# Storage Lab

###### Arbitrage

Arbitrage may not be the most lucrative market yet, but it is substantially larger than ancillary services markets. To give an example from the UK, the total cost of system balancing, congestion management, reserve, and response averaged around GBP 1bn per year during the 2010s, whereas the total wholesale market had an annual value of GBP 45bn.

Arbitrage is also different from other services in that detailed historical electricity price data are readily available in many regions, or can be modelled for hypothetical or future power systems using a variety of available market models. This allows a long-term view on the economic attractiveness of arbitrage to be formed.

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Figure 1 illustrates the optimal dispatch of a pumped hydro system during one week of German power prices.

Figure 1 – Example of the dispatch schedule for a pumped hydro storage device (10 hours, 75% round-trip efficiency) during one week in the German electricity market (8–14 December 2018). Charts show (a) the hourly price in the market with colours signifying the operating schedule for the storage system, and (b) the state of charge of the system. Other market prices and technology configurations can be explored at www.EnergyStorage.ninja.

Three features are evident:

1. The system buys when power prices are low and sells when they are high, which is the cornerstone of arbitrage operation. During this example week, power is purchased for 26 USD/MWh, and discharged sold for 58 USD/MWh on average.

2. Not all of the cheapest hours are exploited for charging (e.g. it sold power on Sunday daytime even though that was cheaper than Tuesday night when it was buying power). This is due to limitations on the storage duration, as it was already fully charged by Sunday morning and could accept no further energy. With longer duration, these lower-priced hours could be exploited, with all of Sunday used for charging, and all of Friday for discharging.

3. More power must be bought than is sold due to the round-trip efficiency. It is therefore only worth charging if there are periods when it can sell that energy for 1.33 times higher price (1 ÷ 75%). With 100% efficient storage and no marginal costs of operation (e.g. due to O&M), almost every hour would be filled with charge and discharge events, as even the smallest price difference would be enough to profit from.

â€‹When this process is applied to longer time series of power prices, it can be used to assess the annual profits and variation from year-to-year. Figure 2 summarizes the value of providing arbitrage with a lithium-ion battery across 162 years of data from 36 global electricity markets (panel a) and in greater detail for 25 European electricity markets (panel b) with data from 2012-2019. These charts show the profit before fixed costs (i.e. the producer surplus), calculated as the revenue from electricity sold through discharging minus the cost of electricity bought for charging. Profit is shown per unit of power per year, i.e. the profit a device would earn factoring in its utilisation: a 100 MW system earning 50 USD/kW-year could anticipate USD 5 million annual profit.

Figure 2 – Profitability for electricity arbitrage from 2012–19 in various global (panel a) and European (panel b) electricity markets, considering a typical lithium-ion system (4 hours, 86% efficient). Each bar covers the 10th to 90th percentile across the national / international markets within each country / region, and the thick line shows the median across markets and years. Coloured lines in panel b highlight the profitability within specific markets, which exemplify an island market (Great Britain), and well-connected markets dominated by fossil fuels (Germany), nuclear (France), and hydro (Norway). Value of arbitrage is estimated by calculating the profit-maximising dispatch against historical power prices, assuming perfect foresight and no uncertainty. Profit refers to revenue from discharging minus cost of charging (ignoring any fixed costs).

Australian markets provide the greatest opportunity in this example, in part because high penetration of renewables and limited availability of other flexible technologies means power prices have very large spikes. Japan also offers relatively high profits with 2012-2019 data as markets were still tight in the wake of the Fukushima nuclear disaster leading to price spikes during high demand periods. European and American markets offer typically half the revenues of the Asia-Pacific markets shown here, as they have a greater capacity margin, greater interconnection between markets, or greater availability of flexible technologies (including pumped hydro storage).

As with other services, the value of arbitrage sees large variation between world regions and also within them. In Europe, during any given year there is a large range in profitability across markets due to their different circumstances. Lithium-ion storage could expect to earn 12 times more per year operating in Great Britain than it could in Norway. Great Britain is among the most lucrative markets in Europe as it is an island nation with relatively little interconnection to its neighbours and relatively little pumped hydro storage, meaning power prices are spiky. At the other extreme, Norway offers consistently low profits for batteries as the electricity market is dominated by flexible hydro plants.

