Thermo-electro-chemical storage (TECS)

of solar energy Erez Wenger1, Michael Epstein2, Abraham Kribus1*

1 School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel

2 Porter School of Environmental Studies, Tel Aviv University, Tel Aviv 69978, Israel

* Corresponding author: kribus@tauex.tau.ac.il

Accepted manuscript

Published paper found in: Applied Energy, Volume 190, March 2017, Pages 788–799

http://dx.doi.org/10.1016/j.apenergy.2017.01.014

© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Abstract

A new approach for solar electricity generation and storage is proposed, based on the concept of

thermally regenerative batteries. Concentrated sunlight is used for external thermo-chemical charging of

a flow battery, and electricity is produced by conventional electro-chemical discharge of the battery. The

battery replaces the steam turbine, currently used in commercial concentrated solar power (CSP) plants,

potentially leading to much higher conversion efficiency. This approach offers potential performance, cost

and operational advantages compared to existing solar technologies, and to existing storage solutions for

management of an electrical grid with a significant contribution of intermittent solar electricity

generation. Here we analyze the theoretical conversion efficiency for new thermo-electro-chemical

storage (TECS) plant schemes based on the electro-chemical systems of sodium-sulfur (Na-S) and zinc-air.

The thermodynamic upper limit of solar to electricity conversion efficiency for an ideal TECS cycle is about

60% for Na-S at reactor temperature of 1550 K, and 65% for the zinc-air system at 1750 K, both under

sunlight concentration of 3000. A hybrid process with carbothermic reduction in the zinc-air system

reaches 60% theoretical efficiency at the more practical conditions of reaction temperature <1200 K and

concentration <1000. Practical TECS plant efficiency, estimated from these upper limits, may then be

much higher compared to existing solar electricity technologies. The technical and economical feasibility

of the proposed cycle are also discussed.

1 Introduction

Energy storage is a crucial issue for an electrical grid with a large contribution of intermittent renewable

resources such as solar and wind. The output of wind turbines and photovoltaic (PV) plants can have sharp

variations that pose a serious challenge to grid stability and power quality. Solar thermal power plants

(CSP-Concentrating Solar Power) offer higher inertia since they rely on rotating machinery, and can be

considered stable on a time scale of minutes. However, CSP plant output is not stable on longer time

scales, due to the variations of insolation and the passage of clouds. Another major issue for the

renewable plants is matching availability to demand, since availability peaks of solar and wind may not

correspond to high demand periods for electricity. Overcoming this problem requires a storage element

that can smooth the variations, by transferring large amounts of energy from periods of high availability

to periods of high demand. Most utility-scale energy storage solutions propose a storage facility that is

separated from the electricity generation facility and charged with electricity [1], e.g., batteries, pumped

hydro, or compressed air [2]. Batteries are well developed for portable applications but battery solutions

suitable for grid-scale storage are still a topic of vigorous research and development [3]. In all cases, it is

necessary to convert the renewable resource into electrical energy, and then convert again into storable

form (chemical or mechanical). To discharge the storage, it is necessary to convert again from the stored

energy form to electricity. These multiple conversions impose higher costs and losses beyond the direct

power generation process, and these grid-scale storage technologies are not yet competitive and not

widely implemented [4]. Pumped hydro is an exception which is competitive, but can be implemented

only in specific geographical locations. The search is still open then for an efficient, flexible, and cost-

effective electricity storage solution.

Some CSP plants offer thermal storage, mostly as sensible heat, integrated into the power plant [5].

Currently, the common storage system in commercial CSP plants comprises large tanks of molten mixture

of nitrate salts, which is heated either directly by concentrated solar radiation, or indirectly with an

intermediate heat transfer fluid such as thermal oil [6]. During power generation from storage, the hot

salt exchanges heat and generates steam, which drives a steam turbine. The plant then includes two or

three fluid circuits that exchange heat, and a thermo-mechanical power cycle. The thermal storage

subsystem has attractive performance with daily loss by self-discharge of 1% or less [4]. However, the

annual average overall conversion efficiency from solar input to electricity in these plants is typically

around 15-18% [7], due to the significant loss in the thermo-mechanical conversion. This relatively low

efficiency and the high cost due to multiple energy conversion steps, result in low economic

competitiveness for current CSP technologies. Therefore, the CSP solution with integrated storage is not

yet satisfactory to address the urgent need for widely acceptable grid-scale storage.

Here we analyze the novel approach of thermo-electro-chemical storage (TECS) for solar electricity, which

offers a unified cycle for both energy conversion and energy storage. It is based on thermally regenerative

cells, an idea that was proposed by Yeager in 1958 [8] but did not reach promising results in subsequent

research, primarily because of the selected materials. We show that using different materials, and

configuring a complete cycle that eliminates some thermodynamic losses, can lead to very high theoretical

performance. The fundamental idea is that concentrated solar radiation can charge a battery externally

but directly without intervening steps, using a thermochemical reaction. Discharging the storage to

generate electrical power is done in an electrochemical cell in the same manner as a conventional battery.

The storage configuration is similar to a flow battery, with the storage medium being transported along a

cycle with three main components: a solar thermochemical reactor/separator (also called regenerator)

for charging, storage tanks, and an electrochemical cell for discharging. The TECS principle is illustrated

schematically in Figure 1, for a generic electrochemical system where electricity is produced in the

reaction: 𝐴 + 𝐵 → 𝐴𝐵, and charging is accomplished in the inverse thermochemical reaction: 𝐴𝐵 → 𝐴 +

𝐵. The TECS cycle converts heat (input at the regenerator) to electricity, and its conversion efficiency is

subject to the Carnot efficiency limit corresponding to the regenerator and electrochemical cell operating

temperatures.

This approach addresses some of the shortcomings of existing CSP technologies, both in conversion and

in storage of solar energy. It eliminates the thermo-mechanical power cycle with its complexity and

thermodynamic loss; it performs the charging process in a single energy conversion step, and it uses a

storable medium directly as the working fluid without need for additional thermal circuits. Compared to

a solar photovoltaic plant with a standard electrochemical battery, the TECS approach performs charging

by direct conversion of solar radiation to storable chemical energy, eliminating the need to convert solar

radiation first to electricity and then converting the electricity again to chemical energy for storage. It also

eliminates the degradation found in many advanced batteries during the charging process. These

perceived advantages of the new concept compared to the established solar technologies need to be

quantified, and the first step of conversion efficiency analysis is presented here.

