Comparing the net-energy balance of standalone photovoltaic-coupled electrolysis and photoelectrochemical hydrogen production

Photovoltaic-coupled electrolysis (PV-E) and photoelectrochemical (PEC) water splitting are two options for storing solar energy as hydrogen. Understanding the requirements for achieving a positive energy balance over the lifetime of facilities using these technologies is important for ensuring sustainability. While neither technology has yet reached full commercialisation, they are also at very different technology readiness levels and scales of development. Here, we model the energy balance of standalone large-scale facilities to evaluate their energy return on energy invested (ERoEI) over time and energy payback time (EPBT). We find that for average input parameters based on present commercialised modules, a PV-E facility shows an EPBT of 6.2 years and ERoEI after 20 years of 2.1, which rises to approximately 3.7 with an EPBT of 2.7 years for favourable parameters using the best metrics amongst large-scale modules. The energy balance of PV-E facilities is influenced most strongly by the upfront embodied energy costs of the photovoltaic component. In contrast, the simulated ERoEI for a PEC facility made with earth abundant materials only peaks at 0.42 after 11 years and about 0.71 after 20 years for facilities with higher-performance active materials. Doubling the conversion efficiency to 10% and halving the degradation rate to 2% for a 10-year device lifetime can allow PEC facilities to achieve an ERoEI after 20 years of 2.1 for optimistic future parameters. We also estimate that recycling the materials used in hydrogen production technologies improves the energy balance by 28% and 14% for favourable-case PV-E and PEC water splitting facilities, respectively.


S.1 Vensim model and calculations for the ERoEI of a PV-E facility
The diagram of the model shown in Figure S1  Figure S1.The model diagram for simulating the ERoEI over time for a PV-AE system is recalculated iteratively every year.Blue arrows point to where each variable participates in a calculation.Grey arrows point to where a parameter is involved as an initial condition.
Electronic Supplementary Material (ESI) for Energy & Environmental Science.This journal is © The Royal Society of Chemistry 2024 meter square of PV active area. (S6) The ongoing operating energy costs of the PV-E facility is the sum of the annual energy cost of running the facility including for power converters, power handling, gas handling and compression.The energy cost of decommissioning the facility depends on whether the spent materials will be landfilled or recycled into new commodity materials or modules.Using Equations (S1)-(S6), the ERoEI as a function of time for a PV-E facility can be simulated with Equation (S7): [( µ  ( -1) -  × µ  ( -1)) × (µ  ( -1) -  × µ  ( -1)) × Similarly to the ERoEI of the PV-E facility, an ERoEI for a PV facility alone may be calculated for electricity output divided by thermal energy inputs as in Equation S8.The numerator may be calculated from the product of the annual insolation, solar-to-electricity conversion rate, and performance ratio, and the denominator is the sum of the energy costs of building, maintaining, and decommissioning the PV facility.
(S8)   (S9) The energy input cost per meter squared of light collection area, detailed in Equation (S11), is the sum of embodied energy cost needed to construct the facility, the cumulative operating energy cost of the facility, and the energy cost associated with decommissioning the facility at the end of its operating lifetime. (S11) The energy cost of constructing the facility, shown in Equation (S12), is the sum of the upfront, embodied energy in the active components of the PEC modules and in the BOS. (S12) Finally, using Equations (S9) -(S12), the ERoEI as a function of time for a model PEC facility can be expressed as Equation (S13): According to this trend, the average efficiency would be expected to reach 21% in the present year 2023 and this value is used as the base-case parameter.In fact, commercial panels with advertised efficiency up to 22.8-23.0%are now available from two manufacturers. 3,4The favourable-case parameter used is the record 26.8% efficiency for a single-junction siliconbased solar cell with an area of 274 cm 2 5 tabulated in the latest Solar cell efficiency tables (version 62). 6It should be noted that multi-junction solar cells involving silicon can achieve higher efficiencies and are being developed at commercial-scale for perovskite/Si cells, 6 which may be important to consider in the future if they ultimately take-up market share from single-junction cells.which is used here in the favourable case.For the optimistic-case parameter, a value of 0.3% is taken from the approximate median degradation rates among recent silicon-based devices in a pair of meta-analyses on PV degradation. 12,13These sources showed a wide range in reported degradation, so the optimistic-case parameter reflects optimal environmental factors rather than an estimate of future technological advancement.

