An important aspect is always the question of efficiency, i.e. the coefficient of performance (COP). This is the question of how much energy is lost during storage, and how much is left for reuse? This is also a criterion for comparison, for which I would like to give values for all the types of storage mentioned.
We will now go through our six different types of storage in our overview. At the bottom end of the page here, there is a link to an overview-table.
• Potential energy in water
-> Input of the energy into the storage:
Even if the typical efficiencies of classical water pumps is said to be between 5 % and 60 % on the internet (see e.g.: https://www.haustechnikdialog.de/SHKwissen/656/Pumpenwirkungsgrad), values of 80 ... 90 % should definitely be achievable with a lifting device as shown here above, if we lift the water specifically, such as with vessels or with pistons in cylinders. The efficiency of the driving electric motor is not usually at about 90 %, and lifting vessels, such as filled buckets at a well, achieves close to 100 % except for a few drops of loss.
-> Keeping the energy inside the storage:
If the upper water-reservoir is a closed vessel, the water remains contained within it at 100% efficiency. If the upper water-reservoir is an open lake, water can evaporate on the one hand, but rainwater can be added on the other hand, resulting in an efficiency of less than or greater than 100 %. On average, we assume 100 % in our considerations.
-> Reconversion of the energy from the storage:
Again, a typical efficiency can be found on the Internet, which is easily surpassed in a real plant. In water turbines with efficiencies between 70 % and 80 % (see e.g.: https://www.energieagentur.nrw/blogs/erneuerbare/faq/wie-berechnet-sich-die-leistung-einer-wasserkraftanlage/), a certain amount of water naturally always runs past the turbine blades unused, which can be prevented by the design with the downward-running buckets in the well. In this respect, the energy reconversion can be expected to have about the same efficiency as the energy storage.
• Gas Pressure Storage
-> Input of the energy into the storage:
In the case of compressors, the search for energy efficiency is a significant issue in those industries which use compressed air. While on one site you can find data for efficiencies of 5 % (http://www.el-com.com/cms/upload/pdf/S28_ELCOM-1.pdf), on other sites you can find efficiencies of up to 60 % (https://energie.ch/kompressoren/). The final pressure to be generated will certainly also play a role. Significant losses, for example, include thermal losses, which are unavoidable due to the laws of thermodynamics when compressing the gas. Since we are looking for a good, yet realistic solution, I decide (by gut feeling) to enter a value of 50% in the summary table of efficiencies (see below).
-> Keeping the energy inside the storage:
Here, the leakage rates of the gas containers play the all-important role. At this point, I decide to be optimistic and assume that we will succeed in producing an ideally leak-proof gas container, so we assume an efficiency of 100 %.
-> Reconversion of the energy from the storage:
Air motors (= pneumatic drives) usually have such a moderate efficiency that I could not find any manufacturer who gives absolute values for efficiency on their website. The manufacturers always compare only the motors among themselves, whereby it is found, that one manufacturer states to consume 90% less energy than the average of the other manufacturers. Whether this is realistic I cannot judge, but it allows me the following estimation: If we assume an efficiency in the bad case of 5%, similar to bad compressors, then one tenth of the energy consumption leads to an efficiency of 50% in the optimal case. Perhaps, this might be a optimistic estimate.
• Chemical energy (hydrogen)
-> Input of the energy into the storage:
For the electrolysis of water, a typical efficiency of 70 ... 80 % can be found on the Internet, and even higher in partial load operation of the electrolysers (https://www.energie-lexikon.info/elektrolyse.html).
-> Keeping the energy inside the storage:
As is well known, hydrogen cannot be stored perfectly, i.e. not without leakage. To minimize losses, so-called liquid organic hydrogen carriers (LOHC) have been developed, which store hydrogen on a liquid carrier medium. This is considered much cheaper than storing the hydrogen in a pressurized gas container. This highlights the problem of storing hydrogen. Even the liquefaction of hydrogen has been addressed (https://emcel.com/de/wasserstoffspeicherung/). Obviously clear is, that the losses are to be understood as a percentage of the hydrogen present per storage time, so the longer one has to store the hydrogen, the worse the efficiency of storing the hydrogen becomes.
-> Reconversion of the energy from the storage:
The efficiency of the fuel cell is usually stated to be comparable or slightly more favourable than the efficiency of the electrolyser, i.e., also in the range of 60 ... 70 ... 80 %. (https://www.sfc.com/glossar/wirkungsgrad-der-brennstoffzelle/)
Typical estimates for the overall efficiency of energy storage using hydrogen are in the range of 40 ... 50 % due to storage losses. For sure, we have concepts to improve the COP (efficiency) of hydrogen-based energy storage remarkably.
