How this fuel cell calculator works
A fuel cell converts the chemical energy of hydrogen (or a hydrogen-rich gas) directly into electricity, heat and water, without combustion. Sizing one comes down to a few practical questions: how much fuel does it consume, how long will the stored hydrogen last, how much heat can be recovered and what does each kilowatt-hour cost? This calculator answers them for the main cell families: low- and high-temperature PEM, solid oxide, phosphoric acid, molten carbonate and alkaline.
- Operating point. Rated power × load gives the electrical output. Efficiency is adjusted for part load: low-temperature PEM gains noticeably as load falls, high-temperature cells much less, and all lose some to balance-of-plant at very low load. Cells with a minimum load (SOFC, MCFC, PAFC) are held at that minimum.
- Fuel. Fuel power = electrical power ÷ efficiency; hydrogen mass = fuel power ÷ 33.33 kWh/kg, or natural gas volume for reformer-based systems.
- Heat and water. The remainder of the fuel energy becomes heat, a share of which you can recover; water output follows from the chemistry.
- Storage and cost. Runtime from common cylinder and tank sizes; fuel cost per kWh, with and without a heat credit, versus a diesel generator at the same load.
The formulas
Worked example: a 5 kW PEM fuel cell
The defaults model a 5 kW PEM system (50% rated efficiency) running at 60% load (3 kW) for 8 hours a day, fed from a 12-cylinder 300 bar bundle holding about 12.6 kg of hydrogen:
- at part load efficiency rises to about 53.5%;
- hydrogen consumption is 0.168 kg/h (1.87 Nm³/h), or 56 g per kWh;
- the bundle lasts about 75 hours, just over three days of continuous running;
- the cell also produces 2.6 kW of heat (1.6 kW recovered at 60–80 °C, for a total CHP efficiency of about 81%) and 1.5 litres of water an hour;
- at €12/kg, fuel costs €0.67 per kWh, close to a small diesel generator at part load (about 0.44 L/kWh at €1.60/L ≈ €0.71/kWh), but silent and with zero local emissions.
The fuel-cell car preset shows a 128 kW PEM stack cruising at 15% load: about 0.95 kg/h, so a 5.6 kg tank lasts close to six hours, consistent with the 500–650 km range of current hydrogen cars.
How to read the results
- Hydrogen consumption: kg/h and Nm³/h at the chosen load; grams per kWh is the fair comparison between systems.
- Efficiency at this load: for backup applications that rarely run at full output, part-load efficiency matters more than the datasheet maximum.
- Runtime from storage: use it to size cylinder bundles for backup autonomy (e.g. 8, 24 or 72 hours).
- Fuel cost per kWh is the dominant running cost; maintenance of fuel cells is usually low compared with engines.
- Efficiency vs load chart shows where the system operates most economically.
Typical values
| Type | Electrical efficiency (LHV) | Operating temperature | Fuel | Typical use |
|---|---|---|---|---|
| PEMFC | 45–55% | 60–80 °C | pure H₂ | vehicles, backup, portable |
| HT-PEM | 40–50% | 120–180 °C | H₂, reformate | micro-CHP, methanol systems |
| SOFC | 55–65% | 600–900 °C | H₂, natural gas, biogas | stationary CHP, data centres |
| PAFC | 40–45% | 150–200 °C | reformed natural gas | commercial CHP |
| MCFC | 45–50% | 600–700 °C | natural gas, biogas | large CHP |
| AFC | 50–60% | 60–90 °C | pure H₂ and O₂/air | space, niche |
Storage reference: 50 L cylinder at 200 bar ≈ 0.8 kg; at 300 bar ≈ 1.05 kg; car tank system at 700 bar ≈ 5–6 kg. Because hydrogen is a real gas, 700 bar stores only about 2.5 times as much as 200 bar.
Tips
- Run at moderate load. PEM systems are most efficient at 30–70% of rated power, so oversizing slightly saves fuel.
- Use the heat. In CHP applications, recovered heat can cut the effective cost per kWh by 10–20%.
- Buy hydrogen in bulk. Cylinder hydrogen is several times more expensive per kg than tube-trailer or on-site electrolysis supply; see the green hydrogen calculator.
- Size backup storage generously. Include a margin for low temperatures, purge losses and cylinders that cannot be fully emptied.
Limitations
Efficiency curves are generic by cell type; real systems differ by manufacturer, age and operating temperature, and stacks lose roughly 0.2–1% of voltage per 1,000 hours depending on duty. Start-up energy (significant for high-temperature cells), purge losses and hydrogen leakage are not modelled. Natural-gas systems include reforming in the efficiency but emit CO₂ at the stack (about 0.2 kg per kWh of gas). The diesel comparison is a generic genset curve; upstream emissions of hydrogen production are not counted.
Method & assumptions
Electrical output P = rated kW × load. Efficiency at load η(x) = ηrated × (1 + k·(1 − x)) minus a small balance-of-plant penalty at low load (k depends on cell type). Fuel power = P ÷ η; hydrogen = fuel power ÷ 33.33 kWh/kg (1 kg = 11.12 Nm³). Heat = fuel power − P; recovered heat = heat × recovery share. Water = 8.94 kg per kg H₂. Runtime = stored kg ÷ kg/h. Diesel comparison uses a generic genset curve (~0.27 L/kWh at full load, rising at part load) and 2.68 kg CO₂ per litre.
Frequently asked questions
How much hydrogen does a fuel cell use per kWh?
How efficient are fuel cells?
How long will a hydrogen cylinder run a fuel cell?
How much water does a fuel cell produce?
Is fuel-cell power cheaper than a diesel generator?
Why does PEM fuel-cell efficiency increase at part load?
Sources & references
- US DOE Hydrogen and Fuel Cell Technologies Office: Fuel cells
- Larminie, J. & Dicks, A.: Fuel Cell Systems Explained, 2nd ed., Wiley, 2003
- Clean Hydrogen Partnership (EU): programme review and KPIs for fuel cells
- NIST Chemistry WebBook: thermophysical properties of hydrogen (density at pressure)
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