PV efficiency degradation
PV performance ratio -The base-case and favourable-case parameters used comes from the latest (4 th ) edition of the Methodology Guidelines on Life Cycle Assessment of Photovoltaic Electricity 10 which reports that typical performance ratios today are 80% -90%, according to the Fraunhofer Institute for Solar Energy Systems latest Photovoltaics Report. 14ese values are a moderate improvement over the values of 70-80% found in a review of life cycle analyses of single-crystalline and multi-crystalline silicon PV systems between 1995 and 2014, 1 and are in agreement with the 0.80 used for ground-mounted utility PV installations. 15,16Although direct PV-coupled electrolysis facility may not require DC-AC conversion, a PV module under optimal conditions may still need a DC-DC converter to ensure the optimal voltage is supplied; this tends to result in a 5-10% power loss, 17 so 95% is chosen as the optimistic-case bound.
PV upfront energy cost -A few sources report the embodied energy cost for constructing PV facilities.In 2013, de Wild-Scholten reported a total primary energy demand for multicrystalline silicon PV systems of 2,661.5 MJ m -2 (739 kWh m -2 ) using the electricity mix in China. 18Meanwhile, Goerig & Breyer reported a market-weighted average primary energy intensity of 3.8 GJ m -2 (1056 kWh m -2 ) for ground-mounted systems and 2.7 GJ m -2 (750 kWh m -2 ) for rooftop systems between 1974-2010. 19Later, Raugei et al. calculated a primary embodied energy cost of 2.76 GJ.m -2 (767 kWh.m -2 ) based on Goerig's work considering 95 % rooftop and 5 % ground-mounted systems in Switzerland. 2750 kWh m -2 is used in this work as an approximate value for the construction energy for ground-mounted systems, given the limited availability of sources.The energy for decommissioning a PV facility is seldom reported 20 nor even tracked. 21Therefore, we use here the approximately 5% energy costs reported for landfilling CdTe thin film modules without recycling. 22Using this value and adding decommissioning costs to construction energy cost yields a final upfront embodied energy cost in the base case of 788 kWh m -2 .
An embodied energy of 537 kWh m -2 is used in this work as the favourable-case present parameter calculated by applying a learning rate of 12% for every doubling of cumulative installed capacity, 23 which agrees with another report of 8-11% and 11-14% for ground-mounted facilities and rooftop systems respectively. 19The IEA's 2023 Snapshot of Global PV Markets report shows that between 2013 and 2022, cumulative PV installations rose from 137 to 1185 GWp, 21 or roughly three doublings.Applying a 12% reduction to the base-case embodied energy three times results in the favourable-case value.(We assume here that these trends are suitable for the silicon-based PV models because silicon-based PV makes up a large majority of the global PV market.) The optimistic future-case value for the embodied energy is calculated as 322 kWh m -2 assuming a moderate slowing in the growth rate resulting in a further four doublings of cumulative installed capacity in the next 20 years.Although this assumption is a rough estimate and ambitious compared to the projections made in a 2019 IRENA analysis, 24 the realised installed PV capacity to 2022 is already ~10% larger 21 than the IRENA projections and the learning curves in past IPCC reports were recently shown by Way et al. 25 to consistently overestimate costs and underestimate improvements.
PV maintenance energy cost -To account for the energy costs for replacing faulty equipment, the 2017 analysis by Raugei et al. use 1% of the total embodied energy cost as an optimistic bound. 2 Specifically, to calculate this value they note a decrease in the incidence of equipment failure by 86% over the decade up until 2013 reported by the company TUV Rheinland. 2Primary literature is, however, difficult to source and other reports on technical risks note clearly that PV inverter failure rates are rarely disclosed by manufacturers. 26One 2020 technical report from NREL for modelling the financial operation and maintenance costs of photovoltaic systems uses an inverter cost of 0.74% of the embodied energy cost for a 10 MW ground-mounted system. 27We conservatively chose a PV maintenance energy costs of 1% of the PV embodied energy costs in each parameters case.In the base case, the maintenance energy cost is 7.9 kWh m -2 and the favourable and optimistic future-case values are 5.4 kWh m -2 and 3.2 kWh m -2 respectively.
