Mapping the techno-economic potential of next-generation CSP plants running on transcritical CO2-based power cycles

Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Mapping the techno-economic potential of next-generation CSP plants running on transcritical CO2-based power cycles Pablo Rodríguez-deArriba a,∗, Francesco Crespi a, Sara Pace b, David Sánchez a aDepartment of Energy Engineering, University of Seville, Seville, Spain bDipartimento di Energia, Poltiecnico di Milano, Milano, Italy ARTICLE INFO Keywords: Supercritical CO2 sCO2power cycles CO2blends CSP plant Techno-economic assessment ABSTRACT Although the thermodynamic potential of transcritical/supercritical power cycles running on CO2mixtures for next generation Concentrated Solar Power plants has been already confirmed in literature, further investigation to assess the actual feasibility of this technology from a techno-economic standpoint is needed. In fact, large uncertainty is found when it comes to the estimation of the 𝐶𝑎𝑝𝐸𝑥 of the power block, and the same can be said for the solar subsystem when higher-than-SoA operating temperature are considered. In this paper, two CSP schemes, with different maximum operating temperatures, are studied: one employing molten salts and another based on solid particles. To overcome the high uncertainty in terms of cost estimation, a two-step analysis is developed: firstly, the 𝐶𝑎𝑝𝐸𝑥 of the entire plant, except for the power block, is calculated assuming correlations from literature. As a result, the minimum power block cost allowing an 𝐿𝐶𝑜𝐸 lower than a certain target is identified. Secondly, an inverse methodology is applied, setting the power block cost and assessing the minimum 𝐶𝑎𝑝𝐸𝑥 of the solar subsystem. As a result, a map is obtained showing the target 𝐶𝑎𝑝𝐸𝑥 to be accomplished by sCO2+CSP if a clear reduction of the 𝐿𝐶𝑜𝐸 of this technology is to be achieved. 1. Introduction Concentrated Solar Power (CSP) plants combined with supercritical carbon dioxide (sCO2) power cycles are widely believed to be a keyenabler of the complete decarbonisation of the power generation sector. This is due to the combination of various outstanding features of this technology, such as the high thermal efficiency, low footprint and high operational flexibility -notable features attributed to sCO2power cycles [1,2]- as well as high dispatchability, brought by the use of Thermal Energy Storage (TES). This last feature stems as a major advantage over variable renewable energy sources such as photovoltaics and wind. Nevertheless, the cost-effectiveness of CSP+sCO2is still unclear, and further investigation is needed to reduce the Levelised Cost of Electricity (𝐿𝐶𝑜𝐸) of this technology in order to make it truly competitive in the energy market. One major drawback of sCO2 power cycles, for instance, is that they exhibit a significant drop in efficiency if compression cannot be performed close to the critical point (31 ◦C). CSP plants are predominantly located in regions characterised by a high solar resource but also by high annually-averaged ambient temperatures. This, combined with the fact that (dry) air-coolers are typically the technology of choice for this kind of plant due to water scarcity in such regions, leads to a rise in the temperature at compressor ∗Corresponding author. E-mail address: [email protected] (P. Rodríguez-deArriba). inlet, with a consequent reduction in the thermal efficiency of sCO2 cycles. Specifically, a drop of about 4 percentage points is anticipated when compressor inlet temperature increases from 35 ◦C, a typical value employed in literature, to 50 ◦C, more representative of CSP applications in arid zones [3]. As a possible solution to this problem, the SCARABEUS project investigated the use of innovative power cycles based on CO2mixtures that can attain higher thermal efficiency than supercritical CO2and steam cycles [3]. The main idea behind the SCARABEUS concept is blending sCO2with certain dopants in order to increase the critical temperature of the resulting mixture above 31 ◦C, enabling condensation of the working fluid even at high ambient temperature, thus overcoming the aforementioned efficiency drop. Extensive research has been conducted by the SCARABEUS consortium to identify the most viable dopants to enhance the performance of sCO2cycles [3–7]. In particular, despite their high thermodynamic performance, mixtures containing TiCl4were deemed unsuitable due to their high toxicity and reactivity with water in air (humidity), which could compromise safety and operational integrity. Other dopants like C6F6, C4F8, and C2H3N exhibited good performance, aligning with the thermal requirements of https://doi.org/10.1016/j.energy.2024.133142 Received 31 January 2024; Received in revised form 31 July 2024; Accepted 8 September 2024 Energy 310 (2024) 133142 Available online 23 September 2024 0360-5442/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/bync-nd/4.0/ ). P. Rodríguez-deArriba et al. Nomenclature 𝑚𝑝Particle mass flow rate [kg/s]  𝑊𝑙𝑖𝑓 𝑡 Power consumption of the particles lift [W] 𝜂𝑙𝑖𝑓 𝑡 Particles lift mechanical efficiency [%] 𝐴𝑆𝑅 Solar receiver external area [m2] 𝐶𝑐𝑎𝑝𝑖𝑡𝑎𝑙 Capital cost [e] 𝑐𝑃 𝐵 Power block specific cost [e/kW] 𝐶𝑆𝐹 Solar field cost [e] 𝐶𝑆𝑅 Solar receiver cost [e] 𝐶𝑆𝑆 Solar subsystem cost [e] 𝐶𝑇 𝐸𝑆 TES cost [e] 𝐶𝑡𝑜𝑤𝑒𝑟 Solar tower Cost [e] 𝐶𝑎𝑝𝐸𝑥 Capital expenditures [e] 𝐶𝐸𝑃 𝐶𝐼 Chemical Engineering Plant Cost Index [–] 𝐶𝑅𝐹 Capital recovery factor [–] 𝐸𝑒𝑙,𝑦𝑖𝑒𝑙𝑑 Annual electricity generation [MWh/year] 𝑓𝑐𝑜𝑛𝑡𝑖𝑛𝑔𝑒𝑛𝑐𝑦 Safety margin factor for direct contingencies [%] 𝑓𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 Indirect