• Phase transition energy
Since only electrical or mechanical energy is converted into thermodynamic energy, but a reconversion into electrical or mechanical energy is not provided, the specification of an efficiency cannot be determined meaningfully for such systems. It makes sense that we always want to relate our efficiency consideration to the same form of energy in the input as in the output.
• Accumulators (electrical energy)
In the internet, accumulators are advertised with an efficiency (total, from input to output) of almost nearly 100%, but I think such a value is unrealistically. The reality is not that good.
https://de.wikipedia.org/wiki/Lithium-Ionen-Akkumulator#Wirkungsgrad
If I remember, for example, that I could operate my small Mignon batteries for 10 hours with a discharge current of 250 mA, but had to charge them for 12 ... 15 hours with 280 mA to recharge them, then I come from my own experience to an (averaged estimated) efficiency of (10h·250mA)/(13.5h·280mA) ≈ 2/3. Since I have gathered this experience on nickel-metal hydride batteries, lead-sulfuric acid batteries or lithium-ion batteries, on the other hand, would be quite conceivable better, I also want to extend the averaged "estimate over all" in the table upwards (see below). Especially for lead-sulfuric acid batteries, efficiencies of just over 80% are given in the optimum case.
• Flywheel mass energy storage
-> Input of the energy into the storage:
Electric motors used to drive the flywheel can be found with typical efficiencies of 90-95%, with large motors also reaching 96% or 97%.
-> Keeping the energy inside the storage:
It is generally known that water bearing run with less friction than the best steel ball bearings. If it were otherwise, we would simply use good steel ball bearings. Their rolling friction coefficient is given as µ R≈5·10 -4 (https://de.wikipedia.org/wiki/Rollwiderstand) To use this value in our calculation would be the most pessimistic possible view, i.e. an unfavourable estimation.
With our dimensioning of the flywheel with a mass of 1.2 tons (see numerical example, above), we would then have a perpendicular force for the sliding pair of F N=12kN. This results in a friction force of F R=µ R·F N≈5·10 -4·12kN=6N. With a mean radius of the flywheel ring of R=1.05m (see numerical example above), we obtain a torque decreasing the angular velocity of the rotation of M=R·F R≈1.05m·16N=6.3Nm.
The extracted power is of course dependent on the angular velocity of the rotation, and at the maximum speed of 7500 rpm (=> angular velocity ω=785rad/sec.) it amounts to P=M·ω=785·1/sec·6.3Nm≈4.9kW. Such losses are actually too high for a long-term energy storage. The situation could be improved only by increasing the radius of the flywheel significantly, thus massively lowering the speed of rotation. With a (larger but) slower running flywheel, the situation would of course occur much more favourable.
Since the flywheel permanently slows down due to friction (without energy supply), the energy loss at the upper speed limit within the first minute is 4.9kW·1min/(100kW·1hr)≈0.08% of the stored energy, and permanently decreases (finally down to zero) when the flywheel slows down. Of course, flywheels with larger diameters provide more favourable values, but the problem that flywheels are only suitable as short-term energy storages, is also clearly evident from the example-dimensioning shown here. At maximum speed, a realistic estimation is, that ½ ... 1 ... 2 % of the stored energy is lost per hour, which becomes a little bit better during the course of the operating period, and can still be improved with different geometrical dimensioning.
-> Reconversion of the energy from the storage:
Power generators for converting the kinetic energy from the flywheel mass into electrical energy can be found with typical efficiencies of 90-95 %, large motors also with 96 % or 97 %.
What would be needed, however, would be a control system to deliver a constant electrical power to the output when the speed of rotation varies greatly (depending on the energy content in the flywheel). To develop something like that is still an open task.
BETTER: FLOATING DISC with MAGNETIC BEARING
Using a simple homemade magnetic bearing with a moment of inertia of rotation of J=0.022 kg·m², I made a simple experiment regarding the angular velocity of rotation due to friction, and I found that the forces of friction corresponds to a coefficient of friction of µ R≈8·10 -5. This is better than the water-bearing by a factor of 6.25.
If the water-bearing flywheel can store energy for a day with reasonable losses, the magnet-bearing flywheel can store energy for a full week with comparable losses. These are reasonably applicable values.
I have put up a summary table for comparison here.
Conclusion:
There are plenty of ways to store energy inexpensively. We just have to make use of them.