AE conversion efficiency -The base-case and favourable-case values are taken as 65% conversion efficiency from a 2018 IRENA report for alkaline electrolysers 28 and predicted to rise to 68% in 2025.This progress agrees with predictions in an expert elicitation study from 2017 that stated system efficiencies would reach 60 to 65% in 2020. 29A separate 2020 IRENA report also uses 65% for present average conditions, and 76% for future conditions in 2050 which is taken as the optimistic-case value. 30 efficiency degradation -There are few specific reports of electrolyser efficiency degradation.Most sources instead state a lifetime between 60,000 to 100,000 hours, 30,28 but without knowledge of the typical operation of electrolysers, an annual degradation rate cannot be extracted.Degradation of electrolyser efficiency was reported in one 2015 study 31 for eleven commercial alkaline electrolysers.Specifically, the efficiency degradation was reported as 1.50% for 2 systems, 1.00% for 4 systems, 0.50% for 2 systems, 0.25% for 2 systems and 0.10% for 1 system.Reviews on alkaline water electrolyzers published in 2018, 32 2019, 33 and 2021 34 have since cited these values.For this work, the parameters will reflect the variation in the reported data, rather than estimates of future improvement.The basecase value is chosen as 1.50% annual degradation whereas the favourable-case is 1.00% degradation and 0.25% annual degradation is used as the optimistic-case value.
AE upfront energy cost -Pellow et al. noted in a 2015 analysis that no peer-reviewed life cycle inventories (LCI) of alkaline water electrolysers were available and so used an empirical LCI of an alkaline fuel cell from 2010 along with Ecoinvent data to estimate an energy cost of 1.36 x 10 6 MJ per MW of capacity for the cell stack (active components) . 35ince then, life cycle assessments of electrolysers have been published, 36 37 after also considering the energy cost of gas compression from Pellow et al. 35 A 2019 energy return on investment comparison by Clerjon et al. 38 and a 2021 net energy analysis by Lee et al. 39 solely use the values from Pellow's work.
Although the total annual solar insolation used for the energy input in this work is 1700 kWh m -2 year -1 , the dimensions of the AE component are sized to match the maximum output from the PV component and lead to an overall capacity factor of ~20% for the electrolyser as was studied by Shaner et al. 40 A 1 m 2 PV illuminated with 1700 kWh m -2 year -1 would have an average power input of 1.94 x 10 -4 MW.For the base-case parameters, after factoring a 21% conversion efficiency and 0.80 performance ratio, the output power would Although development in electrolyser energy inputs is rarely studied, a 2021 Hydrogen Council report on development of electrolyser monetary costs is available and will be used to estimate a learning curve for the embodied energy inputs. 42While a 12% learning rate is expected and used in this work, higher rates of 15-20% may also be feasible considering the early development of other technologies such as batteries, solar PV and wind energy. 42 years. 30Therefore, the base-case energy intensity of 2.79 x 10 6 MJ per MW is reduced to 1.67 x 10 6 MJ per MW and 0.60 x 10 6 MJ per MW in the favourable and optimistic future cases respectively.
Finally, considering the available electricity from the PV modules, in the favourable performance case, with conversion efficiency of 26.8% and 0.90 performance ratio, the power output would be 4.68 x 10 -5 MW and an AE with 2.34 x 10 -4 MW of capacity is needed.
Therefore, the energy intensity of the AE would be 109 kWh m -2 of PV, and the embodied energy including decommissioning would be 119 kWh m -2 of PV.This value will be taken as the favourable case parameter.Similarly, in the optimistic case, the final embodied energy of the AE would be 49 kWh.m -2 of PV.

