# Category Archives: Blog

Disclaimer: information contained herein represents solely the opinion of the author

# My article published in Applied Energy

I have finally managed to get an article about Adiabatic Compressed Air Energy Storage (A-CAES) published in Applied Energy, after starting to think about A-CAES in 2010. Granted, that makes for a disappointing ratio of years-to-articles but whatever, it’s progress!

The link to the article “Adiabatic Compressed Air Energy Storage with packed bed thermal energy storage“, is here.

Anyway, the article deals with an A-CAES systems that uses packed bed regenerators to store the heat of compression and return it again, rather than indirect-contact exchangers and a thermal fluid. As far as I know it is the first article out there to rigorously analyse a system with packed beds, so hopefully it will be a useful contribution. Other articles have considered packed beds for use in Pumped Thermal Energy Storage. I think that an A-CAES system based around packed beds is a better preliminary design than a system which uses indirect-contact heat exchangers (i.e. shell and tube, plate-fin etc) and stores the compression heat in some kind of thermal fluid.

The packed beds allow the stratification of heat at different temperatures to be preserved during the storage process. And we all know that allowing heat at different temperatures to mix involves exergy destruction, so by keeping the heat stratified, a higher efficiency may be achieved. In the system I analyse, most of the exergy is destroyed by the compressors and expanders, with roughly 7% lost as heat escape from the packed beds. The article also explains that due to leftover heat in the beds, during continuous cycling the temperatures of the beds is significantly increased and results in a slightly lower efficiency – reduced from 71.1% to 70.8% in a system with 3 stages. The article develops and validates a numerical model which is available to download. I also made an animation of the simulation which shows how the temperature profile in the packed beds evolves as the system is charged, left in storage, and discharged again (shown below).

The appendix also derives a set of analytical equations for the work available from tank of compressed air in which the pressure in the tank depends on the volume of air contained.

Once more, here’s the link.

# Tesla enters residential battery market with the Powerwall

The big storage news of the week has been the unveiling of Tesla’s new stationary energy storage battery project – the Powerwall. This has inspired me to think a little out-loud about the economics of residential batteries…

The Tesla powerwall: could it become the iphone of residential batteries?

The powerwalls units come in two sizes, 7 kWh and 10 kWh and cost $3000 and$3500 respectively.

Tesla gives the specs as follows:

• Mounting: Wall Mounted Indoor/Outdoor
• Inverter: Pairs with growing list of inverters
• Energy: 7 kWh or 10 kWh
• Continuous Power: 2 kW
• Peak Power: 3.3 kW
• Round Trip Efficiency: >92%
• Operating Temperature Range: -20C (-4F) to 43C (110F)
• Warranty: 10 years
• Dimensions: H: 1300mm W: 860mm D:180mm

Firstly it should be noted that the costs are wholesale costs, and don’t include the price markup – ignore this for the moment. Secondly, and more importantly, you need an inverter, so let’s conservatively add $1500 on to the capital of the battery. So for a 7 kWh system let’s say$4500.

So what can you do with 7 kWh?

The average UK house used about 4200 kWh of electricity in 2013, giving an average demand of very roughly 500 kW (4200 kWh divided by 8760 hours in the year). This equates to around 14 hours of power at this average usage. Of course, sometimes you are asleep or out, so let’s assume that when you are in the average demand is double this at 1 kW (about the power of a medium kettle). Here is a page with estimates of the average power for household appliances in 2008 (they may have got marginally more efficient). So you can probably expect to run your dishwasher and washer in the evening and you’ll have enough juice for lights and TV watching, but you’ll struggle to tumble-dry your clothes too. The peak power is also slightly limiting – you may struggle to run your electric shower, dishwasher and washing machine at the same time.

You would have to be a very frugal user of electricity to consider going off-grid with this battery.

Economics (in UK context)

So how does it stack up economically? Well, obvious things first, you aren’t going to get a saving even if the battery is free unless the price of your electricity varies with time – for example with a time-of-use tariff or if you have your own solar installation that has a different cost associated with the electricity it generates.

Working with a solar PV installation

Let’s say the cost of a solar installation in the UK is roughly £4000 for a 2 kW system, and this produces roughly 2000 kWh per year (that’s about half the yearly average demand for a UK household and equates to roughly 40 kWh a week). Let’s also assume that you get a generation Feed in Tariff of 13.4 p/kWh and an export tariff of 4.8 p/kWh (you get paid 13.4 p/kWh of electricity that you use and 4.8p/kWh of electricity you export), and the price you pay for your grid electricity is 15 p/kWh. Again, if you are using all the solar electricity you generate rather than exporting it, then there isn’t going to be any economic case for a battery. But if you are exporting some to the grid then by storing it you’ll be able to earn the generation tariff and displace the cost of some grid electricity later, but you’ll forfeit any earnings from the export tariff. So, if the round-trip efficiency of the battery is 85% (Tesla say 92% but this will degrade over time so we assume 85% as an average and there will be small losses associated with the inverter), you’ll get an extra 13.4 p/kWh plus 0.85 X 15 p/kWh minus 4.8 p/kWh = 21.35 p/kWh for the electricity you would have exported. Using all of these estimates we conclude that if you exported 50% of the electricity generated by your solar unit, you could save 1000 kWh X 21.35 p/kWh = a princely sum of £214 per year.

