Today, I was reading an article on using concrete blocks lifted by a crane to store energy using gravitational potential energy. This is really just a scaled up version of the gravity light, powering several homes instead of a small LED light.
The inventors are proposing this as a form of energy storage that is reasonably cheap when compared to batteries, estimating a price of $150 per kWh of capacity in contrast to $280-350 per kWh capacity for lithium-ion batteries and has a longer expected useful lifetime and could conceivably be repaired indefinitely. It can be sited in more locations that pumped hydroelectric storage. This is an advantage shared with liquid air energy storage, but with a higher expected round-trip efficiency (85% vs. 35-75% for LAES).
The idea itself is somewhat intriguing, and after a bit of thought, I came up with several ways this could be implemented other than the crane.
Adding this gravity energy storage to wind turbines could make sense. Because winds are stronger and more consistent the higher you go, the tower is already required to lift the blades, usually between 70m and 120m for large turbines. Adding a crane to the tower just below the turbine would add expense, but would cost less overall than building both wind turbine and energy storage separately, would not need an additional connection to the grid, and wouldn't have as much difficulty with siting as most turbines are already far from population centers.
Skip building the crane by using an already existing mountain. This is limited to certain geographic areas (those with high mountains), with more areas suitable than for pumped hydro. Higher vertical differences could also be feasible. This would likely require clearing and flattening a spot on the top of the mountain to store the lifted weights so they don't tumble back down the mountain.
Vertical shaft mines, where a shaft is dug into the ground down some distance to follow a seam of valuable mineral or coal. The large vertical difference involved in such an operation makes gravity energy storage possible. The existing equipment for lifting material and people in and out of the mine could be modified to run as a power storage device.
This is what I came up with in a couple of hours. I've done no research into what any of these would cost to implement, if there are laws that would get in the way, or anything else involved in this. And all of this depends on there being a demand for energy storage. Those people pushing for renewable energy seem to think there is, or will be, that demand. Re-purposing an already existing system seems like it would be cheaper than building a new system, but depends on the retrofit costs, and there is a limited amount of already existing facilities; for any additional capacity, a new system would be required.