High-temperature latent thermal storage system for solar power: Materials, concepts, and challenges

1. Introduction

1.1. Energy storage for renewable resources

Renewable energy resouces can address the challenges faced due to conventional fuels which facilitates the formation of harmony between energy supply, ecological security, and economic viability (Fadl and Eames, 2019).This scenario drives to explore renewable energy resources, such as solar, wind, hydro-energy, biomass, tidal power, geothermal energy, etc. as potential alternatives. In this context, the increase in penetration of renewable sources in the energy market can be easily marked from Figure-1and 2 (Renewable capacity statistics, IRENA, 2016). (see Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Fig. 1, Fig. 4, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 13, Fig. 14, Fig. 15, Fig. 16, Fig. 17, Fig. 18, Fig. 19, Fig. 20, Fig. 21, Fig. 22, Fig. 23, Fig. 24, Fig. 25, Fig. 26, Fig. 27, Fig. 28, Fig. 29, Fig. 30, Fig. 31, Fig. 32, Fig. 33, Fig. 34, Fig. 35, Fig. 36, Fig. 37, Fig. 38, Fig. 39, Fig. 40, Fig. 41, Fig. 42)

Table 1. Energy storage technologies.

Storage technologies		Maximum power rating (MW)	Discharge time (hrs)	Lifetime (years)	Energy density (kWh/m3)	Efficiency (%)
Mechanical	Pumped Hydro	3000	4–16	30–60	0.2–2	70–85
	Compressed air	1000	2–30	20–40	2–6	40–70
	Flywheel	20	Sec-mins	20,000-100000	20–80	70–95
Chemical	Fuel cell	NA	NA	>1000 cycles		2–50
Chemical	Organic molecular storage	NA	NA	>1000 cycles		2–50
Electro-chemical	Li-ion battery	100	1min-8h	6–40	200–400	85–95
Electro-chemical	Lead-acid battery	100	1min-8h	6–40	50–80	80–90
Thermal	Sensible	150	hrs	30	70–210	80–90
	Latent
	Thermochemical
Electrical	Capacitor	0.01–1	Seconds-60min	10,000-100000 cycles	2–10	90–95
	Supercapacitor	0–0.3	Miliseconds-60min	104-106 cycles	1–30	65–100
	Magnetic storage	0.1–10	Miliseconds-8sec	104-105 cycles	0.2–10	75–99
Flow battery		100	hrs	12,000-14000	20–70	60–85
Hydrogen		100	Mins-week	5–30	600 at 200 bar	25–45

Table 2. Comparison between TES and ECS.

TES	ECS
Low-grade thermal energy is stored in the TES system	High-grade electrical energy is stored in electrochemical system
Round trip efficiency is 75%–96%	Roundtrip efficiency is 75–85%
TES with silicon does not experience degradation due to cycling up to 20 years	Cycling operation deteriorates the performance
Storage materials are generally non-toxic	Materials are toxic Example: Lead-Acid battery
Capital cost for long-duration storage can range $70–200/kWh	Capital cost for long-duration storage can range $200–300/kWh
TES can be designed to withstand extreme temperatures (very high or very low)	Electro-chemical battery cannot operate at extreme condition
Durability can stretch more than 15 years	Durability is 3–12 years
Less maintenance is required because of no self-discharge which leads to less life cycle cost	Monitoring and exchanging regularly can increase the lifecycle cost
TES system is most relevant for CST plant or nuclear reactor application	Electro-chemical battery is most relevant for on-grid storage of power from PV or wind plant

Table 3. Central receiver CST plants across world.

CRS plants	Maximum capacity (MW)	No. of heliostats	Tower height (m)	Annual energy production (GWh)	Country	Completion Year
PS 10 Solara	11	624	115	24	Spain	2006
Julich solar towera	1.5	2000	60	NA	Germany	2008
Sierra suntowera	5	24,000	NA	NA	USA	2009
PS 20 Solara	20	1255	165	44	Spain	2009
Gemasolara	17	2650	140	100	Spain	2011
Ivanpaha	392	173,500	139	650	USA	2013
Mersina	5	510	60	NA	Turkey	2013
Crescent dunesb	110	10,347	200	500	USA	2015
Khi solar onea	50	4120		180	SA
Ashalima	121	50,600	260	320	Israel	2018
Mohammed bin Rashid solar parkc	2863	NA	262	460	UAE	2020
Atacamad	110	10,600	243	NA	Chile	2021

a: -Operational.
b: - The Crescent Dunes site has not produced power since April 2019. However, Tonopah Solar Energy has stated to restart of the Crescent Dunes plant by the end of 2020.
c: - This is a hybrid PV/solar thermal plant aims to be completed in 5 phases. The third phase is expected to be completed in 2020. The completed first two phases have 213 MW capacity.
d: Under construction. To be completed in 2021.

