Conservative electrolyser curve from the reviewer's references - #163
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…ences New selectable curve ulleberg_conservative. Both technologies take the steeper of the defensible options, so neither flatters the part-load operation this model is used to argue for. Alkaline. The Faraday term comes from Sanchez et al. 2018, which is the paper Baumhof's own curve depends on, instead of Ulleberg. Ulleberg's f1 puts the knee at 0.016 A/cm2 against a rated density of 0.8, so his term never engages across the operating range and the curve runs below the thermoneutral limit at low load, which is not physical. Sanchez's knee at 0.085 sits just under the operating floor that paper states for alkaline. Specific consumption at 20 per cent load rises 25 per cent and the optimum moves from 49 to 61 per cent. PEM. The shape comes from Astriani et al. 2024, the reviewer's own PEM citation, carried onto the Danish Energy Agency level. That level is 7.6 per cent more conservative than Astriani's own full-load figure, so this is the steeper shape on the higher level. Worth recording: Astriani's curve is monotone with no interior optimum, which disagrees with Baumhof's alkaline curve and with Buttler and Spliethoff. The two references the reviewer raised take opposite positions on the high-load end. That disagreement belongs in the paper's text rather than buried in a fit. Signs in Sanchez's table are dropped by the PDF text layer and were pinned from the paper's own constraints: f2 must be about one at high current density, and f1 rises with temperature per Ulleberg.
Up to standards ✅🟢 Issues
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The first version mixed methods: a physical model for alkaline and an empirical fit to a figure for PEM. If the technologies then differed, part of the difference was the method rather than the physics. That is the same fault the cost basis had before it was moved onto one catalogue. PEM now uses the same three-part construction as alkaline, stack voltage then Faraday then balance of plant, calibrated to the same DEA sheet, with the crossover physics that applies to a solid membrane: permeation is set by the membrane and the pressure difference and is roughly independent of current, so the lost current is a constant and the Faraday efficiency is one minus that constant over the operating current. A porous alkaline diaphragm follows a different law, so using one formula for both would look consistent and be wrong. The crossover current is 1 per cent of rated, giving 99 per cent Faraday efficiency at rated, which is the standard PEM figure. It is validated rather than fitted: 20 per cent load lands at 71.7 kWh/kg against Astriani's 69.4, so it stays conservative against the reviewer's own PEM reference, and the whole 20 to 100 per cent span sits inside the range Buttler and Spliethoff give for PEM systems. Both curves now have an interior optimum because both come from the same physics: alkaline at 61 per cent of load, PEM at 66 per cent. Astriani's own curve is monotone with none, which disagrees with Baumhof and with Buttler. That disagreement is recorded rather than smoothed away.
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Adds one selectable curve,
ulleberg_conservative. Nothing else changes; existing curves areuntouched.
Why
A reviewer raised two references against the part-load sentence: Baumhof et al. 2023 (alkaline) and
Astriani et al. 2024 (PEM). Reading both, plus Sánchez et al. 2018 which Baumhof's curve depends
on, turned up one real error in our parameters.
The Faraday term is about 29x too weak.
η_F = f2 i²/(f1 + i²), so the knee is at√f1:DEA rates the 10 MW alkaline at 0.8 A/cm², so Ulleberg's term never engages. The current curve
reaches 37.96 kWh/kg at 10% load, below the thermoneutral limit of 39.4 — not physical for a
stack releasing heat. Sanchez's knee sits just under the "typically above 100–150 mA/cm²" floor
that paper states for alkaline.
What the new curve does
Both technologies take the steeper of the defensible options, so neither flatters part-load
operation — which is what this model is used to argue for.
optimum moves from 49% to 61% of load.
than Astriani's own 56.3, so it is the steeper shape on the higher level.
Two things worth a reviewer's eye
The references disagree with each other. Baumhof's alkaline curve has a pronounced interior
optimum; Astriani's PEM curve is monotone with none. Buttler & Spliethoff, which the paper already
cites, supports the interior optimum. This is recorded in the code comment rather than smoothed
over, and belongs in the paper's text.
Signs. Sánchez's Table 1 loses its minus signs in the PDF text layer. They are pinned from the
paper's own constraints, not guessed:
f22negative because the paper requiresf2 ≈ 1at highcurrent density (positive gives 1.123, impossible for an efficiency), and
f12positive becauseUlleberg's
f1rises with temperature.Not a straight replacement
Sánchez fitted a 15 kW bench unit; DEA's is 10 MW at 0.8 A/cm². Gas crossover depends on
diaphragm design. Ulleberg is too weak and Sánchez may be too strong, which is why this is added as
a selectable curve for a bounded sensitivity rather than swapped in as the default.