Advances in Power-to-Gas Technologies: Cost and Conversion Efficiency

This paper examines the cost and efficiency dynamics of three prevalent Power-to-Gas technologies. Our results suggest that electrolytic hydrogen production costs will approach but not reach the U.S. Department of Energy's $1.0/kg target by 2030.


Broader Context
With the transition towards sustainable energy technologies gaining momentum, hydrogen is increasingly considered to be crucial for storing and flexibly delivering large amounts of clean energy.Widespread adoption of hydrogen, however, is expected to depend on substantial advances in Power-to-Gas (PtG) technologies that convert renewable electricity to hydrogen.To accelerate the speed of such improvements, governments worldwide have recently introduced sizable subsidy programs for the development, manufacturing, and deployment of hydrogen equipment.This paper provides a comprehensive assessment of the dynamics in system prices and energy efficiency for three prevalent PtG technologies: alkaline, polymer electrolyte membrane, and solid oxide cell electrolysis.By tracking global data points for system prices, energy consumption, and the cumulative installed capacity for each technology, our calculations yield significant and robust learning curves of 83-86% for system prices and 98% for energy consumption over the past two decades.Based on these estimates, we project that, over the coming decade, electrolytic hydrogen produced with any of the three technologies will become cost-competitive with traditional hydrogen supply derived from fossil fuels.Specifically, the life-cycle cost of electrolytic hydrogen production is projected to approach the $1.0/kg cost target set by the U.S. Department of Energy.

Introduction
In the intensifying debate about alternative pathways for rapid decarbonization, hydrogen is increasingly viewed as a critical building block for storing and flexibly dispatching large amounts of carbon-free energy [1][2][3][4] .Among alternative hydrogen production technologies, Power-to-Gas (PtG) in the form of electrolytic hydrogen has received particular attention [5][6][7] .
Large-scale deployment of these technologies, however, is generally expected to hinge on substantial cost declines and energy conversion improvements.To accelerate the pace of these improvements, governments around the world have recently introduced sizeable regulatory initiatives and subsidy programs for the development, manufacturing, and deployment of hydrogen equipment 8;9 .This paper projects cost and conversion efficiency improvements for three prevalent PtG technologies: alkaline, polymer electrolyte membrane (PEM), and solid oxide cell (SOC) electrolysis.Our analysis is grounded in a learning-by-doing model that postulates that system prices for electrolyzers and their conversion efficiency decline at a constant rate with every doubling of cumulative installments of the technology in question.Such learning models have proven highly descriptive in the context of solar photovoltaics 10;11 , onshore wind turbines [12][13][14] , or lithium-ion batteries [15][16][17] .Scarcity of data has so far limited the estimation of learning curves to alkaline electrolysis [17][18][19][20] or to a single equipment manufacturer 21 , resulting in learning estimates with low predictive power.Some earlier studies estimate the rate of past cost declines of PtG technologies against time [22][23][24] or rely on expert opinions about future cost developments [25][26][27] .Both approaches presume that technological progress is an exogenous function of time instead of an endogenous process driven by the rate of technology adoption.
Our analysis provides the first comprehensive assessment of the dynamics in system prices and energy efficiency for the three PtG technologies by tracking global observations on investment expenditures and energy consumption.This information is linked to capacity installations at facilities commissioned worldwide between 2000-2020.Our estimates return significant and robust learning curves for system prices in the range of 83-86%.Thus, system prices declined by 14-17% compared to the price levels prior to the doubling of cumulative installments.The relatively young SOC technology is projected to show the sharpest price decline at a 17% learning rate.PEM electrolyzers, in contrast, have experienced high capacity growth and a rapid price decline between 2003 and 2020.Here, our estimates yield a relatively slow learning rate of 14%.For conversion efficiency, we estimate that every doubling of cumulative installed capacity reduces the required kilowatt-hours (kWh) per kilogram (kg) of hydrogen produced by approximately 2% across all three technologies.
Our regression results can be extrapolated to yield forecasts for the system prices and conversion efficiencies of the three PtG technologies in question by the year 2030.For divergent growth forecasts issued by different industry and policy sources, the extrapolated values fall into ranges that are substantially narrower than most earlier estimates 24;25;28-39 .These calculations, in turn, lead us to conclude that electrolytic hydrogen production will become widely cost-competitive with traditional hydrogen supply based on fossil fuels.Furthermore, the Hydrogen Shot target by the U.S. Department of Energy 9 of producing clean hydrogen at a cost of $1.0/kg by 2030 shows to be ambitious but not unrealistic.Because electricity prices will become the dominant component of the life-cycle cost of hydrogen by 2030, the attainment of the Hydrogen Shot target via electrolytic hydrogen ultimately hinges on the availability of inexpensive and clean electricity.

Learning Curve Estimates
Our analysis considers the three electrolyzer technologies alkaline, PEM, and SOC.For each of these technologies, modules combine electrolysis stacks with so-called balance-ofsystem components 40 .A stack broadly consists of multiple cells where electricity splits water molecules into hydrogen and oxygen.Power electronics, heat and fluid management, and hydrogen treatment comprise the balance of system 41 .Our analysis excludes the pressurization of hydrogen via compressors.
In addition to the acquisition price, the system price for a PtG system reflects project development and installation costs.Since PtG systems have been procured through customized manufacturing contracts in the past, some reductions in system prices have emerged from early efforts to standardize and automate production processes along with increased manufacturing capacity 25;42;43 .Technological improvements have further allowed manufacturers to build larger systems, cut production waste, and save on material costs.Examples of such innovations include better electrode design and bipolar plates, as well as replacing expensive, custom-made components with commercially available ones 41;42;44;45 .
The conversion efficiency of a PtG system is measured in the electricity in kWh required to produce one kg of hydrogen.This includes the energy required for the electrolytic pro-duction process but excludes the energy needed for heat management.Initial improvements in energy consumption have resulted from larger stacks with a better distribution of current density across the reactive surface area, lower system complexity, and improved system integration 17;41 .For PEM electrolyzers, new materials have enabled thinner membranes and more active catalysts at the cell level 44 .
Our global data collection effort tracks system prices, the energy consumption of the PtG systems, and capacity installations at the corresponding facilities for the years 2000-2020.
As detailed in the Electronic Supplementary Information (ESI), the information collected in our database stems from multiple sources, including manufacturers, industry databases, academic articles in peer-reviewed journals, and technical reports by agencies, consultancies, and industry analysts.In particular, information on system prices is based on two earlier reviews 24;39 and a replication of the analyses performed therein (details in Supplementary Note 2).Our search yielded 176 sources, primarily European and North American, containing 264 unique observations from industry or an original review of multiple sources.Of these observations, 105 pertain to alkaline electrolysis over the years 2003-2020, 81 to PEM system between 2003-2020, and 78 to SOC technology spanning the years 2011 to 2020.To focus on recent technological developments, we excluded sporadic estimates for alkaline systems that became available prior to the year 2000 [17][18][19] .

