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arxiv: 2504.18368 · v3 · submitted 2025-04-25 · 📡 eess.SY · cs.SY

Renewable-Colocated Green Hydrogen Production: Optimal Scheduling and Profitability

Siying Li , Lang Tong , Timothy Mount , Kanchan Upadhyay , Harris Eisenhardt , Pradip Kumar This is my paper

Pith reviewed 2026-05-22 17:40 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords green hydrogenrenewable colocated productionoptimal schedulingelectricity market participationprofit maximizationelectrolyzer sizingstochastic optimizationwholesale energy markets
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The pith

Renewable-colocated hydrogen producers can use closed-form policies to optimally split energy between hydrogen and grid sales while sizing assets for maximum profit.

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

The paper models a renewable-colocated hydrogen producer that can turn onsite wind or solar into either green hydrogen or electricity sold to the wholesale market. It derives closed-form optimal scheduling rules for deciding how much renewable output to send to the electrolyzer versus exporting to the grid, under both deterministic and stochastic price and generation conditions. These rules also yield analytical expressions for the resulting operating profit and for the best renewable and electrolyzer capacities. Real-time data from three U.S. system operators are used to test how market prices and environmental policies affect profitability. A reader cares because the results supply concrete, computable recipes for deciding when and how much to invest in colocated green-hydrogen facilities.

Core claim

Under deterministic and stochastic profit-maximization frameworks, closed-form optimal scheduling policies exist that dynamically allocate renewable energy between hydrogen production and electricity export; these policies permit analytical characterization of the RCHP's operating profit and of the optimal sizing of renewable and electrolyzer capacities.

What carries the argument

Closed-form optimal scheduling policies that decide the dynamic split of renewable generation between the electrolyzer and the wholesale electricity market.

If this is right

  • Optimal capacities for the renewable plant and the electrolyzer can be chosen analytically rather than by exhaustive numerical search.
  • Profitability is shown to respond directly to wholesale price levels and to environmental policy incentives such as carbon credits.
  • Multiple market-participation strategies can be compared within the same closed-form framework.

Where Pith is reading between the lines

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

  • Operators could embed these allocation rules in real-time control software to improve daily cash flow without needing heavy computation.
  • The same split-logic might be adapted to other co-located storage or conversion assets such as batteries or ammonia synthesis.
  • Adding constraints for hydrogen storage limits or grid interconnection capacity would be a natural next modeling step.

Load-bearing premise

The models for renewable generation patterns and electricity price dynamics used in the deterministic and stochastic cases are assumed to be accurate enough to represent real market conditions and operating limits.

What would settle it

Apply the derived closed-form policies to fresh real-time renewable output and price traces from any of the three system operators and check whether the realized profit and recommended capacities deviate systematically from the analytical predictions.

Figures

Figures reproduced from arXiv: 2504.18368 by Harris Eisenhardt, Kanchan Upadhyay, Lang Tong, Pradip Kumar, Siying Li, Timothy Mount.

