MAXIMISING THE VALUE OF ELECTRICITY STORAGE

Grid-scale energy storage promises to reduce the cost of decarbonising electricity, but is not yet economically viable. Either costs must fall, or revenue must be extracted from more of the services that storage provides the electricity system. To help understand the economic prospects for storage, we review the sources of revenue available and the barriers faced in accessing them. We then demonstrate a simple algorithm that maximises the profit from storage providing arbitrage with reserve under both perfect and no foresight, which avoids complex linear programming techniques. This is made open source and freely available to help promote further research. We demonstrate that battery systems in the UK could triple their profits by participating in the reserve market rather than just providing arbitrage. With no foresight of future prices, 75-95% of the optimal profits are gained. In addition, we model a battery combined with a 322 MW wind farm to evaluate the benefits of shifting time of delivery. The revenues currently available are not sufficient to justify the current investment costs for battery technologies, and so further revenue streams and cost reductions are required. Highlights:  We demonstrate a simple algorithm for storage providing arbitrage and reserve  This calculates the time profile of storage dispatch to give optimal profits  Our algorithm’s code is made available open source to the community  Battery electricity storage is currently uneconomical when just shifting energy  Providing reserve can triple the revenue for storage in the British electricity market


Introduction
The world's leaders have now pledged to limit global warming to well below 2°C, which will require significant increases in the penetration of intermittent renewables, inflexible nuclear generation and carbon capture and storage, together with electrification of heat and transport sectors. This raises considerable challenges in operating future electrical grids both efficiently and reliably. Electricity storage, demand side response, flexible generation and interconnection all offer methods to alleviate these issues [1]. Currently, storage is proving too expensive to make a significant contribution. Whilst much work is being carried out to reduce costs and improve efficiencies, this paper explores how storage can maximise its revenues through operating in multiple markets.
Previous works have (1) focused on optimising for a single revenue stream such as arbitrage, (2) use global optimisation tools on specific cases, and (3) typically require perfect or very good foresight of future prices.
This work takes an existing algorithm for arbitrage from the EnergyPLAN software by Lund et al. [2] and extends it to co-optimise the provision of reserve, which we show can increase storage revenue by an order of magnitude. A full mathematical description and an open source implementation in MATLAB are given as supplementary material.
The following section evaluates the revenue streams available to storage (focussing on the British market), barriers to its uptake, and the various technologies available. Section 3 describes the algorithm to optimise the operation of storage for arbitrage, with or without reserve services, under perfect and no foresight of future spot market prices and reserve utilisation. Section 4 gives a demonstration of the algorithm, simulating lithium ion and sodium sulphur batteries operating in the British electricity market. The results evaluate the attainable profits and rates of return within the current UK market, together with a sensitivity analysis of various model inputs and an assessment of storage integrated with a wind farm.

Sources of revenue for storage
Storage has the flexibility to operate within energy market, trading energy to gain from arbitrage, and in ancillary markets, offering reserve, power quality and reliability services. It can also be integrated with existing infrastructure: generators such as wind farms (to reduce balancing costs, time-shift delivery or manage constraints); demand centres (to reduce network service charges, e.g. triad avoidance); or networks (deferring costly upgrades to transmission and distribution systems).

The potential and future of arbitrage
The spread between daily peak and off-peak electricity prices depends on a multitude of factors: the difference in fuel costs of baseload and peaking generation, the carbon price, the difference in peak and baseload demand, the penetration of renewables and flexible technologies [3]. Similarly, future electrification of heat and transport has the potential to increase or decrease the spread, dependant on the extent to which the demand is managed in terms of spreading the peaks [4].
Storage that relies on daily energy arbitrage is susceptible to changes in the daily spread.
Renewables may affect the spread by reducing prices when their output is high [5]. Some storage schemes, such as pumped hydro with very large reservoirs, may be capable of arbitrage over longer timescales, perhaps taking advantage of weekly spreads which are driven by lower demand over weekends, rather than renewable penetration [6].
Wind or PV which coincides with peak demand can reduce the spread. This appears to be the case in Germany, where PV coincides with peak daytime demand and suppresses prices during the day, resulting in lower peak prices which now occur in the morning and evening [7]. British peak prices occur in the evening, and so PV may instead increase the daily spread. Wind power has a less systematic diurnal pattern, but the penetrations seen in Germany and Britain are now sufficient to cause negative electricity prices, and thus increase the daily spread. Figure 1 displays the average daily spread in Germany since 2002 (peak minus baseload price) as a proportion of the median spot price, against the growth of solar PV and wind penetration. Before the rise in PV capacity, the cost difference between coal and gas plants was the main driver [3]; however, since 2008, the spread has consistently reduced, as the penetration of PV has dramatically increased. The daily demand profile varies significantly between countries. For example, the UK's peak demand is typically in the evenings, when solar is less likely to displace conventional generation. This greatly reduces its impact on the price spread, though it may still depress average wholesale prices.

