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arxiv: 2501.14576 · v2 · submitted 2025-01-24 · 🧮 math.OC · cs.SY· eess.SY

Dynamic Modeling and Control of Multi-Stack Alkaline Water Electrolysis Systems with Shared Gas Separators and Lye Circulation: An Experiment-Based Study

Yiwei Qiu (1) , Jiatong Li (1) , Yangjun Zeng (1) , Yi Zhou (1) , Shi Chen (1) , Xiaoyan Qiu (1) , Buxiang Zhou (1) , Ge He
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(2) Xu ji Wenying Li (3) ((1) College of Electrical Engineering Sichuan University (2) School of Chemical Engineering (3) Sichuan Tsinghua Energy Internet Research Institute)
This is my paper

Pith reviewed 2026-05-23 04:47 UTC · model grok-4.3

classification 🧮 math.OC cs.SYeess.SY
keywords alkaline water electrolysismulti-stack systemdynamic modelingnonlinear model predictive controlrenewable hydrogenlye circulationgas separationwind power integration
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The pith

A shared 4-in-1 alkaline electrolyzer matches four separate 1-in-1 units within 0.015 MW load error under wind power.

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

The paper constructs a state-space model that describes how multiple electrolysis stacks interact through shared gas separators and lye circulation loops. Experiments on a 4000 Nm³/h 4-in-1 rig supply the data to fit the model's parameters for temperature, gas crossover, and flow dynamics. A nonlinear model predictive controller then uses the model to set stack currents, lye pump speeds, and cooling rates. When the validated model is run with wind-power inputs, the shared configuration produces tracking, temperature, and energy-consumption results nearly identical to four independent single-stack plants. The closeness of these outcomes matters for deciding whether hardware sharing can cut capital cost without sacrificing response to variable renewable supply.

Core claim

A state-space model of lye circulation, temperature, and hydrogen-to-oxygen dynamics, calibrated on experimental data from a 4-in-1 system, combined with a nonlinear model predictive controller that coordinates inter-stack currents and shared flows, yields load-tracking errors, temperature stabilization, and specific energy consumption that differ from four parallel 1-in-1 systems by at most 0.015 MW, 0.346 K, and 0.001 kWh/Nm³ under wind-power supply.

What carries the argument

The state-space model of shared lye circulation, temperature, and HTO dynamics that supplies the prediction model for the nonlinear MPC coordinating stack currents and common flows.

If this is right

  • The shared system can follow wind-power fluctuations with essentially the same accuracy as independent stacks.
  • Temperature control remains within 0.346 K of the separate-stack case without extra cooling hardware.
  • Specific energy consumption stays within 0.001 kWh/Nm³, preserving the efficiency advantage of the multi-stack layout.
  • The NMPC successfully balances load among stacks while respecting shared-separator and circulation constraints.
  • The approach supports direct scaling to larger N-in-1 plants for renewable-hydrogen installations.

Where Pith is reading between the lines

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

  • If the small performance gaps persist at industrial scale, shared-separator designs could materially lower the levelized cost of hydrogen.
  • The same modeling structure might be reused to compare hybrid plants that mix shared and dedicated stacks within one site.
  • Extending the calibration experiments to different stack counts or operating temperatures would test whether the similarity result generalizes.
  • Real-time deployment would require confirming that the shared-loop sensors remain accurate enough for the NMPC to keep the reported error bounds.

Load-bearing premise

The model fitted to one physical 4-in-1 rig still correctly describes all cross-stack interactions when the same equations are used to simulate both the shared and the fully separated configurations.

What would settle it

Side-by-side operation of an actual 4-in-1 plant and four separate 1-in-1 plants under identical wind-power traces, checking whether any of the three performance gaps exceeds the stated simulation bounds.

Figures

Figures reproduced from arXiv: 2501.14576 by ((1) College of Electrical Engineering, (2), (2) School of Chemical Engineering, (3) Sichuan Tsinghua Energy Internet Research Institute), Buxiang Zhou (1), Ge He, Jiatong Li (1), Shi Chen (1), Sichuan University, Wenying Li (3), Xiaoyan Qiu (1), Xu ji, Yangjun Zeng (1), Yiwei Qiu (1), Yi Zhou (1).

Figure 1
Figure 1. Figure 1: (a) Photo of 4-in-1 AWE systems in installation. (b) Schematic diagram of a typical 4-in-1 AWE system. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Topologies for inter-stack lye flow distribution. (a) 4 lye circulation pumps. (b) 2 lye circulation pumps. (c) 1 lye [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Interrelationships between state variables, control, and responses in the [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Polyhedral approximation of the production function of a 1,000 Nm [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Open-loop responses of the 4-in-1 AWE system. (a) Electrolytic currents of the stacks. (c) Lye flow rates of the [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Control and responses of the 4-in-1 AWE system with a 4-pump configuration. (a) Load power reference and overall [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Control and responses of the 4-in-1 AWE system with a 2-pump configuration shown in Fig. 2(b). (a) Load power [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Control and responses of the 4-in-1 AWE system with a 1-pump configuration shown in Fig. 2(c). (a) Load power [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison on control and responses of the 4-in-1 AWE system with 1-pump, 2-pump, and 4-pump configurations. [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Control and responses of four traditional 1-in-1 AWE systems operating in parallel. (a) Load power reference and [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison on control and responses between the 4-in-1 AWE system with a 4-pump configuration and four [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: reference signals based on a wind farm by the Risøe [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: performance metrics of the 4-in-1 AWE systems with different lye circulation topologies and four 1-in-1 systems [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
read the original abstract