Figure 1: Illustration of the TECS cycle for the generic electrochemical system 𝐴 + 𝐵 ⇌ 𝐴𝐵 in (a)

charging mode, (b) discharging mode

During the 1960’s, two general types of thermally regenerative batteries were investigated: (1) metal

hydride or metal halide cells, and (2) bimetallic cells [9]. Significant efforts have been dedicated to

thermally regenerative liquid metal cells such as Na/Sn, Na/Hg and K/Hg [10]. For example, a Na/Sn cell

was built with NaCl-NaI molten salt mixture as the electrolyte operating at 700°C. During discharge, an

alloy of 15-30% molar Na was formed (NaxSn) at the cathode side. The regeneration and release of the Na

from the alloy required temperatures over 1100°C to obtain reasonable kinetics. The theoretical

performance of several bimetallic systems has been calculated, with fairly unsatisfactory results [11]. For

example, the Na/Sn cell with 10-40% mole fraction of the anode metal in the cathode metal should

produce open circuit voltage of 0.47-0.31 V at 500°C, and the ideal regenerative cycle efficiency (heat to

electricity) is only 30-20%, respectively. The Na/Bi bimetallic cell showed the best performance with 0.74-

0.53 volts at 586°C and 41-34% ideal efficiency. Experiments confirmed that Na can be distilled from NaxSn

alloys at temperatures of 1000-1100°C yielding a relatively pure Na vapor [12]. These liquid metal

batteries have some major disadvantages in addition to low efficiency, including: low specific energy

density (typically <200 Wh kg−1 even theoretically), low open cell voltages (typically <1.0 V), highly

corrosive active cell components, and high self-discharge rates when the electrode metal has non-

negligible solubility in the molten salt electrolyte. Moreover, the structure with three liquid layers may be

disrupted under motion or vibration, leading to a short-circuited cell and rapid heat generation. These

features make liquid metal batteries unsuitable for portable applications, leading to a decline of interest

in this direction [9]. Recently, research of liquid metal batteries has been renewed towards applications

of low-cost stationary grid scale storage [9,13].

The second proposed type of thermally regenerative batteries uses metal hydrides or halides. The lithium

hydride chemistry is noteworthy, as lithium is one of the most widely studied negative electrode materials

for electrochemical energy storage due to its high voltage capability, high specific and volumetric energy

density, and good transport properties. The lithium hydride system was one of the first to be envisioned

as a thermally regenerative battery [14]. The electrochemical cell reaction is: 𝐿𝑖(𝑙) +1

2𝐻2(𝑔) → 𝐿𝑖𝐻.

Regeneration (charging) requires decomposition of the hydride, and this system is appealing because LiH

decomposes thermally at 900°C into easily separable liquid lithium and gaseous hydrogen at a pressure

of about 1 bar. Theoretical efficiencies of the LiH thermally regenerative cycle are up to 45% (depending

on cell and regenerator temperatures), but estimates of practical efficiency were much lower, in the range

of 9 – 17% [11]. The available technology for a metal hydride cell does not yet offer a good solution for

the porous or permeable gas side electrode. Another crucial difficulty when considering such a system for

grid-scale storage is the need to store large amounts of hydrogen, either as a large volume at atmospheric

pressure, or compressed to a smaller volume at the expense of significant work investment. Another

proposed version of the hydride cell uses an organic molecule instead of a metal as the hydrogen carrier.

This enables thermal regeneration at low temperature [15], but it would also lead to low conversion

efficiency and low energy density, and raise the same difficulty of hydrogen gas storage.

In summary, both liquid bimetal and metal hydride batteries were investigated as candidates for a thermal

regeneration cycle, and neither showed promising results that would motivate further research. However,

the approach of thermochemical battery charging deserves an updated consideration due to two

advances. First, the range of materials available for electrochemistry is now broader compared to the

1960’s, and new materials may be more suitable for thermal regeneration, as we show here. Second, solar

technologies have matured and can provide today high-temperature thermal power as input to the

regeneration process. Solar concentrator technologies such as tower, parabolic dish, and furnace are now

in operation as industrial large scale plants [7].

The TECS concept offers additional potential advantages compared to current CSP plants. It has the

flexibility to operate at variable power loads without a significant impact on the conversion efficiency,

similar to other electrochemical battery systems, while the efficiency of a solar power plant based on a

steam turbine declines when operating at part load, as well as during the lengthy startup and shutdown

periods [16]. The response of steam based power plants to fast changes, e.g., a sharp increase in demand,

is quite slow due to large thermal inertia, while the TECS flow battery can respond much faster to changes

according to the response time of the pumps between the storage and the EC cell. The steam cycle in a

CSP plant needs to reject a large amount of heat at low temperature, using either a cooling tower with

high water consumption that is problematic in arid sites, or air cooling that reduces plant efficiency and

increases its cost. The solar TECS plant may reduce the amount of heat rejection since its efficiency is

expected to be higher than existing plants. It may reduce or eliminate the need for water cooling, since a

larger temperature difference to the environment is allowed in the absence of the conventional steam

turbine cycle.

The TECS storage can also be equipped with a facility for electrical charging as in a normal flow battery,

using surplus electricity from the grid, in parallel to the thermo-chemical charging. The solar TECS plant

can therefore provide additional services to the grid, for example to store over-production of wind energy

during periods of low demand. This storage capability may also be used to store electricity produced by

baseload power plants at very low marginal cost during the night, and return the electricity to the grid

during daytime peak demand hours, similar to current pumped storage facilities. The daytime discharge

of stored nighttime electricity can take place simultaneously with the charging by solar energy, since they

occur at different parts of the cycle.

In this work, we consider the thermodynamics of TECS cycles with some materials that were not

considered in past work, but are currently used in modern conventional batteries. We derive the upper

limits of conversion efficiency by analyzing a cycle with ideal components. Basic assumptions include:

chemical equilibrium at each point in the cycle; no heat loss from reactors, heat exchangers etc.; no

pressure losses; and an ideal electrochemical cell. For the solar part of the conversion, we assume an ideal

optical concentrator and an ideal blackbody receiver/reactor with thermal emission loss only [17]. Details

of the models for cycle components are discussed. The cycle and its ideal performance are presented

using examples of candidate chemistries: sodium-sulfur and zinc-air, which are currently used in

conventional non-flow electrochemical batteries.