Our data set of cumulative installed capacity is primarily based on the Hydrogen Projects
Database by the International Energy Agency 46;47 (details in Supplementary Note 3).This database includes production facilities that have been commissioned worldwide since 2000 for the generation of clean hydrogen and hydrogen derivatives.In addition, we conducted our own review of hydrogen projects based on industry announcements and media coverage.Our For each PtG technology, the learning effects are assumed to conform to a constant elasticity learning model.Accordingly, both system prices and energy consumption are a function of the cumulative installed capacity of the particular technology 49 .Let v i denote the system prices per Watt (W) of peak power absorption of a technology in year i and Q i the cumulative installed capacity of a technology in kilowatt (kW) in year i.In logarithmic form: where β 1 denotes the learning elasticity parameter and µ i is an idiosyncratic and unbiased error term.Equation 1 predicts that with every doubling of installed cumulative electrolyzer capacity, the system price of a PtG technology declines to 2 β 1 of its previous value.A parallel equation is used to estimate the learning factor of a technology's conversion efficiency.lowest average system prices at $0.9/W (Figure 1a-c, details in Supplementary Note 5).The reduction in system prices across the years 2003-2020 corresponds to a learning factor of 2 β 1 = 84.3% with a 95%-confidence interval of 2.7% (p < 0.0001, adj.R 2 = 0.51).This implies that system prices declined by 15.7% with every doubling of cumulative installed capacity.As of today, SOC electrolyzers, in contrast, have the lowest cumulative installed capacity and the highest system prices at $2.3/W in 2020.Yet, they also exhibit the fastest price decline, described by a learning factor of 83.3 ± 6.5% across the years 2011-2020 (p < 0.0001, adj.R 2 = 0.24).PEM electrolyzers experienced a sharp decline in system prices from $8.3/W in 2003 to $1.1/W in 2020 but also rapid growth in cumulative installed capacity from less than 0.1 to almost 100 MW.The resulting learning factor amounts to 86.2 ± 1.7% (p < 0.0001, adj.R 2 = 0.74).

Report
In terms of energy consumption, alkaline systems have exhibited improvements from above 60 kWh/kg in the early 2000s to 52 kWh/kg in 2020 (Figure 1d-f, details in Supplementary Note 5).Similarly, PEM electrolyzers have witnessed a decline from above 70 kWh/kg in the early 2000s to 57 kWh/kg in 2020, while the SOC technology improved from above 50 kWh/kg in 2011 to around 42 kWh/kg in 2020.Despite the differences in absolute values, our regression analysis yields very similar learning factors for the three PtG technologies.Specifically, the estimated learning factors are 98.3 ± 0.9% (p < 0.001, adj.R 2 = 0.08) for alkaline, 98.3±0.9%(p < 0.001, adj.R 2 = 0.15) for PEM electrolyzers, and 98.4±2.3%(p < 0.2, adj.R 2 = 0.08) for the SOC technology.
To examine the robustness of our learning curve estimates, we first examine the potential effect of changes in the size of PtG systems on the development of system prices.Earlier work suggests that the acquisition price of PtG systems declines at a diminishing rate as the capacity size of the system increases 22;23;40 .While information on system sizes available to us is largely disconnected from the data on system prices, we nevertheless examine multiple different specifications for estimating the potential effect of changes in the size of PtG systems on the trajectory of system prices (details in Supplementary Note 6).The results point towards significant and robust learning coefficients for cumulative installed capacity and a limited effect of capacity sizes.This finding is consistent with studies examining the cost dynamics of onshore wind turbines [12][13][14] , solar photovoltaic modules 10;11 , or lithium-ion batteries [15][16][17] .It is also consistent with the observation that scale economies of PtG plants appear to level off as system sizes exceed a particular threshold 22;23;34 .
Earlier studies have shown that learning curve estimates can be sensitive to the chosen time window 10 .We, therefore, repeat the estimation of learning curves for alkaline and PEM electrolyzers covering the years 2010-2020 to examine the most recent developments in system prices and conversion efficiencies.As detailed in Supplementary Note 7, the learning curves for alkaline electrolyzers improve slightly in terms of both system prices and conversion efficiencies.For PEM electrolyzers, the learning curves for both system prices and energy consumption remain almost unchanged.For both technologies, the 95%-confidence intervals of both learning estimates increase due to smaller sample sizes.Some components of PEM electrolyzers, such as the catalysts, porous transportation layers, and bipolar plates, currently comprise rare earths materials, primarily platinum and iridium.To estimate the potential effect of changes in the market prices of both metals, we calibrate an extension of equation ( 1) for PEM systems that includes the annual average global market price for each metal as an additional regression coefficient.As detailed in Supplementary Note 8, the regression result shows that the learning elasticity of cumulative installed capacity remains unaffected, while the estimated coefficients for both metals are economically and statistically insignificant.Yet, we note that industry observers have pointed out that a rapid increase in PEM electrolyzer production could lead to temporary shortages of these metals.
Earlier studies on the decline in the system prices of alkaline electrolyzers have estimated learning parameters between 82-84% with a 95%-confidence interval of ±6-13% [17][18][19] .While these values are similar in magnitude to our estimate for alkaline electrolyzers (Figure 1a), the larger number of observations in our analysis yields a much tighter 95%-confidence interval at ±2.7%.Aside from sample size, the lower variance in our sample is also likely to reflect standardization in the product offering of electrolysis equipment manufacturers, particularly for alkaline and PEM systems.
An alternative approach to learning curves based on cumulative installed capacity is to estimate technological progress as a function of time.As detailed in Supplementary Note 9, our regressions return annual declines in system prices of 6.0 ± 1.0% for alkaline over the years 2003-2020 (p < 0.0001, adj.R 2 = 0.56), 12.6 ± 1.4% for PEM between 2003-2020 (p < 0.0001, adj.R 2 = 0.77), and 10.6 ± 4.2% for SOC electrolyzers covering 2011-2020 (p < 0.0001, adj.R 2 = 0.25).Furthermore, we identify annual reductions in energy consumption of 0.8 ± 0.4% for alkaline across the years 2000-2020 (p < 0.0001, adj.R 2 = 0.11), 1.4 ± 0.7% for PEM electrolyzers across 2005-2020 (p < 0.0001, adj.R 2 = 0.15), and 1.0 ± 1.4% for the SOC technology between 2011-2020 (p < 0.15, adj.R 2 = 0.07).Earlier studies 24;39 have estimated the annual decline in system prices at 3.0% for alkaline and 4.8% for PEM electrolysis covering the years 2003-2016, and at 9.0% for SOC electrolysis based on data for the years 2011-2019.We attribute the faster estimate regarding price declines emerging from our analysis to the impact of the most recent price observations.At the same time, we note that the estimate for PEM electrolyzers might be somewhat over-optimistic due to the relative richness of observations with lower system prices in recent years.We are not aware of previous studies examining changes in the conversion efficiency of PtG systems.

