Beyond cost reduction: Improving the value of energy storage in electricity systems
Maximilian Parzen, Fabian Neumann, Addrian H. Van Der Weijde, Daniel Friedrich, Aristides Kiprakis
BBeyond cost reduction: Improving the value of energy storage in electricity systems.
Maximilian Parzen , ∗ , , Fabian Neumann , Addrian H. Van Der Weijde , Daniel Friedrich , Aristides Kiprakis University of Edinburgh, Institute for Energy Systems, EH9 3DW Edinburgh, United Kingdom Karlsruhe Institute of Technology (KIT), Institute for Automation and Applied Informatics, Karlsruhe, Germany ∗ Corresponding author email: [email protected]
Abstract
An energy storage technology is valuable if it makes energy systems cheaper. Traditional ways to improve storage technologiesare to reduce their costs; however, the cheapest energy storage is not always the most valuable in energy systems. This paper reviewstechno-economic storage valuation methods and expands them by the new ‘market potential method’ which derives a system-valueby examining the capacities obtained from a long-term investment planning optimisation. We apply and compare this method toother cost metrics in a renewables-based European power system model, covering diverse energy storage technologies. We fi nd thatcharacteristics of high-cost hydrogen storage can be equally or even more valuable than low-cost hydrogen storage. Additionally,we show that modifying the freedom of storage sizing and component interactions can make the energy system 10% cheaper andimpact the value of technologies. The results suggest to look beyond the pure cost reduction paradigm and focus on developingtechnologies with value approaches that can lead to cheaper electricity systems in future. One practical and useful value method toguide energy storage innovation could be the ’market potential method’. Keywords:
Energy storage, Energy system modelling, Techno-economic analysis, Hydrogen, Battery, Technology development
1. Introduction
In the face of global ambitions to reduce greenhouse gas(GHG) emissions, the energy transition characterised by in-creasing shares of wind and solar power will bene fi t from moreenergy storage in the future electricity system [1–3]. How manybene fi ts can be delivered depends, among others, on how futuretechnology will be designed. Consequently, research and devel-opment (R&D) must be improving the techno-economic designof energy storage systems to be most bene fi cial.A traditional approach to improving energy storage designis to reduce its cost [4]. In particular, in the material scienceand chemistry literature, cost reductions of energy storage area pivotal element, alongside maintaining other storage charac-teristics such as a ’su ffi cient’ high e ffi ciency, power and energydensity, and safety [5, 6]. Though, what is ’su ffi cient’ high isoften unclear. Only if one energy storage outperforms the otherin all characteristics it is a superior technology; otherwise, moreexpensive energy storage with suitable technical characteristicscan compete as well (as will be demonstrated in Section 4).Fortunately, material science literature has recognised one ofthe key challenges that energy storage depends on di ff erent ap-plications and the interaction with the electricity system [7].While research on cost reduction of energy storage compo-nents remains a vital element for a successful energy transi-tion, it becomes increasingly important to quantify the valueof energy storage systems under di ff erent circumstances [4].This is a challenging task as the value of a technology dependson the energy system changes [8] which are currently expe-rience constantly infrastructural changes through a transitions towards higher renewable energy shares and increasing sectorcoupling. Consequently, evaluating the value only on today’senergy system might be perceived as naive and risky. Energysystem models can help to investigate the impact of these com-plex changes and guide technology development towards futurevaluable technology.In general, energy storage systems can provide value or ben-e fi ts to the energy system by reducing its total investment andoperational costs; and by reducing risk for any investment andoperation – also known as option value [2]. This paper dis-cusses the bene fi ts of the former by providing energy arbitragewithin a European power system model with hourly temporalresolution. By excluding sub-hourly signals relevant to gridstability, but including scarcity signals relevant for seasonal re-serves mirrored in locational marginal prices or nodal prices.The paper contributes to the existing literature in the followingway: • We review and discuss techno-economic approaches thatare currently used to evaluate and compare energy storagetechnology in Section 2. • We show that current cost metrics can be misleading fortechnology design decisions. Section 4.2 and 4.3 show thata high levelised cost of storage (LCOS) hydrogen storagecan be equally or even more valuable than a low LCOS onefrom the system perspective. We draw this conclusion byobserving deployment of low and high LCOS hydrogenstorage systems in a least-cost power system investmentplanning model.
Preprint submitted to Applied Energy January 12, 2021
We extend the system-value approaches by the newly de-veloped ’market potential method’ in Section 3.1. It isfurther applied and discussed in Section 4. Compared toexisting approaches, the new method uses energy systemmodels to focus on the optimised quantity of a technologyin a set of probable scenarios in a highly resolved, largeregion such as Europe. As a more useful system-valuemetric, research and industry could additionally apply thenew approach to better guide energy storage innovation. • We show that modifying the freedom of storage sizing andcomponent interactions can lead to signi fi cant energy sys-tem bene fi ts (Section 4.1) and impact the system-valueof a technology (Section 4.3). It underlines the impactof developing and o ff ering adaptive components, such ascharger, storage and discharger, separately instead of com-plete storage systems.Our fi ndings suggest that a narrow cost focus on designingenergy storage is not enough. Future R&D design decisionsshould additionally use system-value insights from energy sys-tem models. The presented market potential method could beone approach to accomplish this.