Table 4. Current status of CRS and PTC technology.

Parameters	Values
Parameters	CRS	PTC
Operating temperature (oC)	300–1000	20–400
Solar concentration ratio	150–1500	15–45
Storage integration possibility	Highly possible with low storage cost	possible
Plant peak efficiency (%)	23–35	14–20
Grid stability	High (large TES)	Medium to high (TES)
Annual capacity factor (%)	55 (with 10h TES)	29-43 (with 7h TES)
Installation cost	Relatively high	Relatively low
Thermodynamic efficiency	High due to high operating temperature	Low due to low operating temperature
Maturity of technology	Pilot plants, commercial projects	Commercially proven
Outlook for improvement	Very significant	Limited
Relative rise in efficiency after improvement	40–65	20
LCoE ($/kWh)	0.2–0.29 (with 6–7.5h TES)	0.26–0.37 (no TES)
LCoE ($/kWh)	0.17–0.24 (12–15h TES)	0.22–0.34 (TES)
Capital cost ($/kW)	6400-10700 with TES	6400-10700 with TES

Table 5. Comparison between 2nd and 3rd Gen CST plant.

Generation	2nd Gen	3rd Gen
Receiver outlet temperature (oC)	~500–565	>700
CST technology	PTC, CRS, LFR	CRS
Heat transfer carrier	Steam or salt	Salt, particle, gas
Thermal energy storage	Recent design includes	Implicit
Power cycle	Steam Rankine cycle	Brayton cycle
Design cycle efficiency (%)	38–44	Expected to be > 50
Annual solar-electric efficiency (%)	10–20	25–30

Table 6. Merits and limitations of different integration concepts.

Empty Cell	Two-tank direct concept	Two-tank indirect concept	Passive concept with PCM
Merits	• Heat exchanger is not required between the htf and the storage medium • Hot and cold mediums are kept in different tanks	• Hot and cold mediums are kept in different tanks • As TES material flows between hot and cold fluid, there is less risk of solidification	• Single tank for storage • Simple and compact storage unit • Increasing storage capacity with PCM
Demerits	• Relatively small temperature difference between hot and cold fluid • High cost of storage medium and htf • Antifreeze is required	• High cost of TES materials • Antifreeze is required to prevent storage media to solidify	• Cold and hot mediums are kept at same place • Long term instability • Corrosion issue

Table 7. Comparison of different thermal storage technologies.

Empty Cell	SHS	LHS	TCES
Mechanism	Temperature gradient	Isothermal phase transition	Reversible chemical reactions
Volumetric Density	Small ~50 kWh/m3	Medium~100 kWh/m3	High (500 kWh/m3)
Gravimetric density	Small~0.02–0.03 kWh/kg	Medium~0.05–0.1 kWh/kg	High (0.5-1 kWh/kg)
Storage period	Limited due to thermal losses	Limited due to thermal losses	Theoretically unlimited
Storage Temperature	charging Temperature (More than TCES)	charging Temperature (More than TCES)	Surrounding temperature (Less than SHS & LHS)
Maturity	Industrial-scale	Pilot Scale	Laboratory stage
Technology	Simple	Medium	Complex
Feedback	Large experimental and commercial feedback	Less experimental and no commercial feedback	No feedback
Flexibility	Less time to switch between charging and discharging	Less time to switch between charging and discharging	Switch between charge and discharge takes medium time

Table 8. Correlation between properties of PCM and performance of high-temperature LHS.

Properties of high-temperature PCM	Performance of LHS system
• Phase transition temperature	• Decides the operating temperature during charging/discharging of the TES
• Enthalpy of fusion/solidification	• Amount of energy stored or released
• Coefficient of volumetric change during phase change	• Size of container
• Thermal conductivity	• Rate of energy stored or released
• Vapor pressure	• Thermal stability limit
• Specific heat capacity	• Thermal energy stored in sensible form
• Density	• Density gradient results in increased heat transfer due to convection
• Cost	• Economic feasibility
• Corrosion property	• Manufacturing cost, Reliability, Durability
• Chemical reactivity	• Reliability, system safety

Table 9. Qualitative value of an ideal PCM for high-temperature LHS.

