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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 Fuel-less CAES…

Fuel-less CAES (see the fuel-less CAES variants) is a promising new energy storage technology that stores mechanical work in 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.

The fuelless CAES concept

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

In real systems 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 unhelpful that near-isothermal compression is often dubbed as “isothermal”. Isothermal CAES refers to 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 generally refers to the case in which 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 fuel-less 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 fuel-less CAES concept. There are a number of academic articles that fall foul of this. 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 fuel-less 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 put 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 and hence is not disallowed by the second law. Of course in practice the second law means that no process is perfect and each will introduce losses, and so practically the second law means that the limiting efficiency value of the perfect fuel-less 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. 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 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.

2 stage compression, single stage expansion

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.

Wcomp/m = cpT0((P2/P1)^((γ-1)/γ) – 1) + cpT0((P3/P2)^((γ-1)/γ) – 1) = 2cpT0(r^x -1)                       (1)

Tmax = T0 r^x                                                                                                                                                     (2)

where r = P2/P1 = P3/P2 and x = (γ-1)/γ. The heat removed in each inter-cooling stage is:

Q/m = cp (Tmax – T0) = cpT0 (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:

Wexp/m = cpTmax((P1/P3)^((γ-1)/γ) – 1) = cpTmax(r^(-2x) – 1) = cpT0 (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:

Tout = Tmax r^(-2x) =  T0 r^x  (r^(-2x)) = T0 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:

Bheat flow = Q (1 – T0/T)                                                                                                                                  (6)

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

δBair out  = δQ (1 – T0/T) = mcp δT (1 – T0/T)                                                                                            (7)

Integrating this from T = Ti to T = T0 gives

Bair out = mcp (Ti – T0  – T0ln(Ti/T0)) = mcpT0 (Ti/T0 – 1  – ln(Ti/T0))                                                    (8)

putting in the value for Ti gives

Bair out = mcpT0 (Tout/T0 – 1  – ln(Tout/T0)) = mcpT0 (r^(-x) – 1  – 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:

Bheat leftover = mcpT0 (Tmax/T0 – 1  – ln(Tmax/T0)) = mcpT0 (r^(x) – 1  – 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:

[(r^(-x) – r^x)]/[ 2(r^x -1)]                                                                                                                           (11)

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.

-Wexp/m + Bheat leftover/m + Bair out/m =  –cpT0 (r^(-x) – r^x) + cpT0 (r^(-x) – 1  – ln(r^(-x))) + cpT0 (r^(x) – 1  – ln(r^(x)))

= cpT0 (2r^(x) – 2) = Wcomp/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.

Diabatic CAES 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.

Negative electricity prices and storage

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.

storage schedule 50 per cent storage schedule 100 per cent state of charge 50 per cent state of charge 100 per cent

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.


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.

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