Design considerations for industrial water electrolyzer plants

The motivation of this work is to propose a shared balance of plant (BoP) and power supply (PS) design for industrial scale alkaline electrolyzer plant that has reduced CAPEX with a minimum loss in OPEX for variable load operation. Three important aspects are: a) ﬂowsheet - either shared or individual BoP and PS per stack, b) variable or constant lye ﬂowrate per stack and c) sizing of cooling duty in the lye circulation loop. Steady-state optimization shows that individual BoP per stack (with higher CAPEX) is optimal when the plant is expected to operate at high capacity. For shared BoP and PS, the hydrogen production is higher by 8-12% when operated with variable lye ﬂowrate compared to ﬁxed lye ﬂowrate. Our results further suggest that lye cooling duty should be designed based on the cooling requirements of the degraded electrolyzer stacks at end of life.


Introduction
Hydrogen is an integral part of modern chemical industry.Demands for hydrogen in oil refining, ammonia production, methanol production and steel production has grown significantly and continues to rise.Hydrogen is light, storable, energy-dense, and produces no direct emissions of pollutants or greenhouse gases.However, hydrogen is not available in its pure form in the nature.Currently, hydrogen is almost entirely produced from fossil fuels ( [1], [2], [3]).As a consequence, production of hydrogen is responsible for CO 2 emissions of around 830 million tonnes of carbon dioxide per year [4].Hydrogen can be produced from renewable sources in the form of biomass [5], [6], [7], [8] and through processes utilizing water such as electrolysis, thermal decomposition and photo-catalytic decomposition [9].Hydrogen from water electrolysis process uses direct electrochemical splitting of water into hydrogen and oxygen (2H 2 O = 2H 2 + O 2 ), using water electrolyzer system.Hence the electrolytic hydrogen offers a potential benefit of producing carbon free hydrogen often termed as green hydrogen.Despite being relatively expensive, in recent years electrolytic hydrogen is enjoying increased interest around the world because of declining costs for renewable electricity, in particular from solar PV and wind.There is growing hope that electrolytic hydrogen can now finally fulfil hydrogen's longstanding potential as a clean energy carrier [4].The three main water electrolysis technologies available today are alkaline water electrolysis (AEL) , polymer electrolyte membrane (PEMEL) and solid oxide electrolyte (SOEL) [10], [5], [9].Both AEL and PEMEL are low temperature technologies and provide higher technology readiness levels compared to the SOEL technology which is still in development stage [11].For large scale application, the investment costs and the lifetime determine whether AEL or PEMEL is the most favorable system design [12].The reported investment costs for AEL are from 800 to 1500 €/kW and for PEMEL from 1400 to 2100 €/KW [12].Furthermore, the lifetime and the annual maintenance costs of alkaline water electrolyzers are lower compared to a PEMEL system [10], [13], [14], [15].Therefore, the alkaline water electrolysis is considered as most mature and durable technology, especially for large-scale and longterm renewable H 2 production [16], [17].Hence, this paper focuses on alkaline water electrolysis technology and aims to shed insights into important aspects of the development of large scale industrial hydrogen production plants.We provide an answer to three key questions related to the optimal design of large scale electrolyzer plant flowsheet.These are • Q1: Choice of the flowsheet layout (BoP and power systems) -Should electrolyzer stacks in the plant have shared or separate balance of plant (BoP) and power systems?
• Q2: Variability of the circulating lye flowrate -Should electrolyzer plant have fixed or a variable lye circulation flowrate?
• Q3: Sizing of the heat exchanger in the lye circulation loop -What should be the design basis of the heat exchanger in lye circulation loop?
In the literature several demonstrations projects are reported on hydrogen production.Most projects consume power in kilowatt (kW) range, an early one among them is the HYSOLAR project in 1986 [18].More recent projects for integration of electrolytic hydrogen to renewable energy sources are present in the United States, Canada, Germany, Italy, Norway, Japan, Spain, Finland and United Kingdom [19], [20].Historically, the most extensively investigated pathways include hydrogen to power (HtP) and hydrogen to fuel (HtF) applications [21], [22].Both wind powered hydrogen production systems [23], [24], [25] as well as solar energy based electrolyzer systems are studied [26], [27], [28], [29], [30].The most studied electrolyzer systems in these demonstration projects involve alkaline electrolysis at atmospheric pressure, intermediate pressure (4-30 bar), and even very high pressure (448 bar).These projects mostly discuss their experiences of generating power from hydrogen using fuel cells (HtP) and hydrogen for transport and mobility sector (HtF).