Extrapolating Future Performance
Based on the learning estimates in Figure 1, we now project trajectories of future system prices and energy consumption for each PtG technology.Our projections consider three alternative scenarios to compare different growth scenarios for electrolyzer installations over the coming years.
The first scenario (called "Past Growth") examines the possibility that the cumulative installed capacity for each technology continues to grow at the same rate as observed on average in the past.To estimate this rate, we ran for each technology a univariate regression based on the constant elasticity functional form: ln  The second scenario (called "Policy Target") assumes that the cumulative installed ca-pacity of the PtG technologies will grow such that their total in 2030 reaches the sum of individual policy targets for installed capacity.As detailed in Supplementary Note 10, these targets stem from national hydrogen strategies articulated in recent years and, as of now, amount to about 115 Gigawatt (GW) in total.Since these targets are technology-agnostic and specified for installed capacity, we assume that each technology's share of the total cumulative installed capacity by 2030 is the same as in the Past-Growth scenario.Further, we interpolate the growth in cumulative installed capacity for each technology during the years 2020-2030.Alternative distributions for the technology-specific shares in 2030 have only a small effect on our subsequent findings, especially for alkaline and PEM electrolysis (see Supplementary Note 10 for details).In addition, we account for capacity depletion by adding in each year from 2021 onward the installed capacity expected to have gone offline until that year based on the installation year and a useful lifetime of 20 years 24;39 .Table 1 provides the resulting estimates, with implied annual growth rates for cumulative installed capacity of 63.4% for alkaline, 101.5% for PEM, and 72.8% for SOC electrolysis.
In direct analogy to the second scenario, our third scenario (called "Industry Target") assumes that the cumulative installed PtG capacity grows such that the sum across individual industry targets for installed capacity in 2030 is reached.These targets result from numerous announcements by project developers, hydrogen customers, and industry associations made in recent years and amount in total to about 248 GW.Table 1 shows the resulting estimates for cumulative installed capacity by 2030 for each technology.The implied (interpolated) annual growth rates for cumulative installed capacity amount to 75.9% for alkaline, 117.0% for PEM, and 86.0% for SOC systems.
The resulting trajectories shown in Figure 2 suggest that the system prices of all three technologies are likely to fall substantially over the coming years.Specifically, our calculations project ranges for system prices by 2030 across the scenarios of $285-475/kW for alkaline, $225-352/kW for PEM, and $441-767/kW for SOC electrolysis.The higher values for SOC electrolysis reflect the relative novelty of the technology and its more complex heat management requirements.We also find that, despite the sizable variation in the growth of cumulative installed capacity across the scenarios, the trajectories of system prices for alkaline and PEM electrolysis stay relatively close to each other.For these two technologies, differences in the number of doublings in cumulative installed capacity across the scenarios are smaller than for SOC electrolysis.Regarding the energy consumption of PtG systems, our projections for 2030 yield ranges across the scenarios of 47-49 kWh/kg for alkaline, 47-50 kWh/kg for PEM, and 36-38 kWh/kg for SOC technology.Thus, the energy consumption of alkaline and PEM systems is moving towards the target of 42 kWh/kg by 2050 set by the International Renewable Energy Association 41 .The projected reduction for alkaline systems is also consistent with recent advances in capillary-fed electrolysis cells that exhibit a 15% lower power consumption relative to commercially available systems 50 .SOC electrolyzers are likely to approach the theoretical optimum of 33 kWh/kg towards the end of this decade.Analogous to system prices, the trajectories for alkaline and PEM electrolysis stay relatively close to each other.

SOC Electrolysis f
As a robustness check, we also extrapolate the future performance of PtG technologies based on time.As one would expect, the resulting system prices and energy consumption values are close, if not identical, to the trajectories for the Past-Growth scenario reported in Figure 2 (details in Supplementary Note 11).An exception to this observation is that the time-based projection for system prices of PEM electrolyzers is closer to the trajectory of the Industry-Target scenarios.We attribute this discrepancy to the large share of lower price observations in recent years.Furthermore, we examine a specification based on time and cumulative installed capacity.As detailed in Supplementary Note 11, there is high multicollinearity between the two covariates, which weakens the resulting regression estimates.
Nevertheless, the projected trajectories for system prices and energy consumption are again close to the Past-Growth scenario in Figure 2.
Figure 2 also shows point estimates for future system prices and energy consumption as articulated by industry experts [28][29][30] , technical reports [31][32][33][34][35][36][37] and academic studies 24;25;38;39 .In comparison, our projections for both system prices and energy consumption yield estimates that are consistently and substantially below most of the earlier estimates.We attribute this discrepancy to multiple factors.First, our projections model technological progress not as an exogenous function of time but as an endogenous process driven by deployment rates.In addition, the Policy and Industry Targets suggest a substantial acceleration in the deployment of PtG systems, the magnitude of which is consistent with the projected demand for clean hydrogen by 2030 51 and the ramp-up of manufacturing capacity for PtG systems [52][53][54] .Finally, our calculations are based on recent global information reflecting the rapidly improving system prices and efficiencies as well as the observed recent growth in capacity deployments.