Of course this assumes that the battery has sufficient capacity to store all the electricity that would have otherwise been exported to the grid. 1000 kWh per year is approx. 3 kWh per day and the battery holds 7 kWh, but there is also a huge variation in the daily electricity generated, accounting for seasonal and weather-related variations. But for simplicity let’s assume that out 7 kWh battery can hold all the electricity generated. Approximately then, over the course of 10 years you may be able to save about £2000 using the battery. This is approx. 2/3 the cost of the battery. The figure below shows the expected yearly saving against the percentage of electricity exported by the solar PV system. It also shows the saving associated with the standalone solar PV system.

Saving capability of battery (blue line) against percentage of solar electricity exported (assuming battery always has sufficient energy capacity) – the dotted line shows how I would expect this to vary accounting for the finite capacity of the battery. Estimated saving from 2 kW PV installation also shown (green line)

At 50% electricity export our standalone solar PV system gives us a yearly saving 1000 kWh X (15 p/kWh + 13.4 p/kWh) + 1000 kWh X 4.8 p/kWh = £332. Very approximately that yields a payback of 12 years, which isn’t too far off other estimates (usually around 10 years). The battery-plus-solar system increases the yearly saving to a maximum of ~£500 (with 50% electricity export) and increases the whole system payback in excess of 14 years. Including the inability of the battery to store all the energy exported on summer days I’d expect this to realistically be significantly in excess of 16 years.

Storage and variable grid electricity prices?

The other way electricity storage lets you save is by buying low cost electricity, storing it, and using it when you would otherwise have to buy high cost electricity. Most domestic customers in the UK aren’t on variable tariffs but as an academic exercise let’s consider an Economy 7 tariff, which gives 7 hours (12am – 7 am) at 8 p/kWh and 17 hours at 16 p/kWh (I think these numbers are reasonable estimates). Working at around 80% depth-of-discharge, the battery could displace 5.6 kWh of peak electricity, replacing it with 6.6 kWh of off-peak electricity. If this strategy was run 5 days a week for 52 weeks, then it could generate a saving of around £100 per year. This is a bit less than half of the saving associated with the battery-solar system.

It says quite a lot about the economics to note that at 16 p/kWh, the value of the electricity stored in the battery is ~£1.10. At 3000 cycles this equates to a value of £3300.

Using UK spot market prices from 2013 we find that the 7 kWh battery could have made a maximum of £65 from (wholesale) electricity arbitrage in the year 2013 (to calculate this I use MATLAB and an algorithm available here).

Do combined solar-battery systems reduce the net emissions of the electricity grid?

This is more tricky. Any energy storage device is a net consumer of electricity. From that perspective, unless the electricity would otherwise be wasted it’s better to use it rather than store it. So if you are exporting electricity to the grid and the transport process (to where that electrical energy is used) is more efficient than your round-trip storage efficiency, then storing this electricity instead will increase the global net electricity used. To understand the effect on emissions you’ll need to know what generation source the exported electricity would displace and what generation source the stored electricity would displace. Several other factors also contribute – the battery will contribute to grid reliability and thus reduce the operating reserve margin. If there isn’t much solar in the region then it’s likely that the reserve margins will remain unchanged, however with enough distributed renewable generation at some point another thermal plant will need to be brought online (to deal with the extra fluctuations in supply and demand associated with many distributed renewable generators). In this way, as more and more distributed generation (i.e. residential solar PV) is brought online then storage becomes more important for the grid and is likely to reduce emissions through a meaningful contribution to reliability.

What should be concluded from all of this?

Well firstly it should be pointed out that what Tesla is doing isn’t new – solar plus storage has been done for quite a long time. Traditionally Lead Acid batteries were used, and they still have lower capital costs but are bulkier, require maintenance to replenish the electrolyte and vent hydrogen gas during charge. There are also other residential Lithium ion battery systems out there. Having said that, what this move represents is a big, exciting & fashionable company throwing its weight into the residential storage market. Tesla has the potential to become the iphone of residential batteries.

In terms of the UK economics, the battery and solar option isn’t going to be more economical than using grid electricity. With the current subsidy levels, and given that our estimated system costs are probably on the low-side, I’d imagine that payback for a battery-plus-solar-PV system is in excess of 15 years at present. This is compared to a payback around 10 years for a standalone PV system. The economic case for based on variable prices is much weaker than the case for solar-plus-storage – we anticipate a max saving less than £100 per year.

