The buzzword is "recuperation". With a flywheel (rotating) mass energy-accumulator, energy can only be stored for a fairly limited period of time, because the angular velocity of the rotation of a flywheel mass is permanently by friction. As a result, the energy which can be stored is quite limited, especially with regard to the storage duration.
Free floating magnetic bearings (magnetic levitation) provide a minimum of friction, but we also want to consider other alternatives for cost reasons. Cf: https://www.amazon.de/Levitation-Wunderbarer-physischer-magnetischer-Suspended/dp/B08JFMHHKZ
Air bearings are known as an alternative, but they have the disadvantage that they need a permanent air flow. This also costs energy. Better are water bearings, where the moving components slide on a (thin) film of water. In principle, oil could also be used instead of water, but sliding on the water surface is extremely low-friction as long as the rotating body does not sink into the surface of the water. Important is just to suitably adjust the thickness of the water film and the speed of the moving mass.
If we arbitrarily dimension a flywheel for the purpose of illustration as a numerical example and calculate the rotational energy, as well as the material stress for control purposes, we can set up a numerical example (see here). For simplicity, I take the formulas for material strength analysis (material stresses) from a standard example on the Internet, see:
The flywheel (of our example) has an outer diameter of 2.20 meters and rotates at a speed of 7500 rpm, which is no problem at all for a sliding water bearing. The real limitation of the structure is the material strength of the steel, which must withstand the centrifugal forces. Let us assume a steel with a tensile strength of 2000 N/mm² in our example.
The mass of the flywheel, if we take into account spokes (made of solid steel), is about 1.2 tons. With a (googled) steel price of 480 € per ton, we end up with less than 600 Euros for the material of the flywheel - and this with an energy storage capacity of about 100 kWh !
Now, 6 euros per kilowatt hour (!!) in the purchase price is of course not the total price of the energy storage system (but only the price of the steel for the flywheel).
○ We need a housing. This can be inexpensively cast from concrete or masoned from thick stones, and thus certainly does not generate high costs.
○ We need an electric motor-generator, the price of which is based on its power, not on its energy storage capacity. For example, if I need only 5 kW for my house, I can get the electric motor-generator for few 100 euros.
○ We have to manufacture the flywheel very precisely (in the micrometer range) for the water bearing to work properly, because the thickness of the water layer has to remain small (see below for explanation), which can certainly add a few hundred Euros to the price of the manufacturing technology.
○ If we add a few Euros for a proper electronic control, we will surely end up with less than 2000 € for the entire flywheel energy storage system. That would be a maximum of 20 €/kWh.
○ Furthermore, the flywheel can easily be dimensioned much thicker without having to change anything in all its other components. If we take the flywheel with a thickness of 60 cm, for example, three times as thick as calculated in the numerical example above, we only have to add another 1000 € for the steel, and we end up with about 3000 € for a flywheel energy storage system with an energy storage capacity of 300 kWh. Therefore, a realistic estimate for the achievable final price is perhaps about 10 €/kWh, and that is in the initial cost of the device.
○ So, considering the unlimited lifetime (many 100'000 charge-discharge cycles can be expected), the operating price per stored kilowatt-hour is in the range of fractions of a tenth of a cent per kilowatt-hour. This is a value that pleasantly surprised me even as I was preparing the cost estimate presented here.
What remains to be determined is the load-bearing capacity of the water bearing. Should we be limited by this in terms of the thickness of the disk (namely by its weight), then we would have to live with a purchase price of 20 €/kWh after all. Also this would not be bad. However, I will take this question as an opportunity to write down a few thoughts about the water bearing in the following:
The manufacturing precision for the flywheels must be good enough so that their surfaces can slide on each other with a spacing of a few micrometers, separated by a thin film of water. The thicker the water film between the steel surfaces of the bearing, the greater the risk that vortices can form. What we absolutely need in any case is laminar flow in the water between the steel surfaces.
(see: Laminar flow -> https://de.wikipedia.org/wiki/Laminare_Strömung
We can therefore use the very special water storage to build energy storage systems whose initial costs are in the range of 10 ... 20 € per kWh, with unlimited lifetime, i.e. with an unlimited number of charging and discharging cycles. This represents a genuine technical advance over other energy storage systems.
I will show that magnetic storage can be even more efficient under certain circumstances in a separate overview of the efficiency and effectiveness of energy storage systems.