Techno-economic selection and initial evaluation of supercritical CO 2 cycles for particle technology-based concentrating solar power plants

In this study, the techno-economic performance of supercritical carbon dioxide (sCO 2 ) power cycles in concentrating solar power plants based on particle technology is assessed. A simpli ﬁ ed levelized cost of electricity calculation was used to investigate the effect of cycle parameters, compare cycle layouts and allow for comparing optimized sCO 2 power blocks with steam technology. Results showed that simple cycle layouts with fewer components and lower cycle parameters lead to the lowest energy cost. This is caused by (a) fewer components, (b) lower primary heat exchanger, turbine as well as recuperator cost if the turbine inlet temperatures is limited and (c) a lower cost of the thermal storage system if the sCO 2 temperature increase in the primary heat exchanger is large. Nevertheless, even the most economical sCO 2 variants generate electricity at a 10 % higher cost than a steam reference system and a signi ﬁ cantly lower ef ﬁ ciency. These results held true when changes were made to cost models. Finally, it was shown that the cost of main sCO 2 equipment would have to be reduced by 30 % e 50 % to reach cost parity with steam systems. These ﬁ ndings will need to be con ﬁ rmed with more detailed off-design simulations and optimized solar ﬁ eld components.


Introduction
It is generally agreed on, that future electricity generation has to come predominantly from renewable energy sources. Compared with the other technologies that allow for a large increase in deployment, i.e. wind power and photovoltaics, Concentrating Solar Power (CSP) can be equipped with a cost-effective, multi-hour thermal energy storage. It is, therefore, not a fluctuating source to an electric grid but can offer dispatchable power on demand.
In order to make CSP plants more cost competitive with alternative electricity generation technologies, for example fluctuating renewables plus electric batteries, the levelized cost of electricity (LCOE) generated by them needs to be lowered. Typically, the power block is the subsystem with the lowest efficiency in a CSP plant. An increase in its efficiency would decrease the size of all solar equipment (collector field, receivers, towers and thermal energy storage), which accounts for the majority of a solar tower plant's direct costs [1]. Furthermore, the power block itself accounts for approximately 30 % of these costs. Improvements in its efficiency or cost can, therefore, have a large impact on CSP plants' technical and economic performance.
For many years, power blocks employing supercritical carbon dioxide (sCO 2 ) as the working fluid have been suggested to reach both, higher thermal efficiencies and lower costs, compared with state of the art steam cycles [2]. These potential advantages make the technology attractive for utilization in next generation CSP plants and several studies have been conducted on predicting the performance of such systems [e.g., 3,4].
Most of these studies feature comparisons of different cycle layouts, mainly simple recuperated cycles, recompression cycles, partial cooling cycles and even more complex ones. Glos et al. [5], for example, compared the thermal efficiency of three CO 2 cycles with that of a steam reference system. They found a performance improvement only for a high-performance recompression cycle with reheat and intercooling, not for a simple recuperated cycle, and only if highly effective recuperation is assumed. Ho et al. [6] calculated the investment cost of CSP plants featuring several cycles with identical power rating. A simple recuperated and a recompression cycle had very comparable total cost and thermal efficiency.
Crespi et al. [7] as well as Neises and Turchi [8] modeled CSP systems with molten salt as the heat transfer medium, which induces strict limitations on temperatures and high cost penalties on small temperature differences between hot and cold storage tanks. With these effects considered, they each identified partial cooling cycles as the most economical sCO 2 cycle layouts (excluding configurations that are not suitable for CSP applications). Furthermore, both studies found that a simple recuperated cycle had lower or the same LCOE as a recompression cycle (without reheat or intercooling). Very few studies could be found that compare the techno-economic performance of power plants employing sCO 2 cycles with those employing state-of-the-art steam cycles and none of them included particle technology. Cheang et al. [9] compared a recompression and a partial cooling sCO 2 cycle with two steam cycles. As the modeled plants were designed using molten salt as the heat transfer fluid, the maximum sCO 2 temperature was limited to 580 C and thermal efficiencies were found to be moderate. Cheang et al. concluded that existing steam cycle technology provided higher thermal efficiencies as well as lower installation costs and should therefore be pursued. Crespi et al. [7] derived ranges of LCOE for molten salt CSP plants with a steam and a sCO 2 recompression power block, respectively, using probabilistic cost models. Both configurations resulted in similar ranges, however, the identified spread of LCOE values was large.
Within the CARBOSOLA Project (funded by the German Ministry for Economic Affairs and Energy), Siemens Energy AG and the DLR intend to assess the economic performance of a next-generation sCO 2 CSP plant. In a previous publication by the authors of the present study [10], the techno-economic performance of sCO 2 cycles was compared based on cost models from literature. Under the chosen assumptions, systems based on molten salt as the heat transfer medium were found to lead to higher LCOE values than those based on particle technology.
Due to the lack of agreement in the literature on the optimal sCO 2 cycle for high-temperature CSP applications, a pre-assessment of a multitude of sCO 2 cycles and variants was conducted in the present study, using new cost and performance correlations for major sCO 2 cycle components. The components in the solar particle loop of the plant (namely, heliostat field, receiver, storage system and transport system), were modeled in a simplified manner to attain approximations for the annual electrical output of the plant and, therefore, be able to calculate estimated LCOE values. Based on this figure of merit, the most promising cycle layouts and parameters were chosen for further, more detailed studies. Furthermore, LCOE values of state-of-the-art steam cycles were calculated with the same model, allowing for a direct comparison of the two technologies in a particle technology-based plant.

Modeling and simulations
In this section the boundary conditions, details on the technical and economic modeling and the optimization approach are presented. Furthermore, reference systems featuring a steam power block are defined.

Location, solar field and particle loop modeling
The approximate capacity of the modeled power plant and its location are representative of a typical solar tower plant. The location has a high cumulative annual direct normal irradiation (DNI, see Table 1). In a typical year, the ambient temperature rarely exceeds 35 C or drops below 0 C at an annual mean of 19 C.
The solar receiver is based on the CentRec® technology [11]. As this particle receiver is a cavity receiver with a small aperture opening, multiple towers are foreseen which feature individual heliostat fields. A schematic of such a particle loop is depicted in  Fig. 1. Important performance indicators of the receiver and heliostat field, which are based on initial simulations with the tool Visual HFLCAL [12] as well as of the complete plant are presented in Table 1. The receiver outlet temperature was fixed at 900 C as this has been demonstrated for the technology [13], although higher values promise even better economic performance [14]. The cold tank temperature was calculated for each individual configurations depending on the sCO 2 inlet temperature to the particle heat exchanger and its terminal temperature difference. For a given design point power block efficiency and particle temperature spread, the particle heat exchanger can be sized. The thermal energy storage (TES) system capacity and, therefore, particle inventory are designed to allow for 12 h of full-load PB operation. Under the design point conditions and efficiency estimates defined in Table 1, the heliostat fields, receivers, towers and particle transport systems are sized. Based on this information, the cost of the subsystems can be calculated with the cost models presented in Section 2.3. The annual electricity yield of the plant, E e, a , is estimated in a simplified manner by multiplying the cumulative annual DNI, DNI a , with the collector area, A heliostats , and the annual average efficiencies of collector field, receiver, for dumping and of the power block: Âh collector;a h receiver;a h dumping;a h PB;a : (1)

sCO 2 power cycle modeling
This study's focus is on the performance and economics of sCO 2 cycle power blocks in CSP plants. As a large number of cycle variants is to be compared in the initial stage, the annual energy yield calculation is simplified according to Equation (1). Therein, no hourly calculations are conducted for off-design ambient or load conditions of the power block. Instead, annual average values are used to approximate the electricity generation of any power cycle.
The only PB-related data that is adjusted for every variant in the energetic calculations is the design point net power block efficiency, h PB,net,dp , which is calculated using the power plant simulation tool Ebsilon Professional v.14.03 by STEAG Energy Services GmbH, and, in consequence, the thermal input to the power block. Furthermore, parameters needed as input for the cost model of the sCO 2 power block (see Section 2.3) are derived from these simulations. Thermodynamic results were validated with data from the literature and very good agreement was found.
Based on a literature review, a total of ten process layouts were chosen to be modeled. They were simple recuperated cycles and recompression cycles with or without reheat (RH) or intercooling (IC) as well as partial cooling cycles with or without RH (see Table 2). The respective schematic of two cycles is shown in Fig. 2. The remaining cycle layouts can be derived by removing the highlighted components.

Economic models
The methodology of the economic model is visualized in Fig. 3. The direct cost for power block equipment, C, is calculated according to mostly confidential models based on values of scaling factors (e.g., power rating or conductance-area product, UA), which are outputs of the Ebsilon models The specific values of the parameters a, b, c, d and e as well as the chosen scaling factor, x, are provided in Appendix A except for confidential information. The reference temperature, T reference , for temperature-dependent cost adjustment is the maximum medium temperature in the component. For example, the equipment cost of a primary heat exchanger, PHX, is calculated as with the values of d and e being confidential and T Pa,in representing the particle inlet temperature. It should be noted that no inflation adjustments were made due to the relatively narrow time window in which the cost figures were published (between the years 2018 and 2020). Additionally, indirect costs of a technology provider including profits and contingencies are estimated as a cost adder of 83 % for all steam PBs and of 67 % for all sCO 2 PBs (the latter lower value is meant to account for lower predicted civil and installation costs due to more compact equipment) All items included as indirect costs are listed in Fig. 3.
The costs of all other subsystems of the power plant are calculated on the EPC (Engineering, Procurement and Construction) company level. The underlying correlations for these costs are also given in Table A5. To derive the total investment cost of the project, costs for EPC services and profit as well as owner services are added, which accounts for 31.4 % on top of EPC direct costs. The fixed charge rate, FCR, is calculated as 9.37 % for a project lifetime of 25 years and an annual interest rate of 8 %. Annual operation and Fig. 1. Schematic of the solar particle loop.

Steam reference cycles
In order to compare the cost and performance results of sCO 2 PBs to commercially available technology, two steam cycles were modeled with the identical technological and economic assumptions, except for indirect costs (see Section 2.3) and, of course, PB equipment costs. The two reference cycles are a state-of-the-art subcritical RH steam cycle with a turbine inlet temperature (TIT) of 550 C at a net PB efficiency of 42.7 % and a next-generation subcritical RH steam cycle with a TIT of 600 C and a net PB efficiency of 43.6 %. Cost estimates for steam PB equipment were provided by Siemens Energy.

Simulation and optimization
Each of the ten sCO 2 cycle models was used to calculate net power block efficiencies under varying input parameters. A list of these parameters, as well as the ranges in which they were varied can be found in Table 3. Additionally, some relevant assumptions, which were either derived from component designs by Siemens Energy or estimated based on literature, are presented.
The simulation results were then used to size the remaining components of the CSP plant according to the methodology described in Section 2.1di.e., to achieve the identical design-point electric power output for all configurationsdand to calculate the cost of all equipment and subsystems as well as the respective LCOE values according to Fig. 3. For each configuration, the primary heat exchanger terminal temperature difference was optimized to minimize the LCOE.

Results and sensitivity analysis
In the following, results of the techno-economic pre-assessment are presented in several steps, with different focuses. Firstly, the overall LCOE optimization is presented, followed by a closer look at the optimum values of some varied parameters. Secondly, the calculated LCOE values and power block efficiencies are compared to those of the steam reference systems. Finally, the calculations are repeated with adjusted cost models to show the results' sensitivity to economic assumptions.

LCOE optima with original cost model
The net power block efficiency as well as the resulting LCOE value of all cycle variants are shown in Fig. 4. Several observations can be made from the plot: 1. There is a well defined pareto front marking the configuration with the lowest LCOE for any value of the power block efficiency. 2. The minimum LCOE for the sCO 2 cycles is located at a net PB efficiency of approximately 37 %, which is much lower than that of the steam reference systems. 3. The minimum LCOE of the sCO 2 cycles is considerably higher than that of either of the reference systems (as has been found by Cheang et al. [9] for molten salt plants with a much more restricted temperature range). As the commercially available steam cycle with a TIT of 550 C is more economical than the 600 C variant, the former is used as the reference for comparisons. 4. Very high efficiencies can be reached (greater than 49.0 %), as proposed in various sources in the literature [4,14,16]. This, however, leads to an approximately 30 % higher LCOE compared with the most economical sCO 2 configuration. 5. The lowest-LCOE configurations over the range of PB net efficiencies are predominantly based on cycle types "01", "05", "09" or "10". This is more obvious in Fig. 5, where only the pareto front per cycle layout is shown. This means that IC or RH are not economical under the used cost assumptions (which has also been found by Crespi [17] for molten salt plants), with the potential exception of partial cooling cycles. The sudden increases in LCOE seen in some of the pareto fronts in this plot are caused by discrete changes in TIT. 6. Absolute LCOE values for all variants, including steam systems, are higher than anticipated and calculated in recent studies [e.g., 15,16]. However, these studies' economic assumptions, especially the fixed charge rate and the heliostat costs, are more optimistic than in the present study.

Optimum parameters
The low efficiencies of cost-optimized cycles is surprising given that sCO 2 power blocks are commonly proposed as a highefficiency technology, at least in the field of CSP [8,14]. Interestingly, an optimization for LCOE benefits cycles with comparatively low TITs (see Fig. 6), which is contrary to findings in other studies, where either TITs greater than 700 C are defined [7,16] or even found as an economic optimum [18]. This indicates that those components which are cost sensitive to the cycles' maximum temperature are dominating the overall cost. These are especially the PHXs and turbines through temperature-dependent cost multipliers (see Appendix A), as well as recuperators (due to a larger temperature increase and, thus, more heat being recuperated).
Furthermore, a higher TIT decreases the temperature difference at the hot side of the PHX, meaning that larger and more expensive heat exchangers are needed. This is visualized in Fig. 7, where the particle and sCO 2 temperature evolution in a PHX is shown for two, otherwise identical, configurations with different TITs. Additionally, the sCO 2 temperature at the inlet to the PHX, T sCO2;in , tends to be higher for configurations with a higher TIT or with a greater cycle efficiency, as the latter usually requires more effective recuperation. If the terminal temperature difference of the PHX, i.e. TTD PHX ¼ T cold tank À T sCO2;in , is kept constant, this leads to an increase in the  Table 3 Assumptions and parameters of sCO 2 cycles (y: relative to design inlet pressure; x: pressures below 75 bar were only simulated for partial cooling cycles).

Parameter
Unit cold tank temperature (also visible in Fig. 7) and, consequently, in the needed particle inventory as well as in the TES system's cost. The cost-optimized balance between PHX and TES system is found by iterating the terminal temperature difference of the PHX. The plot in Fig. 8 depicts the sCO 2 inlet temperatures to the PHXs (low-pressure, LP, and high-pressure, HP) as well as the cold tank temperature for those configurations that define the pareto front, i.e., those with the lowest LCOE. When moving towards highefficiency configurations, there is an obvious trend towards higher PHX inlet temperatures, which is partially caused by higher TITs and partially by more effective recuperation in recompression or partial cooling cycles. The cold tank temperature increases at an even higher rate, as the LCOE-optimized PHX terminal temperature difference (green line) increases from approximately 50 K for lowefficiency configurations up to approximately 150 K. The temperature spread in the TES system varies, therefore, between more than 500 K and a minimum of 250 K, with associated cost implications. An additional increase in structural and insulation costs for the cold tank due to higher operating temperatures has been neglected, which would further benefit low-efficiency configurations.
The range of values of further input parameters that resulted in pareto optima are the following: For non-partial cooling cycles, the influence of changes in compressor inlet pressure are small and a value of 75 bar is almost always optimal. Recuperators and cooling heat exchangers (coolers plus ICs) in the optimum configurations are large at optimum parameters of 10 MW/K to 40 MW/K (5 Ke15 K TTD) and 9 MW/K to 15 MW/K, respectively. The optimum recompression fraction ranges mostly from 35 % to 40 % except for partial cooling cycles, where it reached up to 46 %. These ranges are in agreement with other studies on optimum cycle parameters for the chosen boundary conditions, for example by Dyreby et al. [2].

Component costs
The LCOE of sCO 2 systems was found to be considerably higher than that of steam systems (see Section 3.1). In order to identify the main drivers, the direct equipment cost of sCO 2 components, power block indirect cost and relevant subsystem costs are shown in Fig. 9(top). The three configurations being compared are the steam reference case (blue bars), a sCO 2 system with a similar power block efficiency to that of the reference (orange bars) and, lastly, the sCO 2 system with the lowest LCOE (green bars). The main cycle parameters of these configurations are presented in Table 4. Comparing the cost contributions of all three systems, the following can be observed: C There is a significant difference in PHX cost between the sCO 2 case with comparable efficiency to the steam cycle and the other configurations. This is mainly caused by the increased TIT (to 600 C) and the use of RH, which necessitates an additional PHX component.  Table 2).   C Recuperators and coolers in sCO 2 cycles induce much higher costs than internal heat exchangers and condensers in steam cycles. The same is true for compressors, especially in complex cycles featuring several ones, compared with feed water pumps. C Costs for sCO 2 turbosets (i.e., turbines plus generator) and balance of plant (BoP) only have lower costs than the reference if the TIT is low and no RH is employed. C The total cost of the sCO 2 PB far exceeds that of the reference system unless a much lower cycle efficiency is accepted. In that case, the cost for other subsystems increases as they need to provide more energy to the PB. C The higher sCO 2 inlet temperatures of high-efficiency cycles lead to an increase in cold tank temperature (see Fig. 8). This leads to larger particle inventories and, therefore, higher TES system cost. This effect is even more pronounced for recompression cycles (not shown).

Sensitivity
During the definition of equipment cost models, it was observed that there is a large uncertainty associated especially with the costs of particle-sCO 2 PHXs. Due to the lack of any commercial or even demonstrator-size implementations to date, cost models for the component vary widely. Particularly challenging is the correct consideration of the effect of operating temperatures on used materials and, therefore, cost. So far, this has only been investigated in research projects. The PHX cost model, which was employed in all previously presented results of this study, is of the form Therein, f T,PHX is a confidential multiplication factor depending on the TIT and f 700 C represents the value of the factor at a TIT equal to 700 C. The rest of this correlations was derived from literature [14] and converted to be conductance-area product-specific by assuming an overall heat transfer coefficient equal to 300 W/m 2 K. The previously defined cost model results in a strong temperature-dependency of the PHX cost, which leads to potentially unrealistically low costs at low TITs. For a lack of better data available, the sensitivity of overall plant economics on the factor f T;PHX =f 700 + C was assessed by re-evaluating all concepts with the temperature-dependency removed. This is obviously a very conservative assumptions for the lowest TITs. The results derived by use of this cost model ("Carbo_02_fTconst") are shown in Fig. 9(bottom). Naturally, the PHX costs for all variants are higher compared with the previous cost model. Although the absolute costs are, thus, also higher for all sCO 2 cycles, the cost of the reference system increase as well and the difference in minimum LCOE between the fluids is smaller. However, the general trend is unchanged.
Furthermore, it was determined by how much the costs of major sCO 2 equipment would have to be lowered in order to reach cost parity with the steam reference cycle. To achieve this, a lower limit for cooler and IC costs (according to Siemens Energy) is assumed, and direct cost of turboset, recuperators, compressors as well as the indirect cost adder are multiplied by a factor (<1) for every configuration until parity is reached. Using the original cost model ("Carbo_02") as the base, it was found that those costs would have  to be halved to reach cost parity. If cost model "Carbo_02_fTconst" (s.a.) is employed, which penalizes the cost of steam cycles comparatively more than those of sCO 2 cycles, the same analysis showed that those costs would have to be lowered by at least 30 %.

Cycle selection
The selection of a small number of the most promising sCO 2 cycles is one of the key deliverables of this study. The pareto fronts per cycle shown in Fig. 6 imply that if the lowest LCOE is the sole figure of merit, a configuration of Layout 01 should be chosen, while if a higher cycle efficiency in sought after, Layout 05 or one the partial cooling layouts could be beneficial. As cost models have a large influence on the results of the presented analysis, the same comparison is shown in Fig. 10 for the previously introduced cost model with 50 % lower costs for certain equipment (see Section 3.4). It can be deduced that the same cycle layouts would be chosen from an economic point of view. While under these extremely optimistic cost assumptions Layout 01 does not have a clear cost benefit over Layout 05 and the partial cooling cycles any more, it still remains competitive.

Discussion of deviation from other studies' results
There are various reasons for the apparent disagreement of our findings with the common perception of sCO 2 power cycles as a highly promising economical technology.
Firstly, not many studies could be found in which the cost of sCO 2 power blocks is calculated in a similar level of detail as in the presented work. Here, cost assumptions are based on cost figures from an internationally active supplier of power plants and power cycle components. When subsystem-level costs are estimated for the PB, these are commonly significantly lower than those found in this study [e.g. 14]. Often, even cost targets are used [16].
Secondly, compared with studies in which PB costs are calculated, differences in the component cost models compared with the ones used here have been observed. Indirect costs are an important cost driver and there are differences in the way cost items are allocated either as direct or indirect costs. Compared to other studies [e.g. 7,18], our indirect costs are significantly higher, even though optimistic assumptions have been applied.
Thirdly, literature data for steam systems' investment cost or LCOE values are sometimes used as reference values for calculated values of sCO 2 PBs. An analogous modeling of a reference system with comparable input data and boundary conditions can limit the effect that uncertainties, especially of economic and financial models, have on the comparison.

Next steps
As a next step, several areas of the models should be refined. The presented study is based on design point evaluations. Deeper investigations should consider part-load operation conditions of the power cycle. An hourly energy yield model that takes into consideration power block efficiencies under non-nominal cooling conditions will be implemented in a follow-up study. However, as sCO 2 cycles are expected to be penalized more by changing ambient temperatures than steam cycles, these changes are not expected to tilt the scale in their favor.
A further detailed optimization of thermal storage and solar field configuration would help to slightly improve technical configurations and to find global LCOE minima for sCO 2 and the reference systems.
Lastly, many of the cost models for sCO 2 equipment, indirect power block cost and particle subsystems have a large uncertainty due to their low technology readiness level. While we are confident that our models represent the best state of knowledge, extensive component development and testing, which is currently under way in numerous sCO 2 -and particle technology-related pre-commercial projects, will increase accuracy in the future.

Conclusions
A simplified techno-economic model was developed to estimate the LCOE of next-generation CSP power plants utilizing an sCO 2 power block. A multi-tower particle receiver system based on the CentRec® concept with a receiver outlet temperature of 900 C and a 12 h thermal storage is used. Ten different power block layouts (derivatives of simple recuperated, recompression and partial cooling cycles) were modeled and their key parameters varied to find economic optima based on developed cost models for the main power block components and indirect cost. The LCOE optimum was, somewhat surprisingly, found for simple recuperated cycles without reheat or intercooling with a net power block efficiency of less than 37 %, much lower than the one of a state-of-the-art reference system with a steam cycle power block (42.7 %). As a general finding, simple recuperated and recompression cycles resulted in lower costs if reheat and intercooling was omitted.
Furthermore, a comparison with the steam reference system showed that the sCO 2 systems' LCOE is at least 10 % higher. As some of the cost models, especially the one of the particle-to-sCO 2 heat exchanger, have a high uncertainty, the economic comparison was repeated with variations to the original model. However, the general trend appeared mostly unchanged. It was found that the costs of sCO 2 power block main components as well as indirect cost adders would have to be lowered by 30 %e50 % to reach cost parity with steam systems.
Several refinements to the simulations are proposed, namely off-design modeling, solar field and thermal energy storage optimization as well as more accurate component cost models, which will hopefully be available in the future.   Table 2).
Methodology, Writing e review & editing.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Table A5
Cost models (*: confidential data; if no source is mentioned, the correlation was created within the CARBOSOLA Project; assumed exchange rate: 1 EUR ¼ 1.10 USD; _ V in : volumetric flow rate at inlet; H tower : height of receiver center above tower base; _ Q Rec; t : receiver thermal rating; Q TES : thermal storage capacity; y: Buck and Giuliano [14]; x: Weiland et al. [19])