## 2 Methods  
The genuine process to reach the concept of this novel energy storage was actually incremental and dense in back and forth evaluations of numerous alternative solutions.  
The first direction of improvement is related to the underground pumped-hydro reservoir. Because natural caverns or abandoned mines are too scarce and too remote, because salt domes are not suitable for fresh water and because UPHESs of high depth are too costly to excavate and operate, the energy storage must be able to be easily excavated at shallow depth (50-200 m under surface). Because shallow UPHES cannot be of the gravity-type, the energy storage must make use of the hydro-pneumatic type. Because shallow hydro-pneumatic UPHES cannot contain elevated gas pressure through the usual hydrostatic pressure of ground water, tightness toward gas and hydro-water must be achieved with the help of a liner, as in shallow LRCs used for natural gas storage in Sweden [14] and later experimented for shallow CAES pilot programs in Japan [15] and in South Korea [16]. As water appears under three different functions in this work, as the liquid for hydroelectric energy, as the mean of thermal storage and as ground water possibly creating hydrostatic pressure, we opt to name \"hydro-water,\" the use of water as the liquid for hydroelectric energy.  
Consequently, the novel underground PHES presented here uses artificial shallow LRC caverns for pressurized reservoirs. It is pointed-out that, at high operating pressures of 7-15 MPa, cylinder-shaped steel vessels in open-air locations not constrained by rock mass, cannot represent economical solutions for diameters larger than 5 m, since large aerial pressurized vessels benefit of no effect of scale in terms of mass of construction materials and since large thickness of metal are too costly to assemble related to the welding work and its certification. Carbon fibre vessels of a large volume also enjoy no effect of scale and remain uneconomical compared to pressurized caverns.  
The second direction of improvement addresses the warming and cooling irreversibilities created by the compression and expansion of air as the hydro-pneumatic gas. To offer an acceptable RTE, the novel storage needs to replace air pushing on hydro-water by a fluid remaining at constant pressure despite the large variations of volume induced by inflows and outflows of hydro-water. Obviously, gas cannot achieve this constant pressure criterions, so the novel idea is to move hydro-pneumatic UPHES into the domain of liquid-vapour equilibrium (optionally supercritical). Consequently, due to the phase changes expansion and contraction of a fluid at constant pressure, during water inflows (electrical work supplied to the pump), as well as during water outflows (electrical work recovered by the turbine), most of the unwanted warming and of the unwanted cooling of the previous hydro-pneumatic gas solutions are eliminated.  
Since the required volume of pressurized UPHES would grow too large and therefore too costly for long duration storage (5-500 h of operation at nominal power), the third direction of improvement is to realize that the storage of energy per-se must be diverted elsewhere for energy storage of long duration. We opt for large, low-cost, insulated, atmospheric, thermal pits. It will be explained below how a pumped-hydro LRC cavern, coupled with a proper fluid, can become an outstanding locus of conversion from electricity into heat transfer, as well as from heat transfer into electricity.  
The following section reports on the data extracted from literature review. It defines the chosen options for the system and the associated economic evaluation by means of Capex (Capital expenditures) and RTE. Capex of storage is expressed in terms of USD/kW for the power of the conversion system and in USD/kWh for the available energy capacity. RTE is the expression of the ratio of recoverable electricity to the electricity consumed to fulfil storage and is expressed in percentage.