2 Materials and cycles analysis

2.1 Candidate materials

Two examples are considered here to demonstrate the application of the TECS approach with different

electrochemical cells and storage systems. The first is based on the sodium-sulfur (Na-S) battery

technology that has been developed since the 1960’s and is currently used for utility scale storage, but

was not considered in past work as a candidate for thermal regeneration. It offers the advantages of

relatively abundant and low cost materials, long life, high efficiency and high energy density, although

there are still some open questions involving materials stability, safety and fabrication methods, which

limit its implementation [18]. The constituent materials are all in liquid phase at the battery's operating

temperatures around 300℃, and therefore it can also operate as a flow battery. The Na-S battery is based

on a β-Al2O3 solid electrolyte membrane that is highly conductive to Na ions, separating molten sodium

at the anode and molten sulfur at the cathode compartments [19]. During discharge, 𝑁𝑎+ ions cross the

solid electrolyte and electrons flow in the external circuit of the battery, producing a voltage of about 2 𝑉.

The sodium ions combine with the sulfur to form sodium polysulfides [19]:

2𝑁𝑎 → 2𝑁𝑎+ + 2𝑒−

𝑥𝑆 + 2𝑁𝑎+ + 2𝑒− → 𝑁𝑎2𝑆𝑥 (𝑥 = 3 ÷ 5)

(1)

Electrical charging causes the sodium polysulfides to decompose, and the excess 𝑁𝑎+ ions in the cathode

flow back through the solid electrolyte to recombine as elemental sodium at the anode. The alternative

charging method in the TECS cycle is by thermochemical decomposition (regeneration) of the sodium

polysulfides:

𝑁𝑎2𝑆𝑥 + ∆𝐻 → 𝑥

2𝑆2 + 2𝑁𝑎 (2)

The heat of reaction for 𝑥 = 4 in Eq. (2) is ∆𝐻 = 411.4 kJ mol⁄ at 293 K, and 428.5 kJ mol⁄ at 2100 K.

The polysulfides decompose gradually with increasing temperature, releasing sulfur atoms until reaching

finally a mixture of pure Na and S2 vapors. The theoretical specific energy density for a TECS Na-S cycle,

considering the active materials only, is the same as for the conventional Na-S battery: for the case of 1:2

sodium to sulfur molar ratio, it is 580 W h/kg, while practical Na-S batteries demonstrate values of up to

200 W h/kg. This is significantly higher than the abundant lead-acid batteries, and close to Li-ion batteries.

Another interesting comparison is to sensible heat storage in current CSP plants: using the common

molten nitrate salt operating between temperature of 280—560C, and a power cycle with efficiency of

40%, the specific energy density of the storage is less than 50 W h/kg. The round-trip energy efficiency of

currently available Na-S batteries is 85-90% [4]. In a TECS cycle the efficiency of the cell is expected to be

higher, since there is only a single pass of the Na ions through the electrolyte during the discharge.

The second set of materials considered here is the Zn/ZnO system, a distinctly different case compared to

all previously mentioned materials, since the active ingredients are solids rather than liquids. Zinc–air

batteries feature high energy density and long shelf life, and use abundant materials leading potentially

to very low cost [20]. They are used over a wide range of sizes and applications, from portable devices to

electric vehicles [21]. Rechargeable zinc-air batteries, however, are still challenging due to changes in the

morphology of the Zn anode during charging [22], and the need for better catalysts for the air side

reactions [23]. The round-trip efficiency of rechargeable Zn-air batteries is currently less than 60%. The

most critical issue is the dendritic growth and the resulting morphology change of the zinc electrode,

which drastically limits the cycle life of this battery [24]. This issue can be completely resolved by

implementing the external charging as proposed by the TECS cycle.

A zinc-air battery comprises a porous zinc electrode, a membrane separator, and a positive air electrode,

submerged in an aqueous alkaline electrolyte. During discharge, the zinc oxidizes in two steps by reacting

with hydroxyl ions in the electrolyte to form soluble zincate ions, which eventually decompose into

insoluble zinc oxide [21]:

𝑍𝑛 + 4 𝑂𝐻− → 𝑍𝑛(𝑂𝐻)42− + 2𝑒−

𝑍𝑛(𝑂𝐻)42− → 𝑍𝑛𝑂 + 𝐻2𝑂 + 2 𝑂𝐻−

(3)

The hydroxyl ions originate at the cathode by catalytic reduction of atmospheric oxygen:

1

2𝑂2 + 𝐻2𝑂 + 2𝑒− → 2 𝑂𝐻− (4)

During charging, these reactions are reversed, with zinc metal deposited at the anode and oxygen evolving

at the cathode. The proposed TECS alternative is to reduce the zinc oxide by direct thermal dissociation

in a high-temperature chemical reactor heated by concentrated solar energy [25], or to perform

carbothermic reduction with the addition of carbon as a reducing agent [26]. The dissociation reactions

without and with carbon are:

𝑍𝑛𝑂 + ∆𝐻 → 𝑍𝑛 +1

2𝑂2 ; ∆𝐻298 K = 350.5

kJ

mol

𝑍𝑛𝑂 + 𝐶 + ∆𝐻 → 𝑍𝑛 + 𝐶𝑂 ; ∆𝐻298 K = 240kJ

mol

(5)

Operating the Zn-Air system as a flow battery is not easy since both Zn and ZnO are solid at the battery’s

operating temperature. It can be accomplished with mechanical removal of the ‘spent’ zinc oxide and

recharging with fresh zinc powder, either using a replaceable cassette, or in a continuous process where

fresh zinc paste or pellets are pushed into the battery to replace the zinc oxide. Regeneration of the oxide

ex-situ can be more efficient than inside a conventional rechargeable cell, and the process can attain

higher round-trip efficiency of around 70%. Implementing such mechanical transport of solids is

technically challenging and is outside the scope of the current analysis, which deals only with the

thermodynamic point of view.

The theoretical specific energy density of the TECS Zn-Air cycle is very high, the same as the corresponding

conventional battery: 1350 W h/kg when excluding the oxygen that is obtained from the surrounding air

[24], and 1086 W h/kg based on the mass of the stored ZnO in the fully discharged state, which is the

maximum mass stored in the battery. Commercial Zn-air primary batteries already claim specific energy

of up to 470 W h/kg (based on Zn mass) [27], more than double that of current Li-ion batteries. The round-

trip energy efficiency of electrically recharged zinc–air batteries is usually about 60% [23]. Solar external

charging with a TECS cycle will eliminate the substantial over-potential that is usually needed at the

positive electrode, and the hydroxyl ions will need to migrate through the electrolyte only once. It is

expected therefore that the cell efficiency will be substantially increased.