An emerging approach for large-scale renewable hydrogen production is integrating multiple alkaline water electrolysis (AWE) stacks into one balance-of-plant (BoP) system, sharing gas-lye separation and lye circulation components. While this configuration, termed $N$-in-1, reduces cost and complexity, its dynamic performance under fluctuating power remains unclear compared with conventional 1-in-1 systems. This paper develops a state-space model of the multi-stack AWE system, capturing lye circulation, temperature, and hydrogen-to-oxygen (HTO) dynamics, calibrated via experiments on a 4,000 Nm$^3$/h-rated 4-in-1 system. A nonlinear model predictive controller (NMPC) is then designed to coordinate inter-stack current distribution, lye flow, and cooling for load tracking and operational stability. Simulations on the experimental-validated model show that a $4$-in-1 system can achieve very similar performance compared to four parallel 1-in-1 systems. Differences in load-tracking error, temperature stabilization, and specific energy consumption remain below 0.015 MW, 0.346 K, and 0.001 kWh/Nm$^3$ under wind power supply.

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

1 major / 2 minor

Summary. The paper develops a state-space model capturing lye circulation, temperature, and HTO dynamics for an N-in-1 alkaline water electrolysis system, calibrated on experimental step-response and steady-state data from a 4000 Nm³/h 4-in-1 rig. It designs an NMPC to coordinate currents, lye flow, and cooling, then uses forward simulations of the tuned model to compare a single 4-in-1 configuration against four independent 1-in-1 systems under wind power, reporting that differences in load-tracking error, temperature stabilization, and specific energy consumption remain below 0.015 MW, 0.346 K, and 0.001 kWh/Nm³.

Significance. If the central comparison is reliable, the work provides evidence that shared balance-of-plant designs can deliver near-equivalent dynamic performance to conventional parallel systems while reducing capital cost and complexity. The experimental calibration on a full-scale rig supplies concrete grounding that is uncommon in this domain; the NMPC formulation for multi-stack coordination is a practical control contribution.

major comments (1)
  1. [Modeling and simulation sections (model identification and comparative simulations)] The state-space model parameters are identified exclusively from data collected on the physical 4-in-1 rig (shared separators and common lye loop). When the same equations are instantiated four times with independent boundary conditions to represent four 1-in-1 plants, any coupling terms or effective parameters fitted to the shared-flow regime (e.g., lye-flow distribution factors, thermal time constants influenced by common piping) are left unchanged. No separate validation or sensitivity analysis is provided to confirm that these parameters remain valid for the decoupled topology; consequently the headline performance deltas are generated by an unverified model transfer.
minor comments (2)
  1. [Abstract] The abstract states the performance bounds but supplies no detail on validation metrics (e.g., R², cross-validation splits, or residual statistics) for the calibrated model.
  2. [Modeling section] Notation for the state-space matrices and the precise definition of the 1-in-1 boundary conditions should be clarified to allow readers to reproduce the decoupled instantiation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. Below we provide a point-by-point response to the major comment.

read point-by-point responses

  1. Referee: [Modeling and simulation sections (model identification and comparative simulations)] The state-space model parameters are identified exclusively from data collected on the physical 4-in-1 rig (shared separators and common lye loop). When the same equations are instantiated four times with independent boundary conditions to represent four 1-in-1 plants, any coupling terms or effective parameters fitted to the shared-flow regime (e.g., lye-flow distribution factors, thermal time constants influenced by common piping) are left unchanged. No separate validation or sensitivity analysis is provided to confirm that these parameters remain valid for the decoupled topology; consequently the headline performance deltas are generated by an unverified model transfer.

    Authors: The underlying state-space model is derived from first-principles equations governing mass balances, energy balances, and species transport, which are topology-agnostic. For the 1-in-1 configuration, we instantiate the model with independent boundary conditions and disable the shared-flow coupling terms (e.g., by setting lye distribution factors to independent values and removing common piping effects). The fitted parameters primarily capture stack-level phenomena such as electrochemical kinetics and individual thermal capacities, which should remain consistent across configurations. We recognize that a dedicated sensitivity analysis would further substantiate the transferability. Accordingly, the revised manuscript will include a sensitivity analysis on the key parameters (thermal time constants and flow distribution) to verify that the reported performance differences are insensitive to reasonable variations in these values. revision: partial

Circularity Check

0 steps flagged

No significant circularity; simulations are forward runs of an experimentally calibrated model.

full rationale

The paper identifies a state-space model from step-response and steady-state experiments on the physical 4-in-1 rig, then performs forward simulation of both the 4-in-1 and four independent 1-in-1 topologies under the same equations. The reported performance deltas are simulation outputs, not algebraic reductions of fitted parameters or self-citations. No load-bearing step equates a claimed result to its own inputs by construction, and the central comparison rests on the model's predictive use rather than tautological renaming or fitted-input prediction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities beyond the implicit assumption that the calibrated state-space model generalizes across configurations.

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Reference graph

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