Fuel-cell twin

Fuel-cell innovation · Digital Twin Lab

From measurementsto better experiments

An open digital twin for PEM and solid-oxide fuel cells. It compares frozen predictions with measured data, quantifies what it still cannot tell apart, and plans the next test to separate the alternatives. Every result carries its evidence status.

Open the twin workbench See the evidence
Fuel-cell digital twin: a test rig turning into its digital model, surrounded by the loop Measure, Model the physics, Quantify uncertainty, Plan the next test, followed by independent validation: freeze model and predictions, test unseen cells or batches, assess agreed acceptance limits.
Concept illustration. The rig shown is illustrative, not a specific hardware set-up.

How the twin works

A closed loop, not a curve fit

The twin is built to earn trust step by step. Predictions are frozen before data is opened, residuals are kept even when they are unflattering, and the next experiment is chosen for the information it buys.

The twin loop with current figures: Measure, 12,184 PEM samples and a 33-point SOFC impedance record; Model the physics, 36 of 36 balances close and 4 of 4 convergence checks pass; Quantify uncertainty, fixture inductance 0.578 µH; Plan the next test, 3 tests in 78 minutes, proposed.
Figures come from the frozen outputs listed under Evidence. Diagram made with DesignCraft.

Evidence

What has been shown, and what has not

Each card reads straight from a frozen output in the repository. Numerical checks show the code solves its own equations. They do not show the physics is right. Measured comparisons are reported even when the model loses.

Numerically verifiedMeasured gapOpen questionBlocked / withheldProposed
Compare PEM and SOFC for aviation →See the system in 3D →

PEM · proton-exchange membrane

Benefits

  • Starts in under a minute and follows load, including transients [nasa]
  • About twice the power per cm² of the SOFC case here: 0.66 against 0.24 W/cm² [twin]
  • Published flight roadmap: FlyZero 2.0–2.5 kW/kg stack + BoP by 2030 [flyzero]
  • Flown in commuter demonstrators; FlyZero TRL 6 by 2026 [flyzero] [review]

Assumptions in this twin

  • Frozen anchor model at 75 °C, 2.51 bar, RH 0.6, cathode stoichiometry 2
  • Sized at 1.0 A/cm² (0.656 V, 52 % LHV)
  • Mass from FlyZero targets for the step year, not from the twin
  • Measured gap: the model loses to a fixed 0.7 V baseline (120.6 vs 34.2 mV error)

SOFC · solid oxide

Benefits

  • Higher efficiency: 64 % against 52 % (LHV), so 18 % less hydrogen for the same power [twin]
  • Less heat to reject, and at 600–1,000 °C it is high-grade: usable by a turbine or heat exchanger [twin] [review]
  • Fuel flexible and tolerant of CO and other contaminants [nasa] [review]
  • Steady duty suits APU, ground power and turbine-hybrid roles [nasa] [review]

Assumptions in this twin

  • Frozen v1 tubular cell at 800 °C, 3 % steam, 50 mL/min fuel (a single rig cell)
  • Sized at 0.8 V (0.303 A/cm²); below about 0.6 V the rig cell runs short of fuel
  • No mass model and no flight target: published figures span 0.51 kW/kg (cell) to a claimed 2.5
  • Start-up (tens of minutes to hours), thermal cycling and altitude not modelled; acceptance gate blocked
Numerically verified

PEM balances close

36 of 36 casescharge, reaction energy, electrical and coolant balances

Maximum residuals: charge 1.4e-17 mol/s, storage 8.3e-10 J. Water, gas inventory and whole-system energy are not implemented, so no full-system conservation pass is claimed.

Source: output/verification/conservation.json

Numerically verified

Time-step convergence

4 of 4 step caseswithin 1 mV/cell and 0.01 K at the finest step

Production Euler integrator against an independently transcribed reference (DOP853) for load, humidity, pressure and coolant steps. A numerical budget, not an experimental acceptance limit.