2.2 Equilibrium compositions and properties

At each state point in the cycle it is assumed that the mixture is in chemical equilibrium corresponding to

its temperature and pressure. The equilibrium compositions were found by minimization of the Gibbs free

energy of the mixture, subject to the constraints of mass conservation for each element. The Gibbs free

energy of the gas phase takes into account the mixing of the gases and the system's pressure as the

fugacity of the ideal gases. The Gibbs free energy of the liquid phase also takes into account mixing of the

liquid components due to the relevant starting composition. The Gibbs energy of the solid phase does not

take into account mixing or solubility of the solid materials. The total Gibbs free energy of each state was

calculated separately for each phase, and then summed for the total free energy of the mixture. The

materials’ properties were collected from several sources [19,28–32], covering the needed elements and

compounds, and the wide range of pressures and temperatures addressed in this work.

An exception to the assumption of chemical equilibrium was made for the quencher. Due to fast cooling,

the mixture does not react as it passes through the quencher. The outlet composition is then equal to the

inlet composition, except for phase change from gas to liquid where relevant, and does not correspond

to equilibrium at the outlet temperature.

Figure 2 shows the equilibrium composition vs. temperature corresponding to an initial inventory of 1

mole Na2S4 (representing the sodium to sulfur mass ratio of a discharged battery) at pressure of 0.01 bar.

The decomposition proceeds gradually as the polysulfide molecule sheds sulfur atoms with the increase

of temperature: 𝑁𝑎2𝑆4 → 𝑁𝑎2𝑆3 +1

2𝑆2 → 𝑁𝑎2𝑆2 + 𝑆2 (these steps occur at lower temperature and are

not shown in the figure); followed by 𝑁𝑎2𝑆2 → 𝑁𝑎2𝑆 +1

2𝑆2 → 𝑁𝑎2 + 𝑆2, reaching full decomposition

into Na and S2 vapors under chemical equilibrium at 1,580 K. Around 2,600 K the molecule S2 further

decomposes to atomic S, but this is not necessary for the storage cycle. For atmospheric pressure the full

decomposition occurs at 2,090 K, hence the pressure reduction is beneficial to decrease the required

reaction temperature. The low pressure does not require a vacuum pump, and it can be created in the

liquid lines exiting the coolers where the Na and the S condense.

Figure 3 shows the equilibrium compositions vs. temperature for 1 mole of ZnO. The direct dissociation

of ZnO [25] requires a very high temperature of 2,230 K under atmospheric pressure, and therefore it is

shown in Figure 3(a) under a lower pressure of 0.01 bar, similar to the previous case of sodium polysulfide,

leading to dissociation at 1,750 K. The O2 product is in gas phase, and therefore operation at low pressure

will require an investment of vacuum pumping work. The carbothermic reduction [33] occurs at 1,190 K

under atmospheric pressure, as shown in Figure 3(b), and at 950 K under 0.01 bar. Both temperatures are

reasonable for technological implementation, and the atmospheric pressure case should be preferred to

avoid vacuum pumping of the CO product. The zinc can be condensed out of the product gas mixture by

quenching [34]. The CO product after separation can be used as a fuel in direct combustion, or can be

converted to hydrogen using the well-known water gas shift process. The carbothermic process can also

be considered as an alternative method for gasification of the solid carbon. The process eventually emits

CO2, after final conversion of the CO product, and it is desirable to use biomass-based carbon sources to

minimize the greenhouse gas impact.

Figure 2: Equilibrium composition vs. temperature for the Na-S TECS cycle at 0.01 bar, corresponding

to the initial composition of 1 mole Na2S4. Higher polysulfides (𝑥 > 2) have already decomposed

at lower temperatures.

Figure 3: Equilibrium composition vs. temperature for 1 mole ZnO (a) without carbon at 0.01 bar, (b)

with 1 mole of added carbon at 1 bar.

It should be noted that the carbothermic process is a hybrid cycle since it has two energy inputs: the heat

from the solar concentrator, and the energy embodied in the carbon. It also has two outputs, Zn and CO,

both of which are energy vectors. The analysis of conversion efficiency must account for this more

complex situation.

2.3 The Sodium-sulfur TECS cycle

Figure 4(a) shows the layout of a basic TECS cycle based on Na-S chemistry. The discharged medium, a mix

of sulfur and sodium polysulfides from storage tank T1, is preheated in reactor R1 to achieve partial

decomposition of the polysulfides (𝑁𝑎2𝑆4 + ∆𝐻 → 𝑁𝑎2𝑆2(𝑙) + 𝑆2(𝑔), where ∆𝐻823 K = 132 kJ mol⁄ )

and evaporation of the free sulfur. The sulfur vapor is separated in S1, condensed and cooled in heat

exchanger C1, and returned to storage T2. Full decomposition of the remaining polysulfides is achieved in

the high temperature reactor R2. The gas mixture from the solar reactor is cooled rapidly (to minimize the

back reaction) in quencher Q down to the condensation temperature of sodium. The liquid Na is separated

from the sulfur vapor in S2. Both streams of pure sulfur and pure sodium are cooled in C2 and C3,

respectively, and stored in tanks T2 and T3. In practice a small amount of Na vapor may remain with the

gaseous sulfur but in the ideal model we assume full condensation and separation of the Na. When

electricity generation is required, liquid sulfur and sodium are pumped from their respective storage

tanks, T2 and T3, to the anode and cathode compartments of the electrochemical cell. The discharged

mixture of polysulfides with excess sulfur is then returned to storage tank T1.

The cycle can be improved by internal heat recuperation: utilizing some of the rejected heat from the

cooling process to save energy in heating. Figure 4(b) shows an example where heat is diverted from

cooler C1 (state 7) to preheat the stream from state 1 to state 1b. This reduces the amount of external

heat needed in reactor R1. Additional heat might be recuperated from coolers C2, C3 (states 6, 9) if the

heat input and the range of temperatures of reactor R1 allows such additional heat exchange.