2. Storage Valuation Methods
This section reviews and classi fi es currently applied stor-age valuation methods, or in other words, techno-economicanalysis approaches which appraise the competitiveness of en-ergy storage, including both technicalities and economic mea-sures. These methods are broadly employed for industry de-cision making, research focus consolidations and policy regu-lation [2, 9–13], which underlines their importance. Figure 1summaries what components will be discussed and how the lit-erature is classi fi ed.This study classi fi es the literature into two major groups: i)cost analysis and ii) cost and bene fi t analysis. The main di ff er-ence between these two methods is that the cost analysis ignoresthe discharge behaviour of storage, while the cost and bene fi tanalysis takes them into account. Further, we have identi fi edtwo major subgroups of the cost and bene fi t analysis method;we de fi ne one as the pro fi t analysis and the other one system-value analysis, which mainly di ff er in how markets are consid-ered.The pro fi t analysis investigates the value of energy storageprojects which are ’visible’ at present, for a speci fi c location,at current or past real world imperfect and incomplete markets(see Figure 1). In contrast, the system-value analysis estimatesthe value of energy storage which are ’visible’ and ’hidden’ inexisting markets, for longer time horizon and large spatial re-gions by assuming perfect and complete markets in the analysis.Current markets can be considered imperfect and incompletefor multiple reasons: • Markets are not temporally or spatially resolved. For in-stance, spot prices are settled over larger spatial areas andnot in real-time, leading to not perfect spatial dissolvedsocialised grid fees [14]. • Market power can be exploited. Dominant market partic-ipants act for their pro fi t while damaging the average par-ticipant [14]. • Forecast information are imperfect. Forecasts of demand,wind and solar generation underlies uncertainties leadingto imperfect operation and planning [14]. • Other negative and positive externalities exist, related toincomplete markets which distort the price. Negative ex-ternalities can be the non-priced cost for carbon emission,air pollution and biodiversity losses; positive externalitiescan be described as ’hidden values’ or non-priced bene- fi ts such provided by energy storage for network or peakplant deferral, or reduced solar and wind power plant cur-tailments [14, 15].In this context, system-value analysis generally tends to anal-yse markets by partially or entirely reducing these market fl aws.For instance, energy system models can cover higher spatialand temporal resolution, exclude market power, assume perfectforesight and account for externalities. However, not all mod-els idealise. Some try to incorporate the e ff ects of imperfectand incomplete markets by adding cost and bene fi ts related touncertainty and non-optimal operation and investment [16–18].The next subsections will clarify for each techno-economicanalysis class their objectives, methods and users, and further,analyse the grade of technical detail and, fi nally, how the ap-proaches handle the role of competition in uncertain future mar-kets. We categorise the cost analysis of energy storage into twogroups based on the methodology used: while one solely es-timates the cost of storage components or systems, the otheradditionally considers the charging cost, such as the levelisedcost approaches. Their objective is in general to minimise thecost metric for a particular technology or application.An example of the fi rst approach is represented in [19]. Theenergy weighted cost of a storage system (£ / kWh) is min-imised, without any electricity price signal, by a cost optimi-sation model that simultaneously maximise the round-trip e ffi -ciency of the storage. In [20, 21], instead of assuming the costof components, they break down storage components or sys-tems into materials and manufacturing processes. This method-ology, known as process-based cost analysis, allows a deeperunderstanding of cost reductions by mass production or switch-ing to di ff erent manufacturing methods. While both approachesdo not mention competitiveness or the value of energy storage,their outputs combined with cost and bene fi t analysis allows fi nding the value of energy storage solutions.The levelised cost approaches for energy storage includemetrics such levelised cost of storage when electricity is dis-charged (LCOS) and LCOH or LCOM when hydrogen ormethane are discharged respectively [11, 22]. All the levelisedcost metrics above are similarly structured. They divide thetotal cost of the considered system by the discharged energy.2 echno-economic analysis Cost analysis (Tech application specific) Cost and benefit analysis
Profit analysis (Project specific)
System-value analysis (Regional – multinational) • LCOS • LCOH/M • NPV • IRR • Profitability
Index (ROI) • Whole System
Benefit (WSB) • Marginal
WSB • Market potential indicator* M a x . p r o f i t s M i n . t o t a l s y s t e m c o s t M i n . c o s t m e t r i c s Visible value Incl. hidden value
Excl. charging costIncl. charging cost • Cost of component/ system Figure 1: Classi fi cation of current techno-economic analysis methods in the context of energy storage. *Market potential indicator is a suggested decision metricand part of the new introduced market potential method. The abbreviation mean the following: levelised cost of storage (LCOS), levelised cost of hydrogen ormethan (LCOH / M), net present value (NPV), internal rate of return (IRR), return of investment (ROI).
Both parameters must be discounted to represent the time valueof money [23]. We use LCOX in the following equation toindicate that the equation holds for various discharged energyforms: LCOX = ( � T Total cost)
Discounted ( � T Total discharged energy)
Discounted (1)Thereby, the total cost typically consists of capital expendi-tures, operational expenditures and charging expenditures [24–30]. Sometimes additional factors are included that can impacttotal cost and total discharged energy such as degradation rates,taxes, or self-discharging [11].Levelised cost like metrics are used to evaluate many appli-cations, such as energy arbitrage, frequency regulation, volt-age regulation, system restoration and operational management(i.e. redispatch). For this purpose the levelised cost like metricsassumptions must be categorised for the speci fi c application,such charging price, operational time and power to energy ratio[11, 28].While the ’cost of component’ or ’cost of system’ approachis widely used for design decisions with high technological de-tail [19–21], the levelised approaches forego some technolog-ical detail to inform project developer and policy about theirprojected competitiveness in the market [11].The main limitation of the levelised cost approaches regard-ing energy storage is that it ignores the e ff ect and interaction ofthe storage integration on the present or future electricity sys-tem. For instance, they do not account for the bene fi t of reducedwind power curtailments from energy storage; or miss that en-ergy storage competes with other fl exible demands across otherenergy sectors. A further limitation is the absence of a market-driven discharge behaviour in levelised cost studies. Including the discharge behaviour was found to be important for valueidenti fi cation of energy storage due to a more realistic repre-sentation of the operational behaviour determined by marketdynamics [1, 9, 11, 27]. An attempt to include these ’hidden’bene fi ts into levelised cost approaches is presented in [31] byadding integration cost and bene fi ts to technologies, though, itseems challenging to account for each technology the integra-tion cost and bene fi ts separately. Another limitation of levelisedcost approaches is that they are based on many exogenous vari-ables. These exogenous variables are pure assumption, some-times based on historical trends or future expectation. This canbe for instance the fi xed charging prices or operational time andenergy to power ratio assumptions. The use of exogenous vari-ables is in particular a problem when the electricity system is intransition [32, 33]. In contrast, endogenous variables capturedin mathematical models, can account for changing infrastruc-tures more easily.Cost of component or system metrics are excellent for ex-ploring cost reduction opportunities in great technical detail.And cost reductions can be a clear signal for an technologyimprovement under the only condition that the other charac-teristics such as e ffi ciency stay at least the same. On the otherhand, LCOS-like metrics di ff er by being a good fi rst indicatorfor the competitiveness between various technologies for a par-ticular application. However, cost-analysis methods generallymiss market e ff ects and future technology interactions, whichare essential to developing promising storage technologies. fi t analysis The pro fi t analysis describes methods from the investor’s per-spective to choose pro fi table energy storage projects at current3nergy market designs [13, 34–44]. Thereby, the general ob-jective for the investor is to maximise the pro fi t indicator for agiven investment.The inclusion of discharging