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arxiv: 2604.06593 · v1 · submitted 2026-04-08 · 🧮 math.OC · cs.SY· eess.SY

Hot Standby in Ammonia Synthesis Reshapes Market Equilibrium in Renewable P2A Systems: A Potential Game Approach

Yangjun Zeng (1) , Yiwei Qiu (1) , Xiaocong Sun (2) , Jie Zhu (1) , Jiarong Li (3) , Shi Chen (1) , Buxiang Zhou (1) , Kaigui Xie (1) ((1) College of Electrical Engineering
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Sichuan University (2) National Power Dispatching Control Center State Grid Corporation of China (3) Harvard John A. Paulson School of Engineering Applied Sciences Harvard University)
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Pith reviewed 2026-05-10 18:27 UTC · model grok-4.3

classification 🧮 math.OC cs.SYeess.SY
keywords hot standbyammonia synthesispotential gamemarket equilibriumpower-to-ammoniarenewable energy integrationNash equilibriumbest response dynamics
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The pith

Hot standby in ammonia synthesis enables renewable power-to-ammonia producers to increase profits by 20 percent and reach a better market equilibrium.

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

Renewable power-to-ammonia systems couple electricity generation, hydrogen electrolysis, and ammonia production, but limited flexibility puts the ammonia unit at a disadvantage in competitive markets. The paper introduces hot standby operation for the ammonia reactor, which keeps it ready to ramp up without continuous full production and adds discrete on/off decisions. These interactions are cast as a potential game whose best-response dynamics converge to an approximate equilibrium. Case studies reveal that hot standby cuts the ammonia producer's hydrogen purchases from the market and raises its profit by 20.14 percent. This adjustment also moves the overall market outcome to one that benefits all participants more than the original equilibrium.

Core claim

The introduction of hot standby capability in ammonia synthesis reactors relaxes the operational constraints on renewable ammonia producers within the coupled electricity and hydrogen markets. The resulting game is shown to be a potential game, allowing an iterative best-response algorithm to compute an ε-approximate Nash equilibrium despite the presence of integer variables. In numerical case studies, this flexibility reduces the ammonia unit's dependence on external hydrogen supply and boosts its profit by 20.14 percent while producing a more mutually advantageous equilibrium for the entire system.

What carries the argument

Potential game model of the power-to-ammonia market incorporating integer variables for hot standby states of the ammonia reactor, with convergence guaranteed by best-response dynamics to an ε-approximate equilibrium.

If this is right

  • The ammonia producer reduces its purchases of hydrogen from external sources.
  • The ammonia producer's profit increases by 20.14 percent.
  • The market equilibrium shifts to an outcome that is more beneficial for all market participants.
  • Overall coordination between renewable generation, hydrogen production, and ammonia synthesis improves.

Where Pith is reading between the lines

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

  • The same potential-game approach could be used to analyze flexibility options in other power-to-X technologies such as power-to-methanol.
  • Market operators might design incentives to promote hot standby adoption in ammonia plants to enhance system stability.
  • The convergence result suggests that decentralized bidding algorithms could be implemented in real electricity and hydrogen markets.
  • Incorporating stochastic renewable generation into the model would allow testing how hot standby performs under uncertainty.

Load-bearing premise

The interactions among renewable generators, hydrogen producers, and ammonia synthesizers form a potential game whose best-response dynamics still converge to an approximate equilibrium when integer hot-standby decisions are included.

What would settle it

Deployment of hot standby in actual renewable ammonia facilities that fails to produce the modeled profit increase or prevents convergence of bidding dynamics to equilibrium would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.06593 by (2) National Power Dispatching, (3) Harvard John A. Paulson School of Engineering, Applied Sciences, Buxiang Zhou (1), Control Center, Harvard University), Jiarong Li (3), Jie Zhu (1), Kaigui Xie (1) ((1) College of Electrical Engineering, Shi Chen (1), Sichuan University, State Grid Corporation of China, Xiaocong Sun (2), Yangjun Zeng (1), Yiwei Qiu (1).

Figure 1
Figure 1. Figure 1: Schematic a typical multistakeholder ReP2A system. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scenarios of wind and solar power generation, and ammonia price. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Integrating renewable generation, hydrogen production, and renewable ammonia (RA) synthesis into power-to-ammonia (P2A) systems creates interactions across electricity and hydrogen markets. Limited operational flexibility, however, places RA at a disadvantage at the Nash equilibrium (NE). Recent advances in ammonia synthesis reactor design enable hot standby (HSB) operation, improving flexibility but introducing integer decision variables that complicate market equilibrium analysis. To address this challenge, we develop a potential game model and derive a convergent {\epsilon}-approximate equilibrium via an iterative best-response approach. Case studies show that HSB reduces RA's reliance on hydrogen purchases and increases its profit by 20.14%. More importantly, HSB shifts the market equilibrium toward a more mutually beneficial outcome.

