## 1 Introduction
Another technology for the long-duration storage of electricity, PTES (Pumped Thermal Electrical Storage), also called Power to Heat to Power, seems very promising due to the simplicity, the low Capex and the low embodied carbon of its energy storage within two liquid or solid thermal stores (such as water, vegetable oils, sand, boreholes in rock mass, etc.). [PERSON] et al. emphasize the benefits of using CO\({}_{2}\) as the working fluid in a PTES, especially when water is the material for the thermal storages. Using detailed flow sheeting simulation, the authors achieves a RTE of 51% for a hypothetic pilot system of 1 MW using 4 machineries of efficiencies 80-86% and achieves a RTE of 65% for a hypothetic commercial system of 50 MW using 4 machineries of efficiencies 86%-91%, in both case for a CO\({}_{2}\) based system operating between 122 \({}^{\circ}\)C and \(-3\)\({}^{\circ}\)C [5]. Air or argon based power cycles operating over greater temperature ranges can obtain higher theoretical round-trip efficiencies (50%-85%), depending on the design parameters. [PERSON] et al. study in detail all sources of exegetic loss in an attempt to identify the maximum round-trip efficiency that can be achieved and conclude that with an 'optimistic' set of parameters that might be achievable with reciprocating devices, the thermodynamic round-trip efficiency could exceed 85% whilst the system simultaneously achieves an energy density almost an order of magnitude greater than for CAES [6]. [PERSON] et al. perform interesting simulations on the compared performance of PTES versus another long-duration storage technology called LAES (Liquid Air Energy Storage) and state that round-trip efficiencies of PTES at the higher end of pressure ratios reach values of around 80%, adding that these predictions should be seen in light of component performance estimates that have not yet been proven, while for LAES, models show RTE of more than 55% with sufficient utilization of waste cold and heat, when a combination of these two factors is adapted [7]. Unfortunately, as far as pilot systems are concerned, the RTEs of present PTES currently hover around 25%-30% due to the limited efficiencies of two compressors and of two expanders working in gaseous or supercritical phase and due to other thermodynamic irreversibilities. For instance, [PERSON] et al. realized in 2016 a model using butane as the working fluid and computed a maximum RTE of 27.3% [8]. While the Siemens Gamesa company expects a full-scale deployed system to reach in the future round-trip efficiencies of 50%, a RTE of only 25% has been so-far obtained in June 2019 in Hamburg, Germany after several years of development on a pilot plant of 130 MWh per week [9]. Although a dozens of concepts, experimental pilot beds and small-scale demonstration plants have recently entered in development, no grid-scale PTES has been proposed for construction so far. Considering the urgency of addressing climate change by scaling-up the percentage of solar and wind in the energy mix, it is a direction of this work to argue that exists a risk where large efficient gas compressors and gas turbines could not get developed fast enough and to offer the alternative route of a hybrid UPHES-PTES devoid of gas machineries. Electrochemical storages such as batteries are increasingly used by grid-scale operators and in a growing variety of functions but will probably never be considered for long-duration storage because their shorter shelf-life and their heavy embodied-carbon consumed for the production of the battery and the mining of metals can only be compensated by a fast-cycling, meaning the operation of a high number of short storage cycles. Due to the scarcity of suitable and readily approved new mountainous locations for PTES, several types of UPHES (Underground Pumped Hydro Energy Storage) have been considered for many years. For instance, [PERSON] et al. have studied UPHES in deep mines and open pit quarries and their influence on groundwater flow [10].