# PEM Electrolyser and Fuel Cell Models (MathWorks Simscape examples)

> **Markdown report of non-markdown source files.**
>
> | | |
> |---|---|
> | **Sources** | `Simulations/Ready Made PEM Electrolyzer/` · `Simulations/Ready Made PEM fuel cell/` · duplicated in `Simulations/Big Ugly Folder/` |
> | **Origin** | **MathWorks Simscape shipped examples**, obtained via `openExample(...)` |
> | **Licence** | © 2020–2024 The MathWorks, Inc. — see [Provenance](#provenance-and-licensing) |
> | **Status** | Current — but **still at vendor default parameters** |
> | **Report generated** | 2026-07-25 |

## Provenance and licensing

> [!WARNING]
> **This is unmodified third-party code.** Every `.m` and `.ssc` file in both folders carries a
> MathWorks copyright line; not one carries SHIFT attribution. Unlike the
> [EST model](existing-est-model.md) — which ships its MIT LICENSE and upstream URL — this
> vendored code is **marked nowhere in the repository**.

```
Ready Made PEM Electrolyzer/Electrolyzer.ssc:9          % Copyright 2021-2024 The MathWorks, Inc.
Ready Made PEM Electrolyzer/PEMElectrolysisSystemExample.m:57    % Copyright 2021 The MathWorks, Inc.
Ready Made PEM Electrolyzer/PEMElectrolysisSystemParameters.m:6  % Copyright 2021 The MathWorks, Inc.
Ready Made PEM fuel cell/FuelCell.ssc:10                % Copyright 2020-2024 The MathWorks, Inc.
Ready Made PEM fuel cell/PEMFuelCellSystemExample.m:64  % Copyright 2020-2021 The MathWorks, Inc.
Ready Made PEM fuel cell/PEMFuelCellSystemParameters.m:6         % Copyright 2020 The MathWorks, Inc.
…and 8 more Plot*.m files, all MathWorks
```

How they were obtained is recorded only as a comment in `Constants.m`:

```matlab
%openExample('simscape/PEMElectrolysisSystemExample')
%openExample('simscape/PEMFuelCellSystemExample')
```

**Recommended:** add a `PROVENANCE.md` to each folder stating that the contents are unmodified
MathWorks Simscape examples retrieved via `openExample`, and that redistribution is governed by
the MathWorks licence terms.

## The unfinished sizing work

`Constants.m` records the requirement and the plan, verbatim:

> `%Ready made electrolyser -`
> `%Good news: it has a solar profile.`
> `%Bad news: random constants - we want it at 128m3 hydrogen production a day`
> `%I have attempted to find volume via the volumetric flow rate, however this`
> `%uses "standard conditions". THIS BRINGS IT TO 12.8m3, JUST ADJUST (power?)`
> `%SO ITS 10 TIMES BIGGER AND WE ARE GOOD!`
>
> `%openExample('simscape/PEMFuelCellSystemExample')`
> `%This one is also PEM so it should work?`
>
> `%To do: Check if PEM is ok, change parameters for electrolyzer so that`
> `%production is exactely 10times bigger, adjust fuel cell, create grid,`
> `%ensure its power output is appropriate`

> [!IMPORTANT]
> **That TODO has not been carried out.** The parameter files are still at MathWorks demo
> defaults:
>
> - The electrolyser's 24-hour `solar_profile_power` still peaks at exactly **100 kW** — the
>   vendor's round demo number, not a SHIFT-derived profile.
> - The fuel cell still loads **`PEMFuelCellSystemDriveCycle.mat`** — an *automotive drive
>   cycle*, wholly inappropriate for a hospital microgrid.
>
> **No SHIFT-specific hydrogen system parameterisation exists anywhere in this tree**, despite
> `Constants.m` recording the requirement since the earliest revision. This is the single
> largest gap between the [simulator specification](../02-specifications/simulator-io-interface.md)
> and the models that are supposed to implement it.

Note also that the "just multiply by 10" approach to sizing is recorded as an unverified
assumption (*"This one is also PEM so it should work?"*), and that scaling a Simscape
electrolyser's hydrogen output by 10× is not achieved by scaling power alone — cell count,
active area, and current density all enter.

## Electrolyser parameters

`PEMElectrolysisSystemParameters.m` — 71 lines, 11,972 B, MD5 `7871b9ab`. Byte-identical in
`Ready Made PEM Electrolyzer/` and `Big Ugly Folder/`.