Properties		Desirable value	Results
Physical	Density	High	Leads to a small size of storage container
	Vapor pressure	Low	To avoid the complex design of containment
	Volume change	Small	Reduce the containment size
	Phase equilibrium	Favorable	Help towards setting energy storage
Thermal	Phase change temperature	Should match the operating temperature of applications	High operating temperature leads to better efficiency for power generation.
	Energy density	Should be as high as possible	Reduction of weight per unit volume of the storage system
	Thermal conductivity	Should be high	To facilitate high rate of charging and discharging
	Thermal stability	Should be high	Thermally stable material prevents early replacement of storage media leads to a reduction in maintenance costs
Kinetic	Subcooling	Should be less than five degrees	To avoid difficulty in heat extraction from storage
Kinetic	Crystallization rate	Sufficient	Helps to reduce the duration of the cycles
Chemical	Toxicity, flammability Corrosion	PCMs should be non-toxic, non-flammable and non-explosive	Expedites handling and operation of the plant, and, finally, safe transfer
Chemical	Chemically stable	No reaction with PCM containment	Reduction of disposal time of material
Economical	Cost	Low	Addition of financial benefit
Economical	Availability	Plentily available	Ensure a steady supply
Environmental	CO2 footprint	Should be very low	Reduction in pollution

Table 10. Softwares/Online databases for selection of storage medium.

Sl No.	Tool name	Database/Software tool	Description	Reference
1	CES Selector	Material selection software	Mechanical, thermal, physical, optical properties of different materials are compared. Environmental impact and cost analysis are also analyzed.	(“CES selector,” 1994)
2	GRANTA MI	Material database management software	Online tool for material management and also serves as a support to integrate with modeling/simulation software.	(“GRANTA MI,” 1994)
3	IDEMAT	Online material selection database and software	Life cycle analysis for free of cost, sustainability, ecological impact assessment for more than 1000 materials.	(“IDEMAT-Industrial Design & Engineering MATerials database,“)
4	MATERIA	Online directory	Technical specifications and manufacturer details of more than 2600 new materials available without any charge	(“Materia,” 1998)
5	MatWeb	Online bibliography	Freely available content comprising specification sheet and supplier details of nearly 125,000 materials. It can be utilized as a material database in commercial software such as ANSYS Workbench and COMSOL Multiphysics.	(“MatWeb,” 1999)
6	PCMexpress	Modeling tool	Explains the effect of PCM for thermal management of the building and the economic analysis.	(“PCMexpress-A planning and simulation programme for thermal management of buildings using PCMs,” 2008)
7	ThermoCalc	Thermodynamic properties calculation software	Paid tool determines the thermophysical properties of eutectic mixtures using the built-in database of alloys.	(Andersson et al., 2002)
8	Worksheet database with user-defined properties.	Computational Tool	It predicts the composition, thermal & physical properties of eutectic organic PCMs. Provision of expansion of database with user-defined functions are added advantage	(Kahwaji and White, 2018).

Table 11. Merits and limitations of organic and inorganic PCM.

Organic PCM		Inorganic PCM
Merits	Limitations	Merits	Limitations
Solidification takes place without high degree of subcooling	Thermal conductivity is low in solid phase.	Higher thermal conductivity than organic	High degree of subcooling
Ability to be incorporated directly	Low heat of phase transformation	Enthalpy change is more during phase transition	Lack of thermal stability
Low vapor pressure during phase transition	Volumetric storage density is low	Lower volumetric expansion	Phase segregation
Self-nucleating properties	Low heat capacity	High volumetric energy density	Few have more weight
Ability to melt congruently	High volumetric expansion	Large heat storage capacity	Few inorganic PCMs show high volumetric change
Compatible with conventional containment material	Low density	Sharp phase-change	Not suitable for a few building materials
No segregation	Lower operating temperature range than inorganic PCM	Operating temperature spreads over a wide range of temperature to suit high-temperature storage	Incongruent melting and dehydration during thermal cycling
Chemically stable	Flammable	Less costly	Chemical instability
Safe, non-reactive, and recyclable	Require large surface area	Non-flammable, recyclable	Corrosive & Prone to degradation
Organic PCMs have their transition temperature close to human thermal comfort range between 18 °C and 30 °C.	Organic PCMs decompose at higher temperatures	Inorganic PCMs can operate at higher temperature	Inorganic PCMs do not suit for thermal comfort application (Except salt hydrates)

Table 12. Properties of high-temperature inorganic salts and their mixtures.

