Thermo-electro-chemical storage (TECS) of solar energy

Transcription

1 Thermo-electro-chemical storage (TECS) of solar energy Erez Wenger 1, Michael Epstein 2, Abraham Kribus 1* 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 This manuscript version is made available under the CC-BY-NC-ND 4.0 license 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 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.

2 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 costeffective 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

3 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 (Na x Sn) 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 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 volts at 586 C and 41-34% ideal efficiency. Experiments confirmed that Na can be distilled from Na x Sn alloys at temperatures of 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-

4 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) H 2(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

5 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-al 2 O 3 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 Na 2 S x (x = 3 5) 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: Na 2 S x + H x 2 S 2 + 2Na The heat of reaction for x = 4 in Eq. (2) is H = kj mol at 293 K, and kj mol at 2100 K. The polysulfides decompose gradually with increasing temperature, releasing sulfur atoms until reaching finally a mixture of pure Na and S 2 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. (1) (2)

6 Another interesting comparison is to sensible heat storage in current CSP plants: using the common molten nitrate salt operating between temperature of C, 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) e Zn(OH) 4 2 ZnO + H 2 O + 2 OH The hydroxyl ions originate at the cathode by catalytic reduction of atmospheric oxygen: 1 2 O 2 + H 2 O + 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 O 2 ; H 298 K = kj mol ZnO + C + H Zn + CO ; H 298 K = 240 kj (5) mol 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 (3)

7 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 roundtrip 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 Na 2 S 4 (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: Na 2 S 4 Na 2 S S 2 Na 2 S 2 + S 2 (these steps occur at lower temperature and are not shown in the figure); followed by Na 2 S 2 Na 2 S S 2 Na 2 + S 2, reaching full decomposition into Na and S 2 vapors under chemical equilibrium at 1,580 K. Around 2,600 K the molecule S 2 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 O 2 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 CO 2, after final conversion of the CO product, and it is desirable to use biomass-based carbon sources to minimize the greenhouse gas impact.

8 Figure 2: Equilibrium composition vs. temperature for the Na-S TECS cycle at 0.01 bar, corresponding to the initial composition of 1 mole Na 2 S 4. 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.

9 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 (Na 2 S 4 + H Na 2 S 2 (l) + S 2 (g), where H 823 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 electrochemical 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 Q R for the basic cycle configuration, Figure 4(a), is: Q R = Q R1 + Q R2 = H 2 H 1 + H 4 H 3 (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 H 1b instead of H 1. This accounts for the reduced heat input into reactor R1. The ideal work that can be done by the electro-chemical cell W ECC and the accompanying heat transfer Q ECC can be found from the energy and exergy balances on the cell:

10 Q ECC + B 8 + B 10 = W ECC + B 1 B 8 + B 10 + (1 T 0 T ECC ) Q ECC = W ECC + B 1 B = H T 0 S 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. (7) 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)

11 We keep all the storage tanks at the cell temperature, T ECC, and in this case the solution for the ideal work can be expressed as a function of the Gibbs free energy G: W ECC = G 8 + G 10 G 1 (8) The ideal thermal efficiency η th for the basic cycle, representing conversion from heat to work, is then: η th = W ECC Q R (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 W CC is: W CC = W ECC + W HE1 + W HE2 + W HE3 + W HE4 (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. W HE 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: T 8a W HE1 = (1 T 0 )C T 7b T p (T)dT (11) T 0 is the ambient temperature, and C p 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: W HE4 = (1 T 0 T 5 ) (H 4 H 5 ) (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 Q R for both cycles in Figure 5 is:

12 Q R = H 2 H 1 (13) For the basic cycle, Figure 5(a), the ideal work W ECC that can be extracted from the stored zinc in the electro-chemical cell is: W ECC = B 5 + B O2 B 1 (14) B O2 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 η th 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 W vac is: γ 1 W vac = m 7C p [( P 0 γ ) P 7 1] (15) m 7 and P 7 are the flow rate and pressure at point 7 upstream of the pump, respectively, P 0 = 1 bar is the atmospheric pressure, and C p 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 CO 2, and the maximum work output from this reference process is: W ref = B 1b + B O2 B CO2 (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 W tot, then the additional or incremental work W tot W ref is due to the heat input at the reactor. The conversion efficiency relevant to the reactor heat input is then the incremental efficiency [35]: η inc = W tot W vac W ref Q R (17)

13 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 CO 2, and the maximum amount of work that can be done under the assumption of ideal processes is then: W tot = B B O 2 B ZnO + B B O 2 B CO2 (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.

14 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 η sol is then [17]: η sol = 1 σ(t 4 rec T 4 0 ) I C T rec is the receiver effective temperature, and here we assign it as the highest temperature in the reactor, T 4 in Figure 4, or T 2 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/m 2. The total conversion efficiency of the entire system from sunlight input to work or electricity output is then: (19) η tot = η sol η th (20) η th 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, η th 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 thermochemical 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

15 Solar Efficiency (%) CYcle Efficiency (%) 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 (a) Carnot TECS TECS CC Reactor Temperature (K) 80 (b) x1000+carnot 20 x3000+carnot x1000+tecs-cc x3000+tecs-cc Reactor Temperature (K) 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

16 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. Thermal Efficiency Solar Efficiency 100% 80% 60% 40% (a) TECS 20% TECS-CC Carnot 0% Temperature (K) Thermal Efficiency 100% 80% 60% 40% 20% (b) TECS TECS-CC Carnot 0% Temperature (K) 100% 80% 60% 40% 20% (c) x1000+tecs-cc x3000+tecs-cc x3000+carnot 0% Temperature (K) Solar Efficiency 100% (d) 80% 60% 40% x500+tecs-cc 20% x1000+tecs-cc x1000+carnot 0% Temperature (K) 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 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

17 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 higherperformance 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 Znair 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 H 2 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 H 2 /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 CO 2 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

18 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 S 2. 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.