Source: output/verification/convergence.json

Measured gap

Measured PEM challenge: the model loses

120.6 mV vs 34.2 mVmodel RMSE vs a fixed 0.7 V guess, 12,184 samples

Mean residual +92 mV; 0 parameters updated; data previously inspected, so this is a diagnostic, not a blind test. Temperature and humidity are proxies; membrane water is assumed.

Source: output/real/challenge.json

Open question

Two parameter aliases remain

2 aliasesfit the same low-load data within 3 mV

Different concentration-loss and limiting-current pairs reproduce the same low-load voltages. The planner was challenged to separate them; until measured, the twin reports both.

Source: output/verification/identifiability.json

Numerically verified

SOFC conservation and solver checks

8 of 8 checkselement, energy, mesh and cross-solver

Largest energy residual 4.2e-08 J. Mesh study covers the 8/16/32-node baseline only, not domain-wide convergence.

Source: output/sofc-v1/verification.json

Open question

SOFC ohmic resistance vs published

-67% to -58%model vs reported cell resistance

Not a like-for-like comparison: the published value is an open-circuit impedance series resistance that includes electrode losses. Marked not comparable; no parameters were fitted.

Source: output/sofc-v1/public-benchmark.json

Blocked / withheld

Holdout validation gate

Withheld8 reasons, validated = false

The gate stays shut until the hold-out is blind, the hardware is independent, lineage is verified and sensor uncertainty is known.

Source: output/audit/holdout-gate.json

Blocked / withheld

SOFC acceptance gate

Blockedcandidate frozen development not validated

Native processing and units unresolved; No independent fixture calibration; No characterized electrode dynamics or hardware covariance; No approved quantitative hardware-specific acceptance limits or unseen cell/batch custody.

Source: output/sofc-observation-v3/candidate.json

Independent validation · next stage

What it takes to call it validated

  1. Freeze model and predictionsPhysics, adapters, coefficients, covariance and predictions locked and hashed before any new data is opened.
  2. Test unseen cells or batchesWhole cells or batches held by an independent custodian, never rows split from development runs.
  3. Assess agreed acceptance limitsVoltage, transient, settling, temperature-gradient, fuel-utilisation and thermal-cycle limits declared in advance.
Proposed

Next test batch, chosen by information

3 tests · 78 min0.12 kg H₂; best 1.06 nats expected information

Ranked 32 candidate conditions on a 10-cell, 280 cm² stack by expected information gain per rig minute. Status: proposed, not executed.

Source: output/audit/matched-bayesian-plan.json

Why the holdout gate is currently withheld (8 reasons)
  • Development model not ready
  • Acceptance protocol not frozen
  • Measurement audit open
  • Holdout not blind
  • Hardware not independent
  • Lineage not verified
  • Missing or overlapping raw data
  • Sensor uncertainty unverified

Tools

Work with the twin

Twin workbenchReplay scenarios, assurance gates, identifiability, the component model, provenance and the measured challenge. Nyquist Bench · SOFC impedanceOpen the frozen SOFC record in the browser impedance workbench: Nyquist, Bode, circuit fits and a K-K check. Evidence fileEvery figure on this page with its source path and SHA-256, as JSON. Battery twinThe sister Open Pack Designer, built on the same evidence rules.

Data and licences

Where the measurements come from

SourceUsed forLicenceStatus
Schneider et al. 2024, PEM characterisation, 12 cm² cellsDevelopment data: limiting current, EIS, HFR, double-layer capacitanceCC BY 4.0Development only
RealHyFC / Fensterle; BiselloMeasured steady-state challengeCC BY 4.0Inspected, not blind
Nowicki, Wang & Irvine, St Andrews tubular SOFCSOFC impedance record and historyCC BYDevelopment only
Cornet / LEPMINot usedEtalab 2.0Quarantined

This is an independent implementation inspired by published ARCHEE work. It is not code from the University of Bath or ZeroAvia, and it does not describe their hardware. Full attributions are in THIRD_PARTY_DATA.md in the repository.