cost factor over direct costs [%] 𝑓𝑛𝑜𝑚𝑖𝑛𝑎𝑙 Nominal discount rate [%] 𝑓𝑟𝑒𝑎𝑙 Real discount rate [%] 𝐻𝑆𝑅 Solar receiver height [m] ℎ𝑇 𝐸𝑆 TES equivalent storage capacity [h] 𝐻𝑡𝑜𝑤𝑒𝑟 Solar tower height [m] 𝑖Average inflation rate [%] 𝐿𝐶𝑜𝐸 Levelised Cost of Electricity [e/MWh] 𝑁Project lifetime [years] 𝑛ℎ𝑒𝑙𝑖𝑜𝑠𝑡𝑎𝑡𝑠 Number of heliostats [units] 𝑂𝐶𝐶 Overnight capital cost [e] 𝑂𝑝𝐸𝑥 Operating expenditures [e] 𝑃𝑛𝑒𝑡 Net power [MWe] 𝑅𝑀𝑆𝐸 Root Mean Square Error 𝑆𝑀 Solar multiple [–] 𝑆𝑜𝐴 State-of-the-art 𝑇 𝐼𝑇 Turbine inlet temperature [◦C] 𝑇 𝑃 𝐶 Total plant cost [e] ACC Air-cooled condenser ANN Artificial Neural Network CSP Concentrated Solar Power DNI Direct Normal Irradiance [W/m2] FFPR Free-falling particle Receiver g gravity acceleration [m/s2] Gen Generation HTM Heat Transfer Media HTR High-temperature recuperator LTR Low-temperature recuperator PB Power block PCHE Printed Circuit Heat Exchanger PHX Primary heat exchanger SAM System Advisor Model SCARABEUS Supercritical CARbon dioxide/Alternative fluids Blends for Efficiency Upgrade of Solar power plants TES Thermal energy storage conventional CSP plants employing Solar Salts. Nevertheless, their thermal stability above 600 ◦C remains uncertain and this limits their use in next-generation CSP plants that employ high-temperature Heat Transfer Media (HTM) [8]. In contrast, CO2-SO2mixtures, in spite of the risks associated with the high toxicity of sulphur dioxide and the associated corrosion issues if sulphuric acid is formed [6], stand out for their high cycle efficiency and thermal stability at temperatures exceeding 700 ◦C. This has led researchers at University of Seville to select this mixture for further development within the SCARABEUS project, focusing on operational strategies during part-load and off-design conditions [9, 10]. Preliminary characterisations are also underway for other mixtures such as CO2-SiCl4[11]. Several studies presenting the economic assessment of CSP and CSP with sCO2power cycles have been published in recent years, but their results are often inconsistent and strongly dependent on the assumptions considered. NREL’s Annual Technology Baseline (2022) [12] set the Total Plant Cost (TPC) for a 104 MWe (115 MW gross) state- of-the-art SoA CSP plant at 5646 US$/kW (solar multiple -SM- is 2.4, storage capacity is 10 equivalent hours). The cost of the steam turbine is estimated at 1330 US$/kW. The predicted 𝐿𝐶𝑜𝐸 varies with location, from 76 US$/MWh (2800 kWh/m2/year) to 97 US$/MWh (2281 kWh/m2/year), assuming a real Capital Recovery Factor (𝐶𝑅𝐹 , see Eq. (7)) of 4.9%. Locations with lower solar irradiance, such as Seville (reference location in this work), are expected to exhibit a lower capacity factor and, accordingly, higher 𝐿𝐶𝑜𝐸. Manzolini et al. studied various high-temperature CSP schemes in Seville [13]. The authors defined a CSP plant employing conventional Solar Salts as a benchmark. The TPC of this SoA plant was estimated at 8577 US$/kW (SM is set to 3 and the storage capacity is 16 h), with an 𝐿𝐶𝑜𝐸 of 166.8 US$/MWh. Notably, the steam turbine in this study has a rated power output of 20.6 MWe, suggesting that 𝐿𝐶𝑜𝐸 for a 90–100 MWe plant would be lower due to economies of scale. Additionally, a significantly higher 𝐶𝑅𝐹 of 9.36% was used, as compared to the previously mentioned reference value from NREL’s ATB. Neises studied the performance of a 50 MWe Recompression sCO2 cycle for CSP applications and assessed the economic performance of different cycle design points [14]. The expected capital cost of the power block ranged from 1200 US$/kW to 1600 US$/kW, with aTPC of 6200 US$/kW to 7200 US$/kW (2.4 solar multiple and 10 h of TES). The resulting 𝐿𝐶𝑜𝐸 ranges from 80 to 90 US$/MWh (2800 kWh/m2/year), which is higher than the previously mentioned value for SoA technology in the same location. This discrepancy is attributed to the plant’s strategy to maximise revenue from electricity sales rather than maximising power production (i.e.: capacity factor), utilising a dispatch algorithm that accounts for the actual distribution of hourly prices of electricity. Morosini studied various advanced CSP plant configurations in Las Vegas (2672 kWh/m2/year) with a SM of 2.8 and 12 equivalent hours of storage. When employing Solar Salts at 550 ◦C, the estimated cost of a Recompression sCO2cycle rated at 90.4 MWe was 1086 US$/kW, with a TPC of 6195 US$/kW and an 𝐿𝐶𝑜𝐸 of 106.3 US$/MWh. Alternatively, using a 89.6 MWe Recuperated Rankine cycle running on the mixture CO2-C2H3N enabled reducing the capital cost of the power block to 757 US$/kW, and the TPC to 5535 US$/kW; this resulted in an 𝐿𝐶𝑜𝐸 of 95.7 US$/MWh. These 𝐿𝐶𝑜𝐸 figures are significantly higher than those previously reported for similar locations and higher investment costs, primarily because this reference employs a higher discount rate than earlier studies (8%). From these references, it is evident that techno-economic analyses of CSP plants—whether conventional or employing innovative working fluids and/or advanced plant schemes—are subject to substantial uncertainty. Despite 𝐿𝐶𝑜𝐸 being recognised as the primary Key Performance Indicator for economic viability, this metric is highly dependent on factors such as plant location (solar resource), plant layout (scale, solar multiple, storage capacity), and financial parameters (e.g., discount rate, capital recovery factor). Moreover, significant uncertainty exists in estimating the Capital Expenditures (𝐶𝑎𝑝𝐸𝑥) of innovative technologies like power subsystems running on CO2mixtures. The existing literature dealing with 𝐶𝑎𝑝𝐸𝑥 estimation for these power cycles is based on a Energy 310 (2024) 133142 2 P. Rodríguez-deArriba