In addition to the demonstration projects several authors have presented mathematical models to describe water electrolyzer plants [31], [32], [33], [34], [35].David et al. [31] proposed a phenomenological based semiphysical model to replicate the current dynamic response of the experimental self-pressurized electrolyzer assembly.The current-voltage relationship which describes the performance characteristic of an electrolyzer stack was not developed in this work.They reported to use this experimentally validated model as a simulator and as a source for model reduction in order to design control strategies.Persson et al. [32] presented an electrolyzer model which was validated and tested from plant data of a 250kW PEM electrolyzer at Bright Green Hydrogen's Levenmouth Community Energy Project in Methil, Scotland.They concluded that this model can be applied to other commercial electrolyzers of similar type by readjusting the parameters and is useful for whole system modelling for future planning and optimization.Amores et al. [33] investigated electrolyte concentration and electrode/diaphragm distance in the conjunction with the electrochemical and thermodynamic effects in the Ulleberg's model [36] to propose a new model for alkaline water electrolyzer.They introduced two new parameters in Ulleberg's model to take into account the effect of electrolyte concentration and distance between electrodes.The model parameters were estimated, and model was subsequently validated using the experiments at a laboratory scale alkaline water electrolysis system under atmospheric conditions.However, in this work we use the Ulleberg's model to model the electrolyzer as it is well known and tested semi empirical model and several studies have used it or based new models from it [37], [38], [39].To use hydrogen for industry applications large scale hydrogen production systems involving overall power consumption in megawatt (MW) are required.For example energy intensive industrial processes, like ammonia production, steelmaking and oil refining offers significant decarbonisation potential if the electrolytic hydrogen produced using renewable energy sources is utilized in these processes [40].Such a transition from conventional SMR generated hydrogen to green hydrogen requires large scale hydrogen production plants consisting of several hundreds of electrolyzer stacks in gigawatt (GW) range.This paper continues to develop and expand the work presented in the scientific literature on the optimal design of large-scale water electrolyzer plants.Niaz et al. [41] presented a mixed integer dynamic optimization (MIDO) approach for estimating the optimal size and approximate cost of stand-alone renewable energy powered electrolyzer for hydrogen production at any given location.The proposed hybrid system by Niaz et al. was connected to a battery energy storage system (BESS) to ensure the electrolyzer's operation with no support from the grid electricity.The optimal size for such a BESS was determined by solving a MIDO problem that minimize the levelized cost of hydrogen.Along the similar lines, Varela et al. [42] developed a novel scheduling model for AEL to find the optimal number of electrolyzer and production schedules to fulfill the process goals for a given energy scenario.
They presented mathematical description of the operational states, their transitions, and main operational characteristics of AEL, to compute the energy absorption, production of hydrogen, and costs at production level.However, their model was limited to the calculation at production level as the phenomena within the electrolysis cell were not directly computed.The objective of this work is to investigate how to design a shared BoP and power supply system that minimizes the negative effect of sharing on operational flexibility and performance.The electrolyzer stacks in this work are assumed at different stages of their lifetime and hence have non identical performance due to aging.The novelty of the electrolyzer plant flowsheet design in this work is characterized by sharing of BoP and power supply systems between the electrolyzer stacks that reduces CAPEX with minimum loss in OPEX.We answer the three questions Q1, Q2 and Q3 to address related challenges of such a shared flowsheet design for a large-scale electrolyzer system with multiple stacks operating at variable load.This paper is structured as follows, Section 2 introduces the reader to the electrolyzer plant flowsheet and the simplified electrolyzer plant model developed in this study.Thereafter, Section 3 describes the steady state optimization problem used for systematic comparison of the flowsheet designs.Section 4 outlines the results from steady state optimization simulation study.Thereafter Section 5 discusses the impact of some key modeling assumption on the stated results.Finally, Section 6 concludes the paper with observations from our comparative study of different flowsheet configurations.

