Thermo-economic assessment of an innovative power cycle for medium-temperature concentrated solar power plants

Thermo-economic assessment of an innovative power cycle for medium-temperature concentrated solar power plants Antonio J. Subires * , Antonio Rovira , Marta Mu˜ noz Energy Engineering Department, Universidad Nacional de Educaci´ on a Distancia (UNED), c/ Juan del Rosal, 12, 28040 Madrid, Spain ARTICLE INFO Keywords: Organic Rankine cycles Concentrated solar power Thermo-economic optimization Brayton cycles Rankine cycles Levelized cost of energy (LCOE) ABSTRACT Medium-temperature parabolic-trough concentrated solar power (CSP) plants still rely mainly on superheated steam-Rankine cycles, which limit efficiency improvements and cost reductions. This study proposes and evaluates a propane-based hybrid Rankine–Brayton (HRB) power cycle as an alternative for CSP plants operating below 400 ◦C and benchmarks it against steam-Rankine, organic Rankine (toluene), supercritical CO 2 recompression Brayton and HRB-isobutane cycles. A two-stage assessment is performed. First, a non-standardized parametric analysis identifies efficiency optima under identical heat-source conditions. Second, a standardized comparison fixes the solar field, thermal energy storage (TES), and total design-point heat-exchanger size across the cycles; a genetic algorithm optimizes their distribution among components to maximize net power without relying on component-cost models. Annual simulations are performed using hourly meteorological and electricity-price data for Seville, with revenue-maximizing dispatch. Results show that HRB–propane achieves a similar annual energy yield to the steam-Rankine baseline while delivering 1.3 % higher revenue and reducing power-block costs by 9.8–28.6 %, thereby lowering levelized cost of energy (LCOE) by 1.2–4 %. Compared with ORC–toluene, HRB–propane offers similar profitability with lower pressure ratios and above-atmospheric condensation, reducing air-ingress risk and avoiding working-fluid vent losses associated with vacuum operation. These findings suggest that propane-based HRB cycles can improve the techno-economic performance of CSP plants below 400 ◦C, supporting their consideration for next-generation solar-thermal systems. 1. Introduction Current policy frameworks worldwide have driven the rapid penetration of non-dispatchable renewables—primarily wind at utility scale and photovoltaic (PV) generation at both utility and distribution levels [1]. Limited deployment of energy storage, together with the lack of inertia support from PV and wind generation, creates grid challenges such as price volatility and frequencyand voltage-stability issues [2]. In Spain, several events in 2025 reflected these issues: on 28 April, a blackout occurred. Moments earlier, non-synchronous generation accounted for 64 % of total electricity supply, with 54 % coming from solar PV [3,4]. Between January and September 2025, 693 h of zero or negative prices occurred in Spain [5]. In this context, CSP remains a valuable technology due to its dispatchability and its contribution to system stability through synchronous generation. However, its relatively high levelized cost of energy is reflected in a much lower global deployment compared to PV: by the end of 2024, cumulative CSP capacity was about 7.6 GW, while PV accounts for around 1859 GW [6]. To address costs, recent efforts have focused on LCOE reduction. Since 2018, China has been the primary driver of new CSP projects, helping to drive prices down [6]. Although about 70 % of existing CSP plants are still based on parabolic trough collector (PTC) technology, central receiver systems are experiencing significant growth—both in commercial deployment and research—due to their potential to reach higher operating temperatures. These higher temperatures enable greater thermal efficiencies and help reduce the required size of the solar field, which can represent up to 60 % of the total plant CAPEX. This trend is consistent with next-generation CSP roadmaps, such as the U.S. Gen3 CSP program and China’s Solar Thermal Power Generation Blue Book, which prioritize >700 ◦C particle receivers and sCO 2 Brayton cycles [7,8]. These results agree with recent studies. For instance, [9] reported an LCOE of 91.6 $/MWh and annual generation of 277 GWh for a 100 MW tower plant in an arid region (Pakistan) confirming the growing techno-economic viability of tower CSP in arid climates. However, serious issues in recent central receivers CSP projects, particularly molten salt tank leakages, suggest that they have not yet * Corresponding author. E-mail address: [email protected] (A.J. Subires). Contents lists available at ScienceDirect Energy Conversion and Management: X journal homepage: www.sciencedirect.com/journal/energy-conversion-and-management-x https://doi.org/10.1016/j.ecmx.2025.101430 Received 24 October 2025; Received in revised form 15 November 2025; Accepted 26 November 2025 Energy Conversion and Management: X 29 (2026) 101430 Available online 28 November 2025 2590-1745/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC license ( http://creativecommons.org/licenses/bync/4.0/ ). achieved the same level of maturity and reliability as PTC technology [10–13]. Few innovations have been made in CSP technology with PTC over the last decade, when the largest capacity corresponding to this technology was installed [14]. Recent research efforts have mainly focused on exploring heat transfer fluids capable of exceeding the temperature limitations of current thermal oils, which are typically restricted to around 400 ◦C due to thermal degradation. Although commercial molten salts enable the maximum temperature to increase to 