# Understanding the “arbitrage” value of a large battery in SA

Given recent events in South Australia’s energy market and the recent’s tweet by Elon Musk of “100 days or it’s free…” to deliver 100MWh’s of energy storage, there has been much commentary on the value of energy storage. I thought it instructive for *RenewEconomy* readers to delve into the economics of one of the key values of energy storage, “arbitrage”.

As a former energy trader, I would explain this concept simply as “buy low, sell high” or alternatively in the energy spot market it is the concept of purchasing and storing energy at low price times only to generate and sell into the market at high priced times.

Whilst conceptually simple, the purchase price of a battery is high, there are physical limitations on charge/discharge and the frequency of high spot prices is relatively infrequent. The following calculations endeavour to establish a benchmark of the historic economics in South Australia.

To value the arbitrage economics of energy storage I have taken South Australian spot market prices from 1999 to the end of February 2017 and then assumed that we had perfect foresight, i.e. if we had 100% ability each day to charge at the lowest priced periods and then discharge at the highest priced periods (a bold but unrealisable goal).

I then assumed that our round-trip efficiency was 80% (i.e. what we get out compared against what we put in) which is typical for a large lithium-ion energy storage system.

Then, I analysed what I believe is missing in most of the analyses I have seen, which is consideration of how long the battery takes to charge and discharge i.e. most people have assumed simply taking the highest and lowest prices each day to estimate the arbitrage value, but if your battery takes 2 hours to charge and discharge then the total price you receive will be noticeably lower as this means it is the difference between the average of each the four highest and four lowest prices each day. We can then express this as algebraically for a charge/discharge time as:

*Revenue($/MWh) = Round trip efficiency (%) X **(**S**(P _{1}+..P_{n})/n – *

*S*

*(P*

_{(48-n) }+..P_{48})/n)Where n is the number of half hours of storage at full power given that the market settles as 48 half-hours per day and that P_{1} is the highest price, P_{2} is the second highest price, and so on until we get to P_{48} which is the lowest price. If we do this calculation every day for a year these are the results we have are in the following table.

**Table ****1**** – SA Average daily return $/MWh per MWh each year for given charge/discharge durations**

Year |
Days |
4 hours |
2 hours |
1 hour |
30 minutes |

1999 | 365 | $100.40 | $137.42 | $175.33 | $204.55 |

2000 | 366 | $102.63 | $138.39 | $181.25 | $223.47 |

2001 | 365 | $64.58 | $90.00 | $114.90 | $142.16 |

2002 | 365 | $51.84 | $82.99 | $130.45 | $164.49 |

2003 | 365 | $28.87 | $40.47 | $55.30 | $70.07 |

2004 | 366 | $63.91 | $95.87 | $131.94 | $162.55 |

2005 | 365 | $43.99 | $65.60 | $90.97 | $123.00 |

2006 | 365 | $57.39 | $88.40 | $130.66 | $169.07 |

2007 | 365 | $65.62 | $85.41 | $106.54 | $125.58 |

2008 | 366 | $160.72 | $220.34 | $251.29 | $272.18 |

2009 | 365 | $161.98 | $232.78 | $266.47 | $289.57 |

2010 | 365 | $90.32 | $130.03 | $172.59 | $198.01 |

2011 | 365 | $55.09 | $69.31 | $86.48 | $103.62 |

2012 | 366 | $33.06 | $47.31 | $65.56 | $81.17 |

2013 | 365 | $74.82 | $110.95 | $159.82 | $223.36 |

2014 | 365 | $41.97 | $63.24 | $90.94 | $123.72 |

2015 | 365 | $72.92 | $115.04 | $181.50 | $265.48 |

2016 | 366 | $142.62 | $203.95 | $272.54 | $358.10 |

2017 | 59 | $269.38 | $414.70 | $500.49 | $570.15 |

Whole Year Average |
$78.49 |
$112.08 |
$148.03 |
$183.34 |

What this shows is that if we had a battery that cycled daily, this was the return per MWh of energy storage we would expect each day for a given duration of charge/discharge cycle. This duration is also measured alternatively as C rating, where this value is equal to 1/duration (hours) i.e. a 30-minute battery is equal to 1/0.5 = 2.0 C and a 2-hour battery is equal to 1/2 or 0.5 C.

What is important to note is that the shorter duration charge cycle or higher C rating battery has a much higher return per MWh of storage because the highest prices only occur for a single period, so extending the discharge time over lower priced periods reduces the average price received.

Whilst a 2.0 C battery will always have better financial performance than a lower C rating battery, it is often more expensive per MWh of storage. The question then becomes whether a battery system with a lower C rating can be a better choice if its cost per MWh is sufficiently low.

Another way of considering it is that if we look at annual averages, a 2.0 C battery could break even at $183.34/MWh, whilst a 0.25 C battery would need to be as low as $78.49/MWh, and a 0.5 C battery could break even at $112/MWh. This means that whilst Tesla has hit the news with a compelling price offer, if a 2 C battery could be installed at a price 50% higher than Tesla, it would potentially be a better economic choice when considering arbitrage alone.

If we take the example that Elon Musk Tweeted, he talks of $250/kWh of capacity at the Powerpack level but the installed cost will likely be close to double this so around $500,000/MWh installed.

With an expected life of 3650 daily cycles over 10 years and if we ignore the fact that the battery will degrade to as little as 60% of its original capacity and discounted cash-flow analysis, but still considering 80% round trip efficiency, we get an effective price of $500,000/3650/0.8, which is $171/MWh.

The Tesla technology at present is 0.5C which could have returned $203.95/MWh in 2016 but would have averaged only $112.08/MWh in the past, which is insufficient to recover the investment costs at today’s prices.

What this means is that the potential investment is unlikely to make sense at grid scale on pure arbitrage value alone for a battery just yet, but it is getting much closer as the economics are approaching the level of an idealised arbitrageur.

A battery of 100MW would also have a material impact on spot prices in South Australia, such that it would marginally increase the lower prices and potentially reduce some of the peak prices quite significantly, thereby reducing the financial performance of the battery even further.

There are other income streams such as the Frequency Control Ancillary Services (FCAS) market but given that this is a balancing market to respond quickly to differences between dispatched power and system demand, it is not usual that such large MW volumes would be necessary most of the time and hence it may be considered oversized plus FCAS is even more volatile than energy spot markets.

Batteries can also perform “black start recovery”, i.e. return a system from a blackout condition which is an additional source of revenue but unlikely to be politically popular if it is called upon.

However, the operation of a grid connected battery is usually such that providing multiple services often conflict with each other meaning that the total value will be less than the sum of the potential maximum value of all the individual services. i.e. given the payback on arbitrage which is likely to be the largest value is marginal and the uncertainty is high, a commercial investor or battery supplier is not likely to fund a battery wholly themselves and will require “co-investment” or a subsidy before a battery is installed.

This is obviously the case in South Australia, so careful examination of the economics of the battery including both the power (MW) and energy (MWh) requirements will be needed to ensure that the people of South Australia get the right sized solution at the right price.

*Warwick Forster is managing director of Apogee Energy*