Levelized Cost of Hydrogen Production
Recognizing the potential of hydrogen as a decarbonized energy source, the U.S. Department of Energy articulated the Hydrogen Shot initiative in 2021.According to this initiative, the cost of producing hydrogen is to come down to $1.0/kg by the year 2030 9 .The system prices and conversion efficiencies we forecast in Figure 2 are useful in gauging whether the U.S. Department of Energy's goal appears to be a "long shot."To that end, we calculate a life-cycle cost measure termed the Levelized Cost of Hydrogen (LCOH).Analogous to the levelized cost of electricity, the LCOH yields a break-even value for investing in a PtG system.
If an investor were to receive the LCOH as the revenue per kg of hydrogen, the investor would exactly break even in terms of future discounted cash flows, including the initial capacity investment and all subsequent operating expenses (details in Economic Methods).
Earlier studies have established that, in addition to system prices and conversion efficiency, electricity consumption is a major cost component of electrolytic hydrogen 39;55;56 .Our cost calculations are based on a scenario where the electrolyzer operates as a stand-alone PtG system.The operator can purchase power in the wholesale electricity market, subject to a markup for industrial customers.In optimizing the use of its PtG system, the operator has the option of idling the electrolyzer during those hours when the prevailing market price of electricity is high and, therefore, hydrogen conversion would have a negative contribution margin.Accordingly, we initially consider a simple price vector of 8,760 hours, where each entry is calculated as the average across the day-ahead prices observed in the Texas market between the years 2016-2020.Our focus on Texas reflects that the state has deregulated its power market, deployed considerable amounts of renewable energy and hosts several large-scale hydrogen consumers 57 .The resulting annual average electricity purchasing price amounts to ¢3.6/kWh.Fixed operating costs are estimated as a percentage of system prices and account for the replacement of electrolysis stacks during the life of the system.At the suggestion of manufacturers of SOC systems, our calculations increase the assumed energy consumption of such systems by 5 kWh/kg to account for more complex heat management.
The useful lifetime of a system is set to 20 years and the cost of capital to 5.0% for all technologies (details in Supplementary Note 12).

SOC Electrolysis c
Variable operating cost Fixed operating cost Capacity Cost Depending on the growth scenario, our calculations yield LCOH estimates in the range of $1.6-1.9/kgfor alkaline, $1.6-1.8/kgfor PEM, and $1.6-1.9/kgfor SOC electrolyzers (Figure 3, details in Supplementary Note 12).The resulting LCOH ranges may appear surprisingly small, given the large variation in the assumed growth rates under the different scenarios.The main reason for the relatively limited LCOH range is that, depending on the electrolyzer technology, the variable cost of electricity accounts for about 70-90% of the total LCOH by the year 2030.Thus, even large differences in system prices and fixed operating costs as well as the assumed lifetime and the cost of capital have only a minor impact on the overall LCOH.In particular, SOC electrolysis is projected to entail similar LCOH values as the other technologies.The cost disadvantage of higher system prices in comparison to alkaline and PEM systems is compensated by the lower energy consumption of SOC electrolyzers.
To examine the sensitivity of our results in Figure 3, we calculate LCOH values for simultaneous changes in the annual average and the hourly variation of power prices (details in Economic Methods).These changes reflect electricity price distributions of economic market environments characterized by different costs and shares of competing power generation sources as well as the amounts and types of electricity demanded.Our calculations return the LCOH estimates shown in Figure 4. Overall, if the annual average electricity price were to decline by 50% and the hourly volatility to increase by 50%, the LCOH estimates for each technology and growth scenario would fall by about 30% relative to the values shown in Figure 3. Conversely, if the electricity price average were to increase, yet hourly volatility were to decrease by 50%, the LCOH estimates would rise by about 40%.These muted range estimates reflect that it is advantageous to idle the electrolyzers only during hours with relatively high prices. -

Policy Implications
Our findings on the economics of electrolytic hydrogen speak directly to several recent policy initiatives.First, our estimates of the levelized cost of hydrogen indicate that the Hydrogen Shot cost target of $1.0/kg by 2030 appears difficult to achieve if electrolyzer deployments grow at the rates underlying our calculations.We note, however, that most data points underlying our Policy and Industry Targets were set prior to the recent hydrogen initiatives by the European Union 8 and the Inflation Reduction Act in the United States 58 .The production tax credit of up to $3.0/kg of clean hydrogen available under the Inflation Reduction Act is likely to advance the deployment growth of PtG systems significantly in the United States.This growth will be reinforced by the goal of the European Union that seeks to induce its member states to collectively produce 20 million tons of green hydrogen annually by the year 2030 8 .
The level of subsidy support under the recent hydrogen initiatives by the European Union and the United States is tied in both jurisdictions to the carbon intensity of the hydrogen produced.In particular, the production tax credit of up to $3.0/kg available under the Inflation Reduction Act declines monotonically as the kg of carbon dioxide (CO 2 ) per kg of hydrogen produced increases beyond certain threshold levels.Our results in Figures 3 and   4 allow us to estimate the maximum carbon intensity permissible for the LCOH minus the corresponding subsidy support to be equal to or less than $1.0/kg.Absent any changes in the annual average or hourly variation of power prices, we find that all three PtG technologies would need to receive a nominal production tax credit of about $0.9/kg in 2030, which allows a carbon intensity of at most 1.5 kg of CO 2 per kg of hydrogen.Yet, if the annual average electricity price were to decrease by about 25% while the hourly volatility increases by about 25%, then the lowest available nominal production tax credit of $0.6/kg would be sufficient for all three PtG technologies to achieve the $1.0/kg cost target.The corresponding maximal carbon intensity is then 4 kg of CO 2 per kg of hydrogen.These calculations, detailed in Economic Methods, take into account that the production tax credit is only paid for the first ten years of operation and, therefore, the levelized tax credit is less than the nominal one.
We also note that even our most ambitious growth scenario for electrolyzer deployment, that is, the Industry Target falls significantly short of the target for 2030 by the International Energy Agency (IEA).As part of its "Net-zero by 2050" scenario, the IEA postulates 850 GW of installed capacity by 2030 and 3,000 GW by 2045 59 .To examine the implications of the IEA target, we first repeat our calculations in the preceding two sections, assuming that the total global installed capacity will reach 850 GW by 2030.The resulting LCOH ranges, reported in Figure 5, show that the IEA target of 850 GW of installed capacity results in all three PtG technologies reaching LCOH values of $1.0/kg if the annual average electricity price were to decline by about 50% and the hourly volatility were to increase by about 50%.
Achieving the $1.0/kg target with more moderate changes in electricity prices would require even faster growth in the cumulative installed capacity.Ultimately, a key objective of governmental support programs for hydrogen is to make electrolytic hydrogen production cost-competitive with traditional hydrogen supply based on fossil fuels.Transaction prices for traditional hydrogen supply are segmented primarily by scale (volume) and purity: large-scale supply between $1.0-2.5/kg,medium-scale between $2.5-4.0/kg, and small-scale above $4.0/kg 24;60;61 .These values are applicable benchmarks for hydrogen whenever PtG facilities can be installed onsite or adjacent to a hydrogen buying site.Figure 4 shows that all three PtG technologies are projected to become widely costcompetitive with industrial-scale hydrogen supply, even if cumulative installed capacity grows only at the rates observed on average in the past.
Finally, we emphasize that, regardless of the magnitude of the additional growth in deployments resulting from different policy initiatives, the availability of clean and inexpensive electricity will become increasingly important for electrolytic hydrogen, even if it is only available intermittently.It will, therefore, be essential for policymakers to take advantage of the inherent synergies between renewable power generation and electrolytic hydrogen.