565 ◦C, thereby increasing cycle efficiency, the need for heat tracing to prevent the salts freezing (around 220 ◦C) reduces annual net energy production compared with thermal oils [15]. Beyond molten salts, [16] showed that supercritical CO 2 could achieve comparable thermal efficiency to commercial thermal oils in large-aperture parabolic-trough collectors at pressures above 80 bar, although with higher pumping power and strength material requirements. Moreover, advanced silicone-based oils such as HELISOL® 5A offer a wide operating range (−40 to 425 ◦C), and lower flammability and toxicity, although they are costlier than conventional thermal oils [17]. Regarding power block technology, the current state-of-the-art is based on steam-Rankine cycles with superheating, regenerative preheating, and reheating. The turbine inlet temperature for PTC plants ranges from 370 ◦C to 390 ◦C, with a high pressure of around 100 bar [18]. Intermediate reheating increases the steam quality at the turbine outlet to 80–90 %, without the need to decrease the high-pressure level value, which would reduce overall cycle efficiency. Maximum nominal efficiencies for such systems are around 39 % [19] with typical power output values from 50 MW to 200 MW [20]. No alternative power cycles have been identified in the scientific literature that offer comparable performance to the steam-Rankine cycle within the temperature range typical of CSP based on PTC, close to 400 ◦C. According to [21,22] the recompression supercritical CO 2 Brayton cycle (sCO 2 -RB) exceeds the efficiency of the superheated steam-Rankine cycle for turbine inlet temperatures between 450 ◦C and 700 ◦C, but with a CO 2 temperature of 32 ◦C and 53 ◦C at the cooler outlet, respectively. This is consistent with the next-generation CSP roadmaps for central receivers previously mentioned [7,8], but not with the current state of the art in PTC-based CSP, since the 400 ◦C HTF limit prevents the sCO 2 recompression Brayton cycle from outperforming the superheated steam Rankine cycle within the cooler-outlet temperature Nomenclature Acronyms CSP ConcentratedSolar Power HRB HybridRankine −Brayton HTF HeatTransfer Fluid ORC OrganicRankine Cycle PB Powerblock rpm Revolutions per minute sCO2−RB Supercritical CO2recompression Brayton cycle TES Thermal Energy Storage Symbols AMTD Arithmetic Mean Temperature Difference(K) AP Approach Point (K) BcConstant for installation costs(−) C Constant for equipment costs (−) CEPCI Chemical Engineering Plant Cost Index (−) CN CarnotFactor(−) cpSpecific heat (J⋅kg−1⋅K−1) D Diameter(m) DNI Direct Normal Irradiation (W⋅m−2) E Energy(J) Fh,add Qualifying factor for cycle heat supply(−) Fc,rej Qualifying factor for cycle heat rejection(−) FMMaterialFactor(−) FpPressurefactor(−) Fs,gen Entropy generation factor(−) h Enthalpy (J⋅kg−1) K Incidence angle modifier(−) L Length (m) LC Levelized Cost (M € ) LCOE Levelized Cost of Energy ( € ⋅MWh−1) LI LevelizedIncome (M € ) LMTD Logarithmic Mean Temperature Difference(K) ˙ m Mass flow rate (kg⋅s−1) P Pressure(Pa) ˙ P Power(W) rp Pressureratio(−) ˙ Q Thermal power (W) ˙ QhThermal power absorbedby thecycle from the heatsource (W) ˙ QcThermal power rejected by the cycle (W) ˙ qloss Collector thermal power losses per unit length (W⋅m−1) R Gas constant (J⋅kg−1⋅K−1) Re Reynoldsnumber(−) rCI Cost −to−income ratio(−) rPI Profits−to −income ratio(−) s Entropy(J⋅kg−1⋅K−1) SP Sizeparameter(−) T Temperature (K)  ThMean temperature of the heat supply (K)  TcMean temperature of the heat rejection (K) UA Global heat transfer coefficient x Area (W⋅K−1) ˙ V Volumeflow rate (m3⋅s−1) X Characteristic factor(−) x Bypass fraction(−) Subscripts BM Bare module comp Compressor des Design HX Heatexchanger ITD Initial temperature difference INC Income INV Investment is Isentropic mh Mainheater mv Maximum characteristic factor value off Off −design O&M Operation and Maintenance p Polytropic rec Recuperator tbm Turbomachinery turb Turbine Greek letters η Efficiency ΔP Pressuredrop ΔscEntropy decrease of the heat rejection ΔshEntropy increase of the heat supply ΔT Temperature difference(K) A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 2 range. Other studies focus on organic Rankine cycles (ORC), which are considered a competitive alternative to steam-Rankine cycles for lowpower applications (below 1 MW) and for heat source temperatures below 370 ◦C, such as low-grade waste heat recovery [23], biomass [24] and geothermal applications. However, ORCs are less suitable for CSP with PTC technology for several reasons. First, steam-Rankine cycles improve their performance as the size increases [25], mainly due to enhanced turbomachinery and the fact that greater system complexity becomes economically justifiable at larger scales. Second, higher turbine inlet temperatures in steam cycles allow for higher pressures, and therefore greater expansion ratios, improving specific work and efficiency while maintaining a high vapor quality at the turbine outlet. Regarding ORC, the increase in power is a drawback because they require higher mass flow rates, which demand significant pumping power, large inventory of organic fluids, and result in the use of turbines, a technology that is not as established as expanders for ORC [26]. Additionally, increasing the maximum temperature can introduce safety and stability issues, since some organic fluids may degrade [27]. Safety issues become even more relevant in power cycles where condensation takes place below the atmospheric pressure, as air can enter the circuit and be in touch with a flammable fluid. While some studies have investigated the use of ORC in CSP applications, they have focused on systems with low power output and temperature [28,29]. To date, only two commercial CSP-PTC plants with ORC-based power blocks have been developed [30,31]. Both have low power output and low maximum temperature. An alternative power cycle for CSP with PTC technology for high power output is the hybrid Rankine-Brayton cycle (HRB), whose application to CSP with PTC technology was studied in [32]. For a maximum HTF temperature of 400 ◦C, the HRB using propane achieves a higher efficiency than that of both the steam-Rankine cycle and ORC using toluene (one of the best fluids for that technology in terms of efficiency). An off-design analysis of the HRB was done in [33], where the suitability of propane over other fluids was verified. It is important to note that these studies do not include either an economic analysis of the HRB or an annual simulation analysis. As a novelty, this study evaluates the techno-economic and annual performance of a propane-based HRB cycle for parabolic-trough CSP, indicating potential economic improvements over the state-of-the-art superheated steam Rankine cycle, while achieving performance comparable to the ORC–toluene benchmark but without its operational drawbacks (vacuum condensation and toxicity concerns). To benchmark the results obtained, additional representative cycles are also simulated and compared in Section 2 (HRB-propane, HRB-isobutane, ORC-toluene, sCO 2 -RB, and a superheated steam-Rankine cycle with reheat). The calculation methodology follows these steps: In Section 3.1 parametric analyses are carried out to identify the optimal nominal operating conditions for each cycle, aiming to maximize efficiency while considering the same source temperature levels, without equipment sizing (power outputs or heat-exchanger areas). Then, the HRB-propane power block and other CSP components like the solar field and the thermal energy storage (TES) are sized, following the methodology described in Section 3.2 and considering the optimal input conditions previously identified. After that, all other cycles are sized so that their total heat exchanger surface is equivalent to that of the reference HRB–propane, while keeping the solar field and TES unchanged. To achieve this, a genetic algorithm is applied to maximize the net power output, as detailed in Section 3.3. This framework establishes a fair comparison across all cycles avoiding component sizing and cost estimation. Finally, for the economic evaluation, the yearly performance and the costs are required. In Section 3.4 the off-design models and the operation criteria for the annual simulations are defined. Besides, Section 3.5 presents the methodology and models to size the components of the HRB-propane and steam-Rankine power blocks required for applying the cost correlations, prior to its economic evaluation. The cost correlations, viability evaluation parameters, and overall economic scenario are presented in Section 4. The results and discussion are presented in Section 5. The HRB-component sizing results are not included in this work but can be consulted in [34]. Finally, the conclusions and future work are presented in Section 6. 2. Power cycles description The following sections present the layout of the reference power cycle (HRB-propane) and the other cycles considered for comparison (HRB-isobutane, sCO 2 -RB, ORC-toluene and steam-Rankine). The thermodynamic diagrams are provided solely for illustrative purposes. Propane and butane are considered since they are widely used as working fluids in ORC systems due to their favourable thermophysical properties, compliance with current environmental regulations (zero ODP and very low GWP), and suitability for medium-temperature heat sources [35]. Both fluids are classified as A3 according to ASHRAE Standard 34, meaning they are flammable but non-toxic. In addition, their relatively low critical temperature and pressure, together with condensation pressures above atmospheric at standard ambient conditions, offer several advantages: (1) transcritical cycles can be operated without excessively high pressure ratios, (2) turbine, recuperator and condenser size requirements are reduced, and (3) the risk of air ingress into the cycle is minimized. Finally, operating in a transcritical regime improves thermal matching between the sensible heat source and the working fluid during heat addition, which reduces entropy generation in the main heater and can increase cycle efficiency for finite-capacity heat sources. The sCO 2 recompression Brayton (sCO 2 -RB) cycle was included due to its technological similarity to the HRB configuration. Carbon dioxide is widely used in transcritical and supercritical power cycles because it is a natural, non-flammable, and non-toxic refrigerant (ASHRAE A1) with zero ODP and a very low GWP [36]. In addition, CO 2 is chemically stable and, unlike many organic fluids, does not have a temperature degradation limit, which enables its use across a broad range of heat-source temperatures. Although transcritical (Rankine or Brayton) and supercritical CO 2 cycles are both considered for power applications, the transcritical CO 2 configuration was not included in this analysis for two main reasons: (1) the critical temperature of CO 2 (31 ◦C) prevents condensation under the annual operating conditions of the plant location (Seville), disabling the feasibility of a Rankine configuration, and (2) optimization of the transcritical Brayton cycle by varying lowpressure level leads to pressures above the critical point for our application, indicating that the supercritical regime provides the highest efficiency. For these reasons, only the supercritical CO 2 recompression Brayton configuration was considered for comparison. Toluene is considered an appropriate benchmark fluid because its combination of high thermodynamic efficiency and excellent thermal stability makes it representative for medium/high-temperature ORC applications [37,38]. However, its flammability and toxicity, together with the fact that it condenses under vacuum at common ambient temperatures introduce operational and safety challenges; therefore, it is considered here as a theoretical benchmark rather than a practical working fluid. Finally steam-Rankine cycle represents the current state-of-the-art in CSP-PTC plants. 