AE operating energy cost -
The operating energy cost of the AE is taken here as largely made up of the energy cost for hydrogen compression.Adiabatic compression of hydrogen to 200 Bar was reported as 12% of the energy of the hydrogen that is being compressed based on its lower heating value (LHV) 3 , and as low as 8.5%-9% of hydrogen LHV in a 2020 report based on 2019 findings. 30Taking an approximate average of value 10% yields an energy cost of 19 kWh m -2 year -1 for the base case, considering that insolation of 1700 kWh m -2 year -1 leads to 286 kWh m -2 year -1 in electrical output and 186 kWh m -2 year -1 of hydrogen output.
Future improvements in compression energy costs will likely be physically limited.
Therefore, using the average 10% cost of the hydrogen energy produced for the favourable and optimistic-case systems leads to compression energy costs of 28 and 36 kWh m -2 year -1 respectively.These values are larger because more hydrogen is produced.

PEC solar-to-hydrogen (STH) conversion efficiency -
There are few reports of largescale PEC water splitting devices in the literature.A 0.4 % STH efficiency was reported by Domen et al. for a 1 m 2 particulate photocatalyst device in 2018. 43An Sb 2 Se 3 photocathode and BiVO 4 photoanode device with an illuminated area of 0.32 cm 2 showed an overall conversion efficiency of 1.5%. 44Wired photocatalyst systems often use a PV module to drive water splitting with a single photoelectrode.PV-integrated catalysts for water splitting with area of 64 cm 2 showed a 3.9% STH efficiency. 45Another PEC-PV device with area of 64 cm 2 showed 4.67% efficiency using a nickel iron molybdenum catalyst. 46A PEC-PV device with a cobalt-catalyzed tungsten-doped BiVO 4 photocatalyst with 0.24 cm 2 illuminated area showed a 5.5-6.3%STH efficiency but these values drop to 1.9-2.1% when the illuminated area rises to 50 cm 2 . 47Higher demonstrated conversion efficiencies for a PEC-PV device, include a 7.1% STH example with 1.5 x 1.5 cm 2 in area, 48 and the record 8.1% STH device from Pihosh et al.
that reached 90% of the theoretical maximum efficiency for BiVO 4 (although for a 4 x 4 mm 2 illumination area). 49Another BiVO 4 tandem device with Cu 2 ZnSnS 4 showed a STH of ~8% when coupled to a greenhouse thermoelectric device system. 50e Artiphyction project, completed in 2015, yielded the first large-scale 1.6 m 2 PEC prototype using CoPi-catalysed molybdenum-doped BiVO 4 which showed initial conversion efficiency of 3% and concluded that further engineering efforts were needed to improve fluid dynamics and to discover better photo-electroactive materials. 51This value of 3% conversion efficiency will be chosen as the base-case parameter.5% conversion efficiency was their programme target and will be chosen as the favourable-case parameter.Further examples of PEC devices on large-scale demonstration can be found in relevant reviews, 52,53 and at the Solar Fuels Database compiled by EPFL. 54e maximum STH efficiency for dual PEC absorbers using high-performance materials is reported to be 28.3% and 16.2% for earth-abundant materials 55 when considering realistic series and shunt resistances and low-performance external radiative efficiencies and catalytic exchange current densities.These values are close to the range of 20-25% that the US DOE is targeting for solar-driven hydrogen production. 56Predicting near-future conversion efficiency is, however, highly challenging because few PEC devices are in operation and the future materials and configurations of devices may vary greatly from present prototypes.
Improvements in large-scale conversion efficiency may occur in leaps and bounds instead of a gradual climb.10% is taken as an illustrative, optimistic future-case conversion efficiency for large-scale PEC devices in the next 20 years, corresponding to, for reference, five doublings of capacity and a 15% learning curve.Further improvement of the conversion efficiency approaching the theoretical limits will likely require additional research and development, although the required timeframe is beyond the scope of this work.
PEC degradation rate (D PEC ) -Most studies of experimental PEC devices in the literature only show or test for PEC photoelectrode stability over 1 day or less, 57,58 after which time there is already significant degradation, and even if little to no degradation is observed, 59 annual degradation cannot be reasonably estimated from short experiments.One example of a 1 m 2 SrTiO3:Al panel loaded with cocatalysts was tested for 42 days but showed approximately 40% degradation over this time.Another demonstration of a photoelectrochemical cell was a 50 cm 2 hematite photoanode in tandem with two silicon heterojunction solar cells that reported a very stable performance of 0.04% annualised degradation over 42 days. 60Upon close inspection, however, there is a drop when considering early plateau regions and performance later on which indicate a 10% drop in conversion efficiency over the same time.This value will be chosen as the base-case parameter.Other examples of particulate BiVO 4 and photoanodes tested in vanadium-saturated electrolyte showed 1000 and 500 hours of stability respectively. 