behaviour and revenue streamsare distinctive for pro fi t analysis. Depending on the market de-sign, several di ff erent revenue streams for energy storage exist.In the UK, for instance, 14 potential revenue streams exist, suchas frequency response provision or wholesale market arbitrage,which can be power ( e / kW) or energy ( e / kWh) related [45].In general, not every storage has access to the same revenuestreams due to speci fi c characteristics and requirements [11].Most studies include only the energy arbitrage service from en-ergy storage, which means buying cheap electricity and sellingit later more expensive [35]. Other studies co-optimise multipleenergy services which result in higher bene fi ts [35, 46, 47].The pro fi t analysis typically evaluates energy storageprojects with capital budgeting techniques based on discountedcash fl ow methods to acknowledge the time value of money[23]. The energy storage literature uses multiple project assess-ment metrics: present value (PV) is employed to calculate thefeasible cost of a storage project [34], net present value (NPV)to evaluate the pro fi tability of a project [13, 15], and internalrate of return (IRR) to determine at which discount rate or op-portunity cost a project is viable [35, 42]. NPV and IRR aregood investor signals when investment capital can be accessedeasily. However, when investment capital is limited, projectsshould be evaluated by a pro fi tability index, which relates thediscounted bene fi ts to the cost [23]. Many energy storage stud-ies, therefore, investigate energy storage by the pro fi tability in-dex [23], which is also termed cost-bene fi t ratio [37, 38], NPV-ratio [36], return of investment (ROI) [41], return on equity(ROE) [39], all giving the signal of how much money can beachieved per investment. Another common metric in context ofenergy storage is the payback period [40, 42, 44], which [23]judges to be an illustrative but not useful factor for investmentdecisions. Finally, when multiple energy storage technologieswith di ff erent lifetimes are evaluated and compared, such asin [13, 38, 44], an equivalent annual annuity metric is recom-mended [23]. For instance, one could break down the NPV toan equivalent annual annuity where the highest annuity is thepreferable project. There are plentiful limitations for the pro fi tanalysis. One is, similar to LCOS approaches, that many as-sumptions are made exogenous which are increasingly uncer-tain under the current energy transition [32]. Moreover, ques-tions of how electricity prices will develop and how competitionwith other fl exibility providers will e ff ect the revenue streamsat speci fi c locations are not adequately addressed in pro fi t anal-ysis. Examples of such competing fl exibility providers aredemand-side management applications in the electricity, heator transport sector that currently, or even more so in the future,modify the demand behaviour [48].A further limitation of the pro fi t analysis is that it missesthe ’hidden’ or wider power system cost and bene fi ts of energystorage. Because it only focuses on the ’visible’ cost and ben-e fi ts at the current market design. Additionally ’hidden’ costand bene fi ts exist, also called social cost and bene fi ts, that af-fect the value of energy storage [15]. Hidden cost and bene fi ts are, for instance, savings due to investment deferral of networkupgrades or peak plants, or when fewer curtailments increasethe value of renewable generators [32]. Employing a hybridmethod of pro fi t and system-value analysis, the authors in [15]added social or ’hidden’ bene fi ts to the NPV metrics, whichare not directly accounted for in the market design. This leadto a higher value of energy storage solutions. The drawbackof the approach is that again many assumptions are made andadded exogenously to the NPV characteristics ignoring the spa-tial and temporal heterogeneity of the hidden cost and bene fi ts.What may be a good assumption at one location at a speci fi ctime must not be the case at another location at the same oranother time. Including these variables endogenously, as someenergy system models do, can help anticipate better infrastruc-tural changes and reduce risks.As a result, the pro fi t analysis is a useful method to inves-tigate a storage project’s value and competitiveness at presentfor a speci fi c location at current market designs. This mightbe useful for investors to assess short-term projects at speci fi clocations. However, when one looks for the value of energystorage in the long term or across many regions, the followingsystem-value approach can give some extra insights. As previously stated, the system-value analysis estimates thevalue of energy storage which are ’visible’ and ’hidden’ at ex-isting markets, for longer time horizon and large spatial regionsby considering perfect and complete markets in the analysis.Energy system models are used for the system view which op-timises investment and operation of generators, networks andstorage or demand response units at the same time to accom-plish the objective of minimising total system cost. The resultsof such analysis are nowadays mostly applied for policy recom-mendations. However, they also reveal insights for technologydesign. For instance, high capacity factor wind turbines gener-ally lead to less integration costs, or in other words, possess ahigher system-value when similar cost [8, 49].The system-value approaches are important to identify ben-e fi ts of energy storage more comprehensively. Technology de-sign can be shaped to accomplish these bene fi ts. The number ofbene fi ts taken into account depends on the used energy systemmodel. For instance, [3] and [50] neglect network expansion,missing signi fi cant network expansion cost savings from stor-age deployment [2]. On the contrary, the authors in [2, 51, 52]use a model that incorporates generation, network, and systemoperations savings from energy storage in the UK. Its closed na-ture is however criticised for being nontransparent black boxesthat hinder reproductive research [53]. A possible alternative toclosed models, are open energy system models [16, 18, 54].The whole-system bene fi t (WSB) given in e / year and themarginal WSB given in e / kW or e / kWh are two inspiring con-cepts how to attach a system-value to the energy storage inpower systems [2, 3, 51, 52, 55, 56]. Both concepts share acomparison of a none or existing storage scenario with one thatincludes an energy storage expansion. Such approaches are alsoknown as counterfactual scenarios [57]. Thereby, the total sys-tem cost di ff erence between the scenarios is the WSB that the4nergy storage creates [51, 55]. When the marginal WSB curve,given in e / kW or e / kWh, is integrated by the respective storageunit (in kW or kWh), then the WSB is obtained. The marginalWSB is described as vital since it provides the upper-cost limitfor energy storage for a given amount of installed storage [55].Only if the marginal value is above its marginal cost the stor-age is an economically viable option and should be installed.Additionally, to the WSB and its marginal value, the authors in[55], extended the concept by the di ff erentiation of the bene fi tsin net and gross bene fi t. The gross bene fi t excludes the invest-ment cost of energy storage while the net bene fi t includes them.Thereby, the gross value method is used to create a benchmarkof how much the cost can rise for a given technology. The netbene fi t analyses the holistic-value for a speci fi c storage case.Both WSB methods above lead to insightful results. Forinstance, (i) that every additional installed energy storage ca-pacity decreases its marginal value; (ii) that the value of en-ergy storage can su ff er from competition with other fl exibilityproviders, such as demand response or bi-directional chargingof electric vehicle; and fi nally (iii) that energy storage bene fi tscan be decomposed into its origins such as network and peakcapacity savings [2, 51].The major drawback of the WSB approaches is that theyseem to be unsuitable as evaluation metrics to signal betweenmultiple storage alternatives what technology is more compet-itive. The WSB approaches seem to work correctly only fora single energy storage design. When multiple energy storageunits are included in the WSB analysis at the same scenarioand with variable sizing for each location, it becomes di ffi cultwith counterfactual approaches to allocate bene fi ts. Or in otherwords, it becomes unclear which energy storage at what loca-tion is responsible for certain energy storage bene fi ts at a spe-ci fi c time. As a result, WSB approaches are not useful to assigna value to one particular storage or to compare multiple storagetechnology candidates.In the next section, the ’market potential method’ will be in-troduced to extend the system-value literature to circumvent theabove issue and give decision-maker signals even under com-plex competition situations. In short, the new approach movesaway from assigning monetary values directly to individual en-ergy storage units, but instead focuses on the optimised quan-tity. Meaning that a storage is likely to be valuable when acertain amount of storage is built. As in Section 4.4 discussed,the quantity appears to be another useful metric for industry andresearch.