2.1. HRB-propane and −isobutane In an HRB cycle, Brayton and transcritical Rankine cycles take place jointly. Hybridization is achieved by bypassing part of the low-pressure flow that leaves the recuperator through a compressor, as shown in Fig. 1. Most of the main flow follows a transcritical Rankine cycle, while the bypass fraction follows a Brayton cycle. The HRB cycle incorporates specific aspects from both a recuperative transcritical ORC and a sCO 2 - RB. Like in a sCO 2 -RB, a fraction of the vapour leaving the recuperator is A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 3 bypassed through a recompressor. The remaining (main) fraction is condensed and pumped, as in an ORC. Similarly to the sCO 2 -RB, the purpose of the bypass fraction is to reduce irreversibility in the recuperator, with an optimal value that maximizes efficiency. To understand how the cycle contributes to improving efficiency when fed by a finite heat source, a set of factors can be defined [39]. Eq. (1) shows the derivation of these factors from the development of the expression for Carnot cycle efficiency. η cycle =1−˙ Qc ˙ Qh=1− Tc⋅Δsc  Th⋅Δsh=1−Tmin Tmax ⋅Tmax  Th ⋅ Tc Tmin ⋅Δsc Δsh =1−1 CN⋅1 Fh,add⋅Fc,rej⋅Fs,gen (1)  Th is the mean temperature at the heat supply,  Tc the mean temperature at the heat rejection, Δsh the entropy increase of the heat supply, and Δsc the entropy decrease of the heat rejection. CN is the Carnot factor, which accounts for the effect of ratio of the maximum and minimum temperatures of the cycle. Fh,add and Fc,rej are factors qualifying the heat supply and rejection, respectively. These factors take a value of one when the temperature in the heat supply or rejection remains constant, as occurs in latent heat exchange processes. In contrast, for sensible heat exchanges, the value is lower than one. On the other hand, Fs,gen is the entropy generation factor. This parameter accounts for the irreversibility in all the processes of the cycle. For the HRB cycles, Fc,rej is high since the cooling process of the Rankine cycle is a condensing process. Fh,add is also high because the cycle includes a well-balanced recuperator that notably increases the heating temperature although it is well below 1 due to the sensible heating. Finally, the penalisation of Fs,gen in the efficiency can be avoided by selecting a good design. For that, the selection of an optimal compression ratio can move the heat supply process away from the critical point (in pressure), so the specific heat of the fluid remains constant throughout the process. Additionally, the irreversibility of mixing the bypassing flow and the flow heated in the recuperator could be reduced if the thermal state of both incoming streams is similar. Selecting an adequate bypass fraction could balance the heat capacity of the vapor and liquid state flows that exchange energy in the recuperator. Besides the thermodynamic design, it is also important to choose a suitable working fluid. As explained in [39], a high c p /R at ideal gas condition implies a lower difference between the specific heat of the vapor and the liquid state, so a low recompression fraction to balance the recuperator is needed. This leads to a low compression work. However, it should be noted that a very high c p /R value could lead to wet compression, since the slope of the saturated vapor curve could be positive [32]. The proposed fluids, propane and isobutane, meet the above conditions. T-s diagrams for both fluids are shown in Fig. 2. 2.2. sCO 2 -RB The sCO 2 -RB scheme for high-temperature applications commonly has two recuperators. In this case, however, the sCO 2 -RB layout proposed has only one recuperator, since the maximum temperature is not very high (below 400 ◦C). Fig. 3 shows the layout and Fig. 4 the T-s diagram of sCO 2 -RB cycle. As shown in Fig. 1 and Fig. 3, sCO 2 -RB and HRB power cycles share similar layouts, both including a bypass to balance the recuperator and a dedicated compression stage associated with this bypass. Indeed, the only differences (besides the working fluid) are that the HRB uses a pump instead of the main compressor and a condenser instead of a cooler at supercritical pressure. In the sCO 2 -RB, the compressor inlet temperature and pressure are slightly above the critical point. The high specific heat capacity and low compressibility factor around this region lead to low compressor work and low heat rejection mean temperature, which increases the Fs,gen factor. It should be noted that the inlet pressure to the main compressor must be optimized based on the chosen inlet temperature to maximize the cycle efficiency [22]. 