Even after internal recuperation, a large amount of heat must be removed at the quencher and the coolers

to the environment, and this heat can be used to feed secondary thermal converters and generate

additional electricity. This is similar to the combined cycle (CC) arrangement in conventional power plants,

where the exhaust heat from a gas turbine is used to generate steam for a secondary steam turbine at

lower temperature. Figure 4(b) shows several heat engines (HE) receiving heat from the coolers and from

the quencher and generating additional electricity in a combined cycle arrangement (TECS-CC). The heat

engines are shown separately for each point of heat rejection due to their possibly different temperatures.

A TECS-CC will achieve higher overall conversion efficiency, and can also spread electricity generation over

time: the secondary converters generate electricity immediately during charging, while the electro-

chemical cell can operate from storage and generate electricity at any time according to demand from the

grid.

The total heat input into the cycle at the two reactor stages 𝑄𝑅 for the basic cycle configuration, Figure

4(a), is:

𝑄𝑅 = 𝑄𝑅1 + 𝑄𝑅2 = 𝐻2 − 𝐻1 + 𝐻4 − 𝐻3 (6)

𝐻 is the total enthalpy at each state point according to its composition and temperature. When the cycle

contains internal heat recuperation, Figure 4(b), the heat input is modified to use 𝐻1𝑏 instead of 𝐻1. This

accounts for the reduced heat input into reactor R1.

The ideal work that can be done by the electro-chemical cell 𝑊𝐸𝐶𝐶 and the accompanying heat transfer

𝑄𝐸𝐶𝐶 can be found from the energy and exergy balances on the cell:

𝑄𝐸𝐶𝐶 + 𝐵8 + 𝐵10 = 𝑊𝐸𝐶𝐶 + 𝐵1

𝐵8 + 𝐵10 + (1 −𝑇0

𝑇𝐸𝐶𝐶) 𝑄𝐸𝐶𝐶 = 𝑊𝐸𝐶𝐶 + 𝐵1

(7)

𝐵 = 𝐻 − 𝑇0𝑆 is the total exergy at each state point. The Na-S EC cell operates usually at a temperature

around 300℃, and therefore the heat transfer between the cell and the environment affects the exergy

balance.

Figure 4: Layout of the Na-S TECS cycles (R: reactor, S: separator, Q: quencher, C: cooler, T: storage

tank, EC: electro-chemical cell) (a) basic cycle, (b) TECS-CC cycle with recuperation and secondary

heat engines (HE)

We keep all the storage tanks at the cell temperature, 𝑇𝐸𝐶𝐶 , and in this case the solution for the ideal work

can be expressed as a function of the Gibbs free energy 𝐺:

𝑊𝐸𝐶𝐶 = 𝐺8 + 𝐺10 − 𝐺1 (8)

The ideal thermal efficiency 𝜂𝑡ℎ for the basic cycle, representing conversion from heat to work, is then:

𝜂𝑡ℎ =𝑊𝐸𝐶𝐶

𝑄𝑅 (9)

If the charging process is performed at sub-atmospheric pressure, then pumps will be needed in the liquid

lines at points 8 and 10, and their operation will require an investment of work that should be subtracted

in Eq. (9). However, pumping liquid usually requires very little work, and this effect is neglected here.

When the cycle contains also heat engines to convert the waste heat into additional work, as shown in

Figure 4(b), the total ideal work produced by the CC 𝑊𝐶𝐶 is:

𝑊𝐶𝐶 = 𝑊𝐸𝐶𝐶 + 𝑊𝐻𝐸1 + 𝑊𝐻𝐸2 + 𝑊𝐻𝐸3 + 𝑊𝐻𝐸4 (10)

This total work output of the combined cycle is then inserted into Eq. (9) instead of the cell work, to

calculate the overall conversion efficiency.

𝑊𝐻𝐸 is the heat engine work output, defined for the ideal case according to the Carnot efficiency

corresponding to the temperature of operation of each engine. In the three coolers, the temperature

available to the heat engine varies as the stream of product cools, and therefore the heat engine efficiency

varies. For example, the ideal work output of HE1 is:

𝑊𝐻𝐸1 = ∫ (1 −𝑇0

𝑇

𝑇8𝑎

𝑇7𝑏

)𝐶𝑝(𝑇)𝑑𝑇 (11)

𝑇0 is the ambient temperature, and 𝐶𝑝 is the effective specific heat including the effect of phase change

from vapor to liquid, where appropriate. The same expression holds for HE2 and HE3 with the respective

inlet and outlet temperatures of their corresponding coolers. For HE4, due to the rapid quenching process,

heat is available only at the lowest temperature and therefore:

𝑊𝐻𝐸4 = (1 −𝑇0

𝑇5) (𝐻4 − 𝐻5) (12)

2.4 The zinc-air TECS cycle

Figure 5 shows the layout of the TECS cycle with zinc oxide, for the direct dissociation case (a) and the

carbothermal reduction case (b). Both diagrams are for the basic cycle without heat recuperation and

without recovery of waste heat with heat engines. These additional elements can be easily added in

analogy to Figure 4(b). The ZnO in solid granular form (optionally mixed with carbon particles) is heated

and reduced in a single reactor R due to the simple decomposition chemistry, followed by quenching (Q)

to the condensation temperature of the zinc vapor, and separation (S) of the condensed liquid zinc from

the oxygen or CO that remain in gas phase. The separated products are then cooled to room temperature

(C1, C2) and the solid zinc is stored (T2).

The heat input into the reactor 𝑄𝑅 for both cycles in Figure 5 is:

𝑄𝑅 = 𝐻2 − 𝐻1 (13)

For the basic cycle, Figure 5(a), the ideal work 𝑊𝐸𝐶𝐶 that can be extracted from the stored zinc in the

electro-chemical cell is:

𝑊𝐸𝐶𝐶 = 𝐵5 + 𝐵𝑂2− 𝐵1 (14)

𝐵𝑂2 is the exergy of the stoichiometric amount of oxygen from ambient air that is needed to perform the

reaction. The cell is operated close to ambient temperature so that the heat transfer between the cell and

the ambient does not affect the exergy balance. The ideal thermal efficiency 𝜂𝑡ℎ for the cycle is then given

by Eq. (9). Modification of the cycle energy balances for internal recuperation of heat and for conversion

of excess heat in external secondary heat engines follows the same procedure as shown above.

When the charging process is performed at sub-atmospheric pressure, pumping will be needed to

maintain vacuum. This can be done at the liquid zinc line, point 4, with minimal work investment that can

be neglected. But vacuum pumping of the gas exit, point 7, could require a significant work investment.