3. Methodology
The methodology section is built up as follows. First, the newsystem value assessment method, the ’market potential method’is de fi ned in theory. Second, an experimental model setup forhydrogen and battery storage is described that compares costand system-value analysis approaches. Finally, to carry out theexperiment the power system model PyPSA-Eur is introducedwith its problem formulation, set of scenarios and model inputdata. The ’market potential method’ attempts to expand the exist-ing system-value methods to give more useful signals of whichstorage technology is valuable in existing or future energy sys-tems. Figure 2 illustrates that the ’market potential method’consists of: fi rst, the ’market potential indicator’ which corre-sponds to the expanded power or energy capacities of a stor-age component such as charger, discharger or capacity unit;second, the ’market potential criteria’ which seek to supportdesign-decision making of storage technologies. M a r k e t P o t e n t i a l M e t h o d Market
Potential
Indicator
Subjectivedecision
Market
Potential
Criteria
Probable scenario Technology selection
Result (exemplary)
TypeMetric/Approach GW for technology Ain scenario Figure 2: Description of the Market Potential Method. First a market potentialindicator is derived for a single or multiple possible scenarios. The marketpotential indicator is then used by an entity through a market potential criteriato support design-decisions making on energy storage technology.
The foundation of the introduced method is the market po-tential indicator (MPI). The MPI is not a new metric. It is aresult of energy system models that analyse scenarios in futureenergy systems and describes the total quantity of a particu-lar storage technology in a cost minimised electricity system[3, 58, 59]. However, the MPI has never been a central met-ric to improve, compare and explore storage designs in detail; itwas rather used to inform policymakers and market participantsabout probable futures to reduce investors risk [59].In the context of energy system models, we de fi ne the dis-aggregated MPI of a storage unit as optimised (or expanded)power or energy related size at a region. Thereby, the marketpotential focuses on the storage component c , which representsa charger, discharger or capacity unit. The over a region i ag-gregated MPI is determined by:MPI t − t , c = � i ∈ N (MPI) t − t , c , i [ MW or MWh ] (2)It is crucial to consider the MPI by components rather than bya fi xed-sized storage system for mainly two reasons. First, grid-scale energy storage are highly scalable and adaptable [60, 61].For instance, electrolysers (MW), steel tanks (MWh) and fuelcells (MW) composing hydrogen storage systems can be freelyscaled and combined. And in a H -hub operation, two dif-ferent electrolyser could feed the same H -storage tank. Sec-ond, energy storage system components–for instance based onhydrogen–are not required to be at one location. Indicated by[22], hydrogen pipelines can become an economically viable5ption when large amounts of hydrogen need to be transported.Its integration has the consequence that hydrogen electrolyserand fuel cell are not required to be located at one place. Con-sequently, because storage components can be independentlyscaled, adaptable in operation and do not require co-location, itseems advisable to optimise them separately. The use of energy system models is subject to uncertaintyas predicting the future with certainty is impossible. It is im-possible because we can make decisions that impact the futuresuch as done by agreeing on multilateral CO targets which im-proved renewable energy deployment and led to learning by do-ing cost reductions e ff ects [4]. Nevertheless, analysing a broadrange of future scenarios can reduce uncertainty [62]. The mar-ket potential method in linear programming models relies onpossible and probable scenarios. Many di ff erent ways exist tocreate ’possible’ scenarios which di ff er in the set of determinis-tic input assumption and constraints [62, 63]. However, a pos-sible future does not necessarily mean that it is a probable one.A good approach to develop scenarios that can be expected infuture is to follow the ones which are provided and encouragedby either national or multinational institutions - and engage inpublic consultations if they require changes [59]. An exam-ple of the latter one is the European Network of TransmissionSystem Operator for Electricity (ENTSO-E) which provides ev-ery two year an update on multiple, currently three, realisticpathway scenarios based on storylines towards the Europeanagreed targets - known as Ten-Year Network Development Plan(TYNDP) [59]. In the context of the MPI, using a set of proba-ble scenarios helps limit uncertainty of the value indicator. The ’market potential criteria’ give the market potential in-dicator its meaning that can help with decision-making. Thecriteria includes three simple rules. In an optimised energy sys-tem model with many if not all technological alternatives, thetechnology with: • MPI =
0, is unlikely to be valuable in the scenario. • MPI >
0, is likely to be valuable in the scenario. • MPI > ff ects or reduce overhead cost per unit. These cost impactsare not always included in linear programming models as they:First, require some additional computational e ff orts due to re-quired iterative approaches; second, the cost and deploymentrelation is sometimes in fl uenced outside of the energy sector,for instance, the battery market potential and cost relation is in- fl uenced by electric vehicle and electric consumer good sales as the cell technology is sometimes equivalent to the one used forenergy storage purposes. As a result, one can include the MPImagnitude with the following rules: • MPI > X or ’threshold rule’. Where a company or insti-tution decides what minimum market potential X must beachieved. For instance, an alkaline electrolyser needs tobe at least 1 GW in size to be an attractive technology fora company. • MPI A > MPI B or ’bigger is better’ rule. Where if twotechnologies A and B are compared, the one with highermarket potential is more likely to be valuable. Figure 3: Qualitative illustration of market potential criteria applied to a set ofscenarios and technology options. The ” + ” indicates the MPI magnitude. Ad-ditionally, the threshold rule is set to a single plus, meaning that for instance