et al. set of cost correlations for CO2equipment [15], which already exhibits considerable uncertainty even for pure carbon dioxide. The same applies to the cost estimation of the solar subsystem when configurations with high-temperature HTM are adopted. Bearing this in mind, an original two-step upstream analysis is employed to overcome the high uncertainty in cost estimations. This approach is one of the original contributions to literature of this paper, and consists of the following steps: (1) firstly, the 𝐶𝑎𝑝𝐸𝑥 is calculated using correlations taken from literature for all subsystems except the power block, which is the section of the plant with larger uncertainty. The minimum cost of the power block necessary to achieve the target 𝐿𝐶𝑜𝐸 (96 e/MWh) -an arbitrary upper limit set according to the objectives of the SCARABEUS project [16]- is then identified for each case; (2) secondly, an inverse methodology is used to set the cost of the power block and to assess the minimum 𝐶𝑎𝑝𝐸𝑥 of the solar subsystem accordingly, with the final aim of mapping the target 𝐶𝑎𝑝𝐸𝑥 that needs to be achieved by sCO2+CSP to reduce 𝐿𝐶𝑜𝐸 below SoA technologies based on steam turbines. This methodology is applied to transcritical power cycles running on a mixture of 80% CO2and 20% SO2, representing the first economic assessment of its kind in literature. Two CO2-based CSP plants, herein called Generations (Gen), are compared. Gen I considers state-of-the- art Turbine Inlet Temperature (TIT=550 ◦C), and makes use of a conventional solar subsystem technology based on Solar Salt as HTM coupled with two-tank TES. On the other hand, Gen II is representative of next generation CSP plants, capable of achieving 700 ◦C at turbine inlet, based on free-falling particle receivers (FFPR) and combined with a two-tank storage system at ground-level, employing hot and cold particles. 2. Computational environment A Matlab-based computational tool has been developed to aid the design and annual simulation of the solar energy plants. This tool integrates four key subsystems: solar field, solar receiver, Thermal Energy Storage, and the power subsystem. The power subsystem encompasses the power block (PB), the heat rejection unit (HRU), and the primary heat exchanger (PHX). Additionally, the platform employs specific assumptions for estimation of auxiliary loads and thermal losses. It is crucial to highlight that the utilised technology and models are tailored specifically for each generation of CSP plant. Detailed descriptions of these components are provided in the following subsections. The economic assessment is centred on a prototype facility situated in Seville, Spain. The meteorological data for this location was sourced from the EnergyPlus database [17]. The design values for the site’s Direct Normal Irradiance (DNI) and ambient temperature are set at 840 W/m2and 36 ◦C, respectively. These figures correspond to the 95th percentile in the annual distribution curve. The yearly direct irradiance at this site is estimated to be 1773 kWh/m2⋅year. The paper investigates two distinct configurations of CSP plants, each distinguished by the HTM employed: either liquid molten salts (Gen I) or solid particles (Gen II) (see Fig. 1). The molten salt-based solar plant, representing a state-of-the-art scenario, features a circular field around its central tower. Atop the tower sits a cylindrical external receiver, through which molten salts circulate. These salts, integral to the Thermal Energy Storage system, are stored in designated hot and cold tanks. A shell-and-tube heat exchanger serves as the PHX facilitating heat transfer between the salts and the working fluid in the cycle, which operates at TIT of 550 ◦C. Conversely, the solar plant using solid particles utilises free-falling particle receivers — cavitytype receivers — which require polar fields instead of circular fields. This design poses significant challenges in terms of land utilisation and optical performance, especially for large-scale plants, as heliostats located further from the tower have decreased optical efficiency. As proposed by Mills et al. [18], this study adopts a multi-receiver design, which incorporate three FFPRs receivers, facing north, east, and west, on a single tower. Storage of thermal energy is achieved through two ground-level silos, and a particle-to-working fluid moving packed-bed shell-and-tube heat exchanger is employed as the PHX that transfers heat to the power cycle. The use of solid particles enables the power block to operate at a higher temperature, set in this study to a TIT of 700 ◦C, allowing for a greater thermal-to-electric conversion efficiency. 2.1. Solar field For the simulation of the solar field, the SolarPILOT software was employed [21]. The simulation’s design point was established at the summer solstice. The placement of heliostats was guided by the ’representative profiles’ option, a method advocated in Wagner [22], involving simulations across six days at intervals of four hours. In this study, heliostats with a reflective surface measuring 144 m2were utilised. For simulating the multi-FFPR design within SolarPILOT, guidelines were adopted from the studies by González-Portillo et al. [23] and Mills et al. [18]. Essential parameters of SolarPILOT used in this study are concisely presented in Table B.1, found in Appendix B. Initially, SolarPILOT generated a set of 2000 random, viable designs by varying the number of heliostats (3000–20,000), tower height (200–300 m), and receiver height (10–50 m for molten salt receivers; 10–30 m for FFPR). These configurations were evaluated against a variety of sun