In other countries I would expect a similar situation, however in regions where outages are more common, the batteries may add an Uninterruptible Power Supply (UPS) which could drastically increase its value. Though it should be noted that in these areas batteries are already used, and if these are lead-acid type batteries then they will be significantly cheaper. For UPS applications efficiency and cycling are much less important so it’s hard to see the Tesla batteries becoming a better option.

For people who want to use the battery to reduce global net carbon emissions then you’ll need to carefully construct your arguments on why you think this is the case. There are lots of inter-playing effects that, as discussed, can lead to an increase or decrease in global net CO2 emissions. In the UK at present, the grid’s CO2 emissions are fairly consistent at about 500 g CO2 per kWhel­ when the demand is above 25 GW, so it’s hard to imagine that battery use would do anything but lead to a net increase in emissions at the minute in the UK.

However, if you would like to be more independent of the grid, or take a big step towards what many experts believe is a likely possibility for a low-carbon future, and own what could be turn out to be a very fashionable product then this could be the battery for you.

# Energy Policy and the UK 2015 general election

This is just a very quick post to link to some useful resources and discussions regarding energy policy and the UK general election. Although it is very difficult to tell exactly what will arise from the tiny snippets of information given by the manifestos of the UK political parties, I think that energy and climate change are such important questions that these sections of the manifestos are worth looking at.

The Carbon Brief has a good blog post looking at the energy policies of the various parties that I would encourage anyone to read.

Between Labour and the Conservatives there isn’t too much to choose from, both support the climate change, support North Sea oil and see Nuclear as part of the future electricity mix. The Conservative plan to put a blanket halt to the development of onshore wind is slightly worrying, given the sizable onshore resource still available and the huge expense of installing turbines offshore. While onshore turbines aren’t suitable everywhere, current planning restrictions are pretty tight, and given the choice between the pollution and climate change threat associated with fossil fuels or “unsightly” wind turbines, it seems foolish to me to completely rule out the wind turbines! Their stance on fracking is another difference, with the Conservatives more strongly in favour.

The SNP and the lib dems are more supportive of renewables in general and of the development of CCS. The SNP also heavily supports the North Sea Oil and Gas industry.

Obviously the green party has an agenda heavily dominated by climate change, and they advocate ending tax breaks for fossil fuels and oppose nuclear power. They also have some fairly extreme goals for energy efficiency – i.e. a 50% reduction in energy demand by 2030. That’s not to say that with the right measures this isn’t achievable! Their position on nuclear power is difficult and I suspect that a softening on this view would see them gather more support, as many people – including Prof David MacKay – believe that some nuclear is probably a good idea given our current energy needs.

For anyone who believes that climate change poses a clear and present danger the UKIP manifesto is pretty scary – proposing to repeal the climate change act, remove renewable subsidies and use coal for cheap electricity.

# China up to second for installed capacity of Pumped Hydro

While Pumped Hydroelectric Energy Storage (PHES) development has stalled in much of Europe and the USA, in the People’s Republic of China development is booming and the installed capacity had exceeded 22.5 GW by the end of 2014. This moves China into second place for installed pumped hydro globally above the USA which has approx. 21 GW; only Japan has more with 24.5 GW.

In addition, there is currently an additional 11.5 GW of pumped hydro under construction in China which is likely to see it take the lead by 2017. Japan is also currently constructing 3.3 GW of additional pumped storage. Figure 1 shows the development of PHES in Europe, Japan, China, USA and India.

Development of Pumped Hydroelectric Energy Storage in Europe, Japan, China, USA and India

Figure 1: PHES development in Europe, USA, China, Japan and India. Data from numerous sources including US DOE energy storage database. Available in text format here or from the downloads page.

.

While there are undoubtedly many reasons why investors in China and Japan are currently more willing to fund PHES schemes than those in Europe and the USA, the main difference seems to be due to the different regulatory and market structures that exist. In much of the US and Europe, PHES must be rewarded by the market and compete for services that are generally provided by power generation units – and it is treated in a very similar manner to these units. Treating electricity storage as generation makes little sense as storage makes pretty poor generation – the second law of thermodynamics forbids it from outputting more electricity than that which is inputted. Crucially, legislation normally forbids Transmission and Distribution (T&D) network operators from owning PHES (as well as generation). This means it is difficult to reward PHES for its use as a network asset and although the storage could provide benefits across the wider electrical network, the revenue available to them only reflects a small fraction of this value.