61,62An annual degradation rate was not reported for the large-scale prototype built by the Artiphyction project, but they do expect to have achieved a lifetime of 10,000 hours, even though operating current decreases by 5 % after the first 300 hours. 51,63r the theoretical facilities simulated by Sathre et al., 64 the worst case lifetime of the system is 5 years which corresponds to a 4% annual linear degradation rate for a facility that reaches the end-of-life when efficiency is reduced by 20% from the initial value.Their basecase lifetime was 10 years, corresponding to a 2% annual linear degradation rate and these values are chosen here as the favourable-case and optimistic future-case parameters respectively.These metrics are illustrative estimates of the degradation rates of PEC prototypes in the future.
PEC performance ratio (PR PEC ) -Similar to PV modules, this ratio for PEC devices includes losses due to shading of the panel from dust and debris, and losses from temperature fluctuations. 1There is, however, no need to consider losses due to DC to AC conversion or generation and utilisation mismatch so the performance ratio for the PEC device is expected to be higher than for PV and AE modules.Typical performance ratios for PV modules are 0.75-0.8, 1,11,15,16reaching 0.835 for multi crystalline PV systems under optimal conditions of high insolation and low ambient temperature. 65Discounting the losses of 0.1-0.15 to DC to AC conversion, the performance ratio for a PEC module could be expected to reach approximately 0.85-0.95.85% will be used as the base-case value and 95% as the optimisticcase value.
We chose 90% as an average favourable-case performance ratio, which agrees with an estimate of the performance ratio from the expected energy output.Sathre et al. 64 calculates a 31.5 PJ facility -1 year -1 gross energy output.This output (3.15 x 10 10 MJ facility -1 year -1 ) for the 4.57 x 10 7 m 2 total module area facility (4.11 x 10 7 m 2 active area) is an energy output density of 689 MJ m -2 year -1 or 191 kWh m -2 year -1 .At the very beginning of this simulation, modules operate at 100 % performance instead of 90 %, so the energy output should be calibrated to 213 kWh m -2 year -1 .A system PR of 0.88 leads to this value for the very initial hydrogen output when applying the annual solar insolation of 2419 kWh m -2 year -1 and 10% solar-to-hydrogen efficiency used by Sathre et al.  for decommissioning 64 for a total embodied energy cost of 516 kWh m -2 and is chosen as the favourable-case performance parameters for this model.Because these parameters are already predictions, no learning curve is applied although the work was published in 2016.
A low-energy cost facility using only earth-abundant photoabsorbers and catalysts is estimated to cost 373 MJ m -2 (104 kWh m -2 ) for the active components. 64Adding decommissioning and BOS costs assuming that they would be constant whether the active components are energy intensive or not, the low-energy cost scenario has an energy input cost of 104 + 220 + 23 = 347 kWh m -2 .This value is used for the base-case performance parameter.For the optimistic-case future embodied energy cost, a facility similar to the favourable-case system with a mixture of earth-abundant and precious catalysts is assumed to improve over 20 years to an average of the previous cases of 431 kWh m -2 .It is yet to be determined whether low-cost earth abundant PEC catalysts with improved conversion efficiency or higher-cost precious metal catalysts with lowered costs may ultimately be more effective on an overall net-energy basis in the future.
We note here that unlike for other parameters, the base-case value is smaller than (more favourable than) the favourable-case value because of the variation in the materials assumed.No learning curves are applied to calculating the optimistic future case because of the lack of available data surrounding installed capacity and planning developments.
PEC annual maintenance energy cost -The energy for handling and compressing the gas, the energy for module heating, and for managing water supply was reported by Sathre et al. to total an energy cost of 7.3 PJ facility -1 year -1 (49 kWh m -2 year -1 ) for the favourable-case performance system used here. 64This value is comparable with but larger than the 39.2 kWh m -2 year -1 effective maintenance cost for the PV-AE system.
Proportionally, the base-case and optimistic future-performance case maintenance energy costs are 33 and 41 kWh m -2 Year -1 respectively.   296 MJ eq per tonne 70 6,424 MJ eq tonne produced -1 70