Process description and plant model development
In this section we begin by introducing reader to a simplified electrolyzer plant flowsheet which consist of four sub-processes, i.e. electrolyzer stacks, lye circulation system, compressors, and the gas storage system.The later part of this section discusses the mathematical model of the electrolyzer plant.

Process description
The electrolyzer plant (Figure 1) receives renewable power from a solar or wind farm which is adjusted to the desired voltage V el by a transformer and converted to direct current by a rectifier before sending it to the electrolyzer stacks.The peak load from the renewable power system is assumed to be 6.7MW .In the electrolyzer stacks the water is decomposed to produce hydrogen and oxygen according to following electrolysis reaction: The gas-liquid lye mixture from anodic and cathodic chambers of the electrolyzer stack is separated in two gas separators downstream.The gases (H 2 and O 2 ) exit from respective separators and are cooled and stored in storage tanks downstream.The electrolyte from the gas separators is collected in a small buffer tank present in the lye circulation loop.Additional water is added to lye in the buffer tank to replenish the water consumed during electrolysis.The outlet stream from the buffer tank is pumped and cooled in a shared heat exchanger and is returned to the electrolyzer stacks.In this work, the BoP and power systems for the electrolyzer plant include the separators, buffer tank, pump and cooler in the lye circulation loop and the rectifier and transformer.In this study we assume a direct coupling of the electrolyzer stack to the power production system and regard input power as a disturbance to the system (see Section 5 for further discussions).In all flowsheet designs we assume that the lye flow rates q lye,1 , q lye,2 and q lye,3 are manipulated individually.This implies that changing any one of them will change the total lye flowrate across the electrolyzer assembly.To keep the complexity low and clearly illustrate our results we consider flowsheets consisting of three electrolyzer stacks (see Figure 1 and 2).Note that this does limit the generalizability of the answers to Q1 -Q3 because the insights developed extend to flowsheet with more electrolyzer stacks (see discussion in Section 5).The flowsheet with separate BoP and power systems F separate (Figure 2) represents the simplest design strategy in which the single electrolyzer modules (for example atmospheric alkaline electrolyzer A150 from Nel Hydrogen [43]) are directly connected to produce the required hydrogen for large scale industrial processes.This design is the most capital intensive design as each electrolyzer stack has its individual BoP and power systems and thus higher investment costs are needed.On the contrary, the flowsheet with shared BoP and power system (i.e.F shared ) can provide a system with lower CAPEX because in this flowsheet layout, multiple electrolyzer stacks can share the BoP and power supply systems.In Section 3, a nonlinear optimization problem is formulated which provides a basis to decide the trade-off between the low CAPEX and the loss in plant performance because of shared systems.The results from this comparison study are presented in Section 4.

Plant model development
Here we discuss to the mathematical model of the electrolyzer plant.In the developed mathematical model of the electrolyzer plant, the underlying sub-processes i.e. electrolyzer stacks, lye circulation system, compressor and the gas storage system are modelled independently.For brevity and to keep focus on the flowsheet selection problem, we only discuss the electrolyzer stack and heat exchanger model in detail and remaining sub-processes are described in brief.The reader can find complete description of the lye circulation system, compressor and gas storage systems in Appendix A.