In China and Japan PHES plants are rewarded in a cost-of-service manner and can be used as network assets. The network operators can then dispatch these plants as they require for a variety of uses, including ancillary services (frequency response, voltage support, fast reserve etc), peak electric capacity and network congestion alleviation. If the plant can introduce an overall cost saving to the wider network then it is worth the investment.

# Business models for energy storage

A few weeks ago I gave a talk at the UKES energy storage about the work we are doing in Birmingham on the value of distributed energy storage systems. The talk was specifically related to our case study of the Birmingham University main campus as a potential location for a “behind-the-meter” energy storage device. In the introduction I briefly mentioned that there appear to be three main business model classifications for energy storage operation. These are; cost-of-service, direct market participation and behind-the-meter energy storage. This post aims to explain these classifications and expand on how a unique business model for energy storage may use aspects from one or more of these classifications.

There appear to be three main “umbrella” business model classifications under which energy storage could operate in a power market. The term “umbrella” is used because there are very many sub-model variations that can sit underneath one of these terms, and indeed a specific business model can have aspects of all of the umbrella models, however for explanatory purposes still seems useful to broadly classify the models in this manner.

How can energy storage make money?

1. “Cost-of-service”

In this model, the cost of the energy storage is included in the final utility cost (electricity bill) to the customer. Ideally the price would be set based on the costs incurred in providing the service. In practical terms of electricity and electrical energy storage this translates to the storage operator being paid a regulated return on investment. This would probably constitute a part of the final electricity bill to the customer. This is a business model that would be typical of a vertically integrated utility, i.e. a nationalised electricity system. However aspects of this model could be introduced in a competitive electricity market, for example by having third parties compete to provide the energy storage service, but rewarding them in the a regulated manner. Typically this would arise out of an integrated resource plan in line with public policy (for example a mandate requiring a certain level of storage, much like targets for a certain percentage of renewables).

1. Direct participation in a competitive market

In this model, a storage operator would notice that there was an opportunity to earn a return on their investment through taking advantages of the prices offered in the competitive electricity market. Their participation in the market would then reduce the average electricity price slightly (or the price for whatever service they were offering – for example price of fast reserve, frequency response etc) and in doing so increase the global surplus, that is the consumer surplus plus the producer surplus. Consumer surplus is the difference between what the consumers would pay for the commodity of interest and it’s market price, and producer surplus is the difference between the market price and the price they would be willing to accept. To be effective this model ultimately relies on the energy storage being able to provide a market-service cheaper than current alternatives. This market participation could include entering in long term power purchasing agreements with other market players and/or contracting its services to other market players. The government can also perturb the market through the addition of subsidies to attract investment in technologies which would not otherwise be profitable – for example renewable subsidies. These subsidies will then encourage the development of certain technologies favored by public policy.

1. “Behind-the-meter” energy storage

This refers to energy storage devices that are located on the consumer’s/generator’s/end-user’s side of the electricity meter and off-grid energy storage applications. In these cases the generator/consumer/end-user would analyse their own energy economics to determine the viability of the storage unit. This could depend on the available energy-tariffs, any renewable incentives, the value of increased reliability, the perceived value of increasing consumers own renewable energy use, etc. A behind-the-meter energy storage device could also theoretically participate in the competitive electricity market provided there were no regulatory barriers to entry from this point (for example as a form demand response). This model includes energy storage owned by a large utility with a portfolio of power generating plants (etc) that is used for internal trading.

Action under each of these umbrella models has associated issues and barriers. For example the barriers for “cost-of-service” type are probably highest, as it likely requires significant changes in utility planning which are slow to occur even if they are very well aligned with public policy goals. Direct entry in a competitive market has less barriers to entry, however two significant problems are that real electricity markets are never perfectly “competitive” and participation in a competitive market carries a significant risk (i.e. market conditions and thus economics can change over time). In practice there are also market regulations that can stop storage from being able to compete for some market services. The behind the meter case should have the least barriers, but entry into this market would likely require a very cheap technology with good performance. A storage device that could be economical behind the meter of domestic consumers is probably the most favourable for an energy storage developer as it offers the largest customer base for their product.

As I’ve already mentioned, an individual business model may include aspects of some or all three of these umbrella model types. For example, electricity storage would be a useful transmission asset but under current UK market rules transmission and distribution companies are generally prohibited from owning storage assets (as well as generation). To get around this the storage could be owned by a third party but be rented and operated by the transmission/distribution company as a transmission asset, and the storage operator rewarded on a cost-of-service basis. Third parties would then compete with each other to provide this energy storage service. This is essentially what happens with the ancillary services market, except that the storage provider can only provide one use out of many. Another example of a business model involving aspects of two of these umbrella models would be a behind-the-meter storage device used to firm the output from a wind farm that also provided the market with frequency response.