positions throughout the year, based on solar declination angle as per Wagner [22]. Subsequently, an Artificial Neural Network (ANN) was trained using this dataset to predict the optical efficiency of a solar field, based on design variables (heliostat count, tower height, receiver area) and operating conditions (direct normal irradiance, sun position). For designs with multiple receivers, the ANN also calculated the distribution of thermal power across the different receivers. The accuracy of the ANN in estimating solar field efficiency is evident from the low Root Mean Square Error (RMSE) values - 0.38 percentage points for the surrounding field and 0.31 percentage points for the multi-receiver design, as illustrated in Fig. 2. Fig. 3 further confirms the accuracy of the ANNs. This figure compares the ANN-generated predictions of optical efficiency across different sizes of the solar field (as denoted by the number of heliostats) with the results derived from SolarPILOT. A consistent tower height of 210 m was maintained in these comparisons. The size of the molten-salt receiver was varied with the number of heliostats to keep the maximum flux below 1 MW/m2, in line with Eq. (2). The size for Free-falling particle receivers was kept constant at 15 ×15 m2. The comparative results display a robust correlation between ANN predictions and SolarPILOT calculations. 2.2. Solar receiver: Molten-salt receiver and free-falling particle receiver Molten-salt receivers are fundamentally composed of external cylindrical structures, each consisting of an array of panels formed into a cylinder, with each panel containing multiple parallel, vertical tubes. In these systems, a binary mixture of molten salts, commonly Solar Salt (60% NaNO3- 40% KNO3) in SoA CSP tower plants, serves as HTM. For these systems, the molten salt’s temperature typically rises from 290 ◦C to 565 ◦C when integrated with steam turbines in SoA plants. However, in SCARABEUS power cycles operating with a TIT of 550 ◦C, the temperature range for the molten salt is decreased and extends from 387.9 ◦C to 565 ◦C. In this research, the System Advisor Model (SAM) [24] was employed for simulating the thermal behaviour of the receiver. The study 1The schematic for Gen II represents a general concept. This study considered three particle receivers oriented to the North, East, and West, respectively, and used two ground-level particle silos for storage at 800 ◦C and 600 ◦C, instead of the tower-integrated storage option, which is considered not to be cost-effective [20]. Energy 310 (2024) 133142 3 P. Rodríguez-deArriba et al. Fig. 1. CSP plant layouts for Gen I (a) and Gen II1(b) schemes. Source: Adapted from [19]. Fig. 2. ANN’s Optical efficiency error histogram for the circular field (a) and multi-receiver field (b). Fig. 3. Comparative analysis of optical efficiency for various solar field configuration as predicted by the Artificial Neural Network and verified by SolarPILOT. focused on varying the receiver’s height while maintaining consistency in other design parameters such as aspect ratio, number of flow paths, number of panels, tube diameter, and thickness (as detailed in Table 1). In the context of solar plant engineering, the number of panels is typically adjusted to achieve a flow velocity of ≈6 m/s. However, for the sake of simplification in thermal performance characterisation, a constant value of 10 panels was adopted. It was observed that this particular parameter exerts a negligible impact on the thermal efficiency of Table 1 SAM parameters for molten-salt receiver simulation. Parameter Value Aspect ratio [–] 1.25 Tube external diameter [mm] 52.9 Tube internal diameter [mm] 49.6 Number of flow-paths [–] 2 Number of panels [–] 10 Receiver absorptance [%] 93 the receiver, leading to the decision not to vary it in the receiver model. Data tables linking the height of the receiver with corresponding salt mass flow rates and thermal efficiency were generated, to be integrated into a broader system analysis. For the calculation of auxiliary power required for pumping the HTM from the cold tank to the receiver, the methodology outlined by Rodríguez-Sánchez et al. [25] was utilised. For the solid particles-based CSP plant, a configuration incorporating three Free-falling particle receivers was selected. In each FFPR, as described in Ho et al. [26], particles that are directly heated by the concentrated solar radiation fall through the receiver. The chosen HTM is CARBO Accucast ID50, the properties of which are detailed in Ho et al. [27]. Particles are heated from 600 ◦C to 800 ◦C, with a diameter of 350 μm. All receivers were assumed to have an identical aspect ratio of 1 and same aperture area, which was also considered equivalent to the curtain area [18]. A 1-D numerical model of the FFPR was implemented in Matlab as per González-Portillo et al. [23], and the auxiliary power for lifting particles to the top of the tower is calculated using Eq. (1), where 𝑚𝑝denotes the total particle mass flow rate through the three receivers. Lift efficiency (𝜂𝑙𝑖𝑓 𝑡) was assumed to Energy 310 (2024) 133142 4 P. Rodríguez-deArriba et al. Fig. 4. Thermal efficiency of Molten Salt Receiver (a) and Free-falling Particle Receiver (b). Different receiver height. Aspect Ratio of Molten Salt Receiver equals to 1.25. Aspect Ratio of FFPR equals to 1. be 80%.  