2.3. ORC ORCs have different layouts depending on whether they are subcritical or transcritical. In subcritical ORC, the heating process mainly corresponds to an evaporation process, at constant temperature. Conversely, in the transcritical ones, this process is replaced by a sensible heat one, which could lead to lower irreversibility if the heat source is finite. As the recuperator is not balanced (there is no bypass fraction that enables similar heat capacities), fluids with high vapor heat capacity are desirable to balance the recuperator. According to [32,33] toluene is the best candidate since its high c p /R ratio allows achieving a high efficiency. Fig. 5 shows the layout and Fig. 6 the T-s diagram of a subcritical and transcritical ORC-toluene, respectively. Toluene cannot be used in an HRB cycle because the pressure ratio at the compressor would be excessive; and because, as it can be seen from Fig. 6, the compression would be wet. 2.4. Steam-Rankine The superheated steam-Rankine cycle with reheat is the technology currently used in CSP plants. Therefore, it serves as a framework for comparing the HRB-propane cycle. The considered steam power cycle includes four regenerative heat exchangers, three of them are closed feed-water heat exchangers and the other one is a deaerator. Fig. 7 shows the layout. The turbine inlet temperature is set to 391 ◦C, the steam pressure to 80 bar, and the thermal efficiency to 39.7 %, which are typical values for commercial CSP-PTC plants [18,19]. The condensation temperature is 35 ◦C, the same temperature considered for the other cycles. The thermodynamic designs of the other cycles (HRB, sCO 2 and ORC) are not defined in Section 2 because they are later optimized. However, steam-Rankine cycles are well defined and established in commercial PTC plants, so a conventional design is considered. 3. Methodology 3.1. Non-standardized parametric analysis The non-standardized-parametric-analysis enables the comparison of the nominal efficiency of the different cycles without requiring component sizing for the power block (PB) or other CSP subsystems. The optimization objective is to maximize the cycle thermal efficiency, and this is achieved by performing an efficiency map for each configuration using a parametric analysis of the decision variables. In particular, the pressure ratio and the bypass fraction are varied within their feasible ranges (considering also constraints), and the best-performing point in the map is selected as the optimum. Table 1 and Table 2 summarize the fixed input data, the constraints, the decision variables and the objective Fig. 1. HRB layout. A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 4 considered in the analysis. Fig. 8 shows a flowchart of the optimization methodology applied. The maximum pressure ratio value is limited by two constraints: a maximum absolute pressure value of 300 bar, and a turbocompressor pressure ratio limited to 20:1; the latter does not apply to ORC, which has no compressor. Besides, the turbine inlet temperature is constrained by one of the two following factors: either the maximum temperature defined by fluid-specific correlations [40] or a minimum pinch point of 5 ◦C in the main heater. In sCO 2 -RB, the pressure at the inlet of the main compressor is considered also a decision variable to maximize the efficiency since, unlike in HRB and ORCs, there is no link between the heat rejection temperature and pressure. To account for the pressure losses, a pressure drop at the high-pressure side of the cycle is considered at the main heater. Similarly, a pressure drop at the low-pressure side is assigned to the recuperator. In both cases, a linear pressure decrease is assumed along each heat exchanger. Polytropic efficiency is used to calculate the outlet thermodynamic states related to the turbomachinery. Since polytropic efficiency applies to small steps of the compression/expansion process, the total pressure change in each turbomachinery is discretized into 25 parts. This number is a compromise between calculation time and accuracy. Eq. (2) allows for calculating the exit enthalpy of every segment for a turbine, while Eq. (3) is applied to compressors and pumps. For each point of the parametric analysis, all thermodynamic points are solved, and cycle balances are iterated until convergence; the resulting efficiency populates the map, from which the maximum efficiency value identifies the optimal nominal operating point for each cycle. hi+1=hi−(hi−his,i+1)⋅ η p,turb (2) hi+1=hi+(his,i+1−hi)/ η p,comp (3) The specific heat of the propane significantly varies around the critical point, which means that the pinch point in the recuperator can be achieved at either the ends of the heat exchanger or inside it. To determine its position, the enthalpy change has been divided into 25 parts. This number is enough to use the arithmetic mean temperature difference (AMTD) instead of the logarithmic one in each part without introducing significant errors. The pinch-point constraint (5) ◦C) is checked part by part; infeasible points are discarded from the efficiency map. 3.2. CSP-HRB-propane sizing model Main input data used for sizing the power block and the other CSP subsystems is shown in Table 3. The models used are defined in next subsections. 3.2.1. HRB-propane power block and cooling system The UA factor of the recuperator is the sum of the UA of each 25 equal segments. As the temperature variation along a segment is small, the AMTD can be used without significant error. The UA of each small part is then calculated from the heat exchanged ( ˙ Q) and the AMTD (Eq. (4). The correction factor value is one since the heat exchangers considered are in counter-flow with one tube-pass. UArec/mh =∑25 i=1UAi=∑25 i=1 ˙ Qi AMTDi (4) For the cooler, the UA factor is calculated as the sum of the UA Fig. 2. T-s diagram of HRB layout working with propane (left) and isobutane (right). Fig. 3. Sco 2 -RB layout. Fig. 4. T-s diagram of sCO 2 -RB. A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 5 factors associated with the rejection of sensible and latent heat of the cycle (Eq. (5). The correction factor value is approximated to one since most of the exchanged heat is latent. The logarithmic mean temperature for each