Conclusion
Broad adoption of electrolytic hydrogen production will depend on improvements in system prices and conversion efficiency of Power-to-Gas technologies.This paper provides a comprehensive assessment of the dynamics in both parameters for alkaline, polymer electrolyte membrane, and solid oxide cell electrolyzer systems.Our calculations yield significant and robust learning curves of 83-86% for system prices and 98% for energy consumption over the past two decades.Based on these estimates, we project that all three technologies will become substantially cheaper and more energy-efficient.In particular, the life-cycle cost of electrolytic hydrogen production is projected to fall within $1.6-1.9/kgby 2030, approaching the Hydrogen Shot target of $1.0/kg set by the U.S. Department of Energy.
Future studies on electrolytic hydrogen production would benefit from more detailed information on the manufacturing cost and market prices of individual system parts (i.e., electrolysis stacks and balance-of-system components) that is available for multiple years.
They would also benefit from the research and development expenditures and the annual production capacity of equipment manufacturers.Such information could shed further light on the factors driving cost reductions.
It will also be instructive to broaden the line of inquiry in this paper to other technologies for clean hydrogen production, such as anion exchange membrane electrolysis, steam methane reforming with carbon capture and storage, or natural gas pyrolysis.The data available for these technologies has so far been too limited to allow for a similar analysis as conducted in this paper.Naturally, such studies will need to reflect that the tax credits available for hydrogen production under the U.S. Inflation Reduction Act vary greatly with the assessed carbon intensity of the hydrogen produced.
Finally, future work could examine the cost dynamics of hydrogen compression, transmissions, and storage technologies.These components of the hydrogen supply chain can substantially affect the cost of hydrogen supply, especially when the production and consumption of hydrogen are geographically dispersed.However, the data available for these components have so far been too limited and heterogeneous to allow for an analysis similar to the one conducted here for different electrolyzer technologies.

Levelized Cost of Hydrogen
In direct analogy to the commonly referenced levelized cost of electricity 62 , the LCOH identifies the constant price per kg of hydrogen that an investor would have to earn over the useful life of the PtG system in order to break even in terms of discounted after-tax cash flows.
As such, the LCOH enables a cost comparison of alternative PtG technologies that differ in their cost structure and operational characteristics.The following derivation demonstrates that, for a given hydrogen price p, investment in a PtG system is profitable if and only if: The price per kWh at time t at which a PtG operator can purchase electricity from the market is denoted by q(t).Here t is an integer where 1 ≤ t ≤ 8, 760.Since all three of the PtG technologies considered here can be ramped up quickly to operating temperature and conversely can be ramped down rapidly 39 , the capacity utilization factor, denoted by CF (t) can be chosen flexibly on the interval [0, 1] for each hour of the year.Representing the conversion efficiency of a PtG system (in kg/kWh) by the parameter η, where 0 < η < 1, the variable cost for producing 1 kg of hydrogen at time t is given by: Here w h reflects a cost increment incurred per kg of hydrogen produced for consumable inputs, such as water and reactants for deionizing the water.The optimized capacity factor, CF * (t), at time t will then be chosen to maximize η • [p − w(t)] • CF (t).Thus, CF * (t) = 1 if p−w(t) > 0, while CF * (t) = 0 if p−w(t) < 0. This yields the optimized annual contribution margin: For the purpose of the economic model, we can normalize the capacity investment in the PtG system to 1 kW of peak electricity absorption without loss of generality.To be sure, our numerical analysis calibrates the costs and revenues of a PtG facility in accordance with the system sizes that have been built in recent years.We denote the fixed operating costs per kW of installed capacity by F i in year i.In case the productive capacity of a PtG system degrades over time, we denote by x i the share of the initial capacity that is still productive in year i.Given a price for hydrogen p, the overall pre-tax cash flows per kW of peak power absorption capacity of the PtG system in year i is then given by: Let the system prices per kW of peak capacity be given by v.By definition, investment in the PtG system yields a non-negative net present value in terms of after-tax cash flows per kW of peak capacity over the useful life of T years if and only if: where γ = (1 + r) −1 represents the discount factor when r is the applicable cost of capital, and CF L i is the after-tax cash flow in year i.To account for the impact of corporate income taxes, we denote the firm's income tax rate by α with 0 < α < 1. Provided d i ≥ 0 is the percentage of the applicable tax depreciation charge in year i (where d i = 1), the firm's taxable income associated with the investment is Thus, the after-tax cash flow in year i is: Direct substitution shows that the inequality in (2) holds if and only if: Dividing by (1 − α) the inequality in (3) reduces to: where the tax factor ∆, with 0 ≤ ∆ ≤ 1 is defined by: It will be convenient to identify the life-cycle levelization factor as the anticipated number of kilograms of hydrogen that the PtG system will generate per kW of peak capacity over its useful life, given optimized capacity utilization: Since the investment expenditure for capacity is shared by the entire quantity of hydrogen produced over the life-cycle of the facility, the levelized cost of capacity becomes: Similarly, the levelized fixed operating cost per kg of hydrogen becomes: Finally, given optimized capacity utilization, the levelized variable cost per kg of hydrogen is given by: The final step in the derivation is to verify that, for any given hydrogen price, inequality ( 4) is met if and only if: If a PtG system is to receive a production tax credit under the Inflation Reduction Act per kg of hydrogen produced, the resulting profitability condition becomes: where ptc denotes the levelized production tax credit.Let P T C denote the nominal production tax credit and T • the number of years for which the production tax credit is granted.
The levelized production tax credit is then given by:

Estimates of Levelized Cost of Hydrogen
Our calculations are based on the system prices and energy consumption values reported in Figure 2 for the year 2030.Based on discussions with manufacturers of SOC systems, we increase the energy consumption of such systems by 5 kWh/kg to account for heat management.Fixed operating costs are estimated as a percentage of system prices and account for the replacement of electrolysis stacks during the life of the system.Variable operating costs are mainly driven by electricity prices.Since our estimation requires hourly electricity prices, we initially assume a simple price vector where each hourly price is equal to the average across the day-ahead prices observed in Texas between the years 2016-2020 for the corresponding hour: with i reflects the years from 2016-2020.The resulting price vector reflects a deregulated electricity market with a substantial share of renewable power generation.All input parameters used in our calculations and all results are provided in Supplementary Table 11.
Our analysis shows that the resulting LCOH values are mainly determined by electricity prices.To examine the sensitivity of the LCOH values on electricity prices, we consider simultaneous changes in the average of electricity prices as well as changes in the variance of the annual average.In particular, let µ(t) denote the multiplicative deviation factor given by: By construction, Furthermore, let α denote the relative change in the annual average of electricity prices and β the relative change in the hourly variation of electricity prices during hours where prices are above average.In addition, we calculate the corresponding change in the hourly variation of electricity prices during hours where prices are below average, denoted by β, such that the adjusted annual average remains unchanged.Thus, the adjusted electricity price in a particular hour is given by: where β is calculated such that Our sensitivity analysis does not seek a new model for future electricity prices.Instead, we examine the impact of different electricity price distributions on the life-cycle cost of electrolytic hydrogen production.Electricity price distributions are specific to the characteristics of the particular economic market.The rising deployment of intermittent renewable energy sources is expected to cause lower annual average electricity prices and higher hourly price volatility [63][64][65][66] .In contrast, the electrification of transportation services and industrial manufacturing, including hydrogen production, is expected to have a buffering effect on power prices.Naturally, the greenhouse gas emissions associated with electrolytic hydrogen production depend on the carbon intensity of the electricity consumed.Recent studies have examined the effect of different power sources and hydrogen production strategies on the carbon intensity of electrolytic hydrogen production 67;68 .

Overview
This paper provides a comprehensive assessment of the dynamics in system prices and energy efficiency for three prevalent PtG technologies: alkaline, polymer electrolyte membrane (PEM), and solid oxide cell (SOC) electrolysis.We collect and analyze global data points for system prices, energy consumption, and the cumulative installed capacity for each technology.Our regressions yield significant and robust learning curves of 83-86% for system prices and 98% for energy consumption over the past two decades.Incorporating multiple forecasts of future deployment growth, we project that, in the coming decade, all three technologies will become substantially cheaper and more energy-efficient.Specifically, the life-cycle cost of electrolytic hydrogen production is projected to fall in the range of $1.6-1.9/kgby 2030, thereby approaching but not reaching the $1.0/kg cost target set by the U.S. Department of Energy.Supplementary Figure 1 illustrates the main steps of our analysis.

Extrapolating Future Performance
Alternative scenarios of future deployment growth based on past growth rates, policy targets, and industry targets

Levelized Cost of Hydrogen Projection
Life-cycle cost of electrolytic hydrogen production based on projected system prices and conversion efficiency for hydrogen production + system prices'.Industry publications and technical reports were retrieved with a Google search based on the same keywords, where we reviewed the top 100 search results.
Our review procedures retrieved 396 unique sources, which we filtered by multiple criteria to maintain quality and timeliness.We first excluded sources without clear information on system prices (60).We also excluded sources referencing other articles as original sources (66) but then traced the references back to the original sources and added those sources to the pool if they included original data.We further excluded sources without explicit references or methods for obtaining the cost estimate (94).We excluded five articles that were published before the year 2000.Finally, we excluded estimates for alkaline systems manufactured in China 42 , primarily because of differences in technology and manufacturing standards 69 .
To focus on recent technological advances, we also excluded sporadic estimates for alkaline systems from before the year 2000 [17][18][19] .Most of these earlier data points are primarily based on estimates for individual large-scale capacity installations instead of observations for installations of different sizes.
Our procedure yielded 176, primarily European and North American, sources containing For all sources, we focused on system prices that include electrolysis stacks and the balance-of-system, but exclude hydrogen compression.Where available, we also collected system prices for different system sizes.Our main analysis then includes system prices that were normalized to a system size of 1 Megawatt (MW).Yet, we also examine the potential impact of changes in the size of a PtG system on system prices.System prices reported without a system size were interpreted to refer to an average system size for the corresponding year.
We also converted any range estimates to the midpoint in the reported range.Estimates given in currencies other than $US were converted based on the annual average exchange rate of the respective year.We also adjusted historical price information for inflation using the yearly inflation adjustment factor for qualified energy resources as provided by the US Internal Revenue Service.In both adjustments, we accounted for potential differences between the year for which the prices were expressed and the year of publication of the corresponding source.
Finally, all observations of one technology were winsorized at the 5.0% level in combination with a moving time window of 3 years ranging from 1 year before to 1 year after the year in which price estimates are adjusted.Winsorization has only a minor effect on our findings for all technologies.

Review of Cumulative Installed Capacity
Our data set of cumulative installed capacity is primarily based on the Hydrogen Projects Database by the International Energy Agency 46 .The original database includes production facilities that have been commissioned worldwide since 2000 for the generation of clean hydrogen and hydrogen derivatives.Production technologies listed in the database comprise alkaline, PEM, and SOC electrolysis, coal gasification and natural gas steam reforming both with carbon capture and storage technology, and other production pathways such as biogas pyrolysis, biogas steam reforming, or biogas membrane separation.In addition, the database also includes facilities where the type of electrolysis is undisclosed.
The original database lists 445 separate hydrogen production facilities.Since many of these entries miss information on the commissioning date and the installed capacity size, we manually reviewed each entry.We thereby relied on the source provided in the database and on publicly available information from news coverage, industry reports, project websites, and press releases of investors, project developers, and manufacturers.In the course of our review, we could verify information for 186 projects from the original database and amend or adjust entries for 111 projects.We could not verify or complete information for 111 projects due to a lack of publicly accessible information.Furthermore, we excluded 37 projects based on production technologies other than water electrolysis.
In addition, we conducted our own review of hydrogen projects based on industry announcements and media coverage.This review identified 133 additional projects that we added to the data set.Our final data set comprises 430 complete entries, of which 225 represent PtG facilities based on either alkaline, PEM, or SOC technology that were built worldwide between the years 2000-2020.Of these projects, 99 are alkaline electrolysis systems, 112 projects comprise PEM electrolyzers, and 14 facilities are based on SOC technology.If projects had a construction period of more than one year, we use the starting year, that is, the commission date in our calculations.The resulting total cumulative installed capacity across the three PtG technologies amounts to about 200 MW in 2020, which is consistent with recent estimates by industry analysts 41;48 .
The IEA recently published an update of the Hydrogen Projects Database 47 .This update includes some changes to the list of capacity installations in the previous version from which our review departed.However, the total cumulative installed capacity across the three PtG technologies in 2020 resulting from the update is slightly less than the 200 MW resulting from our database.We attribute this difference to the additional review of capacity installations we conducted.