Electrolyzer stacks
The electrolyzer stack model in this work is based on the empirical correlations provided by Ulleberg [36].The electrolyzer stacks has interconnected thermodynamic, electrochemical and thermal effects.The reversible cell voltage, U rev is defined as the electromotive force for a reversible electrochemical process and is expressed as, Here, ∆G represents change in Gibbs free energy, z is the number of electrons transferred in the electrochemical process and F is Faraday constant.Electrolysis of water is non-spontaneous at standard conditions therefore ∆G is positive.The total energy needed for electrolysis to happen is equivalent to change in enthalpy ∆H.The change in Gibbs free energy, ∆G, includes thermal irreversibilities, T ∆S, which is equal to heat demand of a reversible process (as ∆G = ∆H -T ∆S).The cell voltage at which supplied energy participates both in ∆G and T ∆S is referred to as thermoneutral cell voltage, U tn .It is expressed as: In Ulleberg's model [36], the cell voltage (U k ) of an electrolyzer cell of the k th electrolyzer stack when direct current is supplied through it is expressed as sum of reversible cell voltage (U rev ) and ohmic and activation overvoltages i.e.The ohmic overvoltages, U ohm (see second term on right hand side in Equation 5) are because of the ohmic losses in the cell elements (electrodes, current collectors, interconnections, etc.).While activation overvoltages, U act (see last term on right hand side in Equation 5) are due to electrode kinetics as charge transfer between chemical species and electrodes need energy.The performance of the electrolyzer cell is modelled using following empirical voltagecurrent relationship proposed by Ulleberg [36]: Here, k in the subscript refers to the k th electrolyzer stack, r 1,k , r 2,k are ohmic resistance parameters, s k , t 1,k , t 2,k and t 3,k are coefficients corresponding to activation overvoltages, and A is the electrode area.The voltage -current curve (see Figure 3) characterizes the performance of an electrolyzer cell.At lower current densities, a logarithmic relationship is observed which suggests that activation phenomena are predominant while at higher current densities ohmic losses are dominant.At higher temperatures for a given current density reversible cell voltage, ohmic overvoltage and activation overvoltages are reduced, which also reduces cell voltage.At cell voltages lower than U rev , cell current is zero and electrolysis cannot take place.The cell voltage U k for electrolysis reaction is always higher than the reversible cell voltage U rev because of process irreversibilities and as a result water electrolysis is accompanied by the release of heat despite being an endothermic reaction.The rate of heat generated by the electrolyzer is directly proportional to the difference between the cell voltage and the thermoneutral voltage i.e (U k − U tn ).An industrial electrolyzer plant will more likely consist of electrolyzer stacks that are at different stages in their lifetime due to different degradation profiles.Hence, the three electrolyzers in this study are also assumed to be at different stages of their lifetime (i.e new, 51% degraded and 80% degraded).This degradation is represented by choosing different values of the ohmic and activation overvoltage parameters.The electrolyzer 1 is a new electrolyzer at the beginning of the lifetime while the electrolyzer 3 represents a 80% degraded electrolyzer coming to the end of the lifetime .The best performing electrolyzer has lowest cell voltage for a given current density and thus has highest electrical efficiency because of lower power requirements ( Figure 3).The voltage -current curve parameters for these electrolyzer stacks are given in Appendix B. The Faraday efficiency is defined as the ratio between the actual and theoretical maximum amount of hydrogen produced in an electrolyzer.It is also referred to as current efficiency and is caused by the parasitic current losses and the contamination of electrolyte because of dissolution of H 2 in O 2 .The fraction of parasitic currents to total current increases with decreasing current densities.Also, an increase in temperature reduces resistance, hence parasitic current increases which in turn lowers the Faraday efficiency.For a given temperature, Faraday efficiency is described by the following empirical relation [36] η Here, f 1,k and f 2,k are parameters related to the Faraday efficiency, A is the electrode area and I k is the current through the cell of kth electrolyzer stack.According to Faraday's law, hydrogen production rate in an electrolyzer cell is proportional to transfer rate of electrons at the electrodes which is also equivalent to the electrical current in the external circuit.Hence, the hydrogen production rate in an electrolyzer stack is given as: Water consumed during electrolysis to produce hydrogen and oxygen can be calculated from stoichiometry using Equation 1 and Equation 7, i.e.
The energy balance for an electrolyzer is written per stack basis using lumped thermal capacitance model.The schematic of electrolyzer is shown in Figure 4.The energy balance over the control volume, shown with dashed lines in Figure 4 is: Electrolyzer Renewable electric power Feed water + lye Here dE k dt is the energy accumulated in the electrolyzer stack, Ḣin,k is the thermal enthalpy of the incoming lye solution, Ḣout,k is the enthalpy of outlet streams leaving the anodic and cathodic sections of the electrolyzer.Qgen,k is the internal heat generated in the electrolyzer when operating at cell voltages higher than thermoneutral voltage (U tn ).Hence, Qgen,k = n c (U k − U tn )I k , n c is the number of cells in the electrolyzer stack, U k is the cell voltage and I k is current passing through the electrolyzer.The last term, Qloss,k is the total heat loss to the ambient by convection and radiation which is given by [44], Qloss,k Qconv,k and Qrad,k are the heat loss to surrounding by convection and radiation respectively.A s is the active area for radiation and convection, h c is the convective heat transfer coefficient reported to be 5.5[W/m 2 , K] for large scale electrolyzers by Kojima [45], σ is the Stefan-Boltzmann constant, 5.67 × 10 −8 [W/m 2 K 4 ] and is the emissivity constant.Emissivity is assumed to be 0.8 and the area of radiating surface A s is taken to be 0.1 m 2 /kA, cell of nominal current [46].Hence, the energy balance for the electrolyzer is written as: Here, C t,k is the overall thermal capacity of the k th electrolyzer stack.The ambient temperature (T a ) is assumed 20 • C for all calculations and T k is the electrolyzer temperature.We assume there is no mass accumulation inside the anodic and cathodic chambers of the cell, and the heat capacity of inlet and outlet lye streams are assumed to be equal as the change in concentration of the liquid phase is negligible.
The separation of lye and the produced gases (i.e.H 2 and O 2 ) from anodic and cathodic chambers happen in the gas separators.The separation process is assumed to be ideal to keep the model simple and hence, all the losses are neglected.

Heat exchanger
The heat exchanger in the lye circulation loop has counter current flow of hot and cold fluids (see Figure 5) and is used to cool the lye before it is sent back to the electrolyzers.The equations for energy balances on the hot and cold side of the heat exchanger are [47]: Where, subscript h and c denotes the hot and the cold streams respectively.Further, ρ cw is the density of the cooling water, V h and V c are the volumes of the hot and cold side of the heat exchanger respectively, C p is the heat capacity [J/g.K], q cw is the mass flow rate of cooling water [g/s], U is the heat transfer coefficient, and A HX is the heat exchanger area.∆T LM T D is the logarithmic mean temperature difference (LMTD) for counter-current flow and is given by The design of the cooling capacity in the lye circulation loop is directly related to the heat exchanger size (i.e.U A HX value).Appendix D discusses the calculation of the heat exchanger size for new electrolyzer stacks (i.e.HX 0 ) and 80% degraded electrolyzer stacks (i.e.HX 80 ).
The hydrogen and oxygen obtained from the electrolyzer stacks are at atmospheric pressure and therefore, a compressor is needed to compress these gases for storage at high pressure.For the developed electrolyzer plant model, a variable speed centrifugal compressor is considered.The performance of this centrifugal compressor is calculated based on a polytropic compression step.The gases in the storage tanks are assumed to be ideal and storage pressure is calculated using ideal gas law at isothermal conditions.The reader is referred to Appendix A for detailed discussion on modelling of the remaining subsystems and the assumptions considered for the plant model development.
The electrolyzer plant model parameters are estimated based on the specifications from the supplier [43] and state of the art CAPEX data for alkaline water electrolyzers by Proost [48].All the design parameters used in this work for modeling the electrolyzer plant are given in Appendix C.