Ben Cruachan Pumped Hydroelectric plant, Scotland, UK

One interesting point to note is that in the UK, all of our bulk storage facilities (four pumped hydro plants – Dinorwig, Ffestiniog, Ben Cruachan, Foyers) were constructed under cost-of-service models, at a time when the electricity industry was a nationalised utility. They are now all owned by utilities with a portfolio of generation methods, so it seems likely that they are also used for internal trading. The picture above shows the dam for the upper reservoir at Ben Cruachan – I’d definitely recommend walking up to it if you are up that way!

# Can negative electricity prices encourage inefficient electrical energy storage devices?

Following on from my earlier blog post I have written a journal article on this subject which has recently been published in the “International Journal of Environmental Studies”. The article is available to download here. It also gives a nice description of the mechanisms that can lead to negative electricity prices.

One of the main points is that we should only expect a less efficient storage device to be able to generate a higher revenue if the duration of the negative prices is long enough that a more efficient device with the same charging power would become fully charged before the end of the negative price period. Hence whether an inefficient device can indeed generate a higher revenue depends on the ratio between the charging power and the storage capacity. In the case of bulk storage (with the ability to charge and discharge for many hours) it seems unlikely that this situation will arise and the more efficient the device the more revenue it can generate.

# CAES, thermodynamics, efficiency and exergy (part 2)

This is continued from CAES, thermodynamics, efficiency and exergy (part 1)

### A couple of notes on Fuel-less CAES

So now I’ll move on to Fuelless CAES…

Fuelless CAES (see the fuelless CAES variants) is a promising new energy storage technology that stores mechanical work in both compressed air and heat and returns it as mechanical work at a later stage (the mechanical work is usually converted from electricity by a motor and back to electricity by a generator). Fuel-less CAES systems are usually classed as either “Isothermal” vs “Adiabatic” CAES.

Figure 2: The general principle for the Fuelless CAES concept.

In most designs the compression and expansion can be near-isothermal or close to adiabatic – both involve a temperature rise during compression and require separate heat storage. True isothermal compression would be the ideal case it wouldn’t require a separate thermal store, as heat would essentially be stored at ambient temperature in the surrounding environment, however any compression approaching this would be too slow to be practical. It is a little confusing that near-isothermal compression is often dubbed as “isothermal”. Isothermal CAES designs typically propose the use of a near-isothermal compression in which a thermal fluid spray is injected into the compression chamber and which reduces the temperature rise experienced by the air during the compression. This warm thermal fluid must be stored in a separate heat store. Adiabatic CAES designs propose that the compression produces a temperature rise close to the adiabatic temperature rise. The compression heat must then be stored at a much higher temperature than the near isothermal case. This heat is usually removed and stored separately from the compressed air. It is important to note that the energy is stored both mechanically and as heat, and it is only the effective recombination of these two parts that can lead to an efficient system.

Thermodynamic work is path dependent. This has quite a profound consequence on the design of a fuelless CAES system: to maximise the work output of a CAES system the discharging process should follow the exact and opposite path of the compression process. Designs in which this is not the case are intrinsically inefficient and analyses of their efficiency are not reflective of a fundamental limit of the fuelless CAES concept (though this does not mean that they could not ever make economic sense). I have however read a number of academic articles that anaylse systems in which the expansion process is not the same as the compression and then seem to imply general conclusions about the system efficiency, which is misleading. Another common misconception is that the second law of thermodynamics imposes some fundamental limit less than 100% on the efficiency of the system. I think that this comes from a misapplication of the Carnot efficiency for a heat engine, as there is a re-heating element associated with the expansion part of the fuelless CAES process. What the second law of thermodynamics actually states is that even in the limiting case that a reversible system is designed with perfect lossless components, the round trip efficiency cannot be greater than 100%. In a perfect well designed system, the compression takes mechanical work and converts it into potential energy AND takes in heat at ambient temperature and moves it to a high temperature heat store. For perfect intercooling and an ideal gas the heat moved is equal to the work in, discounting the energy stored in the cold compressed air. Of course, this is not a violation of the first law as heat is also taken in with the ambient air. If one were to expand this cold air you would get some work out and you would have moved more heat than the net work put in. This is of course the principle of a heat pump and it is commonly known that these can have COP’s greater than 1. The expansion part then involves recombining the stored heat and the cold compressed air. With no heat losses and perfect inter-heating the compressed air is re-heated to exactly the same temperature as it was after the compression. And finally if the expansion is exactly the reverse of the compression the work out will be the same as the work in for the compression. Heat will be rejected at the ambient temperature with the compressed air. This perfect system does not solely convert heat into work, does not result in a net movement of heat from a lower temperature to a higher temperature without the addition of work and does not result in a net decrease of the entropy of the universe. Hence it is not disallowed by the second law. Of course in practice the second law means that no process is perfect and each real component will introduce losses, and so practically the second law means that the limiting efficiency value of the perfect fuelless CAES process is 100%.