The needed work for adiabatic pumping 𝑊𝑣𝑎𝑐 is:

𝑊𝑣𝑎𝑐 = ��7𝐶𝑝 [(𝑃0

𝑃7)

𝛾−1𝛾

− 1] (15)

m7 and 𝑃7 are the flow rate and pressure at point 7 upstream of the pump, respectively, 𝑃0 = 1 bar is

the atmospheric pressure, and 𝐶𝑝 and 𝛾 are the specific heat at constant pressure and the ratio of specific

heats for the gas at point 7, oxygen or CO for the two configurations shown in Figure 5. The vacuum pump

work is subtracted from the work output of the cycle in the calculation of efficiency.

The hybrid cycle, Figure 5(b), has two energy inputs: the heat provided to the reactor, and the energy

embodied in the carbon that is added upstream of the reactor. The conversion efficiency from heat to

electricity in the hybrid cycle therefore requires special definition. The part of the work output that is

considered to come from the carbon input is the work output of a ‘reference cycle’: a cycle or process

with maximum work output under the same definitions and assumptions as the hybrid cycle, except that

it only uses the carbon as input [35]. The relevant reference process here is the ideal oxidation reaction

of C with atmospheric oxygen to produce CO2, and the maximum work output from this reference process

is:

𝑊𝑟𝑒𝑓 = 𝐵1𝑏 + 𝐵𝑂2− 𝐵𝐶𝑂2

(16)

This is also equivalent to the difference in Gibbs free energy since all reactants and products are taken at

ambient temperature. If the total amount of work that the cycle produces is 𝑊𝑡𝑜𝑡, then the additional or

incremental work 𝑊𝑡𝑜𝑡 − 𝑊𝑟𝑒𝑓 is due to the heat input at the reactor. The conversion efficiency relevant

to the reactor heat input is then the incremental efficiency [35]:

𝜂𝑖𝑛𝑐 =𝑊𝑡𝑜𝑡 − 𝑊𝑣𝑎𝑐 − 𝑊𝑟𝑒𝑓

𝑄𝑅 (17)

Figure 5: Layout of the zinc oxide TECS cycles (R: reactor, S: separator, Q: quencher, C: cooler, T: storage

tank, EC: electro-chemical cell) (a) basic cycle for direct dissociation without carbon, (b) basic cycle

with carbothermic reduction of the zinc oxide

The total work output of the hybrid cycle has to account for the two output streams that can produce

work: pure zinc, state 5 in Figure 5(b); and carbon monoxide, state 7. Both of these streams can react with

the required amount of atmospheric oxygen to produce ZnO and CO2, and the maximum amount of work

that can be done under the assumption of ideal processes is then:

𝑊𝑡𝑜𝑡 = 𝐵5 +1

2𝐵𝑂2

− 𝐵𝑍𝑛𝑂 + 𝐵7 +1

2𝐵𝑂2

− 𝐵𝐶𝑂2 (18)

Modification of the hybrid cycle for internal recuperation of heat and for conversion of excess heat in

external secondary heat engines again follows the same procedure as shown above.

2.5 Solar to electricity efficiency

The ideal solar collector contains an ideal concentrator with no optical losses, and a blackbody receiver

that has only the unavoidable radiative emission loss through the entrance aperture. The efficiency of this

solar collector 𝜂𝑠𝑜𝑙 is then [17]:

𝜂𝑠𝑜𝑙 = 1 −𝜎(𝑇𝑟𝑒𝑐

4 − 𝑇04)

𝐼 ∙ 𝐶 (19)

𝑇𝑟𝑒𝑐 is the receiver effective temperature, and here we assign it as the highest temperature in the reactor,

𝑇4 in Figure 4, or 𝑇2 in Figure 5. 𝐶 is the optical concentration ratio, and 𝐼 is the direct normal flux of solar

radiation, taken at its nominal value of 1,000 W/m2. The total conversion efficiency of the entire system

from sunlight input to work or electricity output is then:

𝜂𝑡𝑜𝑡 = 𝜂𝑠𝑜𝑙 ∙ 𝜂𝑡ℎ (20)

𝜂𝑡ℎ is the heat to work efficiency of the cycle, Eq. (9). In the case of the hybrid cycle with the addition of

carbon as a reducing agent, 𝜂𝑡ℎ is the incremental efficiency of Eq. (17).

2.6 Numerical method

The cycle simulations were performed in MATLAB software. First, the properties of the pure components

over a wide range of pressure and temperature were implemented as MATLAB functions, using

interpolation over the data found in the literature for each material. Then, the mixture composition and

thermodynamic state (mixture enthalpy and entropy) were derived at each state point in the cycle, using

the Gibbs free energy minimization as described in Section 2.2. After all state points were resolved for a

complete cycle, equations (6) to (20) were solved in MATLAB to derive the heat and work exchanges with

the environment, and then the cycle efficiency. Each cycle was simulated over a range of reactor

temperature as a free parameter, while all other interfaces to the environment were set at ambient

temperature and pressure.

3 Results

3.1 Na-S TECS cycle efficiency

Figure 6(a) shows the ideal conversion efficiency from the thermal input into the cycle, to work or

electricity output of the electrochemical cell, for the Na-S TECS cycle at pressure of 0.01 bar. The efficiency

of the simple TECS cycle (with internal heat recuperation but no secondary utilization of excess waste

heat) is close to zero below 1,400 K, where the reaction does not produce free Na; and it reaches a peak

of 40% at reactor temperature of 1,580 K. A significant amount of exergy, or work availability, is embodied

in the waste heat that is removed in the quencher and coolers. Clearly the utilization of this waste heat in

a secondary converter is crucial in this cycle, since the opportunity to reuse heat internally within the cycle

is limited. For the ideal two-stage TECS-CC, where the maximum possible amount of work is extracted

from the waste heat, the peak efficiency is 68.5%. This is close to the Carnot limit at the same temperature,

indicating that the destruction of exergy in the reactor and quencher is relatively small, and the thermo-

chemical process for charging the storage is thermodynamically attractive.

Figure 6(b) shows the conversion efficiency from solar radiation to electricity for the TECS-CC cycle

coupled to an ideal solar concentrating collector, at two levels of concentration. The peak efficiencies are

43% and 60% at concentrations of 1,000 and 3,000 suns, respectively. The higher concentration is

beneficial due to the high temperature of the reactor, which incurs a high thermal emission loss that can

be mitigated with reduction of its aperture area. This range of concentration can be achieved in solar

tower technology with the use of secondary concentrators, or in parabolic dish and solar furnace

concentrators without additional optics. These results are close to the upper limit of an ideal Carnot

engine powered by the same ideal concentrator.

