Proton Exchange Membrane (PEM) electrolysis is a promising pathway for producing low -carbon hydrogen via electrolysis coupled with variable renewable energy (VRE). T his study introduces a physics - based PEM electrolyzer model into a n integrated design and scheduling optimization routine , allowing for a comprehensive evaluation of the impact of reactor level metrics (e.g., cathode pressure, current density) on the levelized cost of hydrogen (LCOH) across various cost, technology, and electricity supply scenar ios. Benefits of static vs dynamic operation of PEM systems are outlined explicitly. The economic viability of a grid -based PEM electrolyzer producing 50,000 kg of hydrogen per day is assessed for both 2021 and 2035 technology scenarios . Results show that dynamic operation reduces the LCOH by 8% under the 2021 Scenario (4.98 to 4.57 $/kg -H2 at maximum current density 2 A/cm2). Under 2035 price, cost and technology assumptions (maximum current density 4 A/cm2), the LCOH ranges between 2.18 - 3.93 $/kg -H2 under static operation, and between 1.42 -2.84 $/kg -H2 under dynamic operation, resulting in LCOH reductions of 20 -50% depending on the electricity price profile. In addition, partial differential pressure mode with a cathode pressure of 5 bar was found to be the most cost -effective way to compress hydrogen to 30 bar in the 2021 Scenario, while full differential pressure mode is preferred in 2035 Scenarios. Finally, the study revealed that grid -based hydrogen production in 2021 does not meet the carbon intensity (CI) criteria for clean h ydrogen in recent U.S. legislation , highlighting the need for dedicated renewable power sources for hydrogen electrolysis to qualify as “clean” . These results suggest that capital cost reduction alone will not achieve low -cost electricity -based hydrogen production, emphasizing the need for further reductions in the cost of low -CI electricity to attain affordable and lower -carbon hydrogen production . 1. Introduction The rapid expansion of renewable energy source s like wind and solar is necess ary to combat climate change . A primary challenge, however, is managing the intermittent nature of such energy in a cost - effective manner . While commercially available Li -ion battery storage is becoming increasingly more cost-effective for storing energy over the period of hours, longer -term energy storage at scale remains challenging1. Hydrogen stands out as a promising low-carbon energy carrier that can provide a means of both long -term energy storage and long -distance energy transport , while serving as a vector for decarbonization end -uses where direct electrification remains challenging. Among the various hydrogen production methods, electrolysis, whereby water is split into hydrogen and oxygen using electricity, offers a less carbon intensive alternative for producing hydrogen in comparison to steam methane reforming and autothermal reforming when driven by renewable power2. Current industrialized water electrolysis technologies for hydrogen production include alkaline and proton exchange membrane ( PEM ) electrolysis. While the alkaline process is more mature, PEM electrolysis is a particularly viable approach in this context, due to faster dynamical response times, wider current density range (0.1 – 6 A/cm2 vs 0.1 -0.4 A /cm2 for alkaline3), reduced corrosion, and fewer components 3,4. However, the current capital cost of PEM electrolysis remains a substantial hurdle , primarily due to membrane and electrocatalyst costs . This contributes the levelized cost of hydrogen (LCOH ), which is estimated to be around $5/kg to $6/kg 5 . This cost is considerably higher than that of steam methane reforming (SMR) , the most widely used industrial process for the generation of hydrogen , which ranges from approximately $1.06/kg -$1.64/kg 6. 7This cost disparity poses a major barrier to the widespread adoption of low-carbon electrolytic hydroge n. This disparity is diminishing however, due to substantial cost reductions in solar and wind electricity generation, as well as reductions in the upfront capital expenses related to electrolyzers 3,8,9. Operating electrically driven processes dynamically in a variable renewable energy (VRE) dominated grid has the potential to drastically reduce operational expenditures, since the process can exploit surplus electricity during low -price periods (e.g., when supply exceeds demand) . This approach presents an interesting optimization problem, since oversizing the system to deal with times of peak production leads to an increase in capital expenditure (CAPEX) and could increase the overall levelized cost of hydr ogen . For electrochemical systems, an additional trade -off to consider is the decreased energy efficiency at high current densities due to increasing overpotentials 10. Several studies have therefore considered the design and operations optimization of electrolyzer systems, with respect to time varying electricity prices. Roh et al. have formulated a total production cost minimization problem for a dynamically operating chlor -alkali electrolyzer 11. Several techniques have been used to make the optimization problem tractable, including a) discretizing the time domain, b) using a piecewise linear approximation for the quadratic power demand function, and c) utilizing a golden -section search (GSS) decomposition method on the electrolyzer size, resulting in a series of mixed -integer linear programs (MILPs). Results have indicated that by oversizing a chlor -alkali electrolyzer and operating dynamically, the total production cost is reduced, provided that the specific capital costs of oversizing are low enough and the electricity price strongly fluctuates. Extending on the concept of oversizing electrolyzers to optimize the least -cost design , Mallapragada et al.12 have developed a techno -economic optimization model to evaluate the economics of a photovoltaic ( PV) PEM system , and have found