𝑊lift =𝑚𝑝⋅𝐻tower ⋅𝑔 𝜂lift (1) Fig. 4 presents the thermal efficiency of both Molten Salt Receivers (a) and Free-falling Particle Receivers (b) over a range of sizes, indicated by receiver height. FFPRs demonstrates a minimum incident power requirement for operation, which increases with receiver size. This effect, highlighted by González-Portillo et al. [28], is linked to the changes in absorptance within the particle curtain at reduced mass flow rates. This variance hinders the attainment of the target outlet temperature under low heat flux conditions. In contrast, such a phenomenon is not observed in molten salt receivers, where the absorptance remains constant across different operational conditions. 2.3. TES A ground-level Thermal Energy Storage system composed of two cylindrical tanks is considered for both Gen I and Gen II, employing molten salts in the former and solid particles in the latter. The height- to-diameter ratio is set to 0.5 and 2 for molten salts in Gen I and for particles in Gen II, respectively. A dead volume of 20% is assumed for both systems. The thermal losses are calculated assuming a thermal resistance of 4 m2K/W [23]. 2.4. Power subsystem The power subsystem includes three modules: power cycle, heat rejection unit and PHX. The power cycle used in this system is a transcritical cycle running on a binary mixture of 80%CO2-20%SO2(molar basis), whose detailed description can be found in previous publications by the authors [6,29]. A modular air-cooled heat exchanger with induced-draft axial fans is used to condense the mixture, thus minimising water consumption of the plant. The final design uses multiple units equipped with three axial fans each, two of them with single-speed drives and the other one with a variable frequency drive. This choice is considered a promising trade-off between enhanced performance and moderate capital cost increase [9]. Further research is needed to determine the optimal number of VFDs. PHX in Gen I and Gen II are different. For Gen I, a shell-and-tube heat exchanger with molten salts on the shell side and the working fluid flowing inside the tubes is employed. For Gen II, a particle-to-working fluid moving packed-bed shell-and-tube heat exchanger is used; for a detailed description of this component and a comparison with other existing technologies, the readers may refer to the work by Ho et al. [30]. Table 2 Power subsystem design parameters for Gen I and Gen II. Parameter Gen I Gen II Turbine inlet temperature [◦C] 550 700 Minimum cycle temperature [◦C] 50 50 Gross power output [MW] 100 100 Cycle thermal efficiency [%] 44.1 51.05 Air-cooled condenser fan power [kWe] 1181 885.0 PHX power consumption [kWe] 239.7 116.6 Net power output [MWe] 90.96 92.43 Net efficiency [%] 40.1 47.1 The power cycle is modelled in Thermoflex environment, modified with a series of user-defined modules to enable the simulation of SCARABEUS-specific components. The air-cooled heat exchanger is modelled in Matlab, as explained in past works by partners of the consortium [31–33], while a numerical code for the particle-to-working fluid shell-and-tube heat exchanger is also specifically developed in the same environment to design and simulate this component. To calculate the total conductance UA, the heat exchanger is modelled as a crossflow heat exchanger. The heat transfer coefficient on the CO2mixture side is determined using Gnielinski’s correlation whereas that on the (dominating) particle side is implemented following the simplified heat transfer model presented in Hertel & Zunft [34]. The Conductance Ratio Method cannot be employed to simulate this component in offdesign conditions, since that method is only valid for counter-flow heat exchangers. Instead, the complete code is simulated. A flow diagram describing the modelling of the power subsystem is provided in Fig. 5. Table 2 compares the main design parameters for the power subsystem of Gen I and Gen II. In this regard, cycle thermal efficiency refers to the ratio from gross power output to heat input to the cycle. On the other hand, net efficiency refers to the ratio from net power output of the power block to total heat input into the PHX. When calculating net power output, several factors are considered, including losses in the electric motor and generator, auxiliary power consumption of the air-cooled condenser, and power consumed by the HTM conveyance system from the hot tank to the cold tank through the PHX. The CSP plant is assumed to operate in base load, thus keeping net power output as close to the rated value as possible. Accordingly, the effect of part-load operation is disregarded in this work, which accounts for the impact of variable ambient temperature only. To provide a comprehensive overview, Fig. 6 illustrates the variations in net power (a) and net efficiency (b) against ambient temperature for two distinct technologies examined in this study: SCARABEUS Gen I and SCARABEUS Gen II. For ambient temperatures lower than design, Energy 310 (2024) 133142 5 P. Rodríguez-deArriba et al. Fig. 5. Flow diagram of the power subsystem simulation. Variables in bold are calculated within each block.  𝑊: electric power,  𝑄: thermal power. Fig. 6. Power subsystem: (a) net power and (b) net efficiency as a function of ambient temperature for SCARABEUS Gen I and SCARABEUS Gen II. the power block operates at its design point with reduced auxiliary power consumption of the air-cooled condenser; this results in a slightly higher net power output and efficiency. For ambient temperatures higher than the rated value, the air-cooled heat exchanger is not able to condense the working fluid at the rated condensation pressure, and this pressure must be increased, resulting in a higher minimum cycle temperature. However, doing so also requires decreasing TIT to keep the return temperature of HTM (i.e., temperature at the outlet from the PHX) equal to its design value. All this results in a drastic drop in both net power and efficiency. 