acompany requires at least two plus to consider a technology as potential candi-date to manufacture or start R&D activities. The open European transmission system model PyPSA-Euris adopted to determine the value of various energy storage sys-tems in a European electricity system. PyPSA-Eur is an adapt-able investment and dispatch model built on the core modelPyPSA that combines high spatial and temporal resolution. Thesuitability of PyPSA-Eur for operational studies and long-termpower system planning studies is described in [64, 65].PyPSA-Eur covers the European transmission model andprocesses electricity system data from diverse sources. Ex-isting conventional generators, transmission lines, substations,and hydro storage systems, as well as planned network rein-forcements, are included with their size and location. Wind andsolar based technologies are green fi eld optimised, which meansthat existing solar and wind capacities disregarded. However,the optimisation is backed with wind and solar satellite datathat will choose the best location of VRE generators to min-imise the total system costs. A spatial resolution of 181 nodesmatched with an hourly resolution across a full year accountsfor the complex spatio-temporal patterns of renewables and gridcongestion events that shape investment decisions [66].In terms of market economics, the model assumes perfectcompetition and foresight for one reference year. A detailedmodel description is included in [64, 65]. Here, we only high-light the key features and constraints. The objective of themodel is to minimise the total system cost in the European elec-tricity system on transmission level. The total system costs con-sists of6 igure 4: Optimal generation, storage and network expansion under a 100% emission reduction scenario and technology data for 2030. Light grey lines showingthe existing installed network capacity. • investment costs, which includes annualised capital cost ofonshore and o ff shore wind turbines, storage componentsand both HVAC and HVDC transmission lines, and • operating costs, which includes fi xed operation and main-tenance, and variable operating cost.The objective is subject to • nodal power balance constraints that guarantee that supplyequals demand at all times, • linearised power fl ow constraints modelling the physical-ity of power transmission, • Solar and wind resource constraint that limits the theoreti-cal generation time-series. We chose a single weather yearfor our analysis; however, this can be extended for a morerobust prediction of weather year anomalies or variations[67]. • Renewable availability constraint which restricts solar andwind technical potential based on environmental protec-tion areas, land use coverage and a distance criteria. • Emission constraint introduces a limit of carbon dioxide CO equivalent emission in the model that impacts tech-nology investment and generation.The model has many adjustable constraints. This study doesnot include the available unit commitment (UC) constraints, since the purpose of this paper does not justify extra compu-tational burdens. These computational burdens are introducedby the UC constraint required mixed-integer formulation thatlosses convexity and hence, leads to a nonlinear program thatrequires more e ff orts to solve. However, if a more detailed tech-nological performance in a high renewable electricity systemwith nuclear power plants is important, this should be included[68].For the input cost and technical assumptions, the documenteddataset provided in [69] is used, referring to an electricity sys-tem scenario in 2030. We only adjusted the dataset of [69] bythe battery and hydrogen storage system inputs summarised inTable 1 and Table 2. Table 1: Power related energy storage model inputs representing 2030 data
Energy storage components Electrolysor Fuel cell Battery InverterLCOS Scenario [Low] [High] [Low] [High] [-]Investment [
EUR / kW el ] 339 677 339 423 a c FOM a [% / year ] 2 3 2 3 3Lifetime [ a ] 25 15 20 20 10E ffi ciency [%] 68 79 47 58 90Discount Rate [%] 7 7 7 7 7Based on Ref. [12] [12] [70] [70, 71] [71, 72]Alkaline SOEC d PEM e SOFC f Li-Ion Battery ga Fixed operation and maintenance cost b Includes fuel cell stack replacement after 10 years which cost 30% of initial cost c Includes 80
EUR / kW balance of plant, mainly assigned to wiring and connection [72] d Solid-Oxide Electrolyser e Proton Exchange Membrane or Polymer Electrolyte Membrane f Solid-Oxide Fuel Cell g Lithium-Ion Battery able 2: Energy related energy storage model inputs representing 2030 data Energy storage components H storage Battery storageLCOS Scenario [High] [Low] [-]Investment [ EUR / kWh el ] 8.4 8.4 188 b FOM a [% / year ] - - -Lifetime [ a ] 20 20 10E ffi ciency [%] - - -Based on Ref. [71] [71] [72] H steel tanks Li-Ion Battery a Fixed operation and maintenance cost b Includes 81
EUR / kW for engineering, procurement and construction costs [72] This study creates energy storage scenarios that focus onenergy arbitrage bene fi ts under spatially resolved perfect andcomplete markets. Scarcity signals relevant to seasonal bal-ancing are considered through locational marginal prices alsoknown as nodal prices. These nodal prices let energy storagebe optimised as seasonal reserve, shifting cheap energy of oneseason to times of high prices. As introduced in Section 2, thecomplete market considerations includes the often unaccountedor ’hidden’ values of energy storage systems, such as: • Avoided investment cost of network expansion • Avoided investment and operational cost of dispatchablegenerators • Increased power plant utilisation / less curtailmentEmission targets play for the energy storage market potentiala vital role. To keep the comparability between scenarios and adecent amount of market potential for energy storage, we set inall scenarios the CO emission reduction target to 100 %.Figure 4 shows an example of the optimised European elec-tricity landscape for the variable energy-to-power ratio sce-nario, which is minimised in terms of total system costs in a 181bus spatial resolution. One should note that the network struc-ture is based on ENTSO-E data which is aggregated to showrealistic line capacities between the buses.Di ff erent to [73], the scenarios include the existing Europeannuclear power fl eet, but acknowledge the German, Spanish,Belgium and Swiss nuclear exit. The inclusion of nuclear