So now on to exergy and CAES. As a physicist I had never come across exergy before I thought as an engineering PhD student that I’d better look at an engineering thermodynamics textbook. It is a very powerful concept. The exergy of a system is a measure of the available work extractable between that system and the “dead state”, which is just the ambient environment. It can be formulated by considering the energy and entropy changes in a general process that involves changes in the enthalpy of a flow through a system, internal energy changes, work in/out and heat flow in/out to the ambient. By simultaneously accounting for both energy and entropy, exergy accounts for the quality of different forms of energy. A good introduction to the concept can be found in most Engineering Thermodynamic textbooks (i.e. Fundamentals of Engineering Thermodynamics by Moran and Shapiro) and there are some good online resources like this. It is an incredibly useful concept in system analysis that accounts for the both the first and second laws simultaneously. In the analysis of engineering systems it allows the irreversibility of different system components to be analysed. In the design of a CAES system this is invaluable as it allows the “exergy destruction” in each component (heat exchangers, compressors, expanders etc) to be estimated. It also allows the maximum extractable work from the system to be easily calculated, which gives an indication of the reversibility of a perfect design.

As an example let’s do an exergy analysis of a CAES system with perfect lossless components with two compression stages and one expansion stage. This will illustrate that the maximum work out of the single expansion stage is less than the compression work put in, and crucially it illustrates where the remaining work is lost. The high pressure air store is considered isobaric so there is no increase in pressure as air is added to the store. The gas is an ideal gas with a constant specific heat capacity. With an isochoric store the equations just become a little more complicated and require more integration.

Consider a system with a 2-stage compression and single stage expansion as illustrated below.

Figure 3: Example asymmetric fuelless CAES system

Each compression increases the pressure ratio by a factor of r, so the total work input in the compression is given by Equation 1.

$\frac{W_{comp}}{m} = c_p T_0 ((\frac{P_2}{p_1})^{\frac{\gamma-1}{\gamma}} - 1) + c_p T_0 ((\frac{P_3}{p_3})^{\frac{\gamma-1}{\gamma}} - 1) = 2 c_p T_0 (r^x-1)$ (1)

$T_{max} = T_0 r^x$ (2)

where $r=\frac{P_2}{P_1}=\frac{P_3}{P_2}$ and $x=\frac{\gamma-1}{\gamma}$. The heat removed in each inter-cooling stage is:

$\frac{Q}{m} = c_p(T_{max}-T_0) = c_p T_0 (r^x-1)$ (3)

The maximum temperature to which the air can be heated without extra heat or work in before the expansion is the same as the temperature from the compression, so the work out of the single stage expansion is:

$\frac{W_{exp}}{m} = c_p T_{max} ((\frac{P_1}{P_3})^{\frac{\gamma-1}{\gamma}}-1) =c_pT_{max}(r^{-2x}-1)=c_pT_0(r^{-x}-r^{x})$ (4)

It has a negative value for r>1 which means work is done by the system. The outlet temperature of the turbine is colder than the ambient as the pressure ratio for the expansion stage is r2 rather than r for each expansion. It is given by:

$T_{out} = T_{max}r^{-2x}=T_0 r^{-x}$ (5)

The work that could be extracted from this cold ambient pressure air can be calculated by considering its exergy. The exergy associated from a flow of heat from some temperature to the ambient T0 is given by:

$B_{heatflow} = Q(1-\frac{T_0}{T})$ (6)

However as the heat is flowing from the body of air it is cooling down so we write:

$\delta B_{airout} = \delta Q (1-\frac{T_0}{T})=mc_p\delta T (1-\frac{T_0}{T})$ (7)

Integrating this from T = Ti to T = T0 gives

$B_{airout}=mc_p(T_i-T_0-T_0 \mbox{ln}\frac{T_i}{T_0}) = mc_pT_0(\frac{T_i}{T_0}-1-\mbox{ln}\frac{T_i}{T_0})$ (8)

Putting in the value for Ti gives:

$B_{airout} = mc_pT_0(\frac{T_{out}}{T_0}-1-\mbox{ln}\frac{T_{out}}{T_0})=mc_pT_0(r^{-x}-1-\mbox{ln}r^{-x})$ (9)

There is also heat left over from the compression, as only the heat from one intercooling stage could be used before the expansion (because no net heat will flow between two identical temperatures). The exergy associated with this leftover heat can also be calculated in the same manner as:

$B_{heatleft}=mc_pT_0(\frac{T_{max}}{T_0}-1-\mbox{ln}\frac{T_{max}}{T_0})=mc_pT_0(r^{x}-1-\mbox{ln}r^x)$ (10)

So now we have accounted for all the work in that went into the compression. With a single expansion stage extracting the work out the efficiency is limited to:

$\frac{r^{-x}-r^{x}}{2(r^x-1)}$

To check we have accounted for all the work into the system we sum the work out and the exergy associated with the cold outlet air and the leftover compression heat.