Figure 6: (a) Heat to electricity ideal conversion efficiency vs. maximum reactor temperature for the

Na-S TECS cycle with internal heat recuperation, and the TECS-CC cycle with full secondary

conversion of waste heat, both at 0.01 bar; the Carnot efficiency is also shown for comparison.

(b) Ideal solar to electricity efficiency vs. reactor temperature for the TECS-CC cycle under solar

concentration of ×1000 and ×3000, compared to a Carnot ideal converter subject to the same

concentration and temperature.

3.2 Zn-air TECS cycle efficiency

Figure 7 shows the ideal thermal and solar conversion efficiencies for the different combinations of Zn-

Air basic TECS cycle and combined cycle, without and with carbon added to the reactor. The thermal

efficiency for the basic cycle without carbon, Figure 7(a), reaches 57% at 1,750 K and 0.01 bar absolute

pressure, while the CC reaches 80% at the same conditions. For the hybrid cycle with carbon at

atmospheric pressure, Figure 7(b), the peak efficiencies (incremental efficiency after subtracting the

contribution of the carbon) are 36% and 68% for the basic and CC cycles, respectively. The hybrid cycle

has maximum efficiency at 1175 K, which is much more accessible for industrial implementation

0

20

40

60

80

100

1500 1600 1700 1800

CYc

le E

ffic

ien

cy (

%)

Reactor Temperature (K)

CarnotTECSTECS CC

(a)

0

20

40

60

80

1500 1600 1700 1800

Sola

r Ef

fici

ency

(%

)

Reactor Temperature (K)

x1000+Carnot

x3000+Carnot

x1000+TECS-CC

x3000+TECS-CC

(b)

compared to the direct thermal reduction case. The hybrid cycle produces 43% of its work output in the

electrochemical cell, and 34% as the work availability in the CO, both of which are storable outputs that

can be used according to demand. The rest, 23% of the work output, comes from the waste heat and

constitutes work that should be used immediately. In both cases, an increase in temperature is not useful

since the reaction is already fully accomplished at these temperatures. The thermal efficiency with carbon

is lower than for direct dissociation, but the advantages of much lower temperature and no need for

vacuum could make this the preferred solution. In both cases, the recovery of waste heat makes a

significant contribution, and leads to a cycle efficiency that is close to the Carnot efficiency for the same

temperature, indicating that the irreversibilities in the cycle due to the reaction and quenching are

relatively small.

Figure 7: Conversion efficiency for zinc-air basic TECS and TECS-CC cycles (a) thermal efficiency, no

carbon, 0.01 bar; (b) thermal efficiency with carbon, 1 bar; (c) solar efficiency, no carbon, 0.01 bar;

(d) solar efficiency with carbon, 1 bar

The solar efficiencies of the direct dissociation TECS-CC cycle with an ideal solar receiver reaches, Figure

7(c), is 66% under the high concentration of ×3,000, but declines sharply to 38% for a more practical

concentration of 1000. For carbothermic reduction, Figure 7(d), a solar efficiency of 61% can be observed

at concentration of 1000, and even a lower concentration of 500 maintains efficiency of 53%.

Concentration of 500 can be achieved with a commercially available solar tower, while 1000 and higher

require additional secondary concentration and higher quality optics. The reduction of required

0%

20%

40%

60%

80%

100%

1700 1800 1900 2000

ThermalEfficiency

Temperature(K)

TECS

TECS-CC

Carnot

(a)

0%

20%

40%

60%

80%

100%

1100 1200 1300 1400 1500

ThermalEfficiency

Temperature(K)

TECSTECS-CCCarnot

(b)

0%

20%

40%

60%

80%

100%

1700 1800 1900 2000

SolarEfficiency

Temperature(K)

x1000+TECS-CC

x3000+TECS-CC

x3000+Carnot

(c)

0%

20%

40%

60%

80%

100%

1100 1200 1300 1400 1500

SolarEfficiency

Temperature(K)

x500+TECS-CC

x1000+TECS-CC

x1000+Carnot

(d)

temperature and concentration with the addition of carbon leads then to a much more technologically

practical solution.

4 Discussion

We have analyzed a unified concept for solar electricity generation and storage, based on thermal

regeneration: an asymmetric flow battery cycle with thermo-chemical charging and electro-chemical

discharging. The analysis presents the upper limits on conversion efficiency in the ideal TECS cycle for two

well-known battery systems, sodium-sulfur and zinc-air. These cases are different from past attempts to

develop thermally regenerative batteries, and suggest new material categories as candidates for higher-

performance cycles. In both cases the efficiency of the ideal cycle (with maximum recovery of waste heat)

is close to the Carnot limit at the corresponding temperature, indicating that the thermo-chemical

charging process does not add significant irreversibility, and the thermodynamic potential to produce

work (availability) remains high. Based on past experience in energy conversion technologies, practical

mature technologies often achieve conversion efficiency which is about 2/3 of the theoretical upper limit.

If the TECS technology will be able to reach a similar level of maturity, then the conversion efficiency will

reach about 40% from solar radiation to electricity, about twice the value for current solar technologies

(both CSP and PV). This indicates a very favorable potential for the new approach, provided of course that

practical and cost-effective engineering solutions can be developed for the envisioned cycle.

Implementation of a solar TECS cycle is a significant technological challenge, and the achievable

conversion efficiency in a real plant needs further analysis. Some of the processes needed for such

implementation have already been demonstrated in a research lab environment, for example for the Zn-

air cycle: solar direct thermal dissociation of ZnO at the scale of 100 kW [25], solar carbothermic reduction

of ZnO at the scale of 300 kW [33], and quenching of the reactor product mix to condense and separate

pure zinc [34]. The carbothermic reduction of ZnO can also be done with other hydrocarbons such as

methane [36], and in this case the product gas contains H2 in addition to CO (syngas). The full

decomposition of ZnO with methane is accomplished at a similar temperature range, up to 1,000℃

depending on pressure. The produced syngas mixture ratio is H2/CO=2/1, which is suitable for the

synthesis of methanol as a path for convenient energy storage in a liquid medium and possible

applications as a transportation fuel.