Review of Conversion Efficiency
Information on specific energy consumption stems from the preceding two reviews.In total, In analogy to system prices, we converted range estimates (if given) to the arithmetic mean of the lowest and highest points in the range.Furthermore, estimates given in units other than kWh/kg were converted based on the lower heating value of hydrogen (120 MJ/kg) and a density of hydrogen of 0.090 kg/Nm 3 .We also checked the boundary and operating conditions of the PtG systems to adjust for factors such as gas compression, water purification, transport and storage of feedstock as well as a potential grid connection.All observations of a technology were winsorized at the 5.0% level in combination with a moving time window of 3 years ranging from 1 year before to 1 year after the year in which the estimates are adjusted.Analog to system prices, this winsorization has a small effect on our findings for all technologies.

Learning Estimates by Deployment
Supplementary Table 1

The Effect of System Sizes
Earlier work suggests that the system prices of a PtG facility decline at a diminishing rate as the capacity size of the system increases 22;23;40 .To examine the potential effect of changes in the size of PtG systems on the trajectory of system prices in our data set, let S i denote the system size in kW of peak power absorption for a particular technology in year i.The functional specification of the extended constant elasticity learning curve in logarithmic form is then given by: where β 2 denotes the size elasticity and µ i the idiosyncratic error term with E[µ i |Q i , S i ] = 0 ∀i.As such, the system prices of a PtG technology is estimated to decline with every doubling of system sizes to 2 β 2 % of its previous value.
Our data set on S i results from our reviews on system prices, energy efficiency, and installed capacity.In total, we gather 125 observations for alkaline system sizes, 114 for PEM, and 18 for SOC 40;46;70 .However, most of these observations are disconnected from our data on system prices.Specifically, only 13 size observations for alkaline and 8 size observations for PEM electrolyzers are connected to information on system prices.Given the data limitations, we implement three different specifications to investigate the potential impact of changes in system sizes on system prices.First, we estimate equation (A1) for each technology with S i given as the annual average system size of the technology.The resulting regression estimates are shown in Supplementary Table 2. Differences between our learning estimates, β 1 , in Supplementary Tables 1 and 2 are small.In addition, the estimated coefficients for size, β 2 , are close to zero and statistically insignificant.For alkaline and SOC, they are even positive.We attribute the results to the set of system prices available to us, which includes in all sample years ranges of price estimates that are likely to originate to some extent from different capacity sizes.Some of our data sources 40;70 provide ranges for system sizes with corresponding ranges for system prices.In the second specification, we first assume that the largest (smallest) system size in the size range of a data source corresponds to the lowest (highest) system price per kW in the cost range.We then interpolate the two ranges following the notion that larger systems entail lower system prices per kW.This procedure yields 18 additional pairs of system prices and sizes for alkaline and 11 additional pairs for PEM electrolyzers.

Supplementary
We replace the average annual system size with the interpolated values for these pairs and add them to our initial pairs of system prices and sizes.We then estimate (A1) again for all technologies.
Supplementary Table 3 Supplementary Table 3 provides the regression results for the second specification.Again, we find no statistically or economically significant parameter estimates for the size coefficient.
Meanwhile, the learning estimates for each technology are close to those reported in Figure 1.
This finding is consistent with analog studies examining the cost dynamics of other clean energy technologies.
Finally, we compare a specification in which we use only the direct matches and interpolated data, which is intended to produce significant size estimators.Consequently, we exclude all data points with matched yearly average system sizes and remain with our original and interpolated pairs only.We employ this specification to assess the impact of a theoretically significant size estimator on our learning parameters.Due to no available data for SOC, we can only carry out this analysis for alkaline and PEM.We find that alkaline electrolyzers exhibit a 2 β 1 = 84.5% learning curve from cumulative installed capacity and a reduction of 1 − 2 β 2 = 5.5% with every doubling of system sizes (Supplementary Table 4).
PEM electrolyzers, in contrast, show an 83.2% learning curve from cumulative installed capacity and a reduction of 7.4% from system sizes.The learning curves for both alkaline and PEM technology are close to those reported in Figure 1, even though the regressions are based on a much smaller data set.

The Effect of Precious Metal Prices
Some components of PEM electrolyzer systems, such as the electrodes, bipolar plates, and porous transportation layers, so far require the precious metals platinum and iridium 41;71 .To examine the potential effect of a change in the market prices of either metal, let P latinum i and Iridium i denote the respective global annual average market prices in year i and β 3 and β 4 the corresponding regression coefficients.The logarithmic form of the extended learning curve is then given by: where µ i is again assumed to have a zero mean and to be uncorrelated with the independent variables.
Market prices for both metals are taken from www.platinum.matthey.com.Supplementary Table 6 provides detailed regression results.Similar to before, we find that the differences between our learning estimates, β 1 , in Supplementary Tables 1 and 6  10 Future Cumulative Installed Capacity Our projections consider three alternative scenarios for the growth of cumulative installed electrolysis capacity over the coming decade.The first scenario (called "Past Growth") assumes that the cumulative capacity of each considered technology continues to grow over the coming decade at the same average rate as in the past.As described in the main body of the paper, we estimate the past average growth rate of cumulative capacity for each technology based on a univariate regression for a constant elasticity model of the form: where i denotes the idiosyncratic error term with E[ i ] = 0 ∀i.Accordingly, the cumulative installed capacity of a PtG technology is predicted to increase every year to e λ 1 of its value in the preceding year.The detailed regression results are provided in Supplementary Table 8, while an illustration is provided in Supplementary Figure 3.
The second scenario (called "Policy Target") assumes that cumulative installed electrolysis capacity will grow such that global installed capacity in the year 2030 meets an aggregate of policy targets.At the point of our analysis, the aggregate target amounts to about 115 GW and stems from the following national and supranational hydrogen strategies: Chile 25 GW 72 and the European Union with 40 GW in Europe and 40 GW in its neighborhood, in particular North Africa 73 , where 36 GW are currently targeted to be built in France (6.5 GW), Germany  In case targets for installed capacity in 2030 were given in a range, we converted these to the arithmetic mean of the lowest and highest targets in the range.All included announcements for installed capacity have a scheduled completion date before 2030.
Some industry observers argue that the growth in PEM installations over the coming years might be slower than in the past because of shortages of rare earth materials and bans on fluoric coatings, which are expected in some jurisdictions, including the European Union.
To examine this possibility, we analyze variants of the Policy and Industry Target scenarios.
Here, we assume that each technology will obtain the same cumulative installed capacity in 2030 as in the Past-Growth scenario.The remaining growth in capacity required to reach the policy (or industry) target is then equally distributed between alkaline and PEM electrolysis, where each one obtains a share of 49%.SOC technology is assumed to obtain the remaining share of 2%, representing the relative youth of the technology.The resulting estimates for the alternative scenarios in cumulative installed capacity are provided in Supplementary Table 9.The corresponding projections for the trajectories of system prices and conversion efficiency are provided in Supplementary Figure 4.
Figure 5.As such, all scenarios and specifications in our calculations yield a consistent assessment of the magnitudes and trends in price and efficiency improvements.12 Levelized Cost of Hydrogen Supplementary Table 11 provides detailed inputs and outputs for our LCOH calculations.
final data set comprises 430 complete entries, of which 225 represent PtG facilities based on either alkaline, PEM, or SOC technology that were built worldwide between the years 2000-2020.Of these projects, 99 are alkaline electrolysis systems, 112 projects comprise PEM electrolyzers, and 14 facilities are based on SOC technology.The resulting total cumulative installed capacity across the three PtG technologies amounts to about 200 Megawatt (MW) in 2020, a figure that is consistent with recent industry estimates 41;48 .Information on specific energy consumption stems from the preceding two reviews (details in Supplementary Note 4).This information includes 130 data points for alkaline systems over the years 2000-2020, 78 for PEM systems between 2005-2020, and 21 for SOC systems across 2011-2020.