$\frac{W_{exp}}{m}+\frac{B_{heatleft}}{m}+\frac{B_{airout}}{m} = -c_pT_0(r^{-x}-r^x)+c_pT_0(r^{-x}-1-\mbox{ln}r^{-x})+c_pT_0(r^x-1-\mbox{ln}r^x)=c_pT_0(2r^x-2)=\frac{W_{comp}}{m}$ (12)

Low and behold the total is the compression work! Therefore we can see where all the work into the system has gone. Even with perfect isentropic lossless components it is not possible to extract all of the 2-stage compression work through a single expansion. The missing work has been accounted for as leftover stored heat and the exit loss from the turbine.

The point of this example is to give a small insight into the power of exergy and encourage its use in both CAES analyses and for informing designs.

# CAES, thermodynamics, efficiency and exergy (part 1)

I thought that I would write a post about CAES and a couple of issues that I feel are commonly misunderstood. This post has been inspired by things that I have heard at academic conferences and things that I have read in both academic and non-academic literature. I also thought that I would share a couple of insights about conventional CAES which have been passed down to me.

### A couple of notes about conventional CAES

Conventional CAES is an energy storage technology that has been around for several decades. It is interesting because although there are two plants currently functional and in existence, no new plant has been built in the last 20 years, despite the fact that both of the existing plants remain open and continue to function economically. This can probably be attributed to high CAPEX costs for CAES and other cheaper generation technologies which represent similar or better investments, added with an uncertainty of how to class CAES and view its efficiency.

Figure 1: The convential diabatic CAES system with a  recuperator. Natural gas is mixed with the compressed air in the generation unit.

Calculating the efficiency of CAES facilities is perhaps not as straightforward as it first seems. The McIntosh CAES plant uses 1 kWh of natural gas and 0.69 kWh of electricity to produce 1 kWh of peak electricity. The energy efficiency in terms of energy-output/energy-input is then around 59%, i.e. quite low for an energy storage technology. However, if instead you consider that the efficiency of a conventional thermal gas generator is around 40%, you would only ever get 0.4 kWh of electricity out of the 1 kWh of gas used in the CAES plant. This makes the efficiency look much better, as now it effectively appears as though you put 0.69 kWh + 0.4 kWh = 1.09 kWh of electricity in and you get 1 kWh of electricity out, giving an efficiency of 92%. Conversely, another argument would be that the 1 kWh of electricity required 2.5 kWh of gas to generate, and hence the energy input is 3.5 kWh of gas to produce 1 kWh of electricity, giving a much poorer efficiency of 29%.

The point of all this is that the “efficiency” values often quoted for CAES must be treated with caution and are generally not comparable with other storage technologies which input and output electricity only, as CAES plants are NEITHER purely energy storage NOR thermal generation, but in reality they represent a mix of both. I haven’t quite decided how to interpret this myself except that when considering CAES as an energy storage option, it is more important to consider from what source the electricity used in charging comes from than other energy storage technologies. For example, using CAES in the context where it would mainly have an electricity-from-renewable input could be regarded as boosting the efficiency of gas generation and hence a good thing under these circumstances, whereas using CAES as a way to store fossil fuel generated electricity would seem like a bad idea. I don’t fully endorse this last statement, rather I’m just using it as an illustration…

Keep an eye on the blog for part 2.

# Negative electricity prices and storage – perhaps not just an academic curiousity

## Why do negative electricity prices occur and can they encourage the use of inefficient energy storage devices?

### What are negative electricity prices and how do they occur?

Negative electricity prices are a relatively recent phenomena in wholesale electricity markets. They were first seen in the German intra-day market in 2007 and are now rare but not extraordinary – there were 56 hours on 15 different days of negative electricity prices in the German day-ahead market in 2012. In modern wholesale electricity markets electricity prices are intended to and broadly do represent supply and demand, with a high price encouraging suppliers to participate in supplying electricity and a low price discouraging suppliers from producing electricity. Negative electricity prices mean that suppliers of electricity must pay consumers to use the electricity that they generate, rather than the usual manner in which consumers pay suppliers for the electricity they use. These negative prices generally arise when a highly inflexible electricity supply meets an exceptionally low demand and the supplier decides that the cost associated with the shutting down and restarting of the inflexible supply is more than the cost of paying an external party to use the generated electricity. Renewable output contributes to negative prices as there is often a protocol in place dictating that green electricity must be used ahead of other generation methods (for example coal and nuclear). Therefore when a time of exceptionally low demand coincides with a time of exceptionally high renewable output conventional base-load generation like nuclear could be asked to power down. A negative electricity price would then occur if the nuclear operator decided that it was cheaper to pay someone to use the nuclear energy generated at that time than to shut down (and subsequently have to re-start) the plant.