The structure of balancing services in the UK
A second type of revenue that storage can access is from balancing services. In the UK, there are three types [9]: 1) Ancillary and Commercial Services 2) Contract Notifications Ahead of Gate Closure 3) Bid -Offer Acceptances (also known as the 'balancing mechanism') The first includes specific services that are contracted for in advance, namely reserve, response, power quality and reliability services. The income is typically based on utilisation volumes (MWh of energy) and/or availability offerings (MW of capacity). The second enables National Grid (Britain's transmission system operator) to contract directly with parties to purchase or sell electricity ahead of gate closure, typically when it predicts system imbalances may occur [9]; however, it is rarely used (most recently in 2012) and is hence not considered further [10]. The third type, the 'balancing mechanism', operated post gate closure (i.e. less than an hour ahead of real-time). Generators and consumers can submit bids to buy electricity (increase demand or reduce generation) and offers to sell electricity (reduce demand or increase generation), indicating the price at which they are willing to deviate from their preferred schedule [9].
The contracted nature of ancillary services results in income streams that are typically more predictable or at least offer some level of certainty, and hence these are considered further for the remainder of this study. Ancillary services consist of frequency response, reserve, black start and reactive power services [9]. In a broad sense, response services balance the power demanded with generation on a second by second basis, whereas reserve provides energy balancing during unforeseen events of longer duration, such as a tripped generator or incorrectly forecast demand.
Black start is required in case of total or partial transmission system failure, to gradually start up power stations and link together in an island system. Finally reactive power services involve maintaining adequate voltages across the transmission network, though such a service may also be useful on distribution networks. A more detailed description of these is given in the online supplement.

Short Term Operating Reserve
It is likely that storage has roles to play in all four elements of ancillary services; however, we focus on the provision of reserve, and specifically short term operating reserve (STOR) for reasons of data availability. STOR is a commercially tendered service, where a constant contracted level of active power (or demand reduction) is delivered on instruction from National Grid, typically when demand is greater than forecast or to cover for unforeseen generation unavailability. The service only requires participants to be available during predefined availability windows, with typically two to three occurring per day [11].
Participants are expected to deliver within 4 hrs of instruction (though most tenders could within 20 mins), with a minimum capability of delivering 3 MW for 2 hrs, followed by a maximum 20 hr recovery period [12]. In 2012/13, the majority of units were less than 10 MW in capacity, with typical utilisation times of 90 mins [12]. Providers are selected through competitive tenders based on economic value, historic reliability and geographic location [11]. Committed providers are expected to remain available for all windows over a season, meaning they cannot generate for other services (e.g. providing arbitrage).

The current value of balancing services
Response, reserve and reactive power services are remunerated for both availability (£/h) and utilisation (£/MWh). Services that include availability windows also receive window initiation payments (£/window) to compensate the participant for readying their plant prior to each window.
The total annual spending on each service by National Grid typically ranges from £50m to £150m per year [18]. The market size for shorter timescale services (frequency response and fast reserve) is

The future of balancing services
Historically, the level of reserve services procured are set to cover three standard deviations of uncertainty, hence can accommodate over 99% of unexpected fluctuations [19]. The uncertainty is formed of error in both the forecast demand and supply. The latter includes unexpected plant outages, loss of the single largest generating unit, and imperfect forecasts for weather-dependent renewables output. Recent forecast requirements for primary and high response have approximately doubled [20,21], in preparation for larger units connecting to the system (new nuclear reactors and interconnectors) and in response to the dramatic increase in wind and solar capacity.
Intermittency increases the standard deviation of supply fluctuations, however the increase is only moderate due to smoothing of outputs up to an hour ahead, and good forecast accuracy up to several hours ahead [19]. The increase does however lead to greater demand for flexible products that can change output rapidly many times per day, as well as maintain a very low or zero standby level [22]. Yet increasing the holding of products such as STOR (of which 2.3 GW is currently considered optimal) may not be the most cost effective way to deal with intermittency [23].
Balancing requirements for wind continuously vary every hour, day or week, whereas STOR is fixed for an entire season. Hence in the future, this could lead to the introduction of new balancing services. A review by Gross et al. found six of seven studies quoting increases in overall reserve requirements of between 3-9% for a 20% penetration of intermittent generation [19]. It is worth noting, that current reserve required to cover wind and PV total about 17% of their output [24].
Other factors such as electrification of heat and transport may also have an effect by making demand more variable between periods and increasing forecast errors [22,25], together with an increase in power plant genset sizes resulting in higher response and reserve requirements [26,27].