2.5. Solar power plant design and annual simulations A comprehensive Matlab-based platform has been developed to perform the design and annual simulations of solar power plants, specifically addressing the specific requirements of both molten salt and solid particle systems. This computational tool requires inputs like the number of heliostats, tower dimensions, receiver size, and storage capacity. The location of the plant, along with relevant climate data, is also a critical input. Energy 310 (2024) 133142 6 P. Rodríguez-deArriba et al. The procedure begins with the initialisation of the ANNs, that are tasked with simulating the solar field’s performance. Distinct networks are utilised for the molten salt plant with a circular field and the solid particle plant with a multi-receiver, polar field design. This ANN is crucial for assessing the field’s optical performance under various configurations of solar field sizes, tower height and receiver dimensions, and solar positions. Following this, a thermal performance interpolation model for the receiver is established, contingent on the incident thermal input. For molten salt applications, receiver sizing tables were generated using SAM, whereas for FFPRs, detailed simulations are carried out within Matlab. In molten salt receivers, a key limitation is the maximum flux that the fluid can tolerate, approximately 1 MW/m2. This requires a minimum receiver size for a specified solar field aperture area. A correlation has been established, derived from SolarPILOT simulations, to determine this minimum receiver size as a function of the number of heliostats (𝑅2= 0.999): 𝐻SR,min = 13.26 + 1.093 ⋅10−3 ⋅𝑛heliostats − 2.305 ⋅10−8 ⋅𝑛2 heliostats (2) Conversely, the scenario for solar plants using solid particles differs significantly. Without practical flux limitations, these systems are not bound by a minimum receiver size relative to the solar field size, as noted in Ho et al. [35], what allows designing the receiver with a ‘closer-to-optimum’ size that balances optical and thermal efficiencies. After a sensitivity study, it was decided to set the size of the FFPRs at 15 ×15 m. This distinction affords solid particle solar plants a design flexibility not present in molten salt configurations. The simulation methodology, adapted from González-Portillo et al. [23], processes hourly data for a year. It aims to keep the CSP plant’s net power output as close as possible to its rated capacity, disregarding part-load operation effects and focusing solely on the impact of variable ambient temperatures. The simulation cycles through all 8760 h of the year. Fig. 7 provides a comprehensive flow diagram of the hourly calculations throughout the year. The simulation’s initial step determines if the solar subsystem can be activated, requiring a DNI above 200 W/m2and wind speeds below 15.65 m/s [23]. If conditions are favourable, the solar power incident on the receiver is calculated using the ANN, based on the current DNI and sun’s azimuth and elevation. The receiver model then assesses the thermal efficiency and heat transferred to the HTM. Subsequent steps involve charging and discharging the TES system. The net efficiency and power output of the power subsystem are determined, considering the ambient temperature and power requirements of the PHX. Based on the heat demand, available TES energy, and energy input from the receiver, the simulation decides whether to operate the power subsystem, also adjusting the TES energy level for the following hour. At the start (hour 0), the TES is assumed to be at its minimum level required to initiate the power subsystem. This minimum is set to 0 for molten-salt-based CSP plants, accounting for an existing molten salt baypass from the receiver to the PHX, and to 3 for particle-based CSP as indicated in González-Portillo et al. [23]. This stage ensures that the storage does not exceed its maximum capacity and maintains the minimum TES level required to operate the power subsystem. If the power subsystem was not in operation in the previous hour, necessitating a startup, there will be a proportional penalty to power production based on the startup duration. The start-up time of a steam turbine depends on the time lapsed from the previous shutdown, varying between 20–30, 30–50, or even 50–100 minutes, depending on whether the start-up is hot (idle for less than 8 h), warm (idle between 8–48 h), or cold (idle for more than 48 h). Considering the large capacity of the thermal energy storage systems addressed in our study, it can be assumed that all start-ups are warm, with a 30-minute start-up time if steam turbines were employed. Nevertheless, a shorter startup time of 10 min is assumed for SCARABEUS Gen I and II, based on the general assumption that supercritical Carbon Dioxide power cycles have better fast response capabilities than steam power plants, thanks to the smaller footprint of these systems, which leads to lower thermal inertia. In cases where the stored thermal energy in the TES is not enough to sustain a full-load operation of the power subsystem for an entire hour, the model assumes that the power subsystem continues to operate at full-load but ceases operation before the hour is completed, once all stored energy is utilised. This scenario ends with the system shutting down, simplifying the complexity of modelling varying load efficiencies and focusing on the efficiency at full operational capacity. In addition to the above processes, the simulation also accounts for auxiliary consumption of various subsystems, including the heliostats’ tracking (55 W per heliostat), startup energy for the heliostats (25 Wh per helisotat) and power consumed in transporting the HTM. The model also considers thermal losses in both the TES and the piping of the tower, ensuring a comprehensive and accurate representation of the plant’s operation. 