Figure 1: Showing the increase in frequency of negative prices in some European electricity markets in 2013 compared to 2012.

### What do negative electricity prices mean for energy storage?

Negative electricity prices indicate inflexibility, and their occurrence essentially reflects a need for energy storage. Their presence should encourage energy storage: instead of buying electricity and then selling it at a later time, storage can “sell” (be paid) taking electricity which can then be sold again at a later period. Of course the action of storage will oppose the prices negativity – storage will tend to push the prices up and a large enough capacity of energy storage should remove negative electricity prices. However apart from Pumped Hydro, energy storage devices are generally small-scale prototypes that are essentially “price-takers” in the market (their effect on the price is very small). These are devices currently being demonstrated and it is thus important to understand them fully in before much larger systems can be developed.

A negative electricity price essentially means that in the absence of any fixed storage operational costs it always beneficial for storage to charge on this negatively priced electricity irrespective of the sell price. By making the observation that an inefficient energy storage device will take more electricity to charge it than an efficient one, one important question is whether these negative electricity prices encourage the use of inefficient energy storage devices.

There appear to be two distinct methods by which energy storage can derive revenue with negative electricity prices. Firstly there the storage can charge at a negative electricity price and discharge at a later positive electricity price or secondly storage can charge at a negative electricity price and discharge at later negative electricity price. Initially I focus on the latter case. This may seem counter-intuitive but given two consecutive price periods with the same negative price the only storage system that will not make a profit by charging at the first and discharging at the second is a device that is 100% efficient (which will simply break even). Of course a more profitable single transaction would be charging at the negative price and discharging at a later positive electricity price, however charging and discharging using negatively priced electricity can still be profitable and will be more profitable the more inefficient the device is. Hence in a sustained period of negative electricity prices if there exists the opportunity for storage to make a complete a charge and discharge cycle before charging on negatively priced electricity and selling at a time with positive electricity prices then this will be the most profitable storage schedule. This represents an unlikely extreme case – it is obviously completely undesirable for storage to discharge at times of negative electricity prices but it is worth mentioning nonetheless. If sustained periods of negative electricity prices do start occurring then policy may need to step in to regulate storage behaviour.

The first method of charging on negatively priced and discharging at positive electricity prices is more intuitive. Generally it is anticipated that this should not encourage inefficient devices as a more efficient device with the same charging and discharging power would always be able to make more money on a single charging and discharging transaction. For example a device with a charging power of 1 MW could take 0.5MWh of electricity from the grid in a 30 minute period. A 75% efficient device would then be able to sell 0.375 MWh at a later positive electricity price while a 50% efficient device would only be able to sell 0.25 MWh. However, again the possibility of the less efficient device making a larger revenue comes with a sustained period of negative electricity prices. For example, consider two 2 MWh storage devices, one 100% efficient and one 50% efficient and each with a charging and discharging power of 2 MW (so in one half hour period 1 MWh can be taken from or exported to the local electricity network) and the price timeseries shown in Figure 1a and 1b. It is assumed that with a round trip efficiency of 50% the charging process and the discharging process each have an efficiency of 70.71%. Therefore only 70.71% of the energy used to charge is stored, and only 70.71% of the energy removed from the store can be sold.

Figure 2: (a) Charging and discharging schedule for 1MW 2MWh 100% storage device. (b) Charging and discharging schedule for 1MW 2MWh 50% storage device. (c) Energy stored corresponding to Figure 1a. (d) Energy stored corresponding to Figure 1b.

As the Figure 1a and 1b show the 50% efficient device uses more energy to charge (the state of charge is shown in Figure 1c and 1d) than the 100% efficient device allowing it to exploit an extra period of negative electricity prices. The 100% efficient device then makes a greater revenue when discharging but not enough to make up for the extra negative electricity price period exploited by the inefficient device. With the price timeseries used the 50% device is able to generate an extra 6% revenue compared to the 100% efficient device.

### Summary

To summarise, negative electricity prices indicate inflexibility in the energy network, and reflect a need for increased energy storage capacities. Energy storage devices should work to counteract these negative electricity prices by increasing demand and a large amount of energy storage should keep the electricity prices positive. However, given that negative electricity prices currently exist, there exists the possibility that these may encourage the use of inefficient energy storage devices that are better able to exploit these negative prices. This is not generally true and depends on the nature of the electricity prices – as well as the degree of positivity versus the negativity. However it is worth recognising the possibility that under certain circumstances negative prices can encourage the use of inefficient devices and this could be a hurdle in the development of effective energy storage techniques, especially given the small-scale demonstration nature of most current energy storage projects.