Figure 1
Figure 1. Figure 1: Schematic of a flexible RCHP. unidirectional interface with the market either as a producer or a consumer, and M2 for the bi-direction interface. Specifically, the four RCHP market participation models are as follows: 1) Standalone Hydrogen Producer (M0): An RCHP under M0 produces hydrogen exclusively from colocated re￾newable. M0 is a benchmark for comparisons. 2) Renewable Producer (M1-p): A renewable en… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Optimal hydrogen production policy for flexible RCHP (M2). (b) Operating profit heatmap as the function of the electrolyzer and renewable nameplate capacities. 2) Short-run Profit and Optimal Nameplate Capacities: We analyze the profitability of the four RCHP models under the optimal hydrogen production policy, deriving closed-form expressions for expected operating profit as functions of re￾newable an… view at source ↗
Figure 3
Figure 3. Figure 3: Optimal production plans of RCHP under different models when QH < QR. See Sec. VII-B for the QH > QR case. the RCHP neither consumes from nor produces to the grid, and a renewable producer in R3 and R4. Under the general prosumer model M2, the RCHP operates as follows in the R1-R4 regions, as shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Annual operating profit in 2022 as a function of solar generation nameplate capacity (x-axis) and electrolyzer nameplate capacity (y-axis). Solid black: Break-even line. Green dashed: Optimal electrolyzer nameplate capacity as a function of solar generation nameplate capacity. (Top: hydrogen price of $1/kg; bottom: $4/kg.) C. Effects of Renewable and Electrolyzer Nameplate Capaci￾ties on RCHP profitability… view at source ↗
Figure 6
Figure 6. Figure 6: illustrates the annual operating profit of the RCHP under varying environmental subsidy factors, which propor￾tionally scale all environmental credit values, including REC prices. We compared the operating profit achieved under the prosumer model with that in the non-colocation configuration, where the electrolyzer and the renewable generator operated independently without co-optimization. When the subsidy… view at source ↗
Figure 5
Figure 5. Figure 5: Mean annual operating profit of the RCHP under varying hydrogen prices (2012-2022), with error bars indicating inter-annual variability. (Left: (45 MW, 20 MW) wind-colocated hydrogen producer; right: (45 MW, 20 MW) solar-colocated hydrogen producer.) The annual operating profit for the two types of renewable had similar characteristics. First, the prosumer model M2 yielded the highest operating profit, and… view at source ↗
Figure 7
Figure 7. Figure 7: Annual operating profit of the (45MW, 20MW) RCHP in different regions in 2022. In NYISO, the mean capacity factors were 0.229 for solar and 0.310 for wind, while in CAISO, they were 0.252 for solar and 0.287 for wind. MISO had a mean wind capacity factor of 0.423. The mean electricity prices were $0.055/kWh in NYISO, $0.073/kWh in CAISO, and $0.057/kWh in MISO [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Percentage allocations of colocated renewables across different models, regions, and resources. VI. CONCLUSION The main contribution of this work is the methodology de￾veloped to analyze RCHP’s operation and profitability, which is applicable to broader contexts, including integrated produc￾tion and energy use in manufacturing, scheduling and energy management in data centers, as well as hydrogen productio… view at source ↗
Figure 9
Figure 9. Figure 9: Optimal production plans for RCHP when QH < QR (including negative LMP cases) [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Optimal production plan for RCHP with a two-segment piecewise linear production function (prosumer model M2). Following the approach outlined in the proof of Theorem 1, the optimal solution for the RCHP’s real-time operation can be derived. Despite the increased complexity, a threshold￾based closed-form solution remains attainable, although it involves more thresholds than in the case of a linear producti… view at source ↗
Figure 10
Figure 10. Figure 10: Optimal production plans for RCHP when QH > QR (including negative LMP cases) [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Prediction errors of LMP, capacity factor, and expected operating profit. F. Empirical Example for Operating Profit Forecasting This example illustrates how Proposition 1 can be applied to estimate the RCHP’s expected operating profit. In practice, theoretical probabilities and expectations can be replaced with empirical counterparts derived from forecasted LMP and renewable trajectories. Since our focus … view at source ↗
read the original abstract

We study the optimal green hydrogen production and energy market participation of a renewable-colocated hydrogen producer (RCHP) that utilizes onsite renewable generation for both hydrogen production and grid services. Under deterministic and stochastic profit-maximization frameworks, we analyze RCHP's multiple market participation models and derive closed-form optimal scheduling policies that dynamically allocate renewable energy to hydrogen production and electricity export to the wholesale market. Analytical characterizations of the RCHP's operating profit and the optimal sizing of renewable and electrolyzer capacities are obtained. We use real-time renewable generation and electricity price data from three independent system operators to evaluate the impacts of market prices and environmental policies on RCHP's profitability.

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

0 major / 3 minor

Summary. The manuscript develops deterministic and stochastic profit-maximization frameworks for a renewable-colocated hydrogen producer (RCHP) that allocates onsite renewable generation between hydrogen production and wholesale electricity export. It derives closed-form optimal scheduling policies for dynamic allocation, provides analytical characterizations of operating profit and optimal renewable/electrolyzer capacity sizing, and evaluates profitability impacts using real-time generation and price data from three ISOs.

Significance. If the closed-form derivations hold under the stated frameworks, the work supplies analytical tools for optimizing colocated renewable-hydrogen systems and sizing decisions, which are relevant for decarbonization efforts. The use of real ISO data for empirical assessment of market prices and environmental policies is a clear strength, offering both theoretical insight and practical grounding beyond purely simulated scenarios.