Steady state optimization problem
In this section we introduce the reader to the steady state optimization problem that we use to systematically compare the flowsheet designs.The nonlinear optimization problem is solved for different values of input power to find maximum overall hydrogen production.The results of this optimization problem for different flowsheet designs provide the basis to compare their performances.This optimization problem is formulated as: max The optimization problem is subjected to process constraints on I den,k , T k and T El,in .In this work N = 3 as we consider three electrolyzer stacks in the plant.I den,k is the current density of the kth electrolyzer stack and should be within the safe limits.At lower current densities, there are technological challenges related to alkaline water electrolysis as the hydrogen concentration in oxygen can increase to dangerous levels (lower explosion limit of hydrogen in oxygen is > 4%) [49].While at higher current density the increased gas production rate results in rapid bubble formation which increases the overpotential due to the greater bubble resistance [50].The high temperature in the electrolyzer reduces the equilibrium voltage.However the higher operating temperature put stringent demands for materials for the structural integrity because of the corrosive effects of the electrolyte [50].Additionally, the inlet lye stream into the electrolyzer should be sufficiently hot so that temperature gradients inside the electrolyzer can be avoided.This is achieved by ensuring that the temperature difference between the inlet lye temperature (T El,in ) and electrolyzer temperature (T k ) is always less than 30 • C. Also the electrolyzer plant is subjected to constraints on the operational decision variables: 0.5 kg/s ≤ q lye,k ≤ 10 kg/s ∀k ∈ {1, 2, 3} q lye,k is the lye flowrate at the inlet of the k th electrolyzer, P El,k is the power consumption by the k th electrolyzer stack, here electrolyzer stack voltage U El,k is used as a degree of freedom to maintain the total power balance (P net ) of the electrolyzer stacks, q cw is the cooling water flow rate in the heat exchanger present in the lye circulation loop and z H2 , z O2 are the outlet valve openings for the hydrogen and oxygen storage tanks.For the flowsheet with the separated BoP and power systems (F separate ) the maximum limit on the cooling water flowrate is 1/3rd of the shared BoP case since each electrolyzer stack has its individual cooler and lye circulation system.Thus the input constraints for F separate (shown in Figure 2) are:

Results
In this section we answer the three key questions Q1-Q3 using the results of the optimization problem described earlier.