Developing a flow system based on Zn/ZnO requires a solution for transportation of both materials in solid

form. Possible solutions include mechanical exchange of pre-fabricated pellets, and pumping a slurry or

paste of the solid particles in a fluid carrier [24]. Another approach is to operate the EC cell and storage

tanks at a higher temperature where the zinc is maintained in a liquid state [37] and can be pumped to EC

cell when needed. The oxide formed in the cell during discharge may be mechanically separated from the

liquid using the density difference.

The reactions in the investigated TECS cycle required high temperatures, implying a technology challenge

and a requirement for high concentration of incident sunlight. An example was shown how to mitigate

this difficulty by introduction of carbon as a reducing agent for ZnO, leading to a considerable reduction

in reaction temperature and required concentration of sunlight. Concern regarding the emission of CO2

from the cycle can be addressed if the source for the carbon is renewable, such as biomass. For example,

wood charcoal was used in [33], which then can then be considered also as part of a biomass gasification

process.

The Na-S technology is well developed for operation around 300℃ but the addition of high temperature

components for the thermo-chemical charging process poses several new challenges. The solar reactor

(R2 in Figure 4) is the most difficult engineering challenge with harsh operating conditions (> 1,400℃ at

vacuum of about 10 mbar), corrosive environment, and requirement for highly efficient heat transfer.

Nevertheless, there are some examples of solar reactors (with different chemical systems) operating at

such temperatures under vacuum [38], indicating that engineering solutions may be found for this

challenge. The handling of the hot gaseous Na-S mixture emerging at about 1,400℃ from the solar reactor

is another challenge for the cycle development. The gases have to be cooled rapidly down to below the

condensing point of the Na to suppress the back reaction and to enable the physical separation of liquid

Na from the gaseous S2. The temperature in the separator exit is estimated to be around 500℃ where

the sodium vapor pressure is sufficiently low for efficient separation. A possible solution is a direct contact

condenser, where a part of the liquid sodium already separated and cooled down to the storage

temperature is pumped back and sprayed into the quenching-separation chamber.

The attractive results for cycle conversion efficiency require the capture of significant amounts of heat at

several points in the cycle, and its conversion in secondary heat engines in parallel to the primary TECS

conversion. This adds complexity and cost to the cycle. An engineering solution may use a secondary fluid

circuit to collect the heat from all the heat exchangers to a single secondary heat engine, as a compromise

to reduce complexity at the expense of some efficiency reduction. The generation of additional electricity

in the secondary stage may offer a natural division between instantaneous electricity generation in the

secondary converter during sunlight hours, and charging of the storage for later generation by the

electrochemical cell.

A full analysis of the expected cost of a TECS plant compared to conventional CSP and other technologies

is not possible at this stage, and must be deferred until the technological challenges are addressed and a

detailed engineering design is developed. However, it is possible to show a very preliminary estimate using

data available for existing CSP plants. A typical installed cost of a solar tower plant based on molten salt

with 9 hours thermal storage (solar multiple 2.1) is about $7,400/kW, and the resulting levelized cost of

energy (LCOE) is about $0.16/kWh for a typical site [39]. We assume that the majority of components in

a TECS plant will be similar to the current technology: solar concentrator field, heat transfer fluid

subsystem, storage tanks, indirect costs, etc. Two aspects will be very different: an electrochemical cell

(installed cost of $300/kW) replaces the turbine power block ($1,100/kW), producing a significant

reduction in capital expense. The TECS plant overall annual average efficiency will be 40% (lower than the

thermodynamic limit to account for additional losses in a real plant, as discussed above) instead of 15%

of the current CSP technology. The financial conditions and the operation and maintenance costs are also

the same as current CSP plants. The result is a levelized cost of $0.053/kWh for the TECS electricity. In a

more conservative case of 30% plant efficiency, the LCOE is $0.071/kWh. This range is similar to the

current LCOE of photovoltaic grid-scale plants, but the TECS solutions will offer the added advantage of

built-in large scale storage that PV plants cannot provide. This estimated cost range is also competitive in

many locations against conventional electricity derived from fossil fuels. This set of assumptions is of

course very rough and will need validation in future research. However, the simple estimate shows the

potential to reach a very competitive cost of energy, if the overall solar plant efficiency is significantly

higher than the current state of the art.

5 Conclusions

We have analyzed two material systems as candidates for the TECS cycle, leading to very promising results

of theoretical performance. The overall conclusions of the analysis are:

• A solar TECS cycle has the theoretical potential to achieve very high conversion efficiency, as well

as other possible advantages in operational flexibility and cost of energy.

• New materials, which have not been considered in the past for thermal regeneration, can lead to

much better results compared to previously proposed systems (e.g. liquid metal batteries).

• Recovery and utilization of waste heat is crucial to achieve high conversion efficiency.

• Several technical challenges (e.g., conversion of closed cell to flow mode, high temperatures solar

decomposition, separation of the decomposition products, transport of solids, etc.) require future

research and development, before this concept can move into practical application.

The high efficiency of ideal TECS cycles serves as motivation to continue work in this direction. Possible

topics for future research may include: investigating a broader range of electrochemical systems to seek

additional storage material options; experimental work to demonstrate that thermo-chemical charging is

feasible, and to understand technological limitations for specific materials; detailed engineering analysis

of the performance of non-ideal system designs, with losses that were not accounted for in this ideal

upper limit analysis; and a detailed analysis of the costs of the materials and of the technology solutions

for the entire plant. If the eventual efficiency of real systems could reach a high fraction of the theoretical

limits shown here, and if low-cost plant engineering solutions can be demonstrated, then the TECS cycle

could be a promising alternative for current solar electricity technologies.

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Nomenclature

𝐵 Exergy, 𝐵 = 𝐻 − 𝑇0𝑆 (kJ)

𝐶 Sunlight concentration ratio (-)

𝐶𝑝 Specific heat (kJ/kg K)

𝐺 Gibbs free energy (kJ)

𝐻, ℎ Enthalpy (kJ), specific enthalpy (kJ/mol)

𝐼 Direct solar radiation flux (W/m2)

𝑃 Pressure (bar)

𝑄 Heat (kJ)

�� Mass flow rate (kg/s)

𝑇 Temperature (K)

𝑊 Work (kJ)

Greek

𝜂 Efficiency

Acronyms

CC Combined cycle

CSP Concentrating Solar Power

EC Electrochemical

PV Photovoltaics

TECS Thermo-electro-chemical storage