Alternative sources of revenue
Further sources of revenue include integrating storage with generators, demand centres or networks. Generators such as wind farms may benefit by utilising storage to improve delivery forecasts and thus reduce balancing costs, and by shifting the time of delivery (effectively arbitrage) to sell for higher prices. This is particularly pertinent if wind penetration increases due to its effect on suppressing spot prices during periods of high national wind output [5]. Many wind farms currently operate under a power purchase agreement (PPA), which typically purchase all wind output at a fixed price [28,29]. This offers a price guarantee, at the expense of including a risk premium. Control over when electricity is delivered may enable better terms to be gained as part of a PPA, or the confidence to operate directly on the spot market. Finally, storage could also be useful if in the future wind farms are offered non-firm connections, i.e. if they are not entitled to receive constraint payments.
Storage can also prove useful for demand sources. Customers on time-of-use tariffs can reduce imports from the grid at times of high prices, as well as reduce network service charges, for instance through triad avoidance [30].
Finally networks may also benefit from storage through deferral of transmission or distribution reinforcement. This is particularly beneficial to distributed storage, in avoiding the significant cost of upgrading distribution networks to meet any future increases in peak demand [1]. However, transmission network operators in the EU are not allowed to own storage assets as they are currently classed as generators. This, together with further barriers to storage, is discussed in the next section.

Undetermined asset classification
Energy storage systems are multifunctional, and may act as generator, consumer or network asset at different points in time or simultaneously. Current regulation classifies storage based on its primary function [33], leading to issues with ownership. According to EU law [22], transmission network operators are forbidden from participating in the electricity markets, and hence would be unable to supplement their return on storage devices through competitive market participation (in addition to network support activities). Whether storage is classed as a generator or consumer also impacts on transmission and distribution use-of-system charges. If a consumer, then often consumers are subject to taxes to subsidise renewables [31]. A new asset class for storage could overcome these issues.

Lack of standards and experience
Other than pumped hydro, storage technologies are still largely developing, hence there is currently a lack of standards on their design, deployment and evaluation of their economic value [31]. For a network operator, investment in traditional network assets offers a low risk investment with guaranteed revenue streams. In contrast, the high capital costs of storage, uncertain future income streams and lack of storage precedents, result in high risk proposition [31]. Hence storage may not 'fit' into the business model of traditional transmission system operators, relying instead on competitive market participants. Furthermore, the benefits storage may offer to grid or centralised generator utilisation and corresponding cost and efficiency benefits are difficult to quantify, although this paper aims to make this more straightforward in future.

No incentive to provide flexible generation
The fixed premia widely used to incentivise renewable generation do not reward dispatchable facilities [34] and are often accompanied by export guarantees [35]. Hence renewable generation often operates at the expense of conventional plant, increasing system-wide integration costs through displacing more energy than capacity, and decreasing asset utilisation. As these costs are socialised, there is a lack of transparency over the true costs of inflexible renewable generation. A two-tier tariff could incentivise owners of renewable energy plants to provide dispatchable energy, as is the case on some Greek islands [36].

Renewable energy subsidies
Whilst storage may provide indirect benefits to renewables in terms of reduced curtailment and hence increased penetration, the electricity itself that is stored may or may not be sourced purely from renewables, if the storage device is connected directly to the grid. This creates difficulty in terms of subsidising storage as a renewable device. However Krajačić et al. propose that a guarantee of origin scheme could alleviate such issues [37]. Even so, under current rules, electricity from renewables that charges storage before entering the grid cannot receive subsidies [22].
Therefore, connecting a wind farm to a storage device would forfeit any renewable incentives.

No incentive to maintain power quality
Power quality is likely to deteriorate as the penetration of renewable energy increases, particularly distributed solar PV or other domestic microgeneration [38]. However, currently there is no incentive to improve power quality and it is difficult to quantify [39].

Reserve market
In liberalised electricity markets, the reserve market may provide a significant income stream for storage technologies [40,41]. According to Wasowicz et al., revenue increases between 6.2% and 19.2% could be obtained for storage operators in Germany if grid support was supplemented with reserve services [34]. However, the state of charge of some storage devices may not be precisely known (lithium ion batteries being a prime example), hindering its operation in the reserve markets [31].

Lack of market liquidity
It is currently estimated that 5% of all trades in the UK market occur on the spot market [42]. The remainder are executed under opaque bilateral contracts, and often between a supplier and its generation arm. This leads to low liquidity in the spot market, increasing the entry barrier to small scale storage and new entrants, as is the case currently with distributed generation [43].