region (de-superheating and condensation) is used. This is justified since the specific heat of the propane remains nearly constant during the de-superheating of the vapor since it is quite far from the critical point, and the temperature is constant during the condensation process. UAcooler =UAsensible +UAlatent =˙ Qsensible LMTDsensible +˙ Qlatent LMTDlatent (5) The cooling system uses air driven from horizontal forced-draft units. The air mass flow rate ( ˙ mair)can be calculated through the heat rejected (˙ Q), the specific heat capacity (cp,air), the cooler initial temperature difference (ΔTITD)and the cooler approach temperature (APcooler)(Eq. (6). The power of the fan is calculated as in [41]: The outlet temperature of an isentropic fan (Tfan,out,is)is calculated considering an isentropic compression (Eq. (7) using the ideal gas model. Then, the actual fan power and enthalpy increase are calculated considering the fan efficiency (accounting for mechanical, isentropic and speed reducer efficiencies) and the air mass flow rate (Eq. (8). ˙ mair =˙ Q cpair⋅(ΔTITD −APcooler)(6) Toutlet,fan,is =Tinlet,fan⋅rpfan R cpair (7) ˙ Pcooler =˙ mair⋅(hfan,out,is −hfan,in) η fan (8) 3.2.2. Solar field: Thermal and piping model Eq. (9) allows for the calculation of the incidence angle modifier of Fig. 5. ORC-layout. Fig. 6. ORC-toluene transcritical (left) and subcritical (right). Fig. 7. Steam-Rankine cycle. A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 6 an Eurotrough-150. This expression includes the cosine effect [42]. Eq. (10) is used to calculate the heat losses per meter of absorber tube [42] of a Schott PTR70 receiver. ΔT is the difference between the average temperature of a collector loop and the ambient temperature, and DNI is the direct normal irradiation. The number of loops, solar field area and HTF mass flow rate are calculated by applying an energy balance and considering the geometrical and optical parameters of the receivers shown in [34]. K=cos(φ)− 2.859621⋅10−5⋅(φ)2−5.25097⋅10−4⋅φ(9) ˙ qloss =0.00154⋅ΔT2+0.2021⋅ΔT−24.899 +[(0.00036⋅ΔT2 +0.2029⋅ΔT+24.899)⋅(DNI 900)⋅cos(φ)](10) It is important to define a model to quantify the pressure losses in the piping and the heating process of the HTF at each startup, since it can amount to up to 3 % of gross power and reduce annual generation by 10–20 % [43,44]. Based on [41], a piping model is used to size the hot/ cold headers and runner pipes to the power block and TES. This model calculates pressure losses from friction in tubes and singular elements (elbows, expansions/contractions, valves, joints) and the fluid inventory inside the circuit. Standardized diameters are used to keep HTF velocities within optimal limits and the solar field is divided into six subfields to achieve a similar number of loops per subfield as Andasol III [45]. In this way, excessively long headers and diameters are avoided. This piping model is shown in [34]. 3.2.3. TES A two-tanks system is considered. The storage fluid is molten salts [46]. The UA factor of the HTF/molten-salt heat exchanger is calculated by the NTU method (Eq. (11): UATES =∈ 1− ∈⋅ ˙ Q Thot,salt −Tcold,salt ;∈= Thot,HTF −Tcold,HTF Thot,HTF −Tcold,salt (11) The tanks have the same diameter-to-height ratio as in ANDASOL I. The minimum and maximum tanks salt level have been calculated using geometric similarity from the reference data [47]. 3.3. Standardized analysis From an economic point of view, the previously described nonstandardized parametric analysis cannot fairly compare different power cycles, because it does not consider the size of the heatexchangers and the solar field. To solve this, a standardized analysis is addressed, which sets both the total heat exchanger UA (sum of the UA of the recuperator, main heater, and cooler), the solar field size and TES size equal to those of the reference HRB-propane CSP. As the solar field is the same for all the analyzed power blocks, the inlet and outlet temperatures of the main heater, as well as the thermal power transferred to each PB are the same and equal to those of the reference plant. The optimization objective is to maximize the net power output (gross power minus parasitic losses) of each power block under these constraints. The optimization is carried out using a genetic algorithm (GA) that simultaneously adjusts the decision variables listed in Table 5—the low-cycle temperature, turbine inlet temperature, recuperator outlet temperature on the high-pressure side, pressure ratio, and bypass fraction—while constraints shown in Table 4 are satisfied. Among the constraints, the total UA factor is treated as a non-linear inequality (UAcooler +UArec +UAmh ≤UAref ), whereas the remaining constraints are implemented as simple upper/lower bounds on the decision variables. In the sCO 2 -RB, the low pressure is also considered a decision variable. The fixed input data (Table 4) is similar to that used in the non-standardized parametric analysis but, in this case, the pinch points are unknowns since are determined by the optimization. Fig. 9 shows a flowchart of the optimization methodology applied. The sum of the UA factors of each power block (cooler, main heater and recuperator) must not exceed the total reference UA factor. In the Table 1 Main input data for each power cycle. HRBpropane HRBisobutane sCO 2 - RB ORCtoluene Fixed data Ambient temperature (◦C) 25 Low-cycle temperature (◦C) 35 Low-cycle pressure (bar) 12.17 4.64 85 0.055 Main heater HTF inlet temperature (◦C) 396 Turbine inlet temperature (◦C) 377 308.85 391 391 Main heater pressure drop (%) 2 Recuperator pressure drop (%) 5 Recuperator pinch point (◦C) 5 Turbomachinery polytropic efficiency (%) 90 Constraints Maximum pressure (bar) ≤300 