There are two ways of combing the SOE with fuel synthesis: 1) the SOE running with steam electrolysis produces hydrogen, which could react with CO₂ for synthesizing fuels; 2) the SOE running with co-electrolysis of CO₂ and H₂O produces syngas, which can be further converted to fuels, as shown in Figure 1. Integrating with intermittent solar energy, the SOE-based power-to-chemical systems should use sufficient electricity and thermal storage and possibly gas storage for continuous operation. When there is enough solar radiation, the power generated by PV and/or MSPT will directly power the SOE subsystem and simultaneously charge the electrical and thermal storage. When the solar irradiation is insufficient, the SOE subsystem will make use of the electricity both stored and generated by the thermal storage. In comparison to electricity storage, intermediate hydrogen storage for steam electrolysis or syngas storage for co-electrolysis may be preferable. Therefore, by choosing a particular SOE mode and effectively sizing and running various subsystems and storage, there should be a minimum levelized cost of fuels produced, depending on the local conditions of solar irradiation and the technology specifications.

The SOE can be operated in endothermic, thermo-neutral, or endothermic modes, depending on its operating point, which also affects the system-level heat integration, particularly, its integration with the downstream chemical synthesis subprocesses. The building and validation of the SOE model and the synergy between the SOE and the chemical synthesis have been provided in a series of publications from the authors (Wang et al., 2019). Coupling of the complete PtX process with solar energy will be further discussed in this paper. Simulations of methane, methanol, and gasoline synthesis processes are carried out in Aspen Plus. A detailed description of the chemical processes is given in the Supplementary Material.

The LCO calculation procedure illustrated in Figure 2 is employed. The LCO of chemicals is determined in Eq. 1, which requires the knowledge of the capital cost of main components (CAPEXs, €) and the annual operating cost (OPEX, €/year) for the considered plant and the production of the product per year expressed in kg for hydrogen Pr. τ is the discount rate and is set at 8%, and the economic lifetime t of the project is set at 20 years. L C O = ∑ t C a p e x + O p e x 1 + τ − t ∑ t Pr 1 + τ − t . (1)

The components involved in CAPEX calculation are MSPT, PV plant, SOE, heat exchanger network, electrical heaters, compressor/pump, and pressure vessel (reactor/flash drum/column) in chemical synthesis. More specifically, evaluation of the MSPT capital cost involves heliostat field, tower, receiver, power block, balance of plant, thermal storage, and indirect capital cost considering land cost, EPC and owner cost, construction cost, and tax. The CAPEX for the high-temperature electrolyzer is based on data representative for 2025 provided by CEA. It includes stacks, piping, enclosure, and DC converter. The OPEX is contributed by each separate piece of equipment, as well as the resource use and waste/pollutant mission of the whole system. For most equipment, the fixed OPEX per year is treated to be simply proportional to its total capital cost. Detailed methods and specified economic parameters to calculate the CAPEX and OPEX are given in the Supplementary Material.

The minimum LCO under different power contribution of MSPT is achieved via optimizing 1) the CSP plant, including MSPT full-load storage hours, MSPT design DNI, MSPT solar multiple, and the oversizing factor; 2) sizes and hourly operating strategies of components (SOE, CSP, PV, and the thermal, chemical, and electricity storage units); 3) heat cascade utilization to calculate the minimal process heat required. Energy balance and mass balance should be satisfied in the optimization. Optimization of those decision variables is obtained by mixed-integer linear programming with the objective of minimum LCO of chemical production. The decision variables are given in Table 1. Moreover, optimization of MSPT is carried out by a genetic algorithm in upper-level optimization as shown in Figure 3, which will be explained in the next section.

The input technical data for the calculation include SOE nominal operating point (steam electrolysis/co-electrolysis, operating pressure, cell inlet and outlet temperatures, and fuel utilization), fuel synthesis design (product type, system type, and operating pressure), and the utility and weather information. The operating conditions of the SOE are unchanged for all solution evaluations at thermo-neutral operation. Technical specifications of major components SOE and MSPT are listed in Table 2. Technical specifications of the chemical synthesis processes are provided in the Supplementary Material.

The input data for the calculation include general system specifications (hydrogen daily production rate and share of MSPT nominal power of the total nominal power), MSPT design variables (design DNI, solar multiple, and full-load hours of storage), SOE nominal operating point (steam electrolysis/co-electrolysis, operating pressure, cell inlet and outlet temperatures, and fuel utilization), fuel synthesis design (product type, system, type and operating pressure), and the utility and weather information. The nominal hydrogen molar production rate per second (mol/s) is first calculated as follows: Y ̇ s,nom = 1000 × Y ̇ d,nom 3600 × 2 × n sun + n ts , (2) where Y ̇ d,nom is the nominal daily hydrogen production (kg/day); n _sun and n _ts are the sun hour and the full-load hours of storage per day, respectively. Given the operating conditions of the SOE, the hydrogen production of a full stack is calculated and then the electrolyzer and the corresponding fuel synthesis process are scaled to meet the required hydrogen yield. Once the system is sized, a heat cascade calculation is performed, and the size of electrical heating and molten-salt hot utility is determined. Afterward, combined with the weather data, the PV and MSPT are designed, optimized, and characterized to obtain the hourly performance, upon which the hourly profