Latent heat thermophotovoltaic batteries

Graphical Abstract Click here to access/download;Graphical Abstract;GraphicalAbstract.tif 1 Latent Heat Thermophotovoltaic Batteries Alejandro Datas(1)(2), Alicia López de Ceballos, Esther López, Alba Ramos(+), and Carlos del Cañizo Instituto de Energía Solar – Universidad Politécnica de Madrid, Madrid, 28040, Spain (1) corresponding author: [email protected] (2) Lead contact (+) currently at Universitat Politècnica de Catalunya, Jordi Girona 1-3, Barcelona 08034, Spain Keywords: energy storage, thermophotovoltaics, power-to-heat-to-power, PHPS, electric thermal energy storage, ETES, thermal energy, high temperature, silicon, phase change materials, cogeneration, combined heat and power, CHP. Summary Latent heat thermophotovoltaic (LHTPV) batteries are power-to-heat-to-power storage systems in which electricity is employed to produce the solid-to-liquid transition in a phase change material (PCM), storing energy in the form of latent heat at very high temperatures (> 1000ºC). When needed, stored energy is released as thermal radiation, and converted back to electricity using thermophotovoltaics (TPV). In this study we discuss on the techno-economics of LHTPV systems, focusing on parameters like the round-trip efficiency, the energy-to-power ratio, the cost per energy and power capacities, and the levelized cost of storage. The relatively low TPV conversion efficiency (< 50 %) and the low cost of the PCMs (< 4 €/kWh) result in optimal designs with high energy-to-power ratios, fitting long duration storage (LDS) applications. The use of lower melting point PCMs, like FeSiB (1157 ºC), allows a significant reduction in the cost of thermal insulation, favouring their use in smaller scale applications. Shorter duration storage applications require lower cost per power capacity, which can be achieved by using higher melting point PCMs such as Si (1414 ºC), or higher round-trip conversion efficiency, which can be achieved through cogeneration, that is, combined heat and power (CHP) dispatchable generation. Results indicate that LHTPV systems can provide lower levelized cost of storage than Li-ion batteries in both LDS and CHP applications. Preliminary experimental results are provided to illustrate the real operation of a LHTPV system. Manuscript Click here to view linked References 2 1 Introduction Latent Heat Thermophotovoltaic (LHTPV) batteries are a kind of power-to-heat-to-power storage (PHPS) system 1–3, also named electro-thermal energy storage (ETES) 4 or thermal energy grid storage (TEGS) 5, that store electricity in the form of latent heat at very high temperatures (>1000ºC) and convert it back to electricity on demand using thermophotovoltaics (TPV) 6,7. High melting temperature phase change materials (PCM), like silicon or silicon alloys 8, enable very dense energy storage (> 1 MWh/m3) at very low cost (< 4 €/kWh) 1, and thus, they are very well indicated for long-duration energy storage applications. Long-duration energy storage systems 9 are characterized by having a high energy-to-power ratio and are intended to store the vast amounts of renewable electricity that would be lost otherwise. The price of this electricity (otherwise wasted) is very low, and the use of high-cost storage systems, like Li-ion batteries (> 80 €/kWh 10), are not indicated in this case. On the contrary, systems with very low-cost per energy capacity (CPE) are preferable, even if they have lower round-trip conversion efficiencies. This is the case of Carnotlimited PHPS systems like LHTPV (in opposition to those that use a heat pump for heating 11) whose round-trip electric-to-electric conversion efficiency is a fraction of the Carnot efficiency, i.e. 1−𝑇𝑐𝑇ℎ ⁄ , being 𝑇𝑐 and 𝑇ℎ the temperature of the cold and hot reservoir, respectively. In addition to long-duration storage applications, PHPS (and LHTPV) systems are well indicated for dispatchable cogeneration from variable renewable energy sources 2. The heat available in the system, either the one that is produced during the thermal-to-electric energy conversion or the one stored within the system, can be used to satisfy the heating demands in this case. The overall conversion efficiency is therefore increased, and the system can be profitable in a wider range of applications. Several PHPS embodiments have been proposed in the recent years using a variety of thermal storage materials (stones, concrete, silicon, carbon, ceramics, etc.). Systems have been proposed in a very wide range of temperatures, ranging from ~ 500 ºC to over 1500 ºC, and use different kinds of thermal-to-electric energy converters 1,4. PHPS systems that operate at very high temperatures (over ~ 1000 ºC) take advantage of the high enthalpy and high energy density of the stored heat 1,12. Most commercial systems use heat engines that are based on well-established Rankine, Brayton, or Stirling thermodynamic cycles 13. More innovative PHPS systems are based on TPV generators. Intended to operate at extreme temperatures (> 1000 ºC), TPV devices enable very dense, modular, silent, and low-cost power generation, ultimately resulting in very compact and scalable PHPS systems. PHPS systems based on TPV have been proposed using either solid1 or liquid5 sensible 3 heat, and latent heat 3 storage options. The main advantage of the latent heat options is the small temperature variation during the discharge (PCM solidification). This enables decoupling the energy storage and power generation capacities of the system. In sensible heat systems, high energy densities require very large variations of the storage media temperature, which imply a variable power generation capacity. As TPV generators require temperatures well over 1000 ºC to operate, most sensible heat options target extreme temperatures, well over 1500 ºC, to get a large temperature range at which the TPV generation is significant. Having such high temperatures in the charged state bring serious challenges on the thermal insulation. On the contrary, latent heat storage systems can be designed to provide an almost constant temperature during the discharge. In this way, a lower temperature can be targeted that relaxes the thermal insulation requirements without deteriorating the TPV power generation capacity. Therefore, the key of LHTPV systems is the selection of a PCM that enables high energy density and low cost (i.e., low thermal insulation requirements) along with reasonably high TPV power generation capacity. In this regard, siliconbased alloys enable very high energy densities (> 1 MWh/m3) and very low costs (< 4 €/kWh) in a ‘moderately high’ temperature range (1157 – 1414 ºC) that mitigates the thermal insulation requirements but is still perfectly suited for TPV power generation. We will see that these features enable the development of very compact, silent, and scalable systems that could be used not only for long duration storage applications, but also for dispatchable cogeneration in space constrained locations such as buildings, factories, or districts. Furthermore, silicon and silicon alloys can be easily obtained from abundant raw or waste materials and eventually recycled after use, and therefore have the potential to minimize the environmental impact of the manufacturing of energy storage systems. In this article we present a techno-economic assessment of LHTPV batteries, with an especial focus on their application for long duration energy storage and dispatchable cogeneration in a fully electrified building. Section 2 describes a LHTPV system configuration; section 3 provides a techno-economic assessment of LHTPV, and section 4 present preliminary experimental results of a LHTPV lab-scale test bed unit that can be used to test different materials and devices under real operation conditions. 2 LHTPV system Figure 1 (a) shows a block diagram of a generic LHTPV system that includes electrical and thermal switches / regulators, a heating system, a thermally insulated heat store (including the PCM and the 4 thermally insulated container), and the TPV generator. Low-cost, high melting temperature and high latent heat PCMs, like silicon, iron, and silicon-iron-boron alloys (see Table 1 and Figure S1 in the Supplemental Information) are, in principle, interesting candidates for LHTPV applications. Silicon is a particularly interesting material due to its low cost and high energy density (both gravimetric and volumetric). However, volumetric expansion upon solidification might be an issue regarding thermal cycling reliability 14,15. The recently proposed Fe-26Si-9B alloy (FeSiB for short) has a volumetric latent heat similar to that of pure silicon and negligible volume expansion upon solidification, allowing for a reliable melting / solidification cycling 16. The lower gravimetric latent heat of FeSiB, which is attributed to the higher density of iron, is not a relevant issue for stationary applications. Moreover, FeSiB could be produced at low cost by using cheap raw and waste materials like silicon, scrap iron, and borosilicate glass. Furthermore, these materials have relatively high thermal conductivities that enable an efficient heat extraction, and can be contained (in liquid state) in carbon and silicon carbide crucibles 5,8. For thermal insulation, a layered system that uses high-temperature and high-cost thermal insulation materials (TIM), like alumina fiber mat, for the inner side, and low-temperature and low-cost materials, like fumed silica board, for the outer side, are used to minimize the overall cost of the system 17 (Table 1). Electric heating can be accomplished using ohmic 18, induction 4, microwave 19, or arc systems 20, and electric switching / regulation can be accomplished by thyristor or IGBT blocks. Thermal switching can be performed by mechanical retracting or introducing the TPV generator in an enclosure within the system, thus, passing from dark to illuminated conditions. Figure 2 shows a possible LHTPV embodiment that is based on the hollow cylindrical crucible units described elsewhere 3,21. In this arrangement, the TPV generators can be mechanically retracted from the emitter, which is a cylindrical enclosure that is made in a crucible that contains the PCM. At the beginning of the discharge, the PCM is in the liquid state near its melting point. When the TPV generator is introduced in the enclosure, the PCM releases latent heat towards the emitter (the inner SiC crucible wall) and starts solidifying. During this process, a solid-liquid interface moves away from the emitter, creating a solid crust around the emitter that hinders heat transfer to the TPV generator. A temperature gradient, which increases over time, is established through the solid crust and the inner walls of the crucible that negatively impacts the TPV output power. In this regard, the advantage of this configuration is that the PCM cross-sectional area (perpendicular to the heat flux) diminishes in the direction of heat flux during the discharge, and thus, the heat flux density (in W/cm2) is maximized at the emitter surface. This results in a small 5 heat transfer that ultimately results in a low temperature gradient through the PCM, subsequently enabling a more efficient thermal-to-electric energy conversion 21. Figure 3 shows the average (solid lines) and the maximum/minimum (colored region) emitter temperatures during the discharge as a function of the discharge duration for two different system designs that have large (Rcont=34 cm) and small (Rcont=19 cm) crucible radius. Results are obtained using a slightly modified version of the quasi-1D heat transfer models described elsewhere 3 that assumes a perfectly adiabatic thermal insulation. This model calculates the temperature gradients in the PCM and the inner crucible walls during the solidification of the PCM. The discharge duration can be varied in this case through the size (the area) of the TPV generator that is introduced in the system, which determines the heat flow. Low temperature gradients in the PCM are expected for small TPV generators that are discharged slowly at a low-power rate. High temperature gradients are expected for large TPV generators that are discharged quickly at a high-power rate. Results in Figure 3 illustrates that smaller container (Rcont = 19 cm) enables much lower temperature gradients, even at high power rates, at the expense of having a lower energy density, as there is large fraction of the volume dedicated to the container rather than the PCM itself. We will see that lower energy densities bring higher costs per energy capacity due to the need of higher amounts of thermal insulation materials. Therefore, a trade-off exists between the cost per power and the conversion efficiency (linked to the average temperature of discharge) and the cost per energy (linked to the energy density) that is determined by the crucible design and the storage duration. 3 Technoeconomics The main technoeconomic parameters of this system (see Figure 1) are: (i) the energy capacity (𝐸=𝑚𝐿), which is proportional to the total amount of PCM (𝑚, in kg) and its latent heat of fusion (𝐿, in kWh/kg); (ii) the cost per energy capacity (CPE, in €/kWh), which accounts for the cost of the PCM, its container, and the thermal insulation system; (iii) the charge and discharge durations at nominal power conditions (𝑡𝑐=𝐸 𝑄𝑖𝑛 ⁄ and 𝑡𝑑=𝐸 𝑄𝑜𝑢𝑡 ⁄), which are determined by the energy-topower ratios at the input and the output, respectively; (iv) the charge conversion efficiency (𝜂𝑐= 𝑄𝑖𝑛 𝑃𝑖𝑛 ⁄) and the cost per input power capacity (CPPin, in €/kWel), which are determined by both the electric switching/regulation and heating systems, and (v) the discharge electric conversion efficiency 𝜂𝑑=𝑃𝑇𝑃𝑉 𝑄𝑜𝑢𝑡 ⁄ and the cost per power capacity at the output (CPPout, in €/kWel), both determined by the TPV energy converter. The heat loss of the system can be accounted for in the overall input and output conversion efficiencies as 𝜂𝑖𝑛 =𝜂𝑐(1+𝑘𝑙𝑜𝑠𝑠𝑡𝑐(𝑡𝑑+𝑡𝑐) ⁄) ⁄ and 𝜂𝑜𝑢𝑡 = 6 𝜂𝑑(1−𝑘𝑙𝑜𝑠𝑠𝑡𝑑(𝑡𝑑+𝑡𝑐) ⁄), being 𝑘𝑙𝑜𝑠𝑠 the fraction of the total energy storage capacity (𝐸) that is lost per cycle through the thermal insulation system. The levelized cost of electricity storage (LCOS) of the system (only accounting for the electricity output) can be formulated as a function of the parameters described above by neglecting the maintenance costs, and assuming a periodic cycling of the system that operates at nominal power conditions 1: 𝐿𝐶𝑂𝑆= 𝑝𝑒 𝜂𝑟𝑡 +1 𝑁𝑐𝑦𝑐𝑙(𝐶𝑃𝑃𝑖𝑛 ∗ 𝜂𝑟𝑡𝑡𝑐+𝐶𝑃𝐸∗ 𝜂𝑜𝑢𝑡 +𝐶𝑃𝑃𝑜𝑢𝑡 ∗ 𝑡𝑑) (1) where 𝜂𝑟𝑡 =𝜂𝑜𝑢𝑡𝜂𝑖𝑛 is the round-trip conversion efficiency, 𝑝𝑒 is the price of the energy input, 𝑁𝑐𝑦𝑐𝑙 =8760/(𝑡𝑑+𝑡𝑐) is the number of cycles in one year, and 𝐶𝑃𝐸∗, 𝐶𝑃𝑃𝑖𝑛 ∗, and 𝐶𝑃𝑃𝑜𝑢𝑡 ∗ are the annualized cost per power and energy capacities that are obtained from the initial capital expenditures CPE and CPPi by 𝐶𝑃𝑋𝑖∗=𝐶𝑃𝑋𝑖∙𝑟(1+𝑟)𝑛((1+𝑟)𝑛−1) ⁄, being 𝑟 the discount rate and 𝑛 the lifetime of the installation (in years). LCOS is given in €/kWh-cycle and represents the average cost of the energy that is released by the system all through its lifetime. LCOS is the key figure of merit that should be minimized, and it increases with the cost per energy and power capacities and the price of input electricity but decreases with the conversion efficiency and the lifetime. Just by looking at this equation one can already understand that systems with high CPE require a high discharge conversion efficiency, and systems with high CPPout require a long discharge duration. On the contrary, systems with very low CPE can tolerate lower discharge conversion efficiencies, and systems with low CPPout can afford short duration discharge cycles. 3.1 Cost per energy capacity The CPE of the system is determined by the PCM, its container and the thermal insulation. Thus, it can be calculated from the cost per volume (CPV, in €/l) and the volume (V) of each of these three elements in the system as 𝐶𝑃𝐸=(𝐶𝑃𝑉𝑃𝐶𝑀𝑉𝑃𝐶𝑀+𝐶𝑃𝑉𝑐𝑜𝑛𝑡𝑉𝑐𝑜𝑛𝑡+𝐶𝑃𝑉𝑖𝑛𝑠𝑉𝑖𝑛𝑠) 𝐸 ⁄ being 𝐸=𝜌𝑉𝐿 the total energy capacity of the system and 𝜌 the gravimetric density of the PCM. The lower bound for CPE assumes negligible cost for the container and the thermal insulation, and it is solely determined by the cost and the energy density of the PCM. Figure S1 in the Supplemental Information shows the volumetric energy density of several storage media, including PCMs (latent heat), as a function of the operation temperature (panel a), and their cost per volume (€/l) and their cost per energy capacity (€/kWh) (panel b) 1. Low costs of the storage media, below 10 €/kWh, are possible with several sensible and latent heat options. However, to reach a low CPE the selected 7 media must not only be cheap but also ensure a low cost of the container and the thermal insulation subsystems. To that end, the storage media should also have a high energy density and a low operation temperature. The so-called ‘solar salt’ (40% KNO3 + 60% NaNO3) used in concentrated solar power plants have low cost (~ 7 €/kWh) at moderate temperatures (up to ~ 560 ºC), but the energy density is low (~ 0.1 MWh/m3). Si and, potentially, FeSiB PCMs provide the highest volumetric energy density at the lowest cost (1.2 MWh/m3 and 2.7 €/kWh), but their operation temperature is very high (1414 and 1157 ºC, respectively). In principle, it is not obvious whether the higher specific cost (in €/m2) of the thermal insulation that is needed at higher temperatures is offset by the higher energy density and the lower cost of the storage media. Panels (a) and (b) in Figure 4 show the overall CPE of a LHTPV system as a function of the melting point and the latent heat of the PCM for different energy storage capacities (1 and 100 MWh, respectively). Two layers of thermal insulation material are considered: the outermost is a silica board that withstands up to 1000 ºC; the innermost is alumina fiber mat that withstands 1650 ºC 17 (see Table 1). The thickness of these two layers is calculated using a 1D heat transfer model to prevent exceeding 1000 ºC in the silica board and to obtain a certain amount of heat loss, which in the case of panels a-d of Figure 4 is 5 %/day (i.e., 20 days of self-discharge duration). The number of crucibles is set to meet the energy storage capacity of the system in each case. As expected, the lowest CPE are obtained by a hypothetical PCM with the lowest melting point and the highest latent heat (Figure 4 a,b). Increasing the temperature implies the use of a thicker thermal insulation material, subsequently increasing the overall cost of the system. Exceeding 1000 ºC is particularly disadvantageous, as this is the temperature limit of fumed silica board, and the inner thermal insulation layer must incorporate the more expensive alumina fiber mat in this case. The impact of increasing temperature is particularly significant for systems with a small energy capacity (Figure 4 a) and using a PCM with a low latent heat. On the contrary, the impact of increasing the temperature is negligible if the energy capacity of the system is high and the PCM has a high latent heat (Figure 5-b), as it is the case of Si and FeSiB PCMs. In other words, the use of Si or FeSiB PCMs is especially well indicated for large scale thermal energy storage. In this case, the amount of thermal insulation that is needed is very small if compared to the amount of thermal energy that is stored, and thus, a thermal insulation system with a higher specific cost (in €/m2) is affordable. At smaller scales, larger amounts of thermal insulation materials are needed per stored energy capacity, and thus, reducing the specific cost of thermal insulation is important. In this 8 regard, the lower melting temperature of FeSiB (m.p. 1157 ºC) is very advantageous. The impact of scale on the CPE is further illustrated in Figure 4 -c, which clearly shows that FeSiB PCM enables the lowest CPE at the smallest scales. Figure 4 -d also shows that using fewer amounts of thermal insulation (i.e., using FeSiB PCM) results in a higher overall energy density. It should be noted that, under the assumptions of this study, PCMs with lower melting temperature (< 600 ºC) must exceed 400 kWh/m3 at costs below 0.8 €/l to reach lower CPE than a system based on FeSiB. Besides, the selected PCM should have a high thermal conductivity. Otherwise, smaller containers with higher surface-to-volume ratios should be used for an efficient heat extraction, which would result in even higher CPEs and lower energy densities. These requirements are hardly attainable by existing PCMs in this temperature range. In the most favorable scenario shown in panels c and d of Figure 4 (FeSiB PCM, H = 1.5 m, and a 100 MWh system capacity), TIM accounts for only 22 % of the total CPE. However, this share increases to 40 % and 84 % if heat losses are reduced to 2.5 %/day and 0.5 %/day, respectively. Figure S2 in the Supplemental Information shows the shares of the three main energy-related system components (PCM, crucible and thermal insulation) to the total CPE of the system for several configurations (energy capacity and heat loss). The general trend is that the share of thermal insulation on the total CPE decreases with the energy capacity and the heat loss. The higher the share of thermal insulation, the higher the total CPE and the lower the energy density. Panels e and f in Figure 4 show the CPE and the energy density, respectively, as a function of the self-discharge duration for a very large (1 GWh) LHTPV system with crucible height values between 2 and 5 m, as represented by the lower and upper bounds of each colored band, respectively. Every selfdischarge duration corresponds to an amount of heat loss, ranging from 10 %/h (10 h of selfdischarge) to 0.24 %/day (10,000 h of self-discharge). The case of current state-of-the-art molten salt TES, with ~ 1 GWh of storage capacity, is indicated with an star (~ 0.36 %/day or ~ 7000 h self-discharge duration, and 0.08 MWh/m3, obtained by assuming ΔT = 250 ºC and the tank dimensions indicated in references 22,23). We see that, under the assumptions of this study, both Siand FeSiB-based LHTPV systems can reach lower CPE (panel e) and higher energy density (panel f) than that of a two-tank molten salt system with the same energy capacity and heat loss (selfdischarge duration). Enabling higher amounts of heat loss (reducing the self-discharge duration in Figure 4-e) comes with a reduction in CPE, as expected. This illustrates an existing tradeoff between cost and efficiency of the thermal insulation. We will see later that this trade-off results in an optimum amount of heat loss that minimizes the levelized cost of storage depending on the 15 that consumes natural gas and grid electricity), assuming simplified models for each component of the system and a relatively simple control strategy. Details on the model are provided in the Supplemental Information. The techno-economic parameters that, otherwise indicated, are fixed, or optimized during the simulations are show in Table 3. Like in our previous work 2, the hourly energy demands of a small residential building in Madrid have been simulated using Energy Plus® 33, resulting in an annual energy consumption of 19.5 MWh, being 3.9 MWh electricity (from which 1.1 MWh are consumed by the air conditioner) and 15.6 MWh heat (14.2 MWh for space heating and 1.4 MWh for domestic hot water). The hourly PV electrical power generation per kW of installed PV capacity is calculated by means of PVsyst® assuming an ideal tilt of the panels 34. To consider different building sizes, these hourly energy demands are multiplied by a scale factor. Despite this approach might not accurately provide the actual energy demand of a large building, it will be useful to illustrate the scaling effects of LHTPV systems. The above methodology has been applied to different configurations of buildings of different sizes, heat consumption, and grid electricity prices with hourly discrimination, to corroborate that the following qualitative results and conclusions are general and valid, even though the quantitative analysis could change depending on the particularities of each application. Figure 11 (panels a and b) show the levelized cost of energy (LCOE, in €/kWh) and the total energy density (in kWh/m3) of the two systems illustrated in Figure 10 as a function of the yearly energy demand, including two kinds of LHTPV systems that are based on InGaAsSb TPV cells and use either Si or FeSiB PCMs. The LCOE has a similar definition than the LCOS (see Supplemental Information) but referring to the average cost of the final consumed energy (heat and electricity) along the entire lifetime of the installation, and it includes both the initial capital expenditures of all components in the system and the cost of the electricity that is purchased from the grid. Any other maintenance costs (e.g., replacement of units) are neglected. The total energy density is defined as the total storage energy capacity of the installation, including the battery (either Li-ion or LHTPV) and the hot water store, divided by the total volume occupied by those components. Each colored band represent the values obtained within each technology’ margin of confidence for their cost (see figure caption). The system has been optimized (see optimized parameters listed in Table 3) at each point targeting the minimum LCOE for each solution. Figure S4 in the Supplemental Information shows the values obtained for all the optimized parameters that are listed in Table 3, i.e., the battery energy storage capacity, the battery output and input power capacity, the PV installed power 16 capacity, the hot water storage capacity, and the optimal crucible height and heat loss of the LHTPV battery. Panel (a) in Figure 11 shows that scaling up LHTPV systems enables a reduction in the LCOE, whereas Li-ion batteries produce a constant LCOE, independently of the scale. This is a direct consequence of the significant reduction of the CPE and the heat loss of the LHTPV systems at large scales. If the yearly energy demand is increased from 0.1 to 100 GWh/year in a Si-based LHTPV system, the optimal LHTPV energy capacity increases from ~ 180 kWh to 800 MWh, the CPE reduces from 40 €/kWh to 5.4 €/kWh and the optimal heat loss reduces from 20 %/day to 0.9 %/day. In a FeSiB-based system, the same tendency is observed but with lower values of CPE (from 18 €/kWh to 4.7 €/kWh) and heat loss (from 8 %/day to 0.5 %/day). At small scales, the cost of thermal insulation is significant, and thus, the optimal amount of losses is relatively high. This results in lower overall conversion efficiencies, higher costs per energy capacity, and ultimately, higher LCOE. The slightly lower LCOE obtained with Si-based systems at large scales is explained by the lower cost per power of the TPV generator, which goes from 362 – 1163 €/kW (at 0.1 GWh/year) to 173 – 444 €/kW (at 100 GWh/year), whereas for the FeSiB system it goes from 601 – 1273 €/kW (at 0.1 GWh/year) to 425 – 1075 €/kW (at 100 GWh/year). This indicates that, to obtain a lower LCOE in this application, having a low cost per power (Si-based systems) is more important than having a low cost per energy (FeSiB-based systems). This is understandable, as the average half-period of PV generation and energy consumption is relatively low in this case (~ 12 hours), and this requires a relatively low energy-to-power ratio. Indeed, the reduction in the cost per power at large scales is also explained by the increment in the energy-to-power ratio, which goes from 5 – 7 hours to 23 – 33 hours in the Si system, and from 18 – 40 hours to 40 – 70 hours in the FeSiB system. A large energy-to-power ratio enables a slow discharge process and a higher average emitter temperature that ultimately results in a lower cost of power capacity (Figure 6). The increment in the energy-to-power ratio is also explained by the fact that, at large scales, a large fraction of the LHTPV storage capacity is dedicated to store the heat that will be eventually used to satisfy the heating demands. At small scales, the large amount of heat that is lost in the LHTPV system prevents its use for this purpose, favoring the use of the hot water tanks, as it will be explained below. Besides of the lower LCOE at large scales, the main advantage of LHTPV over Li-ion is the much higher overall energy density (Figure 11, panel b). A fully electrified system that is based on Li-ion 17 batteries will store large amounts of PV electricity in the form of hot water to eventually satisfy the heating demands. The low energy density of the hot water stores (46.5 kWh/m3 for a temperature difference of 40ºC) results in a very low overall energy density. Most of the volume is dedicated to hot water stores in this case (~ 10,500 m3 for 100 GWh/year, storing ~ 488 MWh of thermal energy), and the Li-ion batteries (assumed to have an energy density of 400 kWh/m3) only represent a small fraction of the total volume (~ 164 m3 for 100 GWh/year, storing ~ 66 MWh of electricity). On the contrary, a LHTPV system can store heat at much higher energy densities (up to ~ 600 kWh/m3 at 100 GWh/year). Consequently, hot water stores are barely needed, and the overall energy density is significantly increased. Most of the volume is dedicated to the LHTPV system in this case (1300 – 1850 m3 at 100 GWh/year, storing a thermal energy capacity of 0.7 – 1.1 GWh), and the hot water tanks represent a small fraction of the total system volume (130 – 180 m3 at 100 GWh/year, storing 6 – 8 MWh of thermal energy), and are only used to store the heat coming from the cooling of the TPV cells. Therefore, a key difference between LHTPV and Li-ion batteries in these applications regards the way of storing the surpluses of PV electricity for delivering the heating demand. In LHTPV systems, these surpluses are stored at high energy density in the LHTPV battery, which is oversized to deliver this additional heating demand. In the case of Li-ion batteries, these surpluses must be stored at low energy density in separate hot water tanks, which occupy a very large volume. The high amount of heat losses that exist in LHTPV systems at small scales favors the use of hot water tanks, and this explains the lower overall energy density of LHTPV-based systems that is obtained in this case. It should be noted that Li-ion batteries could be hybridized with other more efficient heating systems (e.g., heat pumps) and high energy density heat stores (e.g., low temperature PCM) to result in a more efficient and economical solution. The analysis of all these possible scenarios is outside the scope of this study and should be analyzed in future works. The main difference between Si and FeSiB systems that is observed in Figure 11 (panels a and b) is the scale at which LHTPV starts having a clear advantage over Li-ion. Despite Si-based systems provide slightly lower LCOE at large scales, FeSiB-based LHTPV systems become advantageous (i.e., provide lower LCOE and higher energy densities than systems based on Li-ion batteries) at smaller scales. Like in the previous section, this is linked to the lower cost per energy capacity that is attainable at smaller scales (Figure 4-a) due to the lower melting temperature of the FeSiB PCM that allows for a more efficient and cost-effective thermal insulation. Figure 11 (panel c) shows the 18 LCOE for the best-case scenarios of both Li-ion and FeSiB-LHTPV batteries as a function of the yearly energy consumption for different costs of the PV installation, ranging from 600 €/kW to 2000 €/kW and for two cases of LHTPV systems: with an optimized crucible height (solid red lines) and a fixed crucible height of 1.5 m (dashed red lines). These figures show that the scale at which the LHTPV systems outperforms Li-ion batteries increases with the price of PV. This is also the case for the reduction in LCOE that can be obtained at large scales with LHTPV. Therefore, large scales and low PV prices favor the use of LHTPV systems over Li-ion batteries. As lower PV prices are attainable in large-scale installations, this reinforces the conclusion that self-consumption cogeneration solutions based on LHTPV should target very large-scale applications. Moreover, at large scale applications, a dedicated building is probably needed for the LHTPV system, which enables the use of tall crucibles (e.g., over 1.5 m), ultimately resulting in even lower LCOE. Figure 12 shows the LCOE of a LHTPV system optimized at a yearly energy demand of 2 GWh/year, as a function of the TPV conversion efficiency. The optimal size of the LHTPV system ranges from 12 – 15 MWh (for Si systems) to 13 – 15 MWh (for FeSiB systems) and the optimal heat loss from ~ 4 %/day (for Si systems) to ~ 2.5 %/day (for FeSiB systems), independently of the TPV efficiency. The optimal size of the PV installation is ~ 2 MW, also independently of the type of LHTPV system and TPV conversion efficiency. This figure illustrates that a system based on LHTPV can get lower LCOE than those based on Li-ion batteries at a reasonably low TPV conversion efficiency of just over ~ 20 %, which is attainable with current existing technologies. Moreover, the increase in the conversion efficiency over ~ 40 % does not bring a very significant advantage. This is explained by the lower amount of heat that is obtained from the cooling of the cells in this case, which makes necessary to generate this heat by other means. If LHTPV only supplied electricity, one could expect the optimal energy and power capacities of the LHTPV and PV systems to decrease with the TPV conversion efficiency 35. A clear advantage could be expected by increasing the TPV conversion efficiency in this case. However, if LHTPV supplies both heat and electricity in a fully electrified cogeneration application where the heating needs must be satisfied with electricity, either coming from the PV installation or from the grid, the PV and LHTPV installations still need to be sized to deliver the heating needs. This precludes a very significant advantage by increasing the TPV conversion efficiency over ~ 40 %. Increasing the TPV efficiency mostly impacts on the electricity consumption, which represents only 20 % of the total energy demand in this case, and thus, a relatively low TPV conversion efficiency is enough to have a significant impact on reducing the LCOE. The optimal size of the TPV generator that is obtained 19 at 40 % TPV conversion efficiency (e.g., 250 kWel for the best-case scenario of a Si-based system) barely increases at higher efficiencies (e.g., 260 kWel at 80 %), preventing a more significant advantage. It worth noticing that the simulations shown in this section require a very large PV installation (e.g., from 1 to 10 MW for a yearly energy demand from 1 to 10 GWh and a PV cost of 900 €/kW). A large PV installation is needed to minimize the LCOE, i.e., avoid the use of electricity from the grid, due to the assumption of a constant price of grid electricity. In this case, the battery is only charged using electricity from the PV installation. On the contrary, if we assume hourly discrimination for the price of grid electricity, the battery could be charged with grid electricity during the valley periods, and thus, the required PV installation would be smaller. Analyzing this and other possible scenarios is out of the scope of this article and should be studied in future works. 4 An experimental test bed unit An experimental LHTPV test-bed unit has been fabricated in the frame of the EU-funded AMADEUS project 36. The system was designed for crucibles with an inverse truncated cone geometry, following previous designs intended for concentrated solar applications 21,37–39. Like the hollow cylindrical configuration described in the previous sections, the inverse truncated cone geometry has a cross-sectional area (perpendicular to the heat flux) that diminishes in the direction of heat flux. This makes heat flux density (in W/m2) to increase towards the TPV emitter; thus, minimizing the temperature gradient in the PCM during the solidification process. The fabricated system integrates a graphite heater to heat up the crucible from above by thermal radiation. The crucible has 0.63 liters of volume capacity, and it is thermally insulated from the environment by means of a ~ 25 cm cover of graphite fiber mat 17. The TPV cell is mounted in a copper water cooled plate and faces the bottom of the crucible, and it produces electricity from the thermal radiation originating in the crucible walls. The purpose of this system is to be a test bed for the characterization of materials and devices that will be eventually used to develop optimized LHTPV systems. Figure 13 shows preliminary results of the characterizations conducted with this system. Panel a shows the short-circuit current and the complete I-V characteristics (inset) of a 1.48 cm2 GaSb TPV cell (from JX Crystals) as a function of the crucible temperature. Panel b shows the produced TPV power density as a function of the crucible temperature along with the projections made with a TPV 20 cell model that is based in detailed balance calculations 26. A maximum power density of 478 mW/cm2 has been measured at the maximum crucible temperature of 1030ºC, which is 59% of the theoretical maximum of 808 mW/cm2 (assuming an ideal GaSb cell, unity view factor, and a crucible emissivity of 0.81). The highest TPV cell temperature is 37 ºC and it corresponds to the highest crucible temperature (1030 ºC). Figure S5 in the Supplemental Information shows the open circuit voltage and the short-circuit current of the cell under variable irradiance conditions and different controlled temperature, along with the one of real operation conditions. The data in this figure is used to estimate the TPV cell temperature in operation. A linear dependence is found between the produced electric power and the cell temperature according to which cell temperature increases ~ 4 ºC per additional 100 mWel that are produced (panel b in Figure S5). Despite this rate is very dependent on the specific cooling system and the kind of TPV cells that are used (e.g., the cells used in this experiment do not have a back surface reflector, and thus, need to dissipate large amounts of heat), this illustrates that cell cooling might be an issue at very high-power densities. Finally, panel c in Figure 13 shows the time evolution of the crucible temperature, as recorded by a calibrated pyrometer, and the projected TPV power density (dashed lines) calculated using the model mentioned above. The crucible contains 0.357 liters (3.19 kg) of copper in this case, which represents ~ 180 Wh of thermal energy in the form of latent heat. Different solidification processes are shown at different cooling rates, which are controlled by the electric power supplied to the heater from above. During the solidification, the temperature of the crucible keeps at an almost constant temperature in the range of 1050 – 1070 ºC, which is slightly lower than the melting point of copper (1080ºC) due to the temperature gradient in the crucible walls. Projected TPV power densities during the discharge are in the very narrow range of 500 – 550 mW/cm2, almost independently of the cooling rate. The cooling rate, which is linked to the storage duration, barely affects the temperature gradient in this case due to the very high thermal conductivity of copper, although a slightly higher gradient is observed at the highest rate, as expected (Figure 3). From the experiments shown in Figure 13, we can make some projections of the overall system performance. If the bottom part of the crucible (6 cm diameter) would be fully populated with TPV cells, the electricity produced by the system during the discharge would range from ~ 5.5 Wh to ~ 18 Wh for discharge durations between 0.37 and 1.22 hours (the two extreme values shown in Figure 13-c). This is a very small fraction (3 – 10 %) of the total latent heat contained in the PCM (180 Wh), which is attributed to the very high amount of heat loss existing in this lab prototype. 21 Remarkably, the heating electrodes are refrigerated and account for a large fraction of the heat loss, especially for short discharge times, where the input electricity to the electrodes is small and not enough to offset the heat loss. The steady state heat loss through the thermal insulation cover (25 cm of graphite fiber mat) at 1060 ºC crucible temperature is 156 W, as calculated using a CFD model and neglecting heat loss in the electrodes. This means that ~ 1.4 % of the stored latent heat is lost through the thermal insulation per minute. This very high value is attributed to i) the use of copper, which has a much lower energy density than Si or FeSiB; ii) the very small scale of the prototype, which is several orders of magnitude smaller than those considered in the previous sections; and iii) the relatively thin thermal insulation layer. Assuming a TPV conversion efficiency of 22 % (which has been reported for these cells 40) and neglecting heat loss in the electrodes, the discharge efficiency (defined as the delivered electricity during the phase change divided by the total stored energy) and the discharge duration would be 6.6 % and 0.8 hours, respectively, which are in the range of values explored experimentally. If the heat loss would be drastically reduced to 3 %/day (i.e., passing from 156 W to 0.225 W of steady heat loss), the discharge efficiency and the storage duration would be increased to 21.9 % and 2.7 hours, respectively. Obviously, manufacturing such a well thermally insulated system is hardly attainable at these small scales, where the high surface-to-volume ratio leads to very high amount of heat loss. This again points to the relevance of scale in LHTPV systems. 5 Conclusions LHTPV batteries that are based on Si (m.p. of 1414 ºC) or FeSiB (m.p. 1157 ºC) PCM can reach very low costs per energy capacity (< 10 €/kWh) at large scales, and thus, both are appealing solutions for long-duration storage applications. Their very high latent heat (1.2 MWh/m3) enables very dense energy storage and small surface-to-energy ratios, ultimately resulting in relatively low thermal insulation requirements and low cost. The lower melting point of FeSiB further relaxes the thermal insulation requirements and enables lower costs per energy capacity, especially at smaller scales. Systems as small as 1 MWh are in principle possible using FeSiB PCM, whereas systems over 10 MWh are necessary for Si PCM to mitigate the impact of the more expensive thermal insulation system. The combination of high energy density and lower melting temperature of FeSiB makes this system especially appealing for long duration storage applications, where a low-cost and high-efficient thermal insulation is particularly important. Optimal heat losses, resulting from an optimal balance between cost and thermal insulation efficiency, are significantly lower in FeSiB 22 than in Si-based systems, offsetting the higher TPV conversion efficiencies attainable in Si-based systems. Besides, the long discharge duration ensures a minimal temperature gradient through the PCM during discharge, which is particularly important to ensure a low cost per power in such ‘low’ temperature FeSiB-based systems. On the contrary, the higher melting point of silicon enables a much higher TPV power density, ultimately resulting in a lower cost per discharge power capacity. Thus, Si-based systems are better suited for shorter duration applications, where the cost per power is more relevant. The cost per power capacity can be reduced in both kinds of systems by using very low bandgap TPV cells, like InGaAsSb (bandgap of 0.53 eV), or by designing the crucible to minimize the temperature gradients in the PCM during the discharge. In this work, a hollow cylindrical crucible unit has been considered, in which the temperature gradient is minimized by reducing the difference between crucible’ inner and outer radius. This unavoidably brings a reduction in the amount of PCM per unit crucible, ultimately resulting in a lower energy density and a higher cost per energy capacity. Thus, a trade-off exists between cost per energy and power capacities that relies on the crucible design. Besides of long duration storage applications, LHTPV brings some key advantages over Li-ion batteries for dispatchable cogeneration in fully electrified systems. The optimal solution takes advantage of the very low cost and high energy density of LHTPV to store the vast amounts of heat that otherwise should be stored at much lower energy densities in (e.g.) hot water tanks. As a result, the LHTPV-based solution has a slightly lower cost and a much higher energy density than a solution based on Li-ion batteries that relies on hot water tanks for heat storage. Like in long duration storage applications, large scales favor the use of LHTPV over Li-ion due to the lower cost per energy capacity. Large scales also enable lower cost of solar PV installations, which further benefit the use of a (cheaper) LHTPV system over a (more efficient) Li-ion battery in selfconsumption applications. An experimental test bed unit has been fabricated in the frame of the European Project AMADEUS that is intended to test materials and devices that will be eventually incorporated in an optimized LHTPV system. The first experimental results using copper PCM and GaSb TPV cells have been presented, illustrating the capabilities of this experimental setup to guide future developments. 23 6 Resource availability 6.1 Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Alejandro Datas ([email protected]). 6.2 Materials availability This study did not generate new unique materials. 6.3 Data and code availability The data that support the findings of this study are available from the Lead author, upon reasonable request. 7 Acknowledgement This work has been partially funded by the European FET-OPEN projects AMADEUS (grant agreement n. 737054) and NATHALIE (grant agreement n. 945858); by the projects Termocell (ENE2017-86683-R) and GeTPV (PID2020-115719RB-C22) from the National program Retos de la Sociedad funded by the Spanish Ministry of Economy, Industry and Competitivity; and by the project ANDREA from the "programa de apoyo a la realización de Proyectos de I+D para jóvenes investigadores 2019” funded by the Regional Government of Madrid. A. Ramos acknowledges the Serra Húnter Program from the Generalitat de Catalunya for her Serra Húnter Fellow post. 8 Author contributions Conceptualization: A.D.; Funding acquisition: A.D.; Investigation: A.D, A.L.C, E.L., A.R,; Methodology: A.D, A.L.C, E.L., A.R,; Project administration: A.D; Resources: A.D, C.dC.; Software: A.D., A.L.C; Supervision: A.D.; Visualization: A.D.; Writing – original draft: A.D.; Writing – review & editing: A.D, A.L.C., E.L, A.R, C.dC. 9 Declaration of Interest There are no competing interests 24 10 References 1. Datas, A. (2021). Ultra High Temperature Thermal Energy Storage for Dispatchable Power Generation. In Reference Module in Earth Systems and Environmental Sciences (Elsevier). 2. Datas, A., Ramos, A., and del Cañizo, C. (2019). Techno-economic analysis of solar PV powerto-heat-to-power storage and trigeneration in the residential sector. Appl. Energy 256, 113935. 3. Datas, A., Ramos, A., Marti, A., del Canizo, C., and Luque, A. (2016). Ultra high temperature latent heat energy storage and thermophotovoltaic energy conversion. Energy 107, 542–549. 4. Okazaki, T. (2020). Electric thermal energy storage and advantage of rotating heater having synchronous inertia. Renew. Energy 151, 563–574. 5. Amy, C., Seyf, H.R., Steiner, M.A., Friedman, D.J., and Henry, A. (2018). Thermal energy grid storage using multi-junction photovoltaics. Energy Environ. Sci., 334–343. 6. Burger, T., Sempere, C., Roy-Layinde, B., and Lenert, A. (2020). Present Efficiencies and Future Opportunities in Thermophotovoltaics. Joule. 7. Datas, A., and Vaillon, R. (2021). Chapter 11 - Thermophotovoltaic energy conversion. In Ultra-High Temperature Thermal Energy Storage, Transfer and Conversion Woodhead Publishing Series in Energy., A. Datas, ed. (Woodhead Publishing), pp. 285–308. 8. Safarian, J., and Tangstad, M. (2021). Chapter 4 - Phase change materials for high-temperature operation. In Ultra-High Temperature Thermal Energy Storage, Transfer and Conversion Woodhead Publishing Series in Energy., A. Datas, ed. (Woodhead Publishing), pp. 85–111. 9. Albertus, P., Manser, J.S., and Litzelman, S. (2020). Long-Duration Electricity Storage Applications, Economics, and Technologies. Joule 4, 21–32. 10. Mongird, K., Viswanathan, V., Alam, J., Vartanian, C., and Sprenkle, V. (2020). 2020 Grid Energy Storage Technology Cost and Performance Assessment (U.S. Department of Energy). 11. Laughlin, R.B. (2017). Pumped thermal grid storage with heat exchange. J. Renew. Sustain. Energy 9, 044103. 12. Datas, A. ed. (2021). Ultra-High Temperature Thermal Energy Storage, Transfer and Conversion (Woodhead Publishing). 13. Parham, J., Vrettos, P., and Levinson, N. (2021). Chapter 13 - Commercialisation of ultra-high temperature energy storage applications: the 1414 Degrees approach. In Ultra-High Temperature Thermal Energy Storage, Transfer and Conversion Woodhead Publishing Series in Energy., A. Datas, ed. (Woodhead Publishing), pp. 331–346. 14. Rhim, W.-K., and Ohsaka, K. (2000). Thermophysical properties measurement of molten silicon by high-temperature electrostatic levitator: density, volume expansion, specific heat capacity, emissivity, surface tension and viscosity. J. Cryst. Growth 208, 313–321. 31 Table 2. Techno-economic assumptions for the components shown in Figure 10. Ambient temperature is assumed 25 ºC. Component Parameter Value PV installation Cost per power capacity 900 €/kW Nominal PV power installed Optimized (kW) Hot water storage Cost per energy capacity 30 €/ kWh Energy capacity Optimized (kWh) Heat loss 0.1 W⋅K−1⋅dm−3/2 Electric heater efficiency 100 % Temperature of storage 60 ºC Height of the crucibles Optimized (m) LHTPV battery Cost per energy capacity Calculated for each size and heat loss (€/kWh) Energy capacity Optimized (kWh) Cost per input power capacity 20 €/kW Input power capacity Optimized (in (kW) Cost per output power capacity Calculated for each storage duration (€/kW) Output power capacity Optimized (kW) Self-discharge (heat loss) Optimized (%/day) Li-ion battery Cost per energy capacity 87 – 145 €/kWh Energy capacity Optimized (kWh) Cost per input power capacity 52.5 – 60.8 €/kW Input power capacity Optimized (kW) Cost per output power capacity 0 €/kW Output power capacity Equal to the input power capacity Self-discharge 0 %/day Round-trip efficiency 90 % Electric grid Cost of grid electricity 0.17 €/kWh 35 Cost of grid power capacity 50 €/kW 35 Price of electricity injected to the grid 0 €/kWh Other economic variables Weighted Average Cost of Capital 4 % 35 Inflation 2 % 35 Lifetime of all technologies 25 years Figure 1 Click here to access/download;Figure;Fig1.tif Figure 2 Click here to access/download;Figure;Fig2.tif Figure 3 Click here to access/download;Figure;Fig3_new.tif Figure 4 Click here to access/download;Figure;Fig4_new.tif Figure 5 Click here to access/download;Figure;Fig5.tif Figure 6 Click here to access/download;Figure;Fig6_new.tif Figure 7 Click here to access/download;Figure;Fig7.tif Figure 8 Click here to access/download;Figure;Fig8.tif Figure 9 Click here to access/download;Figure;Fig9.tif