Insufficient remuneration for ancillary services
According to Ferreira et al., remuneration for ancillary services within the EU are currently insufficient to make storage economically viable [44]. Storage is not rewarded for its higher accuracy, faster response and greater ramp rates in comparison to conventional ancillary service providers. In the US however, regulation changes in 2013 stipulate that improved performance is now valued [31]. Storage devices (particularly batteries and flywheels) can provide a better service than gas turbines and engines, meaning that the same level of service could theoretically be provided with fewer MW of capacity; however, there is as yet no financial premium available for this.

Small scale storage
It is worth highlighting the importance of small scale distributed storage, particularly for distribution network operators (DNOs). This could help mitigate peaks caused by future electrification of heat and transport [45], and to increase the penetration of distributed generation that can be managed with existing infrastructure. Electrification is an essential part of national decarbonisation strategies across Europe, but will radically alter the profile of electricity demand. For example, a million heat pumps or electric vehicles are estimated to add 1.5 GW to peak demand in Britain and Germany [25]. The distribution cables that serve individual buildings were not designed to handle reverse power flows, where embedded solar panels and combined heat and power units export up to higher-voltage parts of the network [38]. As this 'last mile' of the network is mostly buried under streets, it will be prohibitively expensive to reinforce, and so operators are considering storage as a lower-cost route to balancing microgeneration.
Despite this, current policy development tends to focus on large scale storage [31]. Furthermore, regulation changes could enable DNOs to operate in an active manner, undertaking regional balancing services to better manage power quality and network utilisation [46,47]. Storage could then be used as a regulated asset.

The storage technologies
There are many excellent reviews of the storage technologies available [1,44,48,49];, hence this section simply aims to summarise key points regarding use, and recent data on cost and efficiencies.
The technologies broadly fit into three categories: bulk storage which operates over timescales of several hours to weeks; load shifting (minutes to hours); and power quality (seconds to several minutes) [48]. At the extreme, the UK can store around 50 TWh of natural gas, capable of discharging over 11 weeks [50]. This highlights the potential scale at which hydrogen or synthetic natural gas could be stored, with the ability to operate over seasonal timescales. Battery technologies show lower capacities, and discharge over shorter timescales between several minutes to several hours [48]. Conventional batteries (lead acid and lithium-ion) have higher costs per kWh stored as they require fixed reagents, rather than large natural features to store energy (lakes and caverns). Flow batteries could attain lower specific energy costs ($/kWh) as the reagent volume could be increased with a simple storage tank; however their current low volume of manufacture retains higher costs. The modular nature of batteries favours distributed storage; however the linear economies of scale mean that the cell cost per kW or kWh are similar when moving from residential to utility scale batteries, although the balance of plant costs can reduce dramatically. Finally, electrochemical capacitors (ECs) and flywheels display low energy to power ratios of less than 1, discharging in the seconds to minutes range [48].
The specific costs of the different technologies per kW and kWh are shown in Figure 2 alongside their round-trip efficiencies, based on systematic reviews of hundreds of sources [49,51,52]. It is clear that there is significant divergence between the cost per unit power and unit energy. Bulk energy stores such as PHS and CAES tend to exhibit the lowest $/kWh, as they benefit from economies of scale in storage capacity, but also exhibit the lowest efficiencies. Conversely, electrochemical capacitors exhibit relatively low $/kW, but extremely high $/kWh of over $10,000 / kWh.
This diversity in price and performance highlights the need for a range of market products to allow the different technologies to capture their true value. Bulk energy stores may find arbitrage a viable strategy, however electrochemical capacitors obviously require a market that can adequately reward its extremely fast response and ability to deliver high powers for very short times (for instance primary response).

Previous studies of optimal storage control
Most previous studies that attempt to optimise the control of storage tend to perform global optimisation using mixed-integer linear programming, either to optimise for system-wide benefits or an independent investor. In addition, many previous works have looked only at arbitrage as a revenue source, assuming a price taker analysis [53,54]. Wasowicz et al. includes more applications, obtaining a multi-market optimisation but only under certainty [34]. In particular, they investigated the effect of grid congestion, storage technology and regulatory changes on the economic viability for an independent investor.
Sioshansi et al. investigated the impact large amounts of storage would have on the price spread and value of arbitrage by correlating historic prices to total system demand, and evaluating the extent to which storage would flatten peak demand and off-peak demand [55].

Round-trip Efficiency
forecasts of imbalance prices to investigate the integration of storage with wind, optimising the balance between reducing imbalance charges and gaining from arbitrage [57].
Therefore the aim of this project was to develop a simple algorithm that could optimise multiple revenue streams without the need for foresight. In particular, a simple method that could be run quickly and easily was desired, over a globally optimal solution. Hence the remainder of this paper sets out to explain the algorithm developed and subsequently the key findings.