Single salt	Melting point (°C)	Heat of fusion (J/g)	Density (kg/m3)	Storage Capacity (MJ/m3)	Cost ($/tonne)	Mixture of Salts	Melting Point (°C)	Latent Heat (J/g)
LiF	849	1041	2640 (S) 1810 (L)	2756.2	32,500	KF (55%)/KCl (45%)	605	407
NaF	996	794	2558 (S) 1948 (L)	2031.1	1610	LiF (60%)/NaF (40%)	652	816
KF	858	507	2370 (S) 1910 (L)	1109.2	5300	NaF (65%)/CaF2 (23%)/MgF2 (12%)	743	568
MgF2	1263	938	NA	NA	870	NaF (64%)/MgF2 (20%)/KF (16%)	804	650
CaF2	1418	381	3180 (S) 1910 (L)	1243.4	120	NaF (75%)/MgF2 (25%)	832	627
LiCl	610	416	2070 (S) 1502 (L)	912.9	8000	KCl(21%)/NaF(17%)K2CO3(62%)	520	274
NaCl	801	482	2160 (S)	907.2	49	KCl(40%)/KF (23%)/K2CO3(37%)	528	283
KCl	771	353	1980 (S) 1527 (L)	698.9	455	KCl (45%)/KF (55%)	605	407
MgCl2	714	454	2320 (S) 1680 (L)	1048.6	342	K2CO3 (50%)/Na2CO3 (50%)	710	163
CaCl2	772	253	2150 (S) 2085 (L)	544	200	NaF (75%)/MgF2 (50%)	832	650
Li2CO3	732	509	2110 (S)	1074	7050	LiF (67%)/MgF2 (33%)	746	947
Na2CO3	858	165	2533 (S) 1972 (L)	699.1	324	NaF(65%)/CaF2(23%)/MgF2(12%)	745	574
K2CO3	900	202	2290 (S)	540.4	1100	LiF(33.4%)/NaF2(49.9%)/MgF2(17.1%)	650	860
Mg2CO3	990	698		NA	NA	NaCl (38.5%)/NaBr (23%)/Na2MoO4(38.5%)	612	168
CaCO3	1330	NA	2930 (S)	416.1	NA	CaCl2(38.5%)/CaSO4(11%)/CaMoO4(4%)	673	224

Table 13. Properties of high-temperature metals and cost.

Materials	Melting Point (°C)	Latent Heat (MJ/kg)	Density (kg/m3)	Specific heat (J/kg K)	Thermal Conductivity (W/m K)	Cost ($/lb)
Copper (Cu)	1356	0.193	8800	385	350	3–3.5
Nickel (Ni)	1728	0.3	8908	440	83	6–6.5
Chromium (Cr)	2180	0.4	7140	450	48	5–5.5
Vanadium (V)	2183	0.45	6110	490	51	200–210
Silicon (Si)	1410	1.79	2570	1040	20	1.2–1.5
Boron (B)	2350	4.6	2340	1020	10	20–25
Aluminium (Al)	660	0.397	2800	900	204	1.5–2
Magnesium (Mg)	661	0.388	1746	1270	156	NA
Zinc (Zn)	419	0.146	7140	0.48	112.2	NA

Table 14. Research progess in inorganic salts based PCM for high-temperature LHS.

Reference	Key inference
Kenisarin, 2010	State of art high-temperature PCMs for thermal storage in the temperature range of 120–1000 °C are discussed
Ren et al. (2011)	36 kinds of mixed carbonate molten salts are prepared by mixing potassium carbonate, lithium carbonate, sodium carbonate having melting point close to 400 °C
Olivares (2012)	Thermal stability of current generation Nitrate based salts (solar salt and HITEC) are performed and found that salts decompose above 600 °C
Myers and Goswami (2016)	Alkali metal derived ternary eutectic chloride salt (Nacl-CalCl2-MgCl2) is prepared for thermal storage above 500 °C in a CST system
Dadollahi and Mehrpooya (2017)	Alkali metal (Sodium, potassium,lithium) based chloride and fluoride salts are tested as high-temperature PCM for three different storage configurations
Mohan et al. (2018)	Four ternary chloride mixtures with different cation combinations (Na, K, Li, Mg) were designed using the FactSage® software. Thermal properties and thermal stability of the salts are measured
Mohan et al. (2019)	This paper critically discuses energy storage in fluids having thermal stability over 600 °C. The key focus is fluorides, carbonates and chloride salts
Vidal and Klammer (2019)	For 3rd Gen CST system, nine diffrent mixture of chlorides (Mg,K and Na) are tested with DSC and TGA and lowest melting temperature is found for MgCl2(44.7),KCl (25.8) and NaCl (29.4) (mol%)
Wang et al. (2020)	A mixture of different salts (NaCl–NaF–KCl) is developed by pandat software and experiment. The melting point and fusion enthalpy were found to be 604.1 °C and 398.4J/g.
Ding and Bauer (2021)	This paper discusses recent progress in the selection/optimization of chloride salts, determination of molten chloride salt properties, and corrosion control of construction materials (e.g., alloys) in molten chlorides