Compressor pressure ratio ≤20 Table 2 Variable parameters and objective for each power cycle. Variables Pressure ratio, Bypass fraction Objective Maximize efficiency Fig. 8. Non-standardized parametric flow chart optimization. A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 7 sCO 2 -RB case, in order to consider constant properties in the fluid, the cooling process is divided into small parts, since the fluid is next to the critical point in this process (Eq. (12). Additionally, the correction factor is set to one although the crossflow cooler exchanges only sensible heat. This approximation is valid if the curves that relate the correction factor to the inlet and outlet temperatures of crossflow air-cooled heat exchanger with multiple tube passes are considered, which is a common arrangement in this type of exchanger. UAcooler,CO2=∑25 j=1UAj=∑25 j=1 ˙ Qj AMTDj (12) Additionally, it is assumed that the cooling fluid is heated 7 ◦C in the cooler, so the minimum cycle temperature cannot be lower than 32 ◦C (the nominal ambient temperature is 25 ◦C). 3.4. Annual simulations methodology 3.4.1. General considerations. Operation criteria Hourly data corresponding to the typical meteorological year for Seville have been considered, including the DNI and the dry bulb ambient temperature [48]. However, the simulation time step is set to 30 min. This is because some processes like the start-up process of the power block, take such a time. In this way, the simulation is simplified by considering a single operation per time step. These operations can be: 1) Power generation (with TES charging/discharging, including overnight). 2) TES charging only. 3) Solar field and power block startup. Except for the solar-field startup, all operations are scheduled using a mixed-integer linear program (MILP) to maximize revenue, based on 2022 hourly market prices [49] in Spain. The MILP uses a 48-hour rolling horizon updated every 24 h, assuming that molten-salt tank temperatures remain fixed at the start of each horizon to maintain linearity. Thus, every time that the daily schedule is defined, a detailed model —that considers tank temperature variations in each time step— runs over the first 24 h to refine the results. After that, the MILP is performed again for the next 48 h. The MILP also considers solar-field defocusing to prevent exceeding TES capacity and adds a penalty term to the objective function to discourage multiple or excessive powerblock startups. The following criteria are considered in all operations: 1) The HTF mass flow rate through the main heater and the outlet temperature of the solar field take the design value. 2) The maximum molten salts mass flow rate is its design value. This limits the maximum power that can be stored. 3) During the TES discharging process, the HTF reaches a temperature 5 ◦C below the temperature of the hot salt tank. The same temperature difference is considered for the salts in the TES charging process. 4) The temperature difference between the turbine inlet and the HTF main heater inlet always take the design value. This criterion maximizes the annual production, although the power cycle efficiency is reduced. This is because the salts are discharged to the cold tank with a lower temperature, so higher energy can be stored in the charging process. This approach has been validated in [50]. The thermal energy required to start up the PB and solar field, shading factors, and TES thermal losses are also considered. The methodology used to account for these factors is also described in [34]. 3.4.2. Power block off-design model The following criteria are assumed: 1) The Stodola-Flügel Law is used to describe the behaviour of the turbine at part load (Eq. (13). 2) Constant volumetric flow in the recompressor is considered. 3) The turbomachinery efficiency at off-design conditions is reduced from the nominal value as the capacity moves away from the design value [51]. Eq. (14) relates the turbomachinery efficiency to its capacity. Eq. (15) describes the turbomachinery capacity from the mass flow rate, the pressure, and the inlet temperature. 4) The value of the UA factors at off-design conditions decrease as the mass flow rate of the fluid with the highest thermal resistance also does (Eq. (16). The hypothesis of constant thermal properties (particularly the Prandtl number) of the fluid in the heat transfer correlations is introduced [52]. For the main heater, the mass flow rate corresponds to the HTF while for the cooler it corresponds to the Table 3 Main input data CSP-HRB-propane. Power block Solar field Power gross output (MW) 100 Latitude, longitude Seville, (37.41 N, −5.9 W) Pressure ratio Obtained in Section 3.1 Day and hour June 21 at solar noon Bypass fraction Obtained in Section 3.1 Outlet/inlet Temperature (◦C) 396/290 Other data Same as in Table 1 Solar multiple 2 Air cooling system Collector Eurotrough-150 Fan total efficiency (%) 60 Receiver Schott PTR70 ΔTITD* (◦C) 10 Storage system  APcooler** (◦C) 3 Hot/cold salts temperature (◦C) 391/285 Fan pressure ratio (rpfan) 1.0012 Capacity 12 h *It is the difference between the outlet temperature of the cycle and the air inlet temperature **It is the difference between the condensing temperature and the air outlet temperature Table 4 Fixed data and constraints for the standardized analysis. HRBpropane HRBisobutane sCO 2 - RB ORCtoluene Fixed data Main heater pressure drop (%) 2 Recuperator pressure drop (%) 5 Turbomachinery polytropic efficiency (%) 90 Main heater HTF inlet temperature (◦C) 396 Main heater HTF outlet temperature (◦C) 290 Thermal power required by power block Calculated considering Section 3.2 Air temperature increment (◦C) 7 Ambient temperature 25 Fan total efficiency (%) 60 Fan pressure ratio 1.0012 Constraints Total UA factor ≤Reference UA factor (Calculated considering Section 3.2) Maximum pressure (bar) ≤300 Compressor pressure ratio ≤20 Turbine inlet temperature (◦C) ≤377 ≤308.85 ≤396 ≤396 Minimum low-cycle temperature (◦C) ≥32 A.J. Subires et al. Energy Conversion and Management: X 29 (2026) 101430 8 air. The q exponent value is 0.8 for the main heater and the recuperator while for the cooler is 0.625. 