powerplants reduces the required VRE capacity expansion and at thesame time, increase the share of dispatchable power plants. Ameasure that reduces energy storage demand. However, the fl exibility of nuclear plants is overestimated in this study as typ-ical ramp rates reaching up to 36% / h and minimum allowablepower of 20% per nominal power [74] are ignored. This impliesthat this study will tend to underestimate the energy storage po-tential.Further, similar to [75], an equity constraint is included thatrequires every country to produce at least 80% of its total elec-tricity demand, leading to a smooth distribution of generators inwhole Europe. This constraint is motivated by the fact that po-litical leaders avoid depending entirely on electricity imports,though, are willing to trade a considerable amount to handlethe trade-o ff between economic bene fi ts of importing cheaper electricity and the costly independence of supply from othercountries.The network expansion is constrained to a volume of 25%compared to the existing network capacity, acknowledging theincreasing political di ffi culty to develop new transmission lines.A limited network expansion can potentially lead to higher stor-age demand [76]. Further constrained are hydro storage tech-nologies. These are based on real power plant data, though, aredeactivated for capacity expansion due to natural limitation inmany regions.Figure 5 describes the storage scenario design. First, tech-nical and economic parameters are chosen as model input torepresent a low and high levelised cost of storage (LCOS) casefor a classical LCOS calculation of a hydrogen storage system.Afterwards, the resulting techno-economic details are insertedin the model environment into three scenarios. The scenariosdi ff er mainly in technological design freedoms. Scenario 1 isthe most constrained energy storage scenario having a fi xedenergy-to-power ratio of 100 h for the hydrogen and 4h for thebattery storage technology – applied in a similar range in re-search [11, 34, 77]. Whereby charger and discharger size areequally set. Scenario 2 optimises for the hydrogen storage uniteach component size, charger, storage and discharger so thatthe energy-to-power ratio is variable. The battery is constrainedin fl exible sizing as charger and discharger represent the samecomponent, namely the inverter so that the battery storage canonly size inverter and battery capacity related design separately.Lastly, scenario 3 extends scenario 2 by allowing all hydrogencomponents to mix at a location. While both, scenario 1 and2, run hydrogen low LCOS and high LCOS components sepa-rately, scenario 3 permits cross operation. This can be thoughtof as a H -Hub, having at one location multiple charging anddischarging technologies which operate with the same energycarrier, hydrogen. Cost and technical characteristic selection of storage components Result in one low and high LCOS case
LCOS ranges + market potential indicator S2 – Variable EP ratioS1 – Fix EP ratio S3 – H -Hub Classic
LCOS calculation C a S a D a x 100 x 1 x C a S a D a x y z x y z x z C b C a D a S a D b H y d r o g e n S2 – Variable EP ratioS1 – Fix EP ratio C a S a D a x 4 x 1 x C a S a D a x y x S3 – Variable EP ratio C a S a D a x y x B a tt e r y Figure 5: Description of scenarios set up. The cost and technical storage pa-rameter are chosen once and serve as input for all storage scenarios. Scenario1 shows the fi x energy-to-power ratio of the hydrogen and battery unit a . InScenario 2 and 3 all components can be freely scaled, though, the battery isconstrained to the same charger to discharger ratio. Further, The ’ b ’ in the H − Hub scenario indicates a new technology. . Results and Discussion fi ts As the introduction of the cost and value analysis scenarios,the impact of design freedom on the storage components andthe total system is discussed in this section.Increasing design freedom of energy storage can lead to sig-ni fi cant bene fi ts in the electricity system. When investigatingthe competitiveness of energy storage, many studies assumethat the energy to power ratio is fi xed [3, 27]. Though a fi xed-sized storage unit seems to be far away from an optimal solu-tion. A way to prove this is to investigate the total system costreduction in energy system models as applied in the following.Table 3 shows that the increasing sizing complexity seemsworthwhile to consider as it can lead to per annum total sys-tem cost savings of approximately 13 B e or 10% in the modelledzero CO electricity system scenario while not leading to signif-icant generation portfolio changes (see Figure 6). The total sys-tem cost thereby includes the optimisation relevant costs whichconsist of newly installed generation, storage and network com-ponents, including any operational costs. Another approach tocomprehensively quantify the savings is by calculating the rela-tive investment cost. It shows that the introduction of optimisedsizing can lead to electricity bill savings of roughly half a cent,with the H -Hub scenario contributing only to negligible moresavings. As a result, increasing design freedom of energy stor-age can be desirable for a cheaper electricity system. Table 3: Annual total system costs, relative investment and curtailment data.Variable sizing of energy storage reduces the system costs by 10%.
Scenario Total system cost Relative investment a Curtailment[% of annual demand]Fix EP ratio 152.9 B e / kWh 0.61%Var EP ratio 139.9 B e / kWh 0.73%H2-hub 139.7 B e / kWh 0.37% a Total system cost per annual demand
Figure 6: Installed generation capacity. The optimised capacity looks similarin all three scenarios indicating little in fl uence of the storage scenarios on thegeneration portfolio. Only slightly less generation capacity is required whenvariable sizing of energy storage is permitted. The abbreviations ’ror’ standsfor run of river, o ff wind-ac and -dc for AC and DC connected o ff shore windplants, respectively. The optimal storage design depends on the location and tech-nology. Figure 8 shows the EP-ratio for multiple locations andtechnologies with relevant market potential in an optimal Euro-pean future scenario.Hydrogen charger are larger sized and reveal a wider span ofEP-ratios than its discharger opponents which means that quickcharging and slower release seem to be bene fi cial from a EU Table 4: Additional inputs for LCOS calculation oriented on [11].
