuzzy mem- bership functions for both the inputs and the out- put

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[4] [2]

The amount of hydrogen M d 2 is set as a minimum limit for the operation of the system on day d, and a typical dispatch optimisation determines the opti- mal electrical energy and hydrogen flows for every hour of day d. The dispatch optimisation is similar to that of the benchmark operation, except that this optimisation is performed daily with a constrai...

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[5] [3]

low”, “medium

as well as the hourly day-ahead forecast to determine the optimal flows of electricity and hydrogen that maximise revenue. This process is repeated daily. benchmark operation is performed for a whole year at once with the constraint of supplying M ∗ 2 to the HPA. The fuzzy logic control is implemented using the Python scikit-fuzzy library [33]. Each of th...

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[6] [4]

Calculate the fuzzy membership values for the in- puts and output based on the numerical inputs and the benchmark time series

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[7] [5]

Compute the activation degree for each rule for ev- ery entry in the time series, following the method described in [37]

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[8] [6]

Sum the activation degrees for each rule

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