minor comments (3)
  1. [Abstract] Abstract: The specific ISOs providing the real-time data are not named; adding this detail would aid reproducibility and allow readers to assess data representativeness.
  2. [§5] §5 (or equivalent results section): The profitability comparisons across policies would benefit from explicit discussion of how variability in the stochastic price and generation models propagates into the reported profit ranges.
  3. [Notation/§3] Notation: The distinction between deterministic and stochastic profit expressions could be clarified with a side-by-side summary table to reduce reader effort when comparing the two frameworks.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript, including recognition of the closed-form derivations, analytical characterizations, and empirical assessment using real ISO data. The recommendation for minor revision is noted, and we stand ready to incorporate any editorial suggestions. No specific major comments were enumerated in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper applies standard deterministic and stochastic profit-maximization frameworks to a renewable-colocated hydrogen producer, deriving closed-form optimal scheduling policies for energy allocation between hydrogen production and grid export. Analytical characterizations of operating profit and capacity sizing follow directly from the stated optimization models with explicit assumptions on renewable generation and price dynamics. Profitability impacts are evaluated against real-time data from three independent system operators, providing an external empirical benchmark. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain; the central claims are obtained by applying established optimization techniques to the described setup without circular equivalence to the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Insufficient detail in abstract to identify specific free parameters, axioms, or invented entities. Likely relies on standard assumptions from optimization and stochastic processes in energy markets.

pith-pipeline@v0.9.0 · 5646 in / 884 out tokens · 65154 ms · 2026-05-22T17:40:47.127139+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    eess.SY 2025-07 unverdicted novelty 6.0

    Optimal scheduling of deferrable demands with colocated stochastic supply and piecewise-linear pricing reduces to a finite set of three procrastination thresholds per demand class; a reinforcement learning algorithm l...

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    and excluding the term τRηtQR, which does not affect the operational decision, results in the following optimization. maxmize Pt=(P H t ,P IM t ) (π H + τ H − c W )(γP H t ) − (π LMP t + τ IM REC)P IM t subject to 0 ≤ P H t − P IM t ≤ ηtQR, 0 ≤ P H t ≤ QH, 0 ≤ P IM t ≤ QH. (16) This LP yields the optimal solution P1∗ t = [ P H∗ t , 0, P IM∗ t ] , subject ...

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    However, when QH > η tQR, we have V 1∗ t − V 2∗ t =(π LMP − π LMP t )QH + (π LMP t − π LMP )ηtQR =(π LMP − π LMP t )(QH − ηtQR) > 0

    and ( 19) yield the same solution: P∗ t = [ QH, 0, 0 ] . However, when QH > η tQR, we have V 1∗ t − V 2∗ t =(π LMP − π LMP t )QH + (π LMP t − π LMP )ηtQR =(π LMP − π LMP t )(QH − ηtQR) > 0. Thus, the optimal solution is P∗ t = [ QH, 0, Q H − ηtQR ] . If − τEX REC < π LMP t ≤ π LMP, then for the case QH ≤ ηtQR, V 1∗ t − V 2∗ t = − (π LMP t + τ EX REC)(ηtQR...

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    is expressed as P∗ t = [ QH, η tQR − QH, 0 ] . If π LMP t ≥ π LMP, then V 2∗ t =(π LMP t + τ EX REC)ηtQR =γ(π H + τ H − c W )ηtQR + (π LMP t − π LMP )ηtQR ≥ γ(π H + τ H − c W ) min{ηtQR, Q H} = V 1∗ t , (23) implying that P∗ t = [ 0, η tQR, 0 ] . Combining all these results, we derive the closed-form solution for the original optimization problem ( 5). Th...

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  46. [46]

    We have proved that ∂J OP n (QR, Q H)/∂Q H decreases as QH (or κ) increases

    together with the budget constraint, as described in ( 14). We have proved that ∂J OP n (QR, Q H)/∂Q H decreases as QH (or κ) increases. Similarly, we fix the electrolyzer capacity and consider two renewable capacity values: ˜QR = QH/ ˜κ and ˜Q′ R = QH/ (˜κ + δ) for a small δ > 0. ∂J OP n ∂Q R ( ˜Q′ R, Q H) − ∂J OP n ∂Q R ( ˜QR, Q H) = n∑ t=1 ( ∫ π LMP 0 ∫...

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  47. [47]

    For each capacity pair (QR, Q H) that satisfies the budget constraint, there corresponds a unique capacity ratio κ

    is a monotonically decreasing function of κ. For each capacity pair (QR, Q H) that satisfies the budget constraint, there corresponds a unique capacity ratio κ. This monotonicity implies that searching for the nameplate capacity values along the budget constraint prov ides an efficient approach for guiding the RCHP to the optimal nameplate capacity pair, if...

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  48. [48]

    These empirical values were then substituted into ( 12) to compute the expected operating profit for 2022. Fig. 12 shows the monthly prediction errors for this exam- ple, indicating that the accuracy of operating profit foreca sts is comparable to that of renewable generation forecasts. G. Additional Numerical Results Table V and Table VI present the detail...

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