Methods
The aim of this work was to design and demonstrate a simple algorithm to optimise storage operation for multiple revenue streams: arbitrage, reserve and coupling with a wind farm. We take a deterministic algorithm from Lund et al. [2] and Connolly et al. [56] that finds optimal operation for arbitrage, and add reserve and wind coupling, and demonstrate a selection of findings. The algorithm is technology neutral, and capable of simulating storage for power applications (e.g. batteries for arbitrage and reserve) and for bulk energy applications (e.g. hydro and compressed air for inter-seasonal storage).
Throughout this paper we compare three scenarios: 1. Arbitrage Only -'ArbOnly' 2. Arbitrage with reserve, only taking availability payments -'ArbAv' 3. Arbitrage with reserve, also taking utilisation payments -'ArbAvUt' The two reserve scenarios (ArbAv and ArbAvUt) are designed to explore the minimum and expected levels of income from providing reserve. ArbAv gives the lower bound: earning fixed availability payments for having the store available for reserve provision, but never receiving additional payments for actually providing reserve energy. This requires the store to maintiain charge levels above a set limit and forgo earning revenue from arbitrage during availability windows. ArbAvUt provides a central estimate: earning the availability payments as above and additionally utilisation payments based on the historic need for reserve, which are typically much higher than earnings from arbitrage.

Arbitrage Only (Perfect Foresight)
The EnergyPLAN algorithm for arbitrage described by Lund et al. [2] works by finding optimal charge-discharge pairs: the period with maximum price where discharging should occur, and a corresponding period with minimum price where recharging should occur. If the device can be fully utilised during these periods then they are removed from the series, and the next charge-discharge pair is found. Charge-discharge pairs are only accepted if they are profitable, accounting for the round trip efficiency of the storage device and other marginal costs. Low efficiency devices, or periods with homogenous prices will therefore see limited utilisation.
On the first iteration there are no constraints on which hours or how much capacity is accessible, and so these will be the maximum and minimum priced hours respectively. As the algorithm progresses, constraints on when recharging can occur become binding, so as not to exceed the maximum or minimum possible charge levels.
Lund shows that this arrives at the global optimum for profit [2], which we confirmed using a simple linear program written in GAMS. A simple example is presented in Figure 4, and the online supplement gives a full mathematical description (subroutine A in Figure 3).

Arbitrage + Reserve (Perfect Foresight)
The extension of this algorithm to consider reserve consists of four parts:  First, energy prices are removed during the windows where reserve is provided  The device is then optimised for arbitrage outside of these windows  Additional discharge due to reserve utilisation are added onto the profile  Finally, the operation outside of availability windows is modified to recover any discharges due to reserve utilisation, and ensure that additional constraints are met.
The algorithm initially optimises for arbitrage in all periods outside of availability windows, as it is assumed the device is forbidden from providing arbitrage when committed to provide reserve.
Reserve services are then introduced through a further step. Two scenarios representing extremes of income are considered: with no utilisation (ArbAv), and with typical utilisation (ArbAvUt). In both cases, identical remuneration for availability is received, however the later receives additional payments for energy discharged during availability windows, at the request of National Grid.
For the ArbAvUt scenario, the utilisation volumes are determined based on the input utilisation price and data for STOR utilisation provided by National Grid (2015b). These volumes are then applied during availability windows. We take historic STOR utilisation from 2013/14 STOR year [58]. This gives the average daily profile for working and non-working days during each season, and the total volume for each day of the year. We combine these to form an estimated half-hourly profile of STOR demand, and interpolate the price offered for this utilisation from the supply curve (or 'price ladder') for that season [59].
For the ArbAv scenario, there is no utilisation hence no change in charge level during availability windows. For ArbAvUt, the charge level will decrease during some windows, meaning that additional recharging will be needed between windows. The algorithm then checks that three conditions are met: 1. Minimum charge level prior to every availability window 2. Charge level during all periods is less than or equal to maximum capacity 3. Charge level during all periods is greater than or equal to zero If any are not met, charging/discharging is altered during the most economical feasible periods to accommodate the conditions. Figure 5 gives a graphical explanation of this process, and a mathematical description is provided in the online supplement (subroutines B and C in Figure 3).