system configurations and capital cost targets that result in LCOH that is competitive with hydrocarbon -based production methods 13. In their work, location dependent H2 storage and PV facilities were also considered, and a simple model for the PEM electrolyzer was used, without explicitly modeling the polarization curve (current density – voltage dependence). Ginsberg et al. have considered the optimization of a PEM electrolyzer plants operating dynamically under California and Texas electricity price scenarios 3. The study has considered various operation modes of the electrolyzer, highlighting the temporal variations in current density, ranging from minimum to maximum levels. Results indicate d that dynamic operation reduces the LCOH by up to 63% for 2020 prices and by up to 53% for projected 2030 prices compared to static operation. Furthermore, operation above 2.5 A/cm2 is justified at electricity prices below $0.03 /kWh . In their work, Ginsberg et al. 3 established a voltage -current density dependence in their model by regressing to three specific experimentally measured polarization curves , characterizing high, baseline and l ow electrolyzer efficiencies 14. Our work aims to extend on the work of Ginsberg et al. 3 by modeling the PEM electrolyzer more predictivel y such that different design choice s (e.g., electrolyzer pressure, and membrane thickness ) may be readily analyzed within a n integrated techno -economic optimization framework, without the extensive reliance on experimental data. The p revious literature on PEM electrolysis plants has focused on physics -based models 15,16 or dynamic operation optimization 3,12, but not considered both as part of a design and operations optimization framework . Studies u sing physics -based and cost models typically assess the LCOH under different operating conditions, identifying key drivers for cost reduction. For instance, Orella et. al have presented a generalized techno -economic model that can be used for various electrolytic processes and used it to evaluate the economics of PEM electrolysis 17. In addition , Badgett et. al have provided a techno - economic assessment of the future production of hydrogen based on reduced capital cost as determined from a learning rate, manufacturing economies of scale, reduced material consumption, and improved electrolyzer performance 18. Moreover, James et al. have provide d a detailed techno - economic assessment (TEA) model specific to PEM systems, and conclude that the primary cost drivers are the electricity expenditures to run the electrolyzer and the capital cost of the electrolyzer 19. Furthermore, Yates et. al have evaluated the potential of PV -PEM Electrolyzer systems using a Monte - Carlo approach to identify key drivers for reducing the LCOH 20. Finally, Hancke et al. used a techno - economic model to evaluate the economics of differential -pressure operation of a PEM electrolyzer system by comparing the cost of direct electrochemical compression with the cost of mechanical compression 21. The existing literature on PEM electrolysis plant, while comprehensive in several as pects, has important gaps that this work seeks to address. P revious studies have either focused on physics -based models, as seen in the works of 17–19 , or on dynamic operation optimization3,12,20,21. However, most of these studies have not integrated both aspects: physics -based modeling and dynamic operation optimization with respect to process economics , within a single design and operations optimization framework. This integration is crucial for understanding the interplay between the physical properties of the electrolyzer and operation mode on its operational dynamics, especially under varying economic and environmental conditions. Our work builds on the above literature by: a) developing a physics -based PEM electrolyzer and TEA model that relat es cell-level (e.g., membrane thickness) and plant parameters (e.g., operating temperature and pressure) with process economics , b) integra ting the developed models as part of a techno -economic optimization framework considering dynamic operation , and c) considering a wide range of market scenarios such as region -specific electricity price profiles . The optimization framework allows for evaluating the cost -optimal design and scheduling of a commercial scale PEM electrolyzer plant con nected to the grid with time -varying electricity prices and carbon intensities . We explicitly characterize the CAPEX -OPEX tradeoff under dynamic and static operation and consider a limited treatment of the impact of differential pressure operation of the LCOH. Finally, our analysis considers the LCOH impacts of dynamic and static mode of operation considering today’s grid as well as future renewables dominant power system with increased instances of zero -marginal cost electricity and price volatility. 2. Methodology 2.1. Electrolyzer Model The electrolyzer model uses thermodynamic and electrochemical principles to generate a polarization curve, which describes the electrolyzer’s voltage as a function of current density. The number of electrons transferred directly translates to the moles of products generated in an electrochemical reaction, so the polarization curve is a measure of voltage that is required to produce a unit mass of hydrogen. In this work, t he polarization curve is calculated as the sum of the thermodynamic equilibrium voltag e, ohmic overpotential, and activation overpotential for a given electrolyzer technology and design. The thermodynamic equilibrium voltage necessary to create the chemical potential to drive the electrolysis process, also known as the open -circuit voltage, is given by the Gibbs Free Energy state equation combined with the Nernst Equation (Eq. S2) . Using the state equations allows exploration of much wider temperature and pressure ranges than typical empirical or analytical expressions 16,22,23. In this study, the model was