### Environment

| Parameter | Value | Unit |
|---|---:|---|
| `env_p` | 0.101325 | MPa |
| `env_T` | 20 | °C |

### Solar profile (24 h)

| Parameter | Value | Unit |
|---|---|---|
| `solar_profile_time` | `(0:23)' * 3600` | s |
| `solar_profile_power` | `[0 0 0 0 0 0 0.572 13.1 44.9 74.5 96.4 100 97.5 89.5 65.8 34.0 7.61 0 0 0 0 0 0 0]'` | kW |

### Stack

The comment header in the source says *"Fuel cell stack"* — a MathWorks copy-paste artefact in
the *electrolysis* file.

| Parameter | Value | Unit | Description |
|---|---:|---|---|
| `stack_num_cells` | 50 | – | Number of cells |
| `stack_area` | 280 | cm² | Cell area |
| `stack_t_membrane` | 125 | µm | Membrane thickness |
| `stack_t_gdl_A` | 25 | µm | Anode gas diffusion layer thickness |
| `stack_t_gdl_C` | 250 | µm | Cathode gas diffusion layer thickness |
| `stack_w_channels` | 1 | cm | Gas channel width and height |
| `stack_num_channels` | 8 | – | Gas channels per cell |
| `stack_io` | 1e-04 | A/cm² | Exchange current density |
| `stack_alpha` | 0.7 | – | Charge transfer coefficient |
| `stack_D_gdl_A` | 0.07 | cm²/s | Water diffusivity in anode GDL |
| `stack_D_gdl_C` | 0.07 | cm²/s | Water diffusivity in cathode GDL |
| `stack_membrane_rho` | 2000 | kg/m³ | Density of dry membrane |
| `stack_membrane_MW` | 1.1 | kg/mol | Equivalent weight of dry membrane |
| `stack_mea_rho` | 1800 | **kg/s** *(sic)* | Overall density of MEA — vendor unit typo, should be kg/m³ |
| `stack_mea_cp` | 870 | J/(kg·K) | Overall specific heat of MEA |

### Piping and heat exchanger

| Parameter | Value | Unit | Description |
|---|---:|---|---|
| `water_pipe_D` | 0.01 | m | Water pipe diameter |
| `gas_pipe_D` | 0.01 | m | Gas pipe diameter |
| `exchanger_L` | 1 | m | Overall radiator length |
| `exchanger_W` | 0.025 | m | Overall radiator width |
| `exchanger_H` | 0.5 | m | Overall radiator height |
| `exchanger_N_tubes` | 25 | – | Number of coolant tubes |
| `exchanger_tube_H` | 0.0015 | m | Height of each coolant tube |
| `exchanger_fin_spacing` | 0.002 | – | Fin spacing |
| `exchanger_eta_fin` | 0.7 | – | Fin efficiency |

Derived quantities computed in the script: `exchanger_gap_H`, `exchanger_air_area_primary`,
`exchanger_N_fins`, `exchanger_air_area_fins`, `exchanger_tube_Leq`.

## Fuel cell parameters

`PEMFuelCellSystemParameters.m` — 94 lines, 12,709 B, MD5 `6eaf6bf3`. Byte-identical in
`Ready Made PEM fuel cell/` and `Big Ugly Folder/`. Line 8 executes
`load PEMFuelCellSystemDriveCycle.mat` (13,667 B).

### Environment

| Parameter | Value | Unit |
|---|---:|---|
| `env_p` | 0.101325 | MPa |
| `env_T` | 20 | °C |
| `env_RH` | 0.5 | – (relative humidity) |
| `env_yO2` | 0.21 | – (oxygen mole fraction) |

### Fuel tank

| Parameter | Value | Unit |
|---|---:|---|
| `tank_p` | 70 | MPa |
| `tank_yH2` | `1 − 3e-4` | – (hydrogen mole fraction) |
| `tank_V` | 120 | L |

> `tank_V = 120 L` at 70 MPa is an **automotive** hydrogen tank. The
> [project spec](../02-specifications/simulator-io-interface.md#13-hydrogen-tank) calls for
> **up to 200 kg across two tanks** — roughly three orders of magnitude larger. Another
> consequence of the untouched vendor defaults.

### Stack

| Parameter | Value | Unit | Description |
|---|---:|---|---|
| `stack_num_cells` | **400** | – | Number of cells (vs. 50 in the electrolyser) |
| `stack_area` | 280 | cm² | Cell area |
| `stack_t_membrane` | 125 | µm | Membrane thickness |
| `stack_t_gdl` | 250 | µm | Gas diffusion layer thickness |
| `stack_w_channels` | 1 | cm | Gas channel width/height |
| `stack_num_channels` | 8 | – | Gas channels per cell |
| `stack_io` | 1e-04 | A/cm² | Exchange current density |
| `stack_iL` | 1.4 | A/cm² | Limiting current density |
| `stack_alpha` | 0.7 | – | Charge transfer coefficient |
| `stack_D_gdl` | 0.07 | cm²/s | Water diffusivity in GDL |
| `stack_membrane_rho` | 2000 | kg/m³ | Density of dry membrane |
| `stack_membrane_MW` | 1.1 | kg/mol | Equivalent weight of dry membrane |
| `stack_mea_rho` | 1800 | **kg/s** *(sic)* | Vendor unit typo, should be kg/m³ |
| `stack_mea_cp` | 870 | J/(kg·K) | Overall specific heat of MEA |