There is also a large variation in profitability from year to year within markets, as shown for example by the line for Great Britain. The median inter-annual volatility across all markets – defined as the standard deviation in annual profit across years, divided by the mean profit – is 24% (P10–P90 = 17–36%). For example, annual profit in Great Britain is 50 USD/kW ± 24%. Major markets such as Great Britain, Germany and Japan lie close to this median at 20–24%, and most US markets see year-to-year volatility in the range of 19–26%.

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The profitability of storage is driven by variability in prices. The structure of these prices also matters (e.g. if high and low prices occur each day, or are separated by season), but in general the relative profitability of storage in different markets can be approximated by measures of the price volatility. Two such examples are the standard deviation of prices (across all hourly prices in the year), or the average daily price spread (the difference between maximum and minimum price within each day, averaged across all days in the year). Figure 3 shows a simple relationship between the logarithm of standard deviation in power prices and the profitability of arbitrage, measured across 162 years of market price data.

Figure 3 – Profitability for electricity arbitrage as a function of the amount of variation in hourly market prices. Profitability is estimated for 4 hour, 86% efficient storage from 2012–19 in various electricity markets. Profit is calculated as revenue from discharging minus cost of charging (ignoring any fixed costs).

Figure 3 suggests there is a log-linear relationship between price variation and storage profitability, with each doubling in the standard deviation of hourly prices yielding an extra 35 USD/kW-year arbitrage profit. This relationship is best for describing the relationship across markets, but the data within each region are better described by linear relationships. For example, an additional 1 USD standard deviation in power prices yields an extra 2.10 USD/kW-year arbitrage profit within European markets, versus an extra 0.50–0.75 USD/kW-year within American and Australian markets.

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In most electricity markets, the greatest price variation occurs over short timescales due to the day/night cycle driving demand and solar PV output. Price variations over longer timescales (from day to day or month to month) are smaller, giving diminishing returns to increasing storage duration. The greater problem though is that exploiting price differences over longer time periods gives fewer operating cycles per year, and thus dramatically reduces the additional revenue that can be made.

Figure 4 shows how profitability varies with storage duration, using the same historical market data as in Figure 2. Profit increases with storage duration as fewer periods are inaccessible due to constraints on when charging and discharging can occur. In Australia and Japan, storage with 4 hours duration can earn double the profit of 1 hour duration, but over 40 hours duration is needed to earn triple the profit of 1 hour. Both panels show an elbow around 8 hours. Increasing storage duration beyond this yields very little increase in profit. For example, moving from 4 to 5 hours adds USD 4.65/kW-year in Western markets, but moving from 8 to 9 hours adds USD 1.40/kW-year.

Figure 4 – Profitability for electricity arbitrage from 2012–19 in various electricity markets, as a function of storage duration, assuming constant efficiency. Asia-Pacific and Western markets are shown as separate colours due to their different price levels. Shaded areas cover the 10th to 90th percentile, with a thick line showing the median across markets and years. Value of arbitrage is estimated for storage with 86% round trip efficiency by calculating the profit-maximising dispatch against historical power prices, assuming perfect foresight and no uncertainty. Profit is calculated as revenue from discharging minus cost of charging (ignoring any fixed costs).

Figure 5 shows how profit scales with storage efficiency. More efficient storage is more profitable as less power must be bought for each unit sold (reducing costs), and smaller price differentials are needed to operate profitably (increasing utilisation). In European and American markets, 100% efficient storage could earn twice as much as 75% efficient storage, which in turn earns twice as much as 55% efficient storage. The right panel of Figure 5 shows the marginal benefit of increasing round-trip efficiency. A rise of 1 percentage point increases profits by 0.5–2.2 USD/kW-year in Asia-Parcific markets, or by 0.2–1.4 USD/kW-year in Western markets.

Figure 5 – Profitability for electricity arbitrage from 2012–19 in various electricity markets, as a function of storage efficiency, assuming constant duration. Asia-Pacific and Western markets are shown as separate colours due to their different price levels. Shaded areas cover the 10th to 90th percentile, with a thick line showing the median across markets and years. Value of arbitrage is estimated for storage with 4-hour duration by calculating the profit-maximising dispatch against historical power prices, assuming perfect foresight and no uncertainty. Profit is calculated as revenue from discharging minus cost of charging (ignoring any fixed costs).

Schmidt, O., & Staffell, I. Monetizing Energy Storage - A toolkit to assess future cost and value. Oxford University Press. 2023.