Figure 1 .
Figure 1.Estimates of learning curves.This figure plots the global system prices in 2020 $US against the global cumulative installed capacity together with our estimates of the corresponding learning curves for (a) alkaline, (b) PEM, and (c) SOC electrolyzers.The figure also plots the energy consumption against the global cumulative installed capacity together with our estimates of the corresponding learning curves for (d) alkaline, (e) PEM, and (f ) SOC electrolyzers.Areas shaded in red represent 95%-confidence intervals.Detailed regression results are provided in Supplementary Note 5.

Figure 2 .
Figure 2. Prospects for system prices and conversion efficiency.This figure shows our projections of the potential development of system prices in 2020 $US for (a) alkaline, (b) PEM, and (c) SOC electrolyzers.It also shows our projections of the potential trajectory of energy consumption for (d) alkaline, (e) PEM, and (f ) SOC electrolyzers.Shaded areas represent a joint 95%-confidence interval resulting from the learning curve estimates.Specifically, the upper bounds are derived from the upper bounds of the learning curve estimates in combination with the Past-Growth scenario, while the lower bounds are given by the lower bounds of the learning curve estimates combined with the Industry-Target scenario.

Figure 3 .
Figure 3. Estimates of levelized cost of hydrogen by 2030.This figure shows our estimates of levelized cost of hydrogen by 2030 for (a) alkaline, (b) PEM, and (c) SOC electrolyzers for different growth scenarios.

Figure 4 .
Figure 4. Sensitivity of levelized cost of hydrogen estimates by 2030.This figure shows the sensitivity of our levelized cost of hydrogen estimates by 2030 for changes in the annual average and hourly variation of power prices for (a, d, g) alkaline, (b, e, h) PEM, and (c, f, i) SOC electrolyzers for different growth scenarios.

Figure 5 .
Figure 5. Sensitivity of levelized cost of hydrogen estimates by 2030.This figure shows the sensitivity of our levelized cost of hydrogen estimates by 2030 for changes in the annual average and hourly variation of power prices for (a) alkaline, (b) PEM, and (c) SOC electrolyzers for the growth scenario postulated by the International Energy Agency (IEA).
264 unique observations from industry or an original review of multiple sources.Of these observations, 105 belong to alkaline electrolysis over the years 2003-2020, 81 to PEM system between 2003-2020, and 78 to SOC technology spanning the years 2011 to 2020.Since SOC electrolyzers are reversible, we include estimates for fuel cells in our sample.
we retrieved 229 data points: 130 for alkaline systems over the years 2000-2020, 78 for PEM systems between 2005-2020, and 21 for SOC systems across 2011-2020.We interpret these values as those obtained at full capacity utilization.Alkaline and PEM electrolyzers attain a near-constant energy consumption beyond a small threshold utilization level40 .For SOC systems, existing literature provides little evidence for the change in energy consumption as a function of capacity utilization.For all technologies, the energy consumption values include the energy required for the electrolytic conversion process and the operation of auxiliary systems, such as control systems and monitoring equipment.Yet, the values exclude the energy needed for heat management.

Table 1 .
Estimates of cumulative installed capacity by 2030.

Table 1 .
provides detailed results for our regression estimations of the constant elasticity learning curve in equation(1)in the main body of the paper.Learning estimates for the energy consumption of SOC electrolysis are not statistically significant due to the limited sample size.Yet, the results are consistent with industry estimates and anecdotal evidence from manufacturers.Regression results for equation(1).System prices are in 2020 $US/kW and cumulative installed capacity is in MW.All values are logarithmized using the natural logarithm (ln).Entries in parentheses are standard errors.Key to statistical significance: * * * ≤ 0.001, * * ≤ 0.01, * ≤ 0.05.

Table 2
System prices are in 2020 $US/kW, cumulative installed capacity is in MW, system sizes are in MW.All values are logarithmized using the natural logarithm (ln).Entries in parentheses are standard errors.Key to statistical significance: * * * ≤ 0.001, * * ≤ 0.01, * ≤ 0.05.

Table 7 .
are relatively small.At the same time, the estimated coefficients for both metals are economically insignificant.Regression results for equation (A3).System prices are in 2020 $US/kW and time is given in years.Price values are logarithmized using the natural logarithm (ln).Entries in parentheses are standard errors.Key to statistical significance: * * * ≤ 0.001, * * ≤ 0.01, * ≤ 0.05.

Table 10 .
Regression results for equation (A5)System prices are in 2020 $US/kW, cumulative installed capacity is in MW, average system sizes are in MW.All values are logarithmized using the natural logarithm (ln).Entries in parentheses are standard errors.Key to statistical significance: * * * ≤ 0.001, * * ≤ 0.01, * ≤ 0.05.