5) Pressure drops values (%) coincide with the nominal ones. ˙ m⋅ Tinlet P2 inlet −P2 outlet √=constant (13) η tbm = η tbm,des −1−ϕtbm ϕtbm,des/3 (14) ϕ=˙ m T √ P(15) UAoff =UAdes⋅⎛ ⎝˙ m ˙ mdes⎞ ⎠ q (16) In ORC-toluene, HRB-propane and HRB-isobutane power cycles, the temperature difference between the condensing one and the ambient temperature has the same value as in the design case, while the outlet temperature of the air is the unknown variable. In the sCO 2 -RB case, the air mass flow rate takes the design value when the ambient temperature is higher than the nominal. In this way, the low temperature of the cycle is the lowest possible, and the decrease in efficiency is lower. Fan efficiency and fan pressure ratio take the design value in all cases. 3.5. Component design methodology For all the components, the detailed design equations and correlations are provided in [34]. 3.5.1. Shell and tube heat exchangers Table 6 presents the primary input data and constraints for sizing the shell-and-tube heat exchangers in each power block. Each exchanger is sized using a genetic algorithm that incorporates the UA values calculated through Section 3.3, with the objective of minimizing the heattransfer surface area while satisfying constraints. Geometric constraints are introduced to follow manufacturing recommendations [53]. Pressure drops constraints are determined by the power cycle analysis of the previous section. A minimum Reynolds number is forced to ensure turbulent flow regime. In every heat exchanger, the fluid with higher pressure flows through the tube side except for the boiler, where steam flows on the shell side. In order to avoid excessive wall thickness, the boiler shell diameter must be less than 2 m. The HTF pressure-drop limit is 1.25 bar, which corresponds to the shell-side limit in the HRB-propane main heater and equals the sum of the pressure-drop allowances for the entire steam-generation line in the steam–Rankine cycle (preheater, superheater, reheater, and boiler). The manufacturing material is selected based on the operating temperature. All heat exchangers except for the boiler meet TEMA “DEN” standard, as they have a special high-pressure closure and a fixed tube sheet. The tube thickness is calculated considering the ASME code [54,55]. Single segmental configuration is selected in cases where the shell pressure drop is not very restrictive. Preheater, superheater and reheater do not have tubes in the windows (NTIW), which reduces the HTF pressure drop. A RODbaffle heat exchanger [56] was chosen for the HRB-propane recuperator to meet the restrictive shell-side pressuredrop limits. Its longitudinal shell flow and large hydraulic diameter yield high Reynolds numbers and heat-transfer coefficients at lower velocities, while the baffles prevent tube vibrations with minimal extra pressure drop. Shell clearances, tube arrangements and other geometric aspects of the heat exchangers are calculated considering [57,58]. To calculate the heat transfer coefficient inside the tubes, Jackson correlation [59] is used for the main heater, since it provides high accuracy under conditions close to the critical point, while Gnielinsky’s correlation is used for the steam-Rankine units. The friction factor is calculated using Colebrook-White correlation [60]. To calculate the shell heat transfer coefficient and respective pressure drop, Delaware’s method is used in the main heater, preheater, superheater and reheater. McNaught’s correlation [61] is used for the feedwater heat exchangers since steam is condensed along the shell side. For the kettle reboiler, Ref. [62] is used, and for the recuperator, Ref. [63] is considered. 3.5.2. Air cooler The condenser has been designed as an A-frame air cooler to reduce the total floor area and to improve condensate drainage. The tubes are made of carbon steel with aluminium fins. A standardized high fin tube array has been selected. The tube bundles have 4 rows to avoid excessive pressure drop. The power consumption of the fans and the pressure drop values should match to those calculated through methodology presented in Section 3.2.1 considering a face velocity (air velocity when it crosses the first tube row bundle) in the range of the recommended values given by [64]. The heat transfer coefficient inside the tubes is calculated considering a superheated vapor condensation process with stratified flow [61]. The heat transfer outside the tubes is evaluated using the method explained in [64]. 3.5.3. Propane compressor The objective of the design is to achieve a pre-design with a realistic size while meeting the constraint values shown in Table 7 [65,66]. This compressor model then serves as the basis for cost estimation. The compressor is modelled as an axial flow turbomachine. The main input parameters and design constraints, summarized in Table 7, are consistent with typical compressor design practices, as they ensure high efficiency and stable operation near the design point. 3.5.4. Propane turbine The turbine is modelled as an axial flow turbomachine. The material selected is stainless steel (GTD-450) since the inlet temperature is not Table 5 Variables and objective for the standardized analysis. 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