Figure 5: Example operation with reserve under perfect foresight. Starting from the top, the plots show the charge level, price series (excluding availability windows) and operation profile over the settlement periods. The black circles denote availability windows, as well as the minimum charge level required at the start of availability windows (in this case 300 MWh). From left to right the panels show: (a) After optimising for arbitrage outside of availability windows. (b) After addition of utilisation volumes to operation profile -note the negative charge levels (that are corrected in the next step). (c) After ensuring
charge level is maintained at satisfactory levels. This algorithm therefore assumes perfect foresight of both future prices and utilisation volumes, as ALL volumes are revealed before action (c) is taken.

Introducing no foresight
Under perfect foresight, future market prices are known precisely, hence the storage can take advantage of fluctuations in the market price over periods of hours, days or even months for large capacity seasonal storage. This approach is only practical if a good price prognosis is available, or if used to evaluate the return on storage under future market price projections.
In reality, future prices and utilisation volumes are not known in advance, hence the algorithm's data inputs were modified to operate with no foresight. For the arbitrage-only scenario, a future price series was estimated based on the average daily price profile for each season in the previous year (see supplement section 2.5 for more detail). The model was run with the estimated price series, and the resulting operation profile was combined with the real outturn prices to calculate the profits.
The ArbAv and ArbAvUt scenarios also use these estimated price series to optimise for arbitrage outside availability windows. To accommodate no foresight of future utilisation volumes, the algorithm was modified to form a stepwise process. Utilisation volumes for the first window are revealed, with any recharging to meet the next minimum level requirement, and any corrective actions to retain the charge level between zero and full capacity, made after the first window (i.e. with hindsight of the utilisation volume) and before the next (i.e. with no foresight of future volumes). The process is then repeated for subsequent windows. In contrast, under perfect foresight there was no constraint on when these actions could take place, i.e. they could occur any time prior to or after the corresponding window. This method is further explained and visualised in the online supplement.

Application to a Wind Farm
The above methods were also applied in conjunction with a wind farm, to improve control over when the electricity is delivered. In effect, the wind farm is able to perform arbitrage, with the constraint that storage charging is limited to the output of the wind farm (assuming no import connection to the grid) -as in Figure 6. Hence the scenario considered is arbitrage under perfect foresight. We use Whitelee wind farm as an example, taking its final physical notifications (FPN) of output during the 2013/14 season, retrieved from Elexon.

Financial Calculations
Following the DOE/EPRI convention, the capital cost of battery systems was represented by the sum of a power ($/kW) and energy ($/kWh) term, to allow systems of different c-rates to be compared.
We ignore economies of scale for battery production, and assume that the specific cost (per kW or kWh) is constant regardless of battery capacity. In addition, an efficiency of 80% and cycle life of 5500 cycles (at 80% depth of discharge) was assumed [60,63,64]. Note that lifetime is defined as the number of cycles before a 20 to 30% drop in capacity is observed. Hence the battery may be able to continue running post this period, but with reduced storage capacity and potentially lower power outputs due to an increase in internal resistance [65]. These effects have not been accounted for in this analysis.
For lithium ion (Li) batteries, capital costs of 1000 $/kW plus 700 $/kWh [66,67] were assumed, with operational costs of 9.2 $/kW/yr and an efficiency of 90% [60]. A lifetime of 6000 cycles was assumed [65]. For both technologies, costs of capital have been ignored. For both NaS and Li batteries we note that there is a broad range for system costs and lifetimes, and as these are rapidly evolving any choice of cost data will soon be obsolete. We choose a single, central value for each technology to perform the financial case study, and note that our primary metric (annual return on investment) scales inversely with capital cost. If, for example, capital costs fall by 50% from the values listed above, then annual returns will be double those presented in our results.
For each scenario, the profits of the relevant components are calculated using equations 2-4. The components are then summed to form the total profit for each scenario. This method of calculating profits means that any charging outside of availability windows is associated with the arbitrage component -including charging in preparation for STOR utilisation during a window. Devices can therefore register a financial loss from arbitrage when providing reserve utilisation.
The annual rate of return (ROR) for a device is based on its annual profit divided by the upfront capital cost (i.e. ignoring the time-value of money):

Results and Discussion
This

The effect of efficiency
This section evaluates the effect of round trip efficiency on profits for our three scenarios under perfect foresight: i. Arbitrage only -'ArbOnly' ii.
Arbitrage with availability and utilisation -'ArbAvUt' Assumptions include: c-rate of 0.1, STOR utilisation price of 89 £/MWh, availability price of 5 £/MWh (based on the 2013/14 average for STOR [58]) and no marginal costs of charging/discharging other than electricity purchased.
The total specific profit for each scenario at various efficiencies is shown in Figure 7. At 100% efficiency, ArbOnly offers a specific profit (per kW of discharge capacity) of approximately 70 £/kW-/yr, which lies between the values offered by scenarios ArbAv and ArbAvUt (the extreme cases of arbitrage with reserve). However for efficiencies below 72%, it is more profitable to offer reserve services even with no utilisation, than purely perform arbitrage. This is a result of the fixed payments for available capacity, which are independent of energy production and hence efficiency. This also leads the ArbAv scenario to plateau at even lower efficiencies. This is particularly pertinent for technologies such as compressed air and hydrogen storage, which exhibit round trip efficiencies in the range of 54-74 % and 41-49 % respectively [49].
ArbAvUt offers the greatest specific profits, with smaller devices exhibiting higher values than larger devices. This is discussed further in section 4.