3. Economic modelling The Overnight Capital Cost (i.e. total system cost assuming that design and construction take place instantaneously) is calculated from Eq. (3). Direct costs can be estimated as the capital cost plus a certain safety margin for direct contingencies, while indirect costs are calculated as a percentage of direct costs. Contingency and Indirect cost factors are estimated as 10% and 9%, respectively [23]. 𝑂𝐶𝐶 = (1 + 𝑓𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡)⋅(1 + 𝑓𝑐𝑜𝑛𝑡𝑖𝑛𝑔𝑒𝑛𝑐𝑦)⋅𝐶𝑐𝑎𝑝𝑖𝑡𝑎𝑙 (3) Capital costs are broken down into the cost of the solar subsystem (𝐶𝑆𝑆 ) and the cost of the power subsystem (𝐶𝑃 𝑆 ) (Eq. (4)). The former is calculated as the sum of the cost of the solar field (𝐶𝑆𝐹 ), tower (𝐶𝑡𝑜𝑤𝑒𝑟), solar receiver (𝐶𝑆𝑅) and Thermal Energy Storage (𝐶𝑇 𝐸𝑆 ). The cost of the power subsystem can be estimated from the individual costs of each component of the system or, in the absence of more detailed information, from a cost specific to the installed capacity. 𝐶𝑐𝑎𝑝𝑖𝑡𝑎𝑙 =𝐶𝑆𝐹 +𝐶𝑡𝑜𝑤𝑒𝑟 +𝐶𝑆𝑅 +𝐶𝑇 𝐸𝑆 +𝑐𝑃 𝐵 ⋅𝑃𝑛𝑒𝑡 (4) A cost index is used to compensate for the time value of money, thus reporting all the economic figures indexed to the same year-basis. A correction factor based on the average Chemical Engineering Plant Cost Index (CEPCI) is employed in order to compare the several cost correlations, which refer to different dollar-year basis depending on their publication date. While the values of this index cannot be published here, it is noteworthy that there has been a marked increase in cost reflected in this index. Notably, the CEPCI experienced significant annual surges, with an increase of 19% from 2020 to 2021, and 15% from 2021 to 2022. These changes indicate notable fluctuations in the economic landscape affecting this sector. Actually, these are the most significant increases in recent years, prior to which the highest interannual variation had been 6% only (from 2010 to 2011 and from 2017 to 2018). Having this into account, along with the need to harmonise the reference year of all economic figures (for comparability), all cost estimations were baselined to e2020. The cost of a solar field is commonly reported as a specific cost proportional to the total heliostat reflective surface. This factor is usually divided in two terms, one for the site preparation and another for the mirrors cost. For example, Meybodi et al. [36] reported a likely value of 20 US$/m2for site preparation cost, with minimum and maximum values of 15 and 21 US$/m2, respectively; and a likely value of 120 US$/m2for the heliostats, with minimum and maximum values of 90 and 150 US$/m2, respectively. Meybodi’s costs are not baselined to any specific year but can be assumed representative of 2015US$. The National Renewable Energy Laboratory (NREL), in their Annual Technology Baseline [12], report a value of 16 US$/m2for site preparation and 127 US$/m2for the heliostats (in US$2020), giving a total cost of 143 US$2020/m2. Future projections expects an important cost reduction in site preparation costs, down to 10 US$/m2, and for the cost of the heliostats (down to 50–75 US$/m2) [37]. Energy 310 (2024) 133142 7 P. Rodríguez-deArriba et al. Fig. 7. Flow diagram of the hourly calculations. W: power output in one hour, Q: thermal energy in one hour, E: Energy stored, X: boolean variable (True: on, False: off). It is crucial to note that, while specific costs based on different reference years have been presented, they are utilised as general parameters for scenario definition in the economic analysis within the context of this economic assessment; these values are therefore not linked to any specific year. Rather, two key scenarios are established: the current scenario, with a specific cost of 140 e/m2, and the future scenario, with a reduced cost of 60 e/m2. This distinction allows for the assessment of cost variation impacts on economic projections and the long-term viability of solar field projects. Cost correlations for the tower and solar receiver are reported in Table 3. The costs of the tower and receiver for a plant running on a molten salt receiver are taken from SAM [24]. The latter cost is then replaced by the costs reported by Albrecht et al. [38] for the free-falling particle receiver and the conveyor of particles in the tower. Baselined year of each correlation is indicated in the table. The cost evaluation of the TES system employing Solar Salt is conducted using a proprietary tool of the team at University of Seville, refined from previous research conducted by some of the team members [39]. The specific cost of the TES system based on molten-salts is directly linked to the capacity of the storage system and to the temperature difference between the hot and cold tanks. A reduced temperature gradient incurs a higher specific cost, necessitating a larger Energy 310 (2024) 133142 8 P. Rodríguez-deArriba et al. Table 3 Cost correlations for tower, molten salt rec., and falling particle rec. Equipment Cost Correlation Reference Tower 3⋅106⋅𝑒0.0113⋅(𝐻tower−𝐻SR 2−√𝐴ℎ 2)SAM [24], US$2020. Molten Salt Rec. 103 ⋅(𝐴SR 1571 )0.7SAM [24], US$2020. Falling Particle Rec. 37400 ⋅𝐴SR Albrecht et al. [38], US$2019. Particle Lift 58.37 ⋅𝐻tower ⋅𝑚𝑝Albrecht et al. [38], US$2015. Fig. 8. TES specific cost [e/kWh,th] as a function of storage capacity [GWh,th] for three different configurations: molten salts with temperature difference of 275 ◦C (SoA), molten salts with temperature difference of 177 ◦C and solid particles with temperature difference of 200 ◦C. inventory of storage medium for a certain amount of stored energy. This is notably disadvantageous for SCARABEUS Gen I technology, where the temperature difference is 177 ◦C — substantially lower than the 275 ◦C temperature difference typical of state-of-the-art CSP plants with steam turbines. The implementation of a Thermal Energy Storage system with solid particles has also been studied in literature for CSP plants making use of falling particle receivers. The storage cost can be derived from the methodology proposed by Albrecht et al. [38], which aggregates the costs associated with the hot storage container, the cold storage container, the particles — including the volume of non-storage particles necessary to fill the heat exchanger and particle loss -, the lift from the hot container to the heat exchanger, and the lift from the PHX outlet back to the cold container. To calculate the cost of the lifting mechanism, the same formula used for the receiver’s lift is used, with the appropriate corrections to account for the height of the cold tank and the particle heat exchanger. Fig. 8 compares the specific cost (e2020) of TES based on molten salts and integrated with either a steam turbine or SCARABEUS Gen I power block, against the cost of a solid particle storage system integrated with a SCARABEUS Gen II power cycle. The diagram demonstrates that the cost for molten salt storage significantly escalates with a decrease in temperature difference, surging from 21.4 e/kWh for a 4 GWh system to 32.3 efor a capacity of 1 GWh (50% increase). Conversely, particle-based TES systems emerge as a cost-effective alternative for high-temperature CSP plants, achieving a specific cost of approximately 18.2 eper kWh. The 𝐿𝐶𝑜𝐸 is calculated following the methodology explained in the document issued by the International Energy Agency IEA [40]. This is a simple but widely used approach followed, for example, by NREL’s SAM [24]. Generally speaking, 𝐿𝐶𝑜𝐸 is calculated using Eq. (5). 𝐿𝐶𝑜𝐸 =𝑇 𝑃 𝐶 ⋅𝐶𝑅𝐹 +𝑂𝑝𝐸𝑥𝑓 𝑖𝑥 ⋅𝑃𝑛𝑒𝑡 𝐸𝑒𝑙,𝑦𝑖𝑒𝑙𝑑 +𝑂𝑝𝐸𝑥𝑣𝑎𝑟 (5) Total Plant Cost (TPC) are the capital expenditures required to achieve commercial operation of the power station. TPC differs from Table 4 Financial assumptions and other parameters used in the economic analysis, values taken from González-Portillo et al. [23]. Parameter Value Project lifetime - N [years] 30 Nominal discount rate - 𝑓nominal [%] 7 Average inflation rate - i [%] 2.5 Real discount rate - 𝑓real [%] 4.4 Capital recovery factor - CRF [%] 6.06 OCC in that TPC includes finance cost for the construction of the project. For simplicity, TPC and OCC will be assumed equal.2 Operational and maintenance costs (𝑂𝑝𝐸𝑥) are calculated according to the methodology explained in Appendix A. As indicated in Eq. (5), 𝑂𝑝𝐸𝑥 in power plants consist of both fixed and variable components. Fixed 𝑂𝑝𝐸𝑥 are those that do not change depending on the energy generated but, rather, depend typically on the installed capacity of the plant: r.g., staff salaries and land lease expenses. Variable 𝑂𝑝𝐸𝑥 do, on the other hand, depend on the energy produced by the plant and they typically include including consumables and parts with limited service life. Solar thermal power plants are designed and financed based on typical meteorological conditions for their location and specific operational modes. This allows for the planning of the cumulative operational hours of equipment, elaboration of maintenance plant (Long Term Service Agreements), etc. In this sense, variable and fixed 𝑂𝑝𝐸𝑥 are constant throughout the life of the plant, and both can be counted as fixed costs or as variable costs. In this study 𝑂𝑝𝐸𝑥 are reported as variable costs in e/MWh [41]. The methodology proposed to estimate 𝐿𝐶𝑜𝐸 assumes that the real discount rate (𝑓𝑟𝑒𝑎𝑙) is constant throughout the life of the project. This parameter can be calculated from the nominal discount rate and the inflation using Eq. (6). 𝑓real =1 + 𝑓𝑛𝑜𝑚𝑖𝑛𝑎𝑙 1 + i− 1 (6) The Capital Recovery Factor (𝐶𝑅𝐹 ) is the ratio from a constant annuity to the present value of receiving that annuity for the lifetime of the project, and it can be calculated from Eq. (7). CRF =1 𝑛 ∑ 𝑖=1 1 (1 + 𝑓real)𝑖 =𝑓real ⋅(1 + 𝑓real)𝑁 (1 + 𝑓real)𝑁− 1 (7) The financial parameters have a large impact on 𝐿𝐶𝑜𝐸. For this study, the assumptions made for project lifetime, nominal discount rate, and inflation rate for CSP projects are reported in Table 4. 4. Results 4.1. Annual energy production and reference case The computational platform described in earlier sections is used to calculate the annual yield of both Gen I and Gen II power plants. A sensitivity analysis is also conducted, varying the number of heliostats (equivalently, Solar Multiple) and energy storage capacity (equivalent hours of storage, ℎ𝑇 𝐸𝑆 ). The results are shown in Fig. 9. It is observed that, for the same number of heliostats and ℎ𝑇 𝐸𝑆 , the Gen I system is able to produce slightly more electricity than the Gen II system. This 2The Overnight Capital Cost encompasses not only direct construction costs but also a comprehensive margin for contingencies and indirect costs, thereby accounting for a significant level of financial uncertainty. NREL 2022’s Annual Technology Baseline [12] estimates that the financial costs during construction are approximately 4% of the OCC; nevertheless, this analysis deems that an additional 4% inflation of capital cost might be redundant, yielding overly conservative economic metrics. Energy 310 (2024) 133142 9