### Gas tubes and coolant

| Parameter | Value | Unit | Description |
|---|---:|---|---|
| `anode_tube_D` | 0.01 | m | Hydrogen tube diameter |
| `cathode_tube_D` | 0.05 | m | Air tube diameter |
| `coolant_w_channels` | 1 | cm | Coolant channel width/height |
| `coolant_num_passes` | 12 | – | Coolant channel passes per layer |
| `coolant_num_layers` | 20 | – | Coolant layers in stack |
| `coolant_tube_D` | 0.05 | m | Coolant tube diameter |

### Radiator

| Parameter | Value | Unit | Description |
|---|---:|---|---|
| `radiator_L` | 1 | m | Overall radiator length |
| `radiator_W` | 0.025 | m | Overall radiator width |
| `radiator_H` | 0.5 | m | Overall radiator height |
| `radiator_N_tubes` | 25 | – | Number of coolant tubes |
| `radiator_tube_H` | 0.0015 | m | Height of each coolant tube |
| `radiator_fin_spacing` | 0.002 | – | Fin spacing |
| `radiator_eta_fin` | 0.7 | – | Fin efficiency |
| `radiator_t_wall` | 1e-4 | m | Material thickness |
| `radiator_rho` | 2700 | **kg/s** *(sic)* | Vendor unit typo, should be kg/m³ (2700 = aluminium) |
| `radiator_cp` | 910 | J/(kg·K) | Radiator material specific heat |

### Compressor map

| Parameter | Value | Unit |
|---|---|---|
| `comp_p_ratio_TLU` | `[1; 1.25; 1.5; 1.75; 2]` | – (pressure ratio) |
| `comp_rpm_TLU` | `[0, 1800, 3600]` | rpm |

```matlab
comp_mdot_corr_TLU = [
    0, 0.05,   0.1;
    0, 0.0375, 0.075;
    0, 0.025,  0.05;
    0, 0.0125, 0.025;
    0, 0,      0] * 4;   % [kg/s] Corrected mass flow rate table
```

## Gas properties (shared by both files)

| Gas | `_R` [J/(kg·K)] | `_D` [mm²/s] |
|---|---:|---:|
| H₂ | 4124.48151675695 | 74 |
| O₂ | 259.836612622973 | 18 |
| N₂ | 296.802103844292 | — |

Each gas also carries 52-element lookup vectors sharing the temperature grid
`_T = [-56.55, -50:10:-10, -5:1:5, 10:10:350]` °C, with `_h` in kJ/kg (specific enthalpy),
`_mu` in µPa·s (dynamic viscosity), and `_k` in mW/(m·K) (thermal conductivity).

## What differs between the two models

The two parameter files share identical gas property tables and identical membrane/MEA
parameters. The substantive differences:

| Aspect | Electrolyser | Fuel cell |
|---|---|---|
| `stack_num_cells` | 50 | **400** |
| Limiting current density | — | `stack_iL = 1.4 A/cm²` |
| Gas diffusion layer | Split anode/cathode (`_A` 25 µm / `_C` 250 µm) | Single `stack_t_gdl` = 250 µm |
| Fuel storage | — | `tank_*` block, 120 L @ 70 MPa |
| Air handling | — | `env_RH`, `env_yO2`, compressor map |
| Cooling | Heat exchanger | Coolant channels + radiator |
| Drive input | 24 h solar profile | Automotive drive cycle `.mat` |

## Supporting scripts

Both folders ship MathWorks' plotting and example scripts, all copyright MathWorks:

| Electrolyser | Fuel cell |
|---|---|
| `PEMElectrolysisSystemExample.m` | `PEMFuelCellSystemExample.m` |
| `PEMElectrolysisSystemPlot1IV.m` | `PEMFuelCellSystemPlot1IV.m` |
| `PEMElectrolysisSystemPlot2Power.m` | `PEMFuelCellSystemPlot2Power.m` |
| `PEMElectrolysisSystemPlot3Hydrogen.m` | `PEMFuelCellSystemPlot3Efficiency.m` |
| | `PEMFuelCellSystemPlot4T.m` |
| | `PEMFuelCellSystemPlot5Energy.m` |

The `Plot*.m` files carry polished vendor documentation citing textbook figures — for example
*"The theoretical maximum efficiency for a PEM fuel cell is 83%. However, actual efficiency is
around 60% due to internal losses"*, which lines up with the 40% fuel-cell loss figure in
[AI Efficiency Improvements](../01-project/ai-efficiency-improvements.md).

The `.ssc` component sources use the Simscape `foundation.moist_air.moist_air` and
`foundation.thermal_liquid.thermal_liquid` domains.

## Related

- [Simulink Model Inventory](simulink-model-inventory.md) — including the `Constants.m` staleness
- [Simulator I/O Interface §1.1–1.3](../02-specifications/simulator-io-interface.md#11-electrolyser) — the parameters these should match
- [UCSD Equipment Manual](../03-energy-management/ucsd-equipment-manual.md) — real-world PEM electrolyser specifications
- [AI Efficiency Improvements](../01-project/ai-efficiency-improvements.md) — the loss targets
- [Existing EST Model](existing-est-model.md) — the other vendored subtree