S.5 Recycling energy metrics
was constructed in the system modelling software Vensim PLE+.The arrows show which "variables" are involved with other variable parameters.Variables are recalculated with each iteration if any arrows are pointing into them.They are static if arrows are only pointing out from them."Levels" are parameters summed over iterative time and are boxed in the diagram.

Figure
Figure S2 is the diagram of the model for calculating the PEC ERoEI with its associated relationships.The model follows the approach for simulating the PV-AE system above.Equation 2.1 is again used as the starting point.The model diagram has fewer variables due to the relative simplicity of a PEC water splitting device.

Figure S2 .
Figure S2.The model diagram for calculating the ERoEI of a PEC system with annual iteration

be 3 .
26 x 10 -5 MW.Sizing the AE with an overall capacity factor of 20% then leads to the requirement for an AE that can accept 1.63 x 10 -4 MW of capacity.Therefore, using Pellow's metric of 2.69 x 10 6 MJ per MW, an AE with embodied energy of 438 MJ m -2 of PV is needed, or 122 kWh m -2 of PV.While the energy cost of decommissioning alkaline electrolysers is not available, we approximate the costs using 10% of the energy for construction, consistent with multiple energy life cycle assessments for decommissioning natural gas electricity plants done by the National Energy Technology Laboratory in the United Stated,41 leading to a final embodied energy of 134 kWh m -2 of PV, for the base-case parameter as a conservative value based on the 2015 Pellow et al. analysis .
A 2020 IRENA report showing historical water electrolyser capacity between 2005 to 2019 and predictions to 2030 shows that water electrolysis doubled in capacity approximately four times between 2015 and 2023 and may double in capacity another eight times in the next 20

PEC upfront embodied energy
cost -A theoretical 41.1 km 2 facility with earthabundant photoelectrodes and precious metal catalysts was predicted by Sathre et al. to cost 72.9PJ (493 kWh m -2 ) for the initial construction energy cost, (including 981 MJ m -2 (272.5 kWh m -2 ) for the primary energy to manufacture and construct the PEC system without the balance of systems (BOS) and therefore the BOS costs 220 kWh m -2 ) and 3.4 PJ (23 kWh m -2 )

Figure S3 .
Figure S3.Parameters sensitivity analysis of the ERoEI after 20 years for the PV-E facility for a) varying the individual parameters to their base case in 10% increments while keeping the remaining parameter values at their favourable case estimates, b) varying individual parameters to the favourable case while keeping the remaining parameter values at their optimistic-case values

Figure S5 .
Figure S5.Parameters sensitivity analysis of the ERoEI after 20 years for the PEC facility for a) varying the individual parameters to their base case in 10% increments while keeping the

Table S1 :
Embodied energy metrics for each material in a recycled PV-E system.

Table S2 :
Embodied energy metrics of each material of a recycled PEC system.