Hydrogen storage unit Battery storage unitLCOS scenario [Low] [High] [-]Discharging ratio [ h ] 100 100 4Electricity price [ Eur / MWh ] 50 50 50Yearly full load hours [ h ] 2500 2500 3400Roundtrip e ffi ciency* [%] 32.0 45.8 81,0Lifetime** [%] 25 15 10Static LCOS [ ct / kWh ] 0.21 0.26 0.12*calculated product from energy storage component e ffi ciencies in Table 1 system perspective at most locations. Further, the Li-Ion bat-teries are optimised with a 2-4 h EP-ratio, much smaller thanthe hydrogen components. The reason for that heterogeneousdesign is that local diverse electricity system situations with itsindividual network constraints, supply and demand curves, aswell as the di ff erent storage characteristics (see Table 1 and 2)require a variety of storage scaling to reach an optimal solutionthat minimise the electricity bills. The LCOS is often calculated in the energy storage litera-ture to benchmark technology or even to discuss their compet-itiveness (see section 2). To show the drawbacks of this mea-sure, static and modelled values are calculated according to themethodology described in equation 1.The main di ff erence between static and modelled LCOS iswhat assumptions are used. The static LCOS calculation usesdirectly assumed or exogenous variables such as for full loadhours, electricity prices and energy-to-power ratios. In contrast,the modelled LCOS is based on endogenous variables whichare determined by the energy system model and its inherent as-sumptions. It means that full load hours, electricity prices andenergy-to-power ratios are determined for each location by theEuropean power system model.The static LCOS is calculated with the technical and eco-nomic component characteristics in Table 1 and 2, and theLCOS assumptions given in Table 4. The results of the staticLCOS calculation also given in Table 4 show a 19.2% or 5ct / kWh di ff erence for the two hydrogen storage units, wherebythe battery storage seems much more competitive. It is widelyrecognised that the LCOS is not useful for an ’apple-to-apple’comparison (cf. 2). Nonetheless, energy technologies are opti-mised towards low levelised-cost metrics [78], or others arguethat a reduction of levelised cost of storage will lead to bettercompetitiveness [79]. However, we reveal in the next paragraphthat this can be a misleading idea as a high LCOS technologycandidate can be equally market competitive.The modelled LCOS results are given in Figure 7 for mostbuses in the EU electricity system for the ’variable EP-ratio’scenario. Despite having the same input cost, lifetime, discountfactor and e ffi ciency data as the static LCOS calculation, a wideLCOS range can be observed for each optimised storage unitwhich consists of charger, storage, discharger. One reason isthe heterogeneous charging and discharging behaviour whichis indicated by a range of observed full load hours; another one,the heterogeneous nodal prices or electricity price pro fi les ateach region; and fi nally the heterogeneous sizing of the storagechain.9ser as technology almost negligible in terms of market poten-tial.As a result, what the market potential indicator reveals is thatthe design freedom of storage is important to consider becauseit impacts how valuable technologies seem. For instance, whenvariable component sizing is possible, the PEM fuel cell, aswell as the Alkaline electrolyser, seem to be more desirablewhile Li-batteries loss in importance in the electricity system.Additionally, the complete market potential method is appliedfor Figure 9. Assuming that the scenarios represent probablefutures, all the implemented storage components can be con-sidered according the market potential criteria as valuable as atleast one of the scenario’s possess a positive market potentialindicator. However, only the Li-battery as well as the SOFCfuel cell are the most likely valuable technologies as they areoptimised in all scenario’s and exceed a 1 GW threshold. Thisknowledge can lead to implications, for instance, that the Alka-line electrolyser manufacturer can actively mitigate their valuerisk by promoting variable sizing. Finally, the presented in-sights underline the misleading concept of solely cost minimis-ing technologies approaches and recognising the market poten-tial method as an alternative value indicator that includes thecomplexity of the electricity system. The market potential indicator seems like a useful metricfrom a practical and computer modelling perspective for manu-facturer, developer and research. One reason is that the marketpotential is a driver for business. Successful fi rms want to gen-erate money for its stakeholders and hence are driven by twothings, growth and pro fi tability. The market potential indicatorfor a speci fi c product can relate the growth potential to the prof-itability. For instance, when a company expects to o ff er a future product for net costs of 10 e / kWh then it could include thesecost in the energy system model with a pro fi t and risk premiumof 5 e / kWh (50%). The modelling output is the market poten-tial indicator which is related to the pro fi t and risk premium of50%. As result, the market potential method can be useful forgrowth and pro fi t evaluations of future storage technology.Second, the market potential can give insights where growthmarkets are located and for what reason. This can be achievedsince the disaggregated market potential can identify regionswith future technology expansion (see Figure 10). The elec-trolyser distribution reveals that in many locations high andlow LCOS units complement each other. Additionally, whenstorage components are compared to the generation distribu-tion from Figure 4, most hydrogen units are co-located at re-gions with wind plants (mostly northern regions) while batteriesgravitate towards solar plant optimised areas (mostly southernregions). A reason for the observed co-location might be thediurnal solar power pattern and the multi-day to weekly windpower pattern which creates a network constrained mismatchsuitable for the given storage characteristics [80].Third, the market potential is useful as an indicator of futurecost reductions. Because with the market potential, one can as-sume future technology deployment which is an implicit factorin learning by doing cost reduction e ff ects [4] or a factor thatcan be incorporated into process-based cost analysis to evalu-ate the cost reduction potential [20, 21].Forth, the market potential can reduce the structural uncer-tainty of the linear programming energy system model itself.Initial cost assumptions as model inputs are often made with-out knowing deployment numbers achieved in the optimisation.But it is known that larger deployment can reduce costs due tolearning e ff ects [4]. Since after the fi rst model run the marketpotential can function as a cost reduction signal, one can in an Fix EP ratio. Var EP ratio.
24 44 113 106 4 3 10 0.01 H hub .
80 0.3 54 157 3 14 0.01 H l o w L C O S H h i g h L C O S H l o w L C O S H h i g h L C O S I n v e r t e r r e l a t e d H l o w L C O S H h i g h L C O S B a tt e r y c a p a c i t y r e l a t e d MPI dis /charger [GW] MPI storage [TWh] Figure 9: Market potential indicator for all charging and discharging components in Europe for three technical storage scenarios in a zero emission electricitysystem. Despite having the same economic and technical input data the market potential vary drastically between the scenarios. The SOFC fuel cell and Li-batteryare according to the market potential method, the technologies which are most likely to be valuable in the exemplary set of scenarios. Because they have an optimisedmarket potential indicator in each scenario. *Refers to the total shared storage capacity. igure 10: Optimal energy storage charger distribution in the variable energyto power sizing scenario. Showing the location of market potential in a 100%emission reduction scenario. Comparing to Figure 4, most hydrogen units areco-located with wind plants while batteries gravitate towards solar plant opti-mised areas. iterative or sequential solution approach improve the input ac-curacy and, hence, lower the structural uncertainty.Finally, the operational behaviour can be analysed with thespatial distributed market potential, due to the use of energysystem models which gives operational times series of opti-mised technologies. These time series can be used to identifyoperational patterns and full load hours which both might beuseful for technology design decision.
