Sort the hourly prices, take the round-trip losses off the discharge and haircut for forecasting: a daily high and low are not a revenue model.
Battery arbitrage revenue is the energy discharged times the price in the dearest hours, less the energy charged times the price in the cheapest hours, with the round-trip losses taken off the discharge. On an illustrative day a 50 MW, two-hour battery buys 100 MWh at 39.00 and sells 87 MWh at 141.50, earning 8,410 a day. After availability and an allowance for imperfect forecasting that is 2,531,077 a year, 50,622 per MW. Multiplying the two-hour spread of 102.50 by the full 100 MWh, without losses, would claim 21.9 per cent more.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The calculation looks trivial and is routinely got wrong in three places: the efficiency loss, the hours the battery actually trades, and the assumption that a longer battery earns proportionally more. Each one comes from reading a daily price shape as if it were two numbers.
| Input | Value |
|---|---|
| Power | 50 MW |
| Duration | 2 hours (100 MWh) |
| Round-trip efficiency | 87% |
| Cycles | 1 a day, 365 days |
| Availability | 97% |
| Share of perfect-foresight value captured | 85% |
| Day-ahead prices, per MWh | average 81.38, low 38, high 145 |
The price shape is a solar-heavy day: a midday trough (48 at 11:00, 40 at 12:00, 38 at 13:00, 42 at 14:00) and an evening peak (110 at 17:00, 138 at 18:00, 145 at 19:00, 128 at 20:00).
A two-hour battery at full power charges in the two cheapest hours, 12:00 and 13:00, at an average of 39.00, and discharges in the two dearest, 18:00 and 19:00, at an average of 141.50. Charging comes before discharging, so one cycle fits in the day.
Daily margin = MW × hours × (efficiency × average sell price − average buy price)
Charge: 50 × 2 = 100 MWh at 39.00 costs 3,900. Discharge: 100 × 0.87 = 87 MWh at 141.50 earns 12,310. Margin 8,410, or 168 per MW a day. The 13 MWh lost in the round trip is the difference between 8,410 and the 10,250 the plain spread suggests.
In Excel, with prices in B2:B25: =50*2*(0.87*AVERAGE(LARGE(B2:B25,{1,2}))-AVERAGE(SMALL(B2:B25,{1,2})))
The losses also set the minimum spread worth trading. Each MWh sold costs 39.00 ÷ 0.87 = 44.83 of power bought, so any hour selling below 44.83 loses money against these charging hours: 5.83 per MWh of efficiency cost on top of the purchase price.
A perfect-foresight year of identical days would earn 8,410 × 365 = 3,069,832. Two haircuts bring it to something bankable: the battery is available 97 per cent of the time, and a trader without perfect foresight captures perhaps 85 per cent of the ideal schedule. 3,069,832 × 0.8245 = 2,531,077 a year, 50,622 per MW. In practice the year is built from 365 different days, not one repeated; the method is the same, applied to each.
| Duration, hours | Buy price | Sell price | Spread | Margin a day | Per MW-year | Per MWh of capacity a year |
|---|---|---|---|---|---|---|
| 1 | 38.00 | 145.00 | 107.00 | 4,408 | 26,528 | 26,528 |
| 2 | 39.00 | 141.50 | 102.50 | 8,410 | 50,622 | 25,311 |
| 3 | 40.00 | 137.00 | 97.00 | 11,878 | 71,495 | 23,832 |
| 4 | 42.00 | 130.25 | 88.25 | 14,264 | 85,850 | 21,462 |
Every extra hour of storage trades a worse pair of hours: the fourth hour sells at 110 and buys at 48, against 145 and 38 for the first. A four-hour battery earns 3.24 times what a one-hour battery earns, not four times, and each MWh of capacity earns 19.1 per cent less. That matters because capacity is what the battery costs to build. The spread a longer battery captures is an average over more hours, and averages are flatter than extremes.
| Efficiency | Margin a day |
|---|---|
| 80% | 7,420 |
| 85% | 8,128 |
| 87% | 8,410 |
| 90% | 8,835 |
Pricing the battery off the day's high and low. The peak-to-trough spread here is 107, and 107 × 100 MWh would suggest 10,700 a day. The battery cannot sell 100 MWh in the single dearest hour; it sells 87 MWh over two hours that average 141.50, after buying 100 MWh over two that average 39.00. The same trap scales: a revenue model that applies one daily spread to every duration overstates a four-hour battery most, because it ignores the hours the extra capacity is forced to trade. Build the margin from the sorted hourly prices, with the losses on the discharge, and then haircut for availability and forecasting.
The price shape is illustrative. Real revenue stacks also include ancillary services and capacity payments, are limited by cycling warranties and degradation, and pay grid charges on imports in some markets. Nothing here is investment advice.
The year's 8,760 hours sorted into a price duration curve, and what its averages hide, are in the free workbook for this book. The same hourly logic applied to solar output is in how to calculate a solar capture price and capture rate.
Energy lost in the round trip is power bought and never sold. At 87 per cent, 100 MWh charged returns 87 MWh, and each MWh sold costs 39.00 divided by 0.87, or 44.83, of power bought. On the illustrative day margin moves from 7,420 at 80 per cent efficiency to 8,835 at 90 per cent.
No. The extra hours trade a worse pair of prices. On the illustrative shape, a four-hour battery earns 14,264 a day against 8,410 for two hours, 1.7 times, and 3.24 times a one-hour battery rather than four. Each MWh of capacity earns 19.1 per cent less at four hours than at one.
It depends entirely on the market's daily spreads, the duration and the share captured. In the illustrative case a two-hour battery earns 50,622 per MW a year from energy arbitrage alone, after 97 per cent availability and 85 per cent of the perfect-foresight value; ancillary services and capacity payments come on top.
This article is one calculation from Energy Trading. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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