Green Hydrogen from PV: Electrolyser Size and Cost

For the smooth profile, $P(t)=P_{peak}\sin[\pi(t-t_{rise})/D]$ during daylight and zero outside it, with $P_{peak}=P_{PV}Y\pi/(2D)$. Each hourly average is its exact integral divided by one hour. The alternative profile directly uses entered hourly percentages of PV rating.

Hourly dispatch is $P_{el,h}=0$ below $f_{min}P_{rated}$, otherwise $\min(P_{PV,h},P_{rated})$. Sum power × one hour to obtain energy. Hydrogen equals accepted system energy divided by specific system consumption. Annual production is the available-day output × 365 × availability. Capacity factor uses 8,760 calendar hours; online hours count every productive hour, including part load.

Capital recovery is $CRF=r/[1-(1+r)^{-N}]$, with $CRF=1/N$ at zero discount. NREL 90103 (2024), Eq. 3, provides this annualisation method. A replacement occurs after each input stack-life interval of online hours, at a fractional project year, strictly before project end. Discount each replacement to year zero and annualise its present value with the same CRF.

All-generation billing uses total available annual PV energy, including curtailment and electrolyser downtime. Consumed-only billing uses actual annual electrolyser energy. The 31-point sizing sweep holds PV and all other assumptions fixed while varying PV/electrolyser ratio from 0.5 to 5 in increments of 0.15; infeasible candidates are chart gaps. When every sampled cost is non-finite, no sampled size or cost is reported; the selected design remains independent. No export credit is applied.

The 55 kWh/kg default and LHV efficiency benchmark follow DOE's PEM technical-target table (2022 status). IRENA (2020), pp. 32 and 65, documents load-range variability and system boundaries. NREL 70380 (2017), pp. 28 and 52–58, distinguishes stack specifications, whole-system performance and manufacturing costs; its historical costs are not treated as installed prices today.

• One lumped electrolyser system with constant kWh/kg, no overload, no battery and no grid import.
• A single representative day repeats for a non-leap year. Availability uniformly reduces production and running hours; PV generation continues during downtime.
• Smooth-profile PV yield is net available electrical energy divided by nominal PV power. Its peak must not exceed nameplate. Entered profiles are hourly averages between 0% and 100%.
• PEM 5% and alkaline 30% cutoffs are illustrative. The broad screening ranges in the brief are PEM 3–10% and alkaline 20–40%; IRENA reports some alkaline designs down to 15%. Verify vendor limits, gas purity and operating conditions. The preset changes only cutoff.
• Stack replacements restore performance at constant real cost, scheduled by online hours. Availability includes maintenance downtime; cycling wear is not separately calculated.
• Constant real annual costs and production, initial capital at year zero, end-of-year annual payments, no salvage, tax, subsidy or escalation. Default costs are author-selected examples as of 29 October 2026.
• CU is any single chosen currency. Monetary quantities are numerical accounting values; reference bases of 1 kW, 1 kWh and 1 kg keep units explicit. Monetary input and output bases stay metric under the physical unit switch.

Use for preliminary energy and production-cost comparisons of low-temperature PEM or alkaline electrolysis. Hourly averaging can miss brief cutoff crossings, rapid clouds and startup losses. A representative day cannot reproduce a year's weather or guarantee annual supply.

The lowest sampled LCOH is limited to ratios 0.5–5; it may occur at an endpoint and need not be the continuous optimum. High minimum loads can cause discontinuous changes in online hours, stack replacements and costs. The selected design can lie outside the sweep range.

Use vendor system consumption on the same electrical boundary as PV supply and electrolyser rating. Do not combine a DC stack-only rating with an AC whole-system kWh/kg value. Constant consumption omits part-load and age effects. Validate operating-hour stack life for intermittent operation. No oxygen revenue, water balance, hydrogen storage sizing, delivery-pressure calculation, renewable certification or emissions claim is provided.

Gas separation, ventilation, hydrogen detection and pressure protection are not designed here (hydrogen is flammable and may be produced under pressure); qualified specialists design and install the hydrogen and electrical systems.