5. Critical Appraisal
What the market potential gives its power to resolve the com-plex value of energy storage - the energy system model - alsointroduces typical limitations found in this domain. The funda-mental challenge of any mathematical energy model is to rep-resent a realistic future energy system that includes all relevantphysical, social and political details [81]. Current approachesencounter limitations to represent these details. For instance,models often aggregate in space, time and technological res-olution to reduce the computational requirements losing someaccuracy to represent future scenarios; or assuming perfect andcomplete markets, where actors have perfect foresight. Bothdeviates from what can be accomplished in reality [64] and aspointed out in the introduction this can be important to addressadditional values of energy storage.These energy model limitations can be understood as (1)structural uncertainty related to the imperfect mathematical de-scription of the physics and (2) parametric uncertainty thatrefers to imperfect knowledge of input values, i.e. impacted byinnovation or behaviour. Both compromise every kind of math-ematical models with increasing uncertainty looking into more distant future and vary from model to model [57, 76, 82]. Themost important uncertainties of PyPSA-Eur are summarised in[64], for instance, that demand pro fi les for regions in a coun-try are not disaggregated and only scaled by the GDP of theregions, hence, representing not local di ff erences; or missingmulti-horizon optimisation which can help to describe invest-ment pathways and lock-in e ff ects; or the only focus on the elec-tricity system, missing alternative fl exibility competitors fromother sectors.Nevertheless, most of the uncertainties can be reduced byimproving future mathematical descriptions of the reality andby strategies to reveal remaining uncertainties [81]. This alsoincludes the missing energy storage values of this study for sub-hourly grid services and risk confronted investment and opera-tion. In PyPSA-Eur many of these certainty creating featurescan be implemented in short-term by state of the art techniques.In context of the above-described uncertainties, this studydoes not seek to be the one true future. It rather shows a setof possible future scenarios with di ff erent technological designfreedoms for the only purpose of comparing di ff erent storagedesign evaluation methods.
6. Conclusion
This study analysed recently published literature on energystorage and found three distinctive evaluation approaches to in-dicate how to improve energy storage. We show how these ap-proaches work, what their limitations are and further introducea new energy storage assessment method - the market potentialmethod.The fi rst approach found in literature coined ’cost analysis’identi fi es competitive storage technologies with the objectiveof lowest capital or levelised cost. We argue that this approachshould not be used in isolation to guide storage technology de-velopment or policy recommendations. We quanti fi ed that ahigher LCOS hydrogen storage can be equally or even moredesired than a low LCOS hydrogen storage which questions themeaning of cost like metrics as an evaluation factor.The second ’pro fi t-analysis’ approach considers the desirablestorage projects which maximise pro fi ts. It may sound intrigu-ing for investors at current market design without considerableelectricity system changes, but when the future storage tech-nologies are to be evaluated, this approach is likely to fail. Inthis context, we qualitatively explain that current market de-signs are incomplete and imperfect and might change due tothe energy transition, leading to missing ’hidden bene fi ts’ ofenergy storage when looking into the future. As a result, ratherthan improving technology designs with cost or pro fi t analysismethods, we could design technology with approaches that canlower the total system cost.The third identi fi ed ’system-analysis’ approach can accom-plish this by also including hidden storage bene fi ts and consid-ering future more complete and idealistic markets. However,the review identi fi es a lack of practical system-analysis meth-ods that focus on technology evaluation. Hence, the new ’mar-ket potential method’ is introduced, formulated, applied and12iscussed to improve technology design-decision making. Themarket potential method focuses on components rather than onstorage systems. It is the total sum of the optimised, expandedenergy or power related size in a large spatial electricity sys-tem. As a foundation, the method uses energy system modelsto identify in probable scenarios which technologies potentiallylead to the lowest cost energy system. In a set of scenarioswith a high and low-cost hydrogen storage system and di ff er-ent grades of technological freedoms in sizing and interactionsof the storage, we quantify that a seemingly more expensive en-ergy storage can be the one with higher system-value. Thus, notonly the cost but also the system-value of technology matters ina complex and heterogeneous electricity system.As a secondary result, modifying the freedom of storage siz-ing and component interactions impacts the value of technol-ogy. For example, Li-Ion storage su ff er from variable sized hy-drogen storage. Likewise, increasing these design freedoms canlead to meaningful total system cost savings (10% total systemcost savings compared to a fi x sized storage scenario). But howvariable sizing can be indicated and supported in existing en-ergy planning is a question by itself and should be answered infuture.In summary, the market potential method has implicationson practical and modelling relevant insights for manufacturer,developer and research. It can be used to • support technology design-decision making with growthsignals of magnitude and location, • improve the technology by changing operational be-haviour or adapting material or process selection to bemost valuable for the energy system, • concentrate policy endeavours to come closer to perfectmarket circumstances, or to • enhance energy modelling as evaluation tool itself.Future work can reduce the limitations of this study, suchas the inclusion of sector coupling and multi-horizon optimisa-tion. This study considered energy arbitrage under perfect andcomplete markets. Another branch of work can include moreservices relevant to grid stability and risk approaches. For in-stance, by investigating the impact of imperfect and incompletemarket conditions and higher spatio-temporal resolutions on themarket potential method results. Finally, what might be valu-able in Europe could look di ff erent in other regions. Technol-ogy developer would bene fi t from a global value assessment.Therefore, it is of utmost importance to expand open energysystem models to cover most parts of earth.The economist Milton Friedman said that “there is one andonly one social responsibility of business–to use it resourcesand engage in activities designed to increase its pro fi ts so longas it stays within the rules of the game, which is to say, engagesin open and free competition without deception or fraud” [83].This might sound convenient in many cases. But in the contextof developing energy technology, the game is constantly chang-ing due to the energy transition and sector coupling, aimingcomplete and perfect markets. Thus, maybe it is time to look beyond the cost reduction paradigm and short-term pro fi t focus- to develop technology that leads to lower system cost and win-ning the game of the future. The market potential method couldcontribute to this. Code and Data availability
Code and data to reproduce results and illustrations are avail-able on GitHub https: // github.com / pz-max / beyond-cost. CRediT authorship contribution statement
Conceptualization: M.P.; Methodology: M.P.; Software:M.P.; Validation: M.P.; Formal analysis: M.P.; Investigation:M.P.; Ressources: M.P., A.K; Data Curation: M.P.; Writing -Original Draft: M.P.; Writing - Review & Editing: M.P., F.N.,A.W., D.F., A.K.; Visualization: M.P.; Supervision: M.P., D.F.,A.K.; Project administration: M.P., D.F., A.K.; Funding acqui-sition: M.P., D.F., A.K.;
Declaration of Competing Interest
The authors declare that they have no known competing fi -nancial interests or personal relationships that could have ap-peared to in fl uence the work reported in this paper. Acknowledgements
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