used to evaluate the thermodynamic equilibrium voltage at an operating (cathode) pressure of 1 to 30 bar and an operating temperature of 80 °C. The ohmic resistance results from the resistances from the electron flow, proton flow, electrical contact in the membrane electrode assembly (MEA). The biggest contributor to the ohmic resistance in the PEM electrolyzer is the membrane 22,24. Nafion 117 with a thickness of 178 um is assumed as the membrane technology for the current systems (2021 scenario) while thinner membranes (and thus lower ohmic resistance) is evaluated for the 2035 scenario (see Table 1). The activation overpotential, also known as the kinetic overpotential, is the additional voltage that is needed to supply the activation energy to initiate the exchange of electrons in the electrochemical reactions 25,26. The Butler -Volmer equation (Eq. S12) with the temperature -dependent exchange current density is used to calculate the activation overpotential as a function of current density. Other models also include the concentration overpotential, which arises due to the overpopulation of reacting species near the electrodes interface. However, as long as the flow field is well designed for gas removal and the water circulation rate is high enough, the concentration overpotential can be neglected for PEM electrolysis 23,24,26 –29. For the purpose of making this model a computationally efficient techno - economic optimization tool, the thermal behavior of the electrolyzer was not modeled and it was assumed that an excess amount of water circulates through the system to provide the necessary cooling to control the operating temperature. In addition, the degradation of the electrolyzer stack was not modeled explicitly, but was accounted for in the TEA model by assuming regular refurbishment of the stack every 10 years. A detaile d description of the electrolyzer model is available in SI1. Figures 2a) and 2b) show that the electrolyzer model can be calibrated to make accurate predictions of experimental data 22,30 under various cell configurations and thermodynamic conditions. The model parameters for the 2021 and 2035 technology assumptions were chosen to match the performance of benchmark systems, including commercially available stacks, as shown in Figure S3 . 2.2. Techno -Economic Analysis (TEA) Model The TEA model used in this study was constructed by combining a physics -based PEM electrolyzer model with a system -level cost model for a PEM electrolyzer production plant shown in Figure 2. The production plant consists of the electrolyzer stack, the mechanical balance -of-plant, and the electrical balance -of-plant. a) b) Figure 1: PEM polarization curves under varying thermodynamic conditions. a) Comparison of the electrolyzer model (line) with experimental data30 (circles) at 80°C (red) and 60°C (blue) at ambient pressu re. b) Comparison of the electrolyzer model (line) with experimental data22 (circles) at (a) 55°C and 10 bar (blue); (b) 40°C and 70 bar (red) . The electrolyzer plant cost model was adapted from the Department of Energy (DOE) H2 A model 19, which is based on a detailed ASPEN -model based economic analysis and input from electrolyzer manufacturers. The resultant TEA model serves to determine the net present value (NPV) for the overall production facility, which is subsequently used as the objective function in the integrated design and scheduling optimization problem (see section 2.3). Figure 2: a) Schematic of the PEM electrolysis system showing the electrolyzer stack, the mechanical balance of plant, and the electrical balance of plant. Adapted from 31. KO = Knock Out. b) Illustration of hydrogen flow paths from electrolyzer to storage to system outlet. a) b) 2.2.1. Electrolyzer Cost Model The electrolyzer cost model was adapted from the Department of Energy (DOE)’s H2 A model 19, which considers capital, operational, and overhead costs associated with different components of the electrolyzer plant, such as the stack, the mechanical balance -of-plant (BoP), and the electrical BoP. The stack cost was calculated based on the materials, labor, and capital costs associated with producing the stack. The mechanical BoP includes pumps, compressors, heat exchangers, water filtration system, knockout pots, and temperature swing adsorption system. The electric al BoP includes components such as transformers, rectifiers, switchgear, and control systems. The model also considers the cost of land, site preparation, and installation, as well as indirect costs such as project management, engineering, and contingency. The operational costs include the cost of electricity and feedwater that are necessary to operate the electrolyzer plant. To calculate the total cost of ownership of the electrolyzer plant, the net present value -calculation model was applied to the capital and operating costs over it s expected lifespan. The model adopts the cost assumptions of the H2 A model with modifications to adjust for inflation based on the Chemical Engineering Plant Cost Index (CEPCI) and for the 2021 reference dollar based on the U.S. Bureau of Economic Analysis’s Consumer Price Deflator. A detailed description of the electroly zer techno -economic model is available in SI3. 2.2.2. Compression Cost Model For an electrolyzer plant whose target delivery pressure is 30 bar, the output hydrogen stream can be compressed electrochemically, mechanically, or a combination of both. The higher capital and operating expenses resulting from electrochemical compression were accounted for in the electrolyzer model through a pressure adjustment factor sourced from the literature (see Figure s S4a and S4b ), with the result that 15 -bar stack has roughly a 20% higher capital cost than a stack at ambient conditions 32. For mechanical compression, a separate cost model was developed using the Department of Energy’s Hydrogen Delivery Scenario Analysis Model (HDSAM). The description of the compression model is provided in SI4. 