Q1 -Flowsheet performance with shared or separate
BoP and power systems Choice of the flowsheet layout is decided by comparing the overall hydrogen production by F shared and F separate flowsheet designs.We use the relative loss in overall hydrogen production (l r ) for the comparison, the l r is defined as: The results from optimization problem are shown in Figure 6 which shows the relative loss in production (l r ) with respect to the available power input.Here it is assumed that the lye flowrate for each stack can be used as a degree of freedom.The non-negative loss (l r [%]) in Figure 6 shows that flowsheet F separate has higher hydrogen production rate than flowsheet F shared .The relative loss in production is largest at maximum input power, i.e. 6.7 M W because flowsheet F shared has lower maximum power consumption than flowsheet F separate .This observation holds true irrespective of heat exchanger design basis (i.e.HX 0 and HX 80 ).
The maximum power for flowsheet F shared corresponds to the input power after which we observe a steep increase in the l r % (see red dashed line at 5.8 MW and blue dashed line at 5.5 MW in Figure 6).For the flowsheet F shared electrolyzer stacks are connected in parallel and therefore they operate across a common electrical potential difference.This potential difference is governed by the voltage across the best performing electrolyzer stack (as shown by the horizontal green line in Figure 7).Hence, when the best performing electrolyzer stack reaches the constraint on maximum current density then the degraded electrolyzers are restricted to operate at a lower current density corresponding to the common voltage in this shared flowsheet design.Therefore, the flowsheet F shared has lower maximum power consumption than the flowsheet F separate .The flowsheet F separate operate at higher input power and produces more hydrogen.The maximum power consumption for flowsheet F separate is 6.5 MW with HX 80 (see the red dotted line in Figure 6), which is 0.7 MW higher than maximum power consumption flowsheet F shared with identical heat exchanger size.Also note that the l r is 100% for lower input power (between 1.1 -1.2 MW), this corresponds to the situation when there is no feasible solution for flowsheet F shared while flowsheet F separate is still feasible (Figure 6).This confirms that flowsheet F separate has higher operational flexibility compared to the flowsheet F shared .The decision on the choice of BoP and power system is dependent on the nature of the renewable input power to the electrolyzer plant.In a scenario where the power from the renewable energy source (most likely wind energy farm) is expected to be less than the installed capacity, (for example below 5.8 MW for the installed capacity of 6.7 MW) the electrolyzer plant with shared BoP and power system should be selected.This work compares the electrolyzer stacks that are degraded and have different performance characteristics but it is also worth noting that at the start of the production the electrolyzer stacks have matching performance and the benefits of the separate flowsheet design over shared design will be negligible.Such a situation will make the shared flowsheet design even more attractive.Also interestingly, for input power values less than the maximum power consumption of flowsheet F shared , the relative loss in the production is almost zero.This suggests that both the flowsheet designs have near-identical performances at all these low input powers whenever flowsheet F shared has a feasible solution (Figure 6).Thus, if the input power from the renewable energy source is available in this range (1.2 -5.5 MW) then the electrolyzer plant with shared BoP and power systems is the logical choice.Therefore, we conclude that higher capital investments for flowsheet F separate will pay off only when the electrolyzer stacks are degraded and the electrolyzer plant is operating at input powers higher than the maximum power for flowsheet F shared .For rest of the operating situations the shared flowsheet (F shared ) is the most optimal flowsheet design.Here HX 0 and HX 80 denotes heat exchanger sizing for electrolyzer stack cooling requirements at beginning of life (i.e.0% degraded) and when it is 80% degraded respectively.Dotted vertical lines represent maximum power consumption of the flowsheet Fseparate for a given heat exchanger size which is higher than the maximum power consumption for the flowsheet F shared shown with dashed vertical lines.
4.2.Q2: Impact of the variable inlet lye flowrate on steady state performance Impact of the variability of the lye circulation flowrate is described by comparing the hydrogen production of a given flowsheet design with fix and varying inlet lye flowrate.From the results we see that the flowsheet design with separate BoP and power systems (F separate ) having heat exchanger design based on the cooling demand at 80% degradation (HX 80 ) is the flowsheet design with highest overall hydrogen production.Therefore it is considered as  basis to compare remaining flowsheet designs to highlight the loss in production incurred because of fixed inlet lye flowrate (see Figure 8).Fixing the inlet lye flowrate to each electrolyzer stack reduces the flexibility of the plant which decreases the overall hydrogen production.The loss in production for flowsheet with shared BoP and power systems (i.e.F shared ) increases by around 8-12% when inlet lye flowrate is fixed (see red and blue plots in Figure 8).This loss in production is irrespective of the heat exchanger size in flowsheet F shared .On the contrary, the effect of fixing inlet lye flowrate on the overall hydrogen production in flowsheet F separate is insignificant (see black and magenta plots in Figure 8), the maximum increment in loss is only around 1.3%.With fixed inlet lye flowrate the electrolyzer stacks in flowsheet F separate use individual cooling water flowrate q cw to control the inlet lye temperature T Elin and therefore avoid becoming constrained by limit on electrolyzer temperature (i.e.T k < 80).Thus, the electrolyzer stacks in the flowsheet F separate are able to operate at higher voltage and thereby produce more hydrogen even when the circulating lye flowrate is fixed.
Hence it is concluded that if the input power from the renewable energy source is close to maximum installed capacity (for example more than 5 MW for the 6.7 MW installed capacity in this study) fixing input lye flowrate is near-optimal for the plant flowsheet with separate BoP systems and can potentially simplify the control structure design later.However, for plant flowsheet design with a shared BoP and power system, the losses because of fixed lye flowrate are significant at higher input power (around 8-12%).In this flowsheet (i.e.F shared ) all the electrolyzer stacks have same inlet lye temperature (T Elin ) and fixed lye circulation flowrate constrains the heat that can be removed from the system (since maximum outlet temperature T k = 80 • C and Ḣin − Ḣout = q lye,k C p,lye (T Elin −T k )).Therefore, fixing the inlet flowrate for the electrolyzer stacks in the flowsheet with shared BoP and power systems is a bad idea and is not recommended.The varying lye circulation flowrate provides an additional degree of freedom to manage the heat removal which helps to increase the hydrogen production for the shared flowsheet design.Nevertheless the effect of the variability of the inlet lye flowrate on the maximum hydrogen production is negligible at lower input power (i.e.below 5 MW in this work).Therefore, this study recommends to operate the plant at varying lye circulation flowrate if flowsheet F shared is selected and higher input power is expected.Effect of cooling capacity in the lye circulation loop is discussed by comparing hydrogen production from both the flowsheet designs (i.e.F shared and F separate ) for different different heat exchanger sizes.The maximum hydrogen production by the flowsheet designs F separate and F shared with different heat exchanger size is shown in Table 1.The maximum hydrogen production is higher for larger heat exchanger size.This is because as electrolyzer stack is degraded (i.e.electrolyzer 2 and 3 in this study), it will generate more heat because of reduced energy efficiency (see Figure 9 for specific electricity consumption of three electrolyzers which is inversely related to the energy efficiency).In such situation the performance of degraded electrolyzers is limited by the maximum operating temperature of the electrolyzer.The larger heat exchanger size allows for more cooling in the lye circulation loop.This in turn allows the degraded electrolyzers to operate at the higher current densities for the longer part of their lifetime and produce more hydrogen (see Table 1).Also, in the situation when the electrolyzer plant flowsheet with shared BoP and power system is selected the loss in the hydrogen production at the maximum input power can be narrowed by oversized cooling capacity in the lye circulation loop.This is useful in situation where the renewable energy source is capable of providing the maximum installed power only for limited time but not at all the times.Hence, the compromised flexibility of the selected flowsheet having shared BoP and power system is improved by larger heat exchanger.This observation concludes that the cooling capacity in the lye circulation loop should be designed based on the cooling requirements of the degraded electrolyzer stacks.The larger heat exchanger results in higher overall hydrogen production for both flowsheet designs.