The effect of discharge capacity
The specific profit is independent of discharge capacity for the ArbOnly and ArbAv scenarios.
However it does affect the ArbAvUt scenario, via interaction with the volume of STOR utilisation that occurs. As STOR requires a generator to run at a fixed output level, smaller discharge capacities can As the discharge capacity reduces, the profit attributed to utilisation increases, in line with an increase in STOR utilisation (this equally causes a drop in the 'arb' component due to increased charging required outside of availability windows to cover the utilization). In actual fact, the utilisation price was set to 89 £/MWh, which essentially places this device first in the 'merit order' for STOR despatch [59]. Thus the assumptions of the model mean that despatch occurs as long as national demand for STOR is greater than the device's discharge capacity.   Whilst the specific profit earned is greatest for smaller devices, the absolute profit increases with size. Figure 9 highlights this, where the highest utilisation profit component is obtained for a 100 MW device. Above this, the increase in MW offered is outweighed by the reduction in the number of times the device is called upon, resulting in a net reduction in utilisation MWh. Naturally however, the availability and arbitrage components increase in an approximately linear fashion, resulting in an overall increase in total profits.

The rate of return attainable for arbitrage and availability
To place the specific profits discussed earlier into context, rates of return on exemplar sodium sulphur (NaS) and lithium ion (Li) batteries have been evaluated. The specific profit for the ArbOnly and ArbAv scenarios is dependent on the efficiency and c-rate, but is independent of discharge capacity (in contrast to the ArbAvUt scenario -discussed in section 4.2). Figure 10a and b present the variation of specific profit and rate of return with c-rate. Li batteries achieve greater specific profits due to their efficiency advantage, but the lower cost of NaS batteries result in higher rates of return. Furthermore, the greatest specific profits (at low crates) do not result in the greatest rates of return, as the increase in capital cost outweighs the additional revenue captured. Nevertheless, a peak rate of return of only 1.98% is achieved, which is too low to be viable, as discussed in section 4.4.  Devices with lower discharge capacities tend to exhibit greater specific profits (as discussed in section 4.2). Moreover, devices with the lowest c-rates (longest discharge times), tend to offer the highest specific profits. This is due to the nature of the measure of specific profit, where inevitably devices with equal discharge capacities but larger energy stores are able to capture greater profits.

The rate of return attainable for arbitrage and reserve
However, the highest specific profits do not result in the highest rates of return (as can be observed comparing Figure 11 (top and bottom)). For a given capacity, there appears an optimal c-rate to maximise rate of return. This behaviour is a result of the interaction between a reduction in specific profits as c-rates increase, but also a reduction in specific capital costs.  For a round trip efficiency of 1, the profits with no foresight range between 88% (ArbOnly) and 98%

Sensitivity to assumptions for STOR utilisation
(ArbAvUt) of those with perfect foresight. With an efficiency of 0.8, this drops to 75% for ArbOnly and 96% for ArbAvUt. The certainty of availability payments makes reserve more favourable with no foresight: the ArbAv scenario is more profitable than the ArbOnly scenario for efficiencies of less than 0.72 with perfect foresight; however for no foresight, this crossover point increases to 0.85.
These observations can be explained by the two factors that no foresight introduces: i) The use of estimated future prices, which affects the arbitrage component of all scenarios.
This is due to the difference between the estimated and real prices. The ArbOnly scenario is most exposed as all profits are derived from arbitrage, whereas for the ArbAv and ArbAvUt scenarios, the proportion of profits from arbitrage are lower, due to the fixed availability and utilisation payments. Furthermore, the sensitivity of ArbOnly with no foresight to efficiency is likely due to the significantly fewer hours over which arbitrage operates at lower efficiencies (due to the higher price spreads required). Hence any discrepancies between the predicted and actual prices are magnified. At very low efficiencies, hardly any arbitrage is performed at all, resulting in the convergence of the profits for ArbOnly with perfect and no foresight.
ii) The unknown future STOR volumes, which results in increased restrictions over when corrective action can take place. For instance, following utilisation in an availability window, the storage device may have to charge up prior to the next window, even if the price is high.
Under perfect foresight, advanced planning is effectively permitted, such that the device could charge up ahead of both windows, avoiding the high prices in between.
A final point of note is that for the ArbOnly scenario, the algorithm with no foresight achieves 88% of the optimal profits, with an efficiency of 1. This can be considered quite high for having simply used a price profile based on averages over the previous year's STOR season. This is due to the importance of profile shape for arbitrage rather than mean value: it is safe to assume that on most days, discharging between 5-7pm would be optimal (due to likelihood of high prices relative to other times of day).  Greatest returns were obtained for the smallest capacities, as the arbitrage benefits diminish as more storage is employed. The optimal c-rate is between 0.3 and 0.4 (3.3 to 2.5 hours of storage capacity), implying that around 1 MW of battery capacity was optimal. Note that we ignore economies of scale in producing batteries, and so this result may change if larger batteries are significantly cheaper per MW.