Table 15. Research progress in metallic PCM for high-temperature LHS.

Reference	Key inference
Riechman and Birchenall (1980)	They were the first to analyze the metals as suitable high-temperature PCM. Various alloys of Al,Cu,Mg and Si are tested and verified that Al and Si alloys have best storage densities per mass or volume
Wang et al. (2006)	They developed a novel high-temperature phase cahnge storage system using AlSi12 having high heat of fusion (560 kJ/kg) and thermal conductivity (160 W/mK).
Rodríguez-Aseguinolaza et al. (2014)	The eutectic Mg49–Zn51 alloy was identified as suitable PCM for LHS. Both solid-solid and solid-liquid phase transitions were characterized
Kotzé et al. (2013)	A concept was developed to integrate LHS with AlSi12 as PCM with steam generator. The analysis indicated that the cost of the AlSi12 storage material is 14.7 US$ per kWh of thermal energy storage.
Wang et al. (2015)	Four binary and 2 ternary alloys of Aluminum and Silicon were investigated for potential high-temperature storage
Wei et al. (2016)	The aluminium alloy samples are preapred and thermophysical properties are measured using DSC, laser flash apparatus. They observed that adding Cu, Zn, and Si to an aluminum alloy reduces the melting point of the alloy.
Fang et al. (2016)	This study characterized Mg–36%Bi, Mg–54%Bi and Mg–60%Bi (wt. %) alloys as phase change materials for thermal energy storage at high temperature and established Mg based alloys have hgih corrosion resistance than Aluminium based alloys
Polkowski et al. (2018)	Silicon and Boron alloys were fabricated as high-temperature PCM and their high temperature interaction with refractories was examined
Zeneli et al. (2019)	Numerical investigation of silicon based latent storage system was performed considering volumetric change during phase change and dendritic formations.Silicon melting was reduced with increase in Stefan number
Safarian and Tangstad (2020)	The properties of pure metals and alloys and specifically Si-based alloys are proposed as suitable PCM

Table 16. Comparison between DSC and DTA technique.

DSC	DTA
• Both phase transition temperature and heat of phase transformation can be determined	• Only phase change temperature can be determined
• The two peaks in the DSC curve describes the amount of heat release and heat intake	• The peaks on the DTA curve do not represent any definite physical interpretation
• The thermal stability limit using DSC can go up to 1000 °C	• The thermal stability limit using DTA can go up to 1500–1700 °C
• Better sensitivity and precision	• Lower sensitivity and precision

Table 17. Comparison between steady and transient method for thermal conductivity measurement.

Steady method	Transient method
The governing equation for a steady method is 1-D steady-state Fourier law	The working principle is established from the unsteady heat conduction equation
Conductivity measurement using steady-state includes guarded hot plate (GHP) technique	Transient thermal conductivity measurement techniques include Transient hot-strip (THS), laser flash analysis (LFA), transient plane source (TPS), and transient hot-wire (THW)
Because of steady behavior, this method makes the signal analysis straightforward	Transient behavior makes the signal analysis complex due to temporal variation
This method requires a long duration of time to attain a steady-state in actual experiments	This method provides quick and highly accurate results.
This is a more accepted and appropriate method to measure relatively low thermal conductivity samples	The laser flash method can measure samples with high thermal conductivity.

Table 18. Thermophyscial properties of htfs.