Discussion
In this section we discuss the impact of the simplifying assumption related of the electrolyzer plant flowsheet on the results of this study.Number of electrolyzer stacks: In this work, we choose to consider only 3 electrolyzer stacks in the plant flowsheet to keep the calculations simple and to make the benefits and the associated trade-off to the shared BoP and power systems distinct.The results from this work are generic and apply to the flowsheet with an even higher number of electrolyzer stacks.The electrolyzer stacks in the flowsheet with shared BoP and power systems are arranged in a parallel electrical arrangement and thus operate across a common electrical potential.Having additional electrolyzer stacks in the shared flowsheet design will add lines to the current-voltage characteristic plot corresponding to respective electrolyzer stacks.However, these stacks will always be constrained to operate across a common electrical potential dictated by the best performing electrolyzer stack (as shown by the green horizontal line in the Figure 7).This leads to limited overall hydrogen production by the flowsheet designs that have degraded electrolyzer stacks and share BoP and power systems.Hence, the simplifying assumption regarding the number of electrolyzers does not impact the general conclusions from this work.
Power system modelling: In this work we focus on the hydrogen production system to explain how multiple electrolyzer stacks can be configured for large scale industrial hydrogen production.It is assumed that the electrolyzer stacks are properly controlled to follow a reference power profile from a renewable energy source.The integration of the renewable energy to the grid power is not studied in this work.Such complex configurations wherein the grid power is integrated with the renewable power will require power system modelling to cover the non ideal situations and load balancing during the electrolyzer plant operations.The future work can model these electrical behaviors to design power management system together with the hydrogen production system.Distribution in the degraded state of the electrolyzer stacks: In an industrial operating environment, the stacks will degrade differently and also be replaced at different point in time (due to maintenance principles where one and one stack are taken out of service and replaced with a refurbished stack).As such, it is important to investigate how different BoP and power supply designs will be affected operationally by differences in stack performance.To illustrate this point we select three stacks at different point in their life cycle.We assume electrolyzer stacks at different stages of their lifetime, i.e. new (0% degraded), 51% degraded and 80% degraded.This degradation is assessed based on the specific electricity consumption by the electrolyzer stack at full load.The 80% degraded electrolyzer (i.e.Electrolyzer 3 in this study) is representative of an electrolyzer that despite being degraded will remain in the operation for sometime before replacement.This case study illustrates that with proper design we can have a reduction in CAPEX (by sharing BoP and power supply) with a minor effect on OPEX (the exact value of which will depend on the level of difference in degradation of the three stacks).