Integrating storage with wind
The maximum rates of return of only 1.89% and 1.22% was recorded for NaS and Li batteries respectively, hence battery-based arbitrage with a wind farm is not viable with current battery costs and wholesale prices. Either further revenue streams must be sought, the capital cost of storage must dramatically fall, or the value of shifting the time of delivery must increase. The latter may occur in the future if wind penetration increases, and hence periods of high output depress the spot price more markedly.
Alternatively, integrating storage with a wind farm enables some level of control over the farm's output. This could provide operators with enough confidence to sell output directly on the spot market as opposed to via a power purchase agreement (PPA). The fixed price per MWh offered in PPAs is lower than the average spot price of power as the counterparty is exposed to the risk of price volatility. If this risk premium is assumed to be 10% of the output-weighted average spot price, this would result in an additional income of 4,200,000 £/annum (£13,000 per MW of wind capacity), irrespective of storage size. It is not meaningful to add this to the rate of return of the storage device as this is a qualitative benefit, based on operator confidence in the marketplace. The size of storage has plays a qualitative role in reducing perceived investor risk.

Conclusions
As the penetration low carbon intermittent or inflexible forms of generation increase, system integration costs inevitably rise. Storage offers a solution to limit these costs, however to date it is still considered too costly to be an effective solution. Either costs have to decrease or storage operators have to maximise use of the devices to obtain as much profit as possible. Most studies in literature have aimed to optimise some form of storage either for a single revenue stream such as arbitrage, or performed analyses using computationally expensive global optimisation tools.
Additionally, a good prognosis of future prices was typically required.
This research has developed and demonstrated a simple, generic algorithm that can optimise a storage device for arbitrage, with or without reserve services, under both perfect and no foresight.
We make the Matlab implementation of this algorithm available to the community to help foster future research.
For an exemplar sodium sulphur battery, the maximum annual rate of return obtained for performing arbitrage only in the British market was 1.98%, but this increased to 7.50% for arbitrage with reserve, both under perfect foresight. For a lithium battery, returns were lower at 1.28% and 4.4%, due to the higher capital cost. Operation under no foresight was found to reduce profits by 5-25%. Also, integrating a sodium sulphur battery with a wind farm to shift time of delivery was found to produce a maximum rate of return of 1.89%, compared to 1.22% for a lithium battery.
With current battery lifetimes and electricity prices, the rates of return obtained even under perfect foresight are unlikely to prove viable. Either costs must reduce, alternative technologies with longer lifetimes (such as PHS) must be sought, additional revenue streams must become accessible, or the fundamental dynamics of the electricity market must change (e.g. daily price spread increasing due to increasing wind penetration).
Despite finding that storage would not be viable in any of the considered scenarios, the algorithm developed was successful at providing a simple means of optimising the control of storage, and future work should extend it to further revenues streams. In particular, the lack of transparent data resulted in the use of STOR market data for reserve services, however the technical properties of storage mean that it may gain greater benefit from operating in shorter timescale markets, such as fast reserve or response. Alternative income may also be gained from:  Triad avoidance in order to minimise transmission use of system charges (or maximise payments in the case of distributed generation);  Reduce imbalance costs for a wind farm;  Participate in flexible reserve in conjunction with a wind farm (assuming good forecasts are available at the week ahead stage in case opt out is required).
The algorithm could also be further developed to include impacts on lifetime within the decision process. Currently lifetime is post-processed as a result rather than an optimisation variable.
Furthermore, refinements to the no foresight algorithm could be made through improved forecasting of future prices using correlation with temperature forecasts.

Acknowledgements
We thank the Engineering and Physical Science Research Council, via Project EP/K002252/1 (Energy Storage for Low Carbon Grids) for funding Iain Staffell.