2.3. Techno -Economic optimization framework An optimization framework was formulated to ascertain the ideal plant sizing ( specifically, the electrolyzer surface area and storage capacity), and optimal scheduling of the process -related operational variables (e.g., current density) over the course of year under time -varying electricity prices. The net present value of the plant cost was used as the objective function to be minimized. Since all scenarios considered in this work assume the same average daily production rate (see Section 2.5) this is equivalent to minimizing the LCOH. The LCOH was calculated by dividing the total discounted cost by the total discounted hydrogen production over the lifespan of the plant. The optimization problem was given by: 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑁𝑃𝑉 (𝐶𝑇𝑜𝑡𝑎𝑙 )=𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐶𝐶𝐴𝑃𝐸𝑋 +𝐶𝑠𝑡𝑜𝑟𝑎𝑔𝑒 +∑ [(𝐶𝑃𝑅+𝐶𝑈𝑃𝑅 +𝐶𝑓𝑂𝑃𝐸𝑋 +40 𝑦=1 𝐶𝑣𝑂𝑃𝐸𝑋 )(1+𝜋)𝑦 (1+𝑑)𝑦] . (1) Where 𝐶𝐶𝐴𝑃𝐸𝑋 is the capital expenditure ($), 𝐶𝑠𝑡𝑜𝑟𝑎𝑔𝑒 is the capital expenditure for storage ($), 𝐶𝑓𝑂𝑃𝐸𝑋 are the fixed operating expenses, 𝐶𝑣𝑂𝑃𝐸𝑋 are the variable operating expenses, 𝐶𝑃𝑅 is the planned replacement cost, and 𝐶𝑈𝑃𝑅 is the unplanned replacement cost. Throughout, we assume a plant lifetime of 40 years , an inflation rate ( 𝜋) of 1.9 %, and a discount rate adjusted for inflation ( 𝑑) of 8 %. The variable OPEX expenditures were determined by: 𝐶𝑣𝑂𝑃𝐸𝑋 =∑ ∑ 𝑃𝑒𝑙𝑒𝑐(𝑡)×𝑃𝑜𝑤𝑒𝑟 𝑜𝑝(𝑗𝑜𝑝(𝑡))+𝑃𝑒𝑙𝑒𝑐(𝑡)×𝑈𝑒𝑙𝑒𝑐ℎ𝑜𝑢𝑟𝑙𝑦×𝑚̇𝐻2,𝑝𝑟𝑜𝑑ℎ𝑜𝑢𝑟𝑙𝑦(𝑡)+24(𝑑+1)−1 𝑡=24𝑑364 𝑑=0 𝑃𝑤𝑎𝑡𝑒𝑟 ×𝑈𝑤𝑎𝑡𝑒𝑟ℎ𝑜𝑢𝑟𝑙𝑦×𝑚̇𝐻2,𝑝𝑟𝑜𝑑ℎ𝑜𝑢𝑟𝑙𝑦(𝑡). (2) Where 𝑃𝑒𝑙𝑒𝑐(𝑡) is the electricity price at time 𝑡, 𝑃𝑜𝑤𝑒𝑟 𝑜𝑝(𝑗𝑜𝑝(𝑡)) is the electrolyzer stack power which is a function of current density ( 𝑗𝑜𝑝(𝑡)), 𝑈𝑒𝑙𝑒𝑐ℎ𝑜𝑢𝑟𝑙𝑦 and 𝑈𝑤𝑎𝑡𝑒𝑟ℎ𝑜𝑢𝑟𝑙𝑦 are the hourly electrical usage and water usage respectively, and 𝑚̇𝐻2,𝑝𝑟𝑜𝑑ℎ𝑜𝑢𝑟𝑙𝑦 is the hourly mass flow of hydrogen produced. In equation (2), we sum over all hours of the year, and 𝑃𝑒𝑙𝑒𝑐 is a yearly electricity price profile, discretized in hours. Note that by substituting 𝐶𝑣𝑂𝑃𝐸𝑋 in the NPV optimization (1), we assum e that model dispatch over 1 year is duplicated over the other 39 years. Under dynamic operation, a hydrogen storage device at the electrolyzer outlet (see Figure 1b) is modelled so that the system is allowed to store excess hydrogen during periods of low electricity prices and discharge it later, while meeting a fixed daily production rate. For simplicity, the storage can be charged or discharged, but not both at the same time. The storage model is described in more detail in SI6. A minimum current density limit for the electrolyzer is applied due to safety and efficiency consi derations, and this is achieved via a big -M formulation (see SI Eqs S49 and S50 ). The optimization problem is discussed in more detail in SI 6. 2.3.1. Solution method Two techniques were used to make the optimization problem ( 1) numerically tractable. Firstly, due to the nonlinearities present in the electrolyzer model equations, a piecewise linear approximation was used to determine the stack power density as a function of current density (see SI6, SI Figure S24). This method improves optimization time and allows for implementation in Gurobi as the global optimization solver. Secondly, a golden section search (GSS) decomposition method is used to determine the optimal electrolyzer capacity (see SI6 , and figures S23, S26 and S27 ), which results in the solution to many smaller MINLP subproblems with fixed ele ctrolyzer capacity The overall LCOH minimization problem is a mixed -integer linear program (MINLP), was implemented in Gurobi 9.5 , and solved to a 1 % optimality gap. The optimization model consists of approximately 250,000 equations, 50,000 continuous variables and 60,000 binary variables. Typically, about 10 GSS iterations were required to reach a convergence tolerance of 1 tonne H2/day (2% of the baseline value) . Since the electrolyzer capacity was fixed in the subproblem, the objective function in the inner loop of the GSS algorithm was simplified as: 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐶𝑠𝑡𝑜𝑟𝑎𝑔𝑒 +∑ [𝐶𝑣𝑂𝑃𝐸𝑋(1+𝜋)𝑦 (1+𝑑)𝑦]40 𝑦=1 (3) Where 𝐶𝑠𝑡𝑜𝑟𝑎𝑔𝑒 is the capital cost of the storage device, which increases linearly with storage inventory. 2.4. Grid electricity input data sources In order to assess the impact of electricity price on the levelized cost of hydrogen (LCOH) in the 2021 Scenario, historical hourly locational marginal prices (LMP) from Southern California in 2021 33 were used in the cost model. In addition, a typical grid interconnection cost of $0.03/W was added to the total electricity price. For the 2035 scenario, multiple regional system electricity price projections for 2030 -2040 from the National Renewable Energy Laboratory (NREL) 2021 Cambium Project 34 and the FLECCS Program 35,36 were used in the simulation. Brief descriptions of each of the electricity price scenarios used in this study are available in SI5. 2.5. Scenarios evaluated Throughout this work, we employ a case study that uses grid electricity to supply 50,000 kg of H2 per day, generated at an outlet pressure of 30 bar, in line with central, large, plant size H2 production system described by 19 . The electrolyzer temperature is assumed to be 80 C. The minimum operating current density, 𝑗𝑚𝑖𝑛, is assumed to be 0.5 A /cm2. The cathode and anode exchange current densities are assumed to be 2.3x10-3 and 3.0x10-6 A, respectively. Two modes of operation are considered: static and dynamic. Under static operations, the electrolyzer was constrained to operate at a constant nominal current density, producing a constant stream of hydrogen at the outlet. In this mode of operation, the electrolyzer plant was sized to exactly match the demand rate, thereby removing the need for a storage facility . In dynamic operations, the electrolyzer was allowed to vary the operating current density subject to technical and operational constraints . In addition, a storage facility is necessary to insulate the consumers from variable production of dynamic operations . 2.6. Cost and technology assumptions A sensitivity study was carried out in order to assess the impact of different cost drivers on the LCOH. The sensitivity parameters include different technology, cost, and price assumptions on the basis of available calculations and projections in the literature. To ensure consistency in the assessment of plant costs, adjustments were made using the Chemical Engineering Plant Cost Index (CEPCI). This index accounts for changes in the costs of equipment, construction, and plant expenses, providing a relia ble standard for evaluating the actual costs of the project. Additionally, all monetary figures were standardized to 2021 values employing the Consumer Price Deflator. By converting all financial data to a common base year, this adjustment ensures a comparative analysis based on the prevailing economic conditions of 2021 . Table 1 shows the electrolyzer model parameters assumed for the 2021 and 2035 Scenarios. Table 2 shows the cost model parameters assumed for the 2021 and 2035 Scenarios. In section 3.3 we also consider modifying the cathode pressure. Table 1: Electrolyzer Model Parameter s for various technology scenarios. Parameter 2021 Scenario 2035 Scenario Unit Membrane Thickness 17830 12710 μm Cathode Exchange Current Density 2.3x10-3 2.3x10-3 A/cm2 Anode Exchange Current Density 3.0x10-6 3.0x10-6 A/cm2 Temperature 80 80 C Cathode Pressure 30 30 Bar Anode Pressure 1 1 Bar Maximum or Nominal Current Density 1,2,3,4 4 A/cm2 Minimum Current Density 0 0.5 A/cm2 Table 2: Key technology cost assumptions across the two technology scenarios . See SI 3 and SI4 for details. eBoP is the electrical balance of plant consists of an AC transformer to change the voltage of the AC power supply from the grid and a rectifier to convert the AC current to a DC current . The mechanical BoP (mBoP) consists of subsystems that perform secondary functions to support the electrolyzer stack 14. Parameter 2021 Scenario 2035 Scenario Unit Electrolyzer Stack Cost 2 0.7 $/cm2 mBoP Cost 117 54 $/(kg H2 /day) eBoP Cost 126 80 $/kW electric Total CAPEX 1,006 421 $/kW input Storage CAPEX 500 300 $/kg Grid interconnection cost 30 $/kW Discount rate for annualizing capital costs 8% 3. Results And Discussion In this study, we explore three main aspects that influence the LCOH for a PEM electrolysis plant: 1) static vs dynamic operational modes considering design and operational cost trade -offs, 2) system design parameters like maximum current density and differential pressure operations and 3 ) the influence of different electricity price profiles and technology cost assumptions. We also include a brief discussion of the potential cost and design implications of the H2 production tax credits available in the U.S. as part of the Inflation Reduction Act of 2022 with a more thorough discussion on this subject available elsewhere 37. 3.1. Impact of Dynamic vs Static Operations on LCOH Under 2021 Technology and Cost Assumptions Under 2021 cost and technology assumptions noted in Table 1 -2, dynamic operations reduce the LCOH by 5 - 11% compared to the equivalent static operations delivering the same hourly hydrogen production rate of 50 tonnes/day (Figure 3) . The cost savings is attributed to the reducing variable operating costs (mostly power purchase costs), which account for up to 82% of the LCOH shown in Figure 3. Under dynamic operations, the cost -optimal electrolyzer dispatch results in increasing hydrogen production (by increasing current density) when the electricity is cheap and decreasing production when the electricity is expensive, as highli ghted in temporal patterns in current density and electricity prices in Figure 4. By contrast, the electrolyzer in a static mode produces a constant stream of hydrogen by operating at a constant nominal current density of 2 A/cm2 regardless of the fluctuations in the electricity prices. Figure 3: Optimized LCOH contributions under 2021 cost and technology assumptions. LCOH has units $/kg -H2. For static operation, the current densities mentioned refer to the unchanging operation at the specified current density. Under dynamic operation, the current densities indicate the maximum permissible current density. The electrolyzer is given the flexib ility to operate below this maximum limit on an hourly basis. Electricity price scenario based on the historical data for node LAFRESA_6 in Southern California. Although operational costs are lower under dynamic operation as compared to static operation, in order to achieve the same production target, the lower utilization rate in a dynamic mode was compensated with a larger production capacity (and thus greater fixed costs) . For example, across the current density scenar ios evaluated in Figure 3, the installed production capacity† is 4-38 % greater than the average H2 production rate. Furthermore, investment in a compressed H2 storage facility is necessary to buffer out the mismatch between a variable supply and a fixed H2 demand. As shown in Figure 4, t o compensate for this mismatch the electrolyzer produces more hydrogen at high current density and charges this to storage during low-price hours . During high price hours, hydrogen production is reduced by lowering current density and storage is discharged to meet the demand. There is also evidence of long -term hydrogen storage, where the longest continuous period where storage remains above 20% of the capacity is 46 days (starting on day 30 ). The increme ntal cost of H2 storage in the dynamic operation case is relatively minor (< 2% ) compared to the other variable and fixed cost s of the electrolyzer , even while considering relatively expensive above -ground H2 storage . The attractiveness of this approach is likely to increase if salt cavern -based H2 storage , which has lower capital costs 38, becomes feasible . Despite an increase in the electrolyzer nameplate capacity and the addition of the storage facility, the LCOH of dynamic operations is less than that of static operations. For the case study simulated for Southern California, oversizing the plant capacity by 33% with a nominal/maximum current density of 2 A/cm2 led to an 8% decrease in LCOH, from 4.98 $/kg to 4.57 $/kg. Even with dynamic operation, the LCOH values in Figure 3 for current technology and grid conditions are still much greater than the cost of H2 production from fossil options, which range between 0.5 - 1.7 $/kg, depending on natural gas prices (International Energy Agency, 2021). This gap suggest s that further reductions in capital costs and electricity prices are needed to make H2 production via PEM electrolyzers an economical option. † The installed production capacity of the electrolyzer is evaluated at the maximum current density, which represents the upper limit on the hydrogen production rate. The calculation involves multiplying the maximum current density by the total cell area determined from the optimization algorithm, and applying Faraday's law to translate the electrical input into the mass flowrate of hydrogen (see SI Eq. 39) Figure 4: Optimal plant dispatch under 2021 cost and technology assumptions under dynamic operation . The electricity price corresponds to the LMP at the node LAFRESA_6 in Southern California. The maximum current density is set to 2A/cm2. Negative values of storage charge refer to discharge. Operating at a high current density is crucial to reducing the LCOH in both static and dynamic operational modes , enabling more hydrogen production per unit of cross -sectional area of electrolyzer cells, which in turn reduces the capital expenditure and other fixed costs associated with scaling the plant size ( as depicted in Figure 3). Although variable operating expenses increase with increasing current density due to efficiency losses (see Figure 3), an ove rall cost reduction of 9.8% to 12.8% was achieved by increasing the current density from 1 A/cm2 to 2 A/cm2. The benefits of dynamic operations also increase with increasing current density. Since the cell is less efficient at higher current densities, a greater reduction in variable OPEX was achieved when the cell operates at part -loading. As shown in Figure 3, the LCOH is reduced by 5% at 1 A/cm2, 8% at 2 A/cm2, which is the typical limit of present systems, and 11% at both 3 and 4 A/cm2 when transitioning from static to dynamic operations. A corollary observation from this result is that commercially alkaline electrolyzers that have much lower current density ranges (typically around 0.1-0.4 A /cm2) may be less valuable to exploit electricity price volatility for low -cost H2 production as compared to PEM systems. 3.2. Impact of Electricity Price Profil e on LCOH Under 2035 Technology and Cost Assumptions Figure 5 LCOHs with different electricity price projections with 2035 technology and cost assumptions. A nominal /maximum current density of 4 A/cm2 is used for the static/dynamic operation scenarios . Each panel represent different set of electricity price scenarios retrieved from the literature. See further explanation on the price scenarios used here in section SI5. Here we explore the LCOH impact of future projected cost and performance of electrolyzers and electricity price scenarios on the LCOH under static and dynamic operations. First, e lectrolyzers, particularly PEM systems, are relatively nascent technology, with global installed capacity at 90 MW as of 202 0 39. Therefore, many studies expect that the capital costs for electrolyzers will significantly decrease in the future due to advancements in flow fields, membrane electrode assembly (MEA), labor, economies of scale, quality control, and larger cell areas 19,40,41. Studies suggest that the learning rates for electrolyzers are comparable to those for solar PV, between 16% and 21% 42,43. Additionally, IRENA 2020 predicts that a cost reduction of more than 40% can be achieved by 2030. With an annual decline rate of 4.8% 8, the cost of an electrolyzer stack is expected to decrease from 2.0 $/cm2 in 2021 to 0.7 $/cm2 in 2040. As the technology scales up, capital costs for balance -of-plant equipment are also expected to decrease, resulting in a total capital cost of $421 /kW for the 2035 scenario (Table 2). Second, technology improvements are expected to enhance the operational performance of electrolyzers. The development of thinner membranes and optimized catalyst layers can improve electrolyzer performance while also reducing the cost of the electrolyzer stack. While it is difficult to predict which technological advancements will be succ essful, it is anticipated that future electrolyzers will be able to use thinner membranes without compromising structural integrity and crossover resistance. Third, as power costs are the biggest contributor to the total cost of electrolytic hydrogen production , we evaluated the impact of different future electricity price scenarios in order to understand the range of possible LCOH values under different grid context s. As previously mentioned, the projections include 16 different hourly prices series forecasts for 2030 -2040 from the NREL 2020 Cambium Scenarios 34 and the FLECCS Program 35,36. The five NREL Cambium Scenarios use the Regional Energy Development System (ReEDS) model to simulate the electricity price series under different assumptions of renewable energy penetration (high/low renewable energy cost) and policy support (decarbonize 95% by 2035 or 2050). The price series data are obtained for 2040 in a balancing region corresponding to Southern California. In addition to the NREL Cambium Scenarios, the NREL price scenarios from the FLECCS program 35 also provide hourly price series data for 2035. These data are simulated with the reference natural gas prices from the EIA’s Annual Energy Outlook study ( AEO2020 ) and different carbon tax assumptions ($100/tonne or $150/tonne), for each of the major grid operators in the United States, including CAISO, ERCOT, MISO -W, NYISO, and PJM. In addition, the FLECCS Princeton data set offer region -agnostic hourly price series data for 2030, simulated with the assumptions of $60/tonne carbon tax, AEO2020 REF natural gas prices, and mid/low costs for solar and wind clusters located across the country. According to the simulation /optimization results depicted in Figure 5, dynamic operations become more valuable with future cost, technology, and electricity price assumptions. In comparison to the 5-11% reduction in the 2021 Scenario, dynamic operations in the 2035 Scenarios lead to a 20 -50% reduction in LCOH from the equivalent static operations baselines. Oversizing plant capacity up to four times the target production rate enables this cost reduction . Oversizing plant capacity is advantageous due to several reasons. The future grid systems with more renewable power integration are expected to have higher price volatility (see section SI5 and Table S8 in SI) , which provides more opportunities to dynamically vary the electrolyzer power loads. Additionally, lower capital costs reduce the opportunity cost of oversizing the plant capacity. Although there are clear benefits of dynamic operation , there are technical and operational challenges to be addressed to realize the full potential of dynamic operations as modeled in this study. For instance, h ydrogen crossover from cathode to anode, which is likely to be more prevalent at lower current densities (near zero) may limit the duration up to which the electrolyzer can continue to operate low current densities. In addition, h igh-frequency cycling may limit the number of cycles due to degradati on, and the response times of the balance -of-plant equipment may not be fast enough to exploit every trough in the price fluctuations. Nevertheless, the trend is clear that dynamic operations will play an increasingly important role in reducing the cost of hydrogen production in the future with lower capital costs, cheaper and more volatile electricity prices, and technological improvements. Overall, F igure 5 shows that the cases simulated with an assumed capital cost of $421/kW e had an LCOH ranging from $1.4/kg to $3.6/kg, with an average of $2.5/kg , which is still higher than fossil -based production costs of $0.5/kg to $1.7/kg . We tested a bookend case where we adopted the electricity price scenario that resulted in the lowest LCOH (FLECCS MiNg_$150_ERCOT) and assumed a highly optimistic capital cost of $200/kW (see section SI7) . This bookend case resulted in a LCOH of $1.20/kg (Figure S28) . This finding suggests that reducing capital costs of existing technologies alone may not meet the U.S. Department of Energy’ s Hydrogen Shot target of $1/kg. It emphasizes t he necessity for continued investments in low -cost renewable power and breakthrough technology research to achieve low-carbon and affordable hydrogen production. 3.3. Differential Pressure Operations Most of the commercial electrolyzers available in 2021 come with a standard feature of 30 bar outlet pressure. Differential pressure operation is one way to achieve this, where the anodes remain at ambient pressure (1 bar), and the cathodes are pressurized to 30 bar. Another method is to carry out electrolysis at ambient pressure on both anode and cathode sides and then use mechanical compressors to pressurize the produced hydrogen. A hybrid solution is also possible, where the electrolysis occurs at an int ermediate pressure on the cathode side, and the mechanical compressors then pressurize the hydrogen to the desired level. Under the modeled 2021 scenarios , we find that the operating at differential pressure is has minor impact on overall LCOH, with the most economical option being to operate cathode at 5 bar , as depicted in Figure 6. As the cathode pressure increases, the thermodynamic efficiency loss and higher pressure requirements increase operating expenses and capital costs. In comparison to ambient p ressure operations, the increased operating expenses and capital costs required for differential pressure operation at 5 bar are more than offset by avoiding inefficient mechanical compression at low pressure ranges (compression ratio of 5 from 1 bar to 5 bar). Under the 2035 scenario , full electrochemical compression with a differential pressure of 30 bar is projected to be the most cost -effective mode of operation, eliminating the requirement for bulky and noisy mechanical compression systems. This is bec ause the impact of higher pressure operation is mitigated by the lower average electricity price and electrolyzer capital costs. 2021 Scenario 2035 Scenario Figure 6: Optimized LCOH contributions under 2021 and 2035 cost and technology assumptions, with varying cathode pressures. Results correspond to dynamic operation. Left: LMP Southern California electricity price profile, maximum current density of 2 A/cm2. Right: ERCOT electricity price profile, maximum current density of 4 A/cm2. 3.4. Impact of the Inflation Reduction Act on LCOH The Inflation Reduction Act (IRA) legislation in the U.S. introduces a 10 -year production tax credit (PTC) mechanism under section 45V, based on the carbon intensity (CI) of the produced hydrogen as shown in Table 3 . We examined whether any of the modeled scenarios align with the IRA's criteria, specifically exploring the carbon intensity (CI) thresholds for eligibility when accounting for embodied CI of grid electricity supply . Furthermore, we sought to explore strategies that could enable more effective utilization of the IRA's provisions, investigating potential avenues to optimize and fully capitalize on its benefits for hydrogen production. Table 3: IRA 45V Production Tax Credit (PTC) by Hydrogen Production Carbon Intensity (CI) . Carbon Intensity (CI , kg CO 2/kg H 2) Production Tax Credit (PTC , $/kg H 2) 2.5 – 4 0.50 1.5 – 2.5 0.75 0.45 – 1.5 1.00 <0.45 3.00 For the 2021 scenario, the hydrogen CI was calculated using the average seasonal (quarterly) carbon emission intensity of the California grid system available at hourly resolution (annual average CI of 274 kg CO 2/MWh). Hourly carbon emission s were calculated by multiplying the CI with the electrolyzer power load. Then, the total carbon emissions are divided by the total mass of the produced hydrogen , which yields a CI of 13.18 kg CO 2/kg H 2. For the 2035 scenarios, the hourly marginal CI of the grid in Southern California is obtained from the NREL Cambium database. Under the Mid Scenario (average grid CI of 117 kg CO 2/MWh), the resulting hydrogen CI is 6.27 kg CO 2/kg H 2. In the 95% Decarbonization by 2050 Scenario (average grid CI of 146 kg CO 2/MWh), the CI stands at 7.78 kg CO 2/kg H 2. The 95% Decarbonization by 2035 Scenario (average grid CI of 18 kg CO 2/MWh) notably attains a CI of 0.79 kg CO 2/kg H 2, which underscores the critical need to reduce grid CI to minimize hydrogen CI. It reveals that only the most aggressive scenario, aiming for 95% decarbonization by 2035, manages to produce grid- based electrolytic hydrogen with a CI meeting the IRA standards , qualifying for $1.00/kg H 2 assuming that the 45V PTC is still in effect by 2040 . The notable increase in PTC for the lowest CI bracket suggests a potential economic advantage in configuring the electrolyzer to follow the low -emissions grid hours , thereby reducing the hydrogen CI. We explored this scenario by adding a constraint in the optimization model to limit the CI of the produced hydrogen to not exceed 0.45 kg CO 2/kg H 2 in the case with electricity prices defined as per the 95% Decarbonization by 2035 Scenario . Implementing this constraint le ads the optimization model to oversize the production capacity by 2.6 1 times the average H 2 demand, producing hydrogen at a CI of 0.43 kg CO 2/kg H 2. As can be seen in Table 4 , this strategy le ads to higher pre -PTC LCOH . However, the subsequent application of the PTC significantly reduce s the post -PTC LCOH to below the post-PTC LCOH of the strictly pricing -following case without the emissions constraint . This result provides another illustration of the utility of dynamic operation in optimizing the long -term return on investment for a hydrogen production asset . All the major U.S. grid systems in 2021 operate with a far higher CI (average of 379 kg CO 2/MWh) than what is necessary to qualify for the PTC credit , which implies that grid-connected electrolytic hydrogen production facilities that do not procure additional renewable power will not qualify for the PTC provisioned by the IRA. In other work, we have explored the emissions and cost impacts of alternative additionality and time -matching requirements being contemplated to implement the PTC policy 37. Table 4: Electrolyzer production c apacity, Carbon Intensity (CI), Pre -PTC LCOH, and Post -PTC LCOH of 2021 Baseline and 2040 Future Scenarios. The 10 -year PTC is postprocessed by levelizing the annual PTC with a discount rate of 8% and an effective tax rate of 20%. Electrolyzer production capacity, defined as per footnote† and reported relative to the average H2 demand. The 2040 electricity price scenarios are s ourced from the NREL cambium database 34 and correspond to the grid in Southern California. Scenario Assessment Year Mode Capacity CI (kg CO 2/ kg H 2) Pre-PTC LCOH ($/kg) Post -PTC LCOH ($/kg) 2021 Base 2021 2A Dynamic 1.32x 13.18 4.57 4.57 Mid 2040 4A Dynamic 1.36x 6.27 2.59 2.59 Decarbonize 95% by 2050 2040 4A Dynamic 1.33x 7.78 2.73 2.73 Decarbonize 95% by 2035 2040 4A Dynamic 1.89x 0.79 3.67 3.22 Decarbonize 95% by 2035 2040 4A Dynamic + Emissions 2.61x 0.43 4.03 2.67 intensity constraint ( ≤ 0.45 kgCO 2/kgH 2) 4. Conclusions In this study, a techno -economic optimization framework was developed to compute the LCOH of a PEM hydrogen production facility under various price, cost, and technology assumptions. The framework was used to evaluate the benefits of dynamic operations and differential pressure operations under various grid scenarios. The results showed that dynamic operations lowered the LCOH by 8% under the 2021 scenario and by 15 -20% under the 2035 sensitivity scenarios, indicating that dynamic operations would become mo re advantageous in the future. Partial differential pressure mode with a cathode pressure of 5 bar was identified as the most cost -effective way to compress hydrogen to 30 bar under the 2021 Scenario, while a full differential pressure mode was preferred u nder the 2035 scenarios. The emissions analysis showed that grid -based hydrogen production in 2021 does not meet the CI criteria for the IRA 45V PTC. Thus, future hydrogen electrolysis projects in the next decade will require a dedicated renewable power so urce to take advantage of the PTC. This study comes with some model limitations that should be factored when interpreting the findings and form the basis for future work . First, the absence of modeling hydrogen crossover could lead to an over -estimation of hydrogen production efficienc y and under -estimation in LCOH . Second, the electrolyzer model does not incorporate an explicit model for membrane degradation, and it is anticipated that dynamic operations and high current densities could negatively impact the lifespan of the electrolyzer 3. Although a stack replacement cost is incorporated in the TEA analysis, the model does not account for the variation of degradation with dynamic operation or current density. Lastly, the price - taker assumption used as part of the LCOH calculation might simplify market dynamics and neglect potential impacts on hydrogen pricing due to variations in supply and demand. Future studies should address these gaps to provide a more realistic evaluation of PEM production facilities. 5. Acknowledgements The authors acknowledge funding from Analog Devices Inc. for supporting the research undertaken in this project. 6.