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

2 major / 2 minor

Summary. The manuscript develops a potential game framework to model interactions among renewable generation, hydrogen production, and renewable ammonia (RA) synthesis in power-to-ammonia (P2A) systems. Hot standby (HSB) operation is introduced to improve reactor flexibility, adding binary decision variables. An iterative best-response algorithm is used to compute an ε-approximate Nash equilibrium, with case studies claiming that HSB reduces RA's hydrogen purchases and raises its profit by 20.14% while shifting the equilibrium to a mutually beneficial outcome.

Significance. If the potential-game property holds and best-response dynamics converge despite the mixed-integer HSB decisions, the framework could provide a useful tool for equilibrium analysis in integrated renewable energy markets with discrete operational modes. The reported profit gain and equilibrium shift indicate practical value for P2A system design, but the absence of explicit verification for the game-theoretic assumptions limits the strength of these conclusions.

major comments (2)
  1. [Model and Algorithm Sections] The assertion that the multi-player game with integer HSB decisions forms a potential game is not supported by an explicit potential function or a proof that payoff differences equal potential differences for unilateral deviations involving the binary HSB variables. This is load-bearing for the claim that iterative best-response converges to an ε-approximate equilibrium (see the model development and algorithmic approach sections).
  2. [Case Studies Section] The case-study result of a 20.14% RA profit increase and the associated equilibrium shift lack error bars, sensitivity checks on key parameters, or details on data sources, undermining the robustness of the quantitative claims about HSB benefits.
minor comments (2)
  1. [Abstract] The abstract states specific numerical outcomes without cross-references to the relevant tables or figures in the main text.
  2. [Notation and Formulation] Notation for the binary HSB variables should be more clearly distinguished from continuous decision variables to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our potential game framework for P2A systems with hot standby operation. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: The assertion that the multi-player game with integer HSB decisions forms a potential game is not supported by an explicit potential function or a proof that payoff differences equal potential differences for unilateral deviations involving the binary HSB variables. This is load-bearing for the claim that iterative best-response converges to an ε-approximate equilibrium (see the model development and algorithmic approach sections).

    Authors: We acknowledge that an explicit potential function and the corresponding proof for binary deviations were not detailed in the original submission. In the revised manuscript, we will add a new subsection in the model development section that constructs the potential function Φ explicitly as the sum of all players' quadratic utility terms minus the cross-market interaction penalties in the hydrogen market. We then prove that for any unilateral deviation by player i (including flipping the binary HSB variable b_i ∈ {0,1}), the change in i's payoff exactly equals the change in Φ, satisfying the potential game definition even with the mixed-integer decisions. This directly supports the convergence guarantee of the iterative best-response algorithm to an ε-approximate Nash equilibrium. revision: yes

  2. Referee: The case-study result of a 20.14% RA profit increase and the associated equilibrium shift lack error bars, sensitivity checks on key parameters, or details on data sources, undermining the robustness of the quantitative claims about HSB benefits.

    Authors: We agree that the quantitative claims require additional robustness verification. In the revised case studies section, we will add: (i) error bars computed from 100 Monte Carlo runs using stochastic renewable generation profiles; (ii) sensitivity tables varying electricity prices (±20%), hydrogen purchase costs, and ammonia demand levels, confirming the profit gain remains between 18-23% and the equilibrium shift persists; (iii) explicit data source citations, including NREL 2023 renewable profiles and IRENA cost parameters. These additions will substantiate the reported 20.14% profit increase and mutual-benefit equilibrium shift. revision: yes

Circularity Check

0 steps flagged

No significant circularity in claimed derivation

full rationale

The paper models P2A market interactions as a potential game and computes an ε-approximate equilibrium via iterative best-response dynamics. This is an explicit modeling choice and standard algorithmic procedure rather than a reduction of outputs to inputs by construction. No equations or claims in the abstract equate a derived equilibrium or profit gain to a fitted parameter or self-referential definition; the 20.14% profit figure and equilibrium shift are presented as simulation outcomes under the stated model. The derivation chain remains self-contained and does not rely on load-bearing self-citations or smuggled ansatzes for its central results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the multi-market interactions constitute a potential game and that the iterative best-response procedure converges to an ε-equilibrium even after introducing integer hot-standby variables. No free parameters or new entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption The electricity, hydrogen, and ammonia markets interact in a way that admits a potential function whose minimization yields Nash equilibrium.
    Invoked to justify the use of best-response dynamics and the existence of an ε-approximate equilibrium.
  • domain assumption Hot-standby operation can be represented by integer decision variables without destroying the potential-game structure.
    Required for the model to remain tractable after adding flexibility.

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Works this paper leans on

11 extracted references · 11 canonical work pages · 1 internal anchor

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