Htf		MP (°C)	Thermal Stability limit (°C)	Viscosity (Pa.s)	Thermal Conductivity (W/m. K)	Specific heat (kJ/kg.K)	Cost ($/kg)
Air		–	–	0.00003@ 600 °C	°0.06@600°; C	1.12 @600 °C	0
Water/Steam		0		0.00133@ 600 °C	°0.08@600°; C	°2.42@600°; C	~0
Thermal oil		−20	300–400	°0.001@300°; C	~0.1	°2.436@300°; C	0.3–5
Organics (Biphenyl/Diphenyl oxide)		12	393	°0.0006@300°; C	~0.01	°1.93@300°; C	100
Molten salts	Nitrate and nitride	~65–220	500-600	0.003–0.03	<0.5	1–1.5	0.5–1.1
	Fluorides and carbonates	~400	800–900	~0.004@800 °C	~1.2	1.2–1.3	1.2–1.3
	Chlorides	200–650	850	°0.004@600°; C	°0.325@300°; C	0.81	1
Liquid metals	Na	98	883	°0.0002@600°; C	46@600 °C	°1.25@600°; C	2
	Na–K	−12	785	°0.00018@600°; C	°26.2@600°; C	°0.87@600°; C	2
	Pb–Bi	125	1533	°0.00108@600°; C	12.8@6000C	0.15@6000C	13

Table 19. Merits and limitations of htf.

htf	Merits	Limitations
Thermal oil	• Commercially used • Moderately operating pressure	• Expensive • Flammable • Stable up to 400 °C
Molten Salt	• Ambient pressure operation • Industrial use • Temperature upto ~ 565 °C possible	• Antifreeze is required • Corrosion issue
Direct steam	• Inexpensive • Nontoxic • No upper-temperature limit • Directly used in Rankine cycle power block	• High pressure in the field • Multiphase operation adds complexity to system design
sCO2	• Inexpensive • Nontoxic • No upper-temperature limit • Directly can be used in Brayton cycle power block • Single-phase throughout operation	• High pressure in the field • Still in the research & development stage

Table 20. Comparison between fixed and variable domain method.

Fixed domain method	Variable domain method
• The total domain is considered a single region	• The total domain consists of 3 regions i.e 2 phases and the phase change interface
• Mass and energy conservation are satisfied for the complete domain, therefore known as the fixed domain method.	• Each region is treated separately using mass and energy conservation principles, leads to the name variable domain method.
• A single governing equation is used for both phases	• Each phase has its governing differential equation
• No interface boundary condition is required	• The solid-liquid interface utilizes Stefan boundary condition to evaluate the velocity
• The interface location draws an inference from the solution of the governing equation.	• The interface location is explicitly defined as a priori.
• Multidimensional problems can be effectively formulated	• Formulation of multidimensional problems is complex
• Stepwise increase of temperature and enthalpy with time for pure metal is the limitation of this method	• No explicit relation between temperature and enthalpy
• This method is suitable for alloys to predict the correct temperature and enthalpy relations.	• Suitable for pure metals
• As fixed domain method is easy to program, multidimensional problems can be easily handled.	• Extension to multidimensional problems make the model very complex

Table 21. Charging, discharge and overall exergy efficiency of LHS.

Efficiency	Expressions	Description
Charging (Φcharge)	ψstored/ψhtf	Exergy efficiency during charging is the ratio between exergy stored to total exergy entered to TES during charging
	ψstored/ψhtf	Rate of change Exergy efficiency
	ψstored/ψhtf + Pump work	Pump work is also included
	ψstored/ψinit	Maximum possible exergy stored
Discharging (Φdischarge)	ψhtf/ψpcm, init	Discharge efficiency is ratio between exergy retrieved to total exergy stored in the TES system
	ψhtf/ψpcm	Presents the maximum possible exergy retrieved
Overall (Φoverall)	ψrecovered/ψsupplied	Total exergy efficiency for the complete cycle
	Φoverall = Φcharge × Φdischarge	Product of charging and discharging efficiency

Table 22. Layouts of sCO2 Brayton cycle.

Single flow layout	Split flow layout
Recuperation	Recompression
Intercooling	Modified recompression
Reheating	Preheating
Inter-recuperation	Turbine split flow-1
Pre-compression	Turbine split flow-2
Split-expansion	Turbine split flow-3

Table 23. Novel high-temperature TIM.

TIM	Thermal stability (oC)	Thermal Conductivity (W/mK)	Price (€/dm3)
Zirconia fibre board	2000 in Air	0.36 @ 1800 °C	585
Graphite fibre board	2000 in inert gas	0.82@ 1800 °C	15
Alumina fibre board	1600 in Air	0.25@1200oC	165
Fumed silica	1000 in Air	0.034@600oC	2.5