Conclusion
This work investigate flowsheet design for industrial electrolyzer systems and how the steady state operational performance of the electrolyzer stacks is affected by sharing BoP and power systems.The flowsheet layout with separate BoP and power systems has higher capital investments and offer greater operational flexibility when the electrolyzer stacks are degraded.However these higher investments can only payback if the renewable power supply is expected to provide input power higher than the maximum power consumption of the shared flowsheet with degraded electrolyzer stacks.In this work the maximum power consumption of the shared flowsheet with degraded electrolyzer stacks is 5.8 MW and the installed capacity is 6.7 MW.The installed capacity corresponds to the power requirements of the shared and separate flowsheet designs when all electrolyzer stacks are new.When the electrolyzers stacks are new, shared and separate flowsheet designs have similar performances for all input power values.Also, the two flowsheet designs (i.e.separate and shared) with degraded electrolyzer stacks have identical performances for input power in range from 1.2 MW to 5.5 MW.Therefore there are no incentives of additional investments in the separate flowsheet design for these operation scenarios.Hence, it is concluded that shared flowsheet layout is most optimal design.At input power values less than 1.2 MW, when electrolyzer stacks are degraded significant loss in production is noted in shared flowsheet design compared to separate flowsheet design.This is because of process constraints in shared flowsheet design while the electrolyzer stacks in separate flowsheet design remain operational because of higher operational flexibility.For this case shutting down one of the stacks in shared flowsheet design could be an option to be explored.The loss in the performance because of fixed lye circulation flowrate is significant for shared flowsheet design with degraded electrolyzer stacks especially at higher input power.That is why fixing lye flowrate for shared flowsheet is a bad idea.On the contrary, for flowsheet with separate BoP and power systems fixing the circulating lye flowrate causes insignificant increment in loss in the performance.Thus the inlet lye flowrate can be fixed if separate flowsheet design is selected.Heat exchanger design has a significant impact on the performance of both the flowsheet designs and a higher hydrogen production rate is achieved with the larger heat exchanger sizes.This is because larger heat exchanger allows for more cooling capacity that enable the degraded electrolyzer to operate at the maximum temperature at higher current density.Therefore, it is recommended to decide the size of heat exchanger in lye circulation loop based on the cooling demand of the electrolyzer stacks at the end of the lifetime.where w is the polytropic work, α is the compressor efficiency, for this work we have used α = 0.63.P ower comp is compressor power, T el and p el are inlet gas temperature and pressure to the compressor, p sto is the outlet gas pressure from the compressor and is equal to the hydrogen pressure in the storage tank and R is the gas constant.
As shown in the plant flowsheet, (Figure 1) ṅcomp H2 is assumed to be equal to the total flowrate of hydrogen out from all the electrolyzers, ṅel H2 .Solving Equation A. (A.9) A centrifugal compressor is a type of rotary compressor and has fixed pressure ratio, therefore P ower comp is a dependent variable that is calculated from Equation A.9.As given in [53] the polytropic exponent, x is related to adiabatic component γ, through polytropic efficiency E p as, The polytropic efficiency of the centrifugal compressor is between 0.7 to 0.75 as mentioned in [53].For the calculations in this study, it is assumed that E p = 0.75.The adiabatic exponent γ for hydrogen which is a diatomic molecule is 1.4.For this study, from Equation A.10 polytropic exponent x = 1.62, which is used for all the simulations.
Similarly, since O 2 is also a diatomic molecule, therefore γ and x for oxygen are same as that for hydrogen.Also, to keep the model simple, we have used Equation A.9 to calculate power requirements of the oxygen compressor ( ṅcomp is calculated from stoichiometry).

Figure 1 :Figure 2 :
Figure 1: F shared : Simplified flowsheet for state of the art electrolyzer plant with shared BoP and power systems

Figure 3 :
Figure 3: Performance characteristics of the electrolyzer stacks considered in this study.Electrolyzer 1 is the best performing electrolyzer while Electrolyzer 3 is representative of the electrolyzer with 80% degradation.The dashed magenta lines show the minimum and maximum current density during plant operation.

Figure 4 :
Figure 4: Schematic diagram of an electrolyzer stack

Figure 5 :
Figure 5: Schematic diagram of counter-current flow heat exchanger

Figure 6 :
Figure6: Relative loss in overall hydrogen production, lr for flowsheet F shared and flowsheet Fseparate.Here HX 0 and HX 80 denotes heat exchanger sizing for electrolyzer stack cooling requirements at beginning of life (i.e.0% degraded) and when it is 80% degraded respectively.Dotted vertical lines represent maximum power consumption of the flowsheet Fseparate for a given heat exchanger size which is higher than the maximum power consumption for the flowsheet F shared shown with dashed vertical lines.

Figure 7 :
Figure 7: Performance characteristics (U-I curve) of the electrolyzer stacks in this study.The horizontal green line represents the operating voltage of electrolyzer stacks in flowsheet designs with shared BoP and power systems.In shared flowsheet (F shared ) the electrolyzer stacks are connected in parallel configuration and hence operate across a common potential difference governed by the best performing electrolyzer stack (i.e.Electrolyzer 1 in this study).Dashed magenta lines show minimum and maximum operating current density.

Figure 8 :
Figure 8: Loss comparison of all the flowsheet designs w.r.t.flowsheet design having highest overall hydrogen production.Solid lines represent the flowsheet designs having variable inlet lye flowrate while dashed lines correspond to the flowsheet designs with fixed inlet lye flowrate

Figure 9 :
Figure 9: Specific electricity consumption of the electrolyzers considered for the study

Figure A. 1 :
Figure A.1: Schematic diagram of the lye circulation system.The control volumes are marked with a dashed line.

Figure A. 2 :
Figure A.2: Schematic diagram of a buffer tank 7 and Equation A.8 for P ower comp , P ower comp = ṅcomp

Table 1 :
Comparison of plant flowsheets designs with different heat exchanger sizes for maximum H 2 production