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Reduced PEM fuel-cell stack

Prescribed gas/temperature Nernst potential with activation, ohmic and limiting-current losses plus an identified polarization lag. No humidity, gas-flow or thermal network states.

Implementation ID
battery-pem-stack
Reviewed
2026-10-27

Behavior

Computes a reduced PEM stack polarization from prescribed hydrogen/oxygen pressures and temperature. Nernst potential, activation, ohmic and limiting-current losses determine cell voltage. An identified first-order polarization lag adds dynamics. Faraday balance gives reactant consumption.

Interface

Reduced PEM fuel-cell stack interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Reduced PEM fuel-cell stackStudio blockcurrenttemperaturehydrogenPressureoxygenPressurevoltagepowerheathydrogenoxygenreversiblepolarizationactivationTargetconcentration
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
currentinputAStack current; scalar.
temperatureinputKCell temperature; scalar.
hydrogenPressureinputPaHydrogen partial pressure; scalar.
oxygenPressureinputPaOxygen partial pressure; scalar.
voltageoutputVStack voltage; scalar.
poweroutputWElectrical output power; scalar.
heatoutputWThermoneutral power difference; scalar.
hydrogenoutput1Hydrogen consumption (mol/s); scalar.
oxygenoutput1Oxygen consumption (mol/s); scalar.
reversibleoutputVPer-cell reversible voltage; scalar.
polarizationoutputVPer-cell polarization state; scalar.
activationTargetoutputVSteady activation loss; scalar.
concentrationoutputVConcentration loss; scalar.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
ParameterUnitDefaultMeaning and limits
Number of series cells
seriesCells		15Number of series cells. This is an editable model input; the default belongs to the synthetic worked example.
Reference reversible cell voltage (V)
reversibleV		V1.229Reference reversible cell voltage (V). This is an editable model input; the default belongs to the synthetic worked example.
Reversible-voltage temperature slope (V/K)
temperatureSlopeVPerK		V/K-0.00085Reversible-voltage temperature slope (V/K). This is an editable model input; the default belongs to the synthetic worked example.
Reference temperature (K)
referenceTemperatureK		K298.15Reference temperature (K). This is an editable model input; the default belongs to the synthetic worked example.
Reference pressure (Pa)
referencePressurePa		Pa100000Reference pressure (Pa). This is an editable model input; the default belongs to the synthetic worked example.
Liquid-water activity
waterActivity		11Liquid-water activity. This is an editable model input; the default belongs to the synthetic worked example.
Per-cell ohmic resistance (Ω)
resistanceOhm		Ω0.01Per-cell ohmic resistance (Ω). This is an editable model input; the default belongs to the synthetic worked example.
Effective exchange current (A)
exchangeCurrentA		A1Effective exchange current (A). This is an editable model input; the default belongs to the synthetic worked example.
Limiting current (A)
limitingCurrentA		A20Limiting current (A). This is an editable model input; the default belongs to the synthetic worked example.
Effective transfer coefficient
transferCoefficient		10.5Effective transfer coefficient. This is an editable model input; the default belongs to the synthetic worked example.
Polarization time constant (s)
timeConstantS		s1Polarization time constant (s). This is an editable model input; the default belongs to the synthetic worked example.
Initial polarization loss (V)
initialPolarizationV		V0Initial polarization loss (V). This is an editable model input; the default belongs to the synthetic worked example.
Thermoneutral cell voltage (V)
thermoneutralV		V1.48Thermoneutral cell voltage (V). This is an editable model input; the default belongs to the synthetic worked example.

Equations and rules

  • Vstack = cells * (E_Nernst - eta_activation - I*R - eta_concentration)
  • tau*deta_activation/dt = eta_steady - eta_activation
  • hydrogen mol/s = cells*I/(2*F)
  • oxygen mol/s = cells*I/(4*F)

Worked example

Reduced PEM fuel-cell stack worked example

Use the defaults below with Stack current = 2 A, Cell temperature = 298.15 K, Hydrogen partial pressure = 100000 Pa, Oxygen partial pressure = 100000 Pa. At 0 s, Stack voltage is 6.038232542 V. Additional checks are listed below.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Stack voltage
voltage		06.03823254153795V1e-08
Hydrogen consumption (mol/s)
hydrogen		05.1821348283088646e-0511e-08
Oxygen consumption (mol/s)
oxygen		02.5910674141544323e-0511e-08
Stack voltage
voltage		105.811795216042423V1e-06

Explore the recorded outputs

Reduced PEM fuel-cell stack recorded example

Reduced PEM fuel-cell stack / Stack voltage
Reduced PEM fuel-cell stack / Stack voltage against timeRecorded synthetic simulation values. Time in seconds; output in V.5.7936805.8593472.55.92501455.9906817.56.05634810VTime (s)
Reduced PEM fuel-cell stack / Stack voltage: 6.038233 V at 0 s

103 actual recorded samples. Lines are visual guides between samples. Synthetic example, not measured cell data.

Download the recorded samples (JSON) · Open this Studio example after release

Use in a workflow

Reduced PEM fuel-cell stack worked example

Prescribed gas/temperature Nernst potential with activation, ohmic and limiting-current losses plus an identified polarization lag. No humidity, gas-flow or thermal network states.

  1. Reduced PEM fuel-cell stack: Computes a reduced PEM stack polarization from prescribed hydrogen/oxygen pressures and temperature. Nernst potential, activation, ohmic and limiting-current losses determine cell voltage. An identified first-order polarization lag adds dynamics. Faraday balance gives reactant consumption.
    • Use the parameter values in the block reference.
    • Implementation tested locally; public release pending.
Open Studio example after release

Connected concepts

Limits and interpretation

  • Positive gas pressures and temperature are required; current is nonnegative and below the limiting current. No hydration, gas-channel flow, internal thermal or conserving network states. Literature supplies background, not a claim to reproduce a full published model.
  • The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

  1. Non-linear dynamic modeling of proton exchange membrane fuel cell

    A. Haddad, R. Bouyekhf, A. El Moudni, M. Wack · Journal of Power Sources · 2006

    Technical reference · Primary background on dynamic PEM modeling. The Lemonergy prescribed-gas polarization model is a bounded original reduction and does not reproduce the full model.

  2. Fuel Cell Handbook, seventh edition

    U.S. Department of Energy / National Energy Technology Laboratory · 2004

    Technical reference · Thermodynamic potential, polarization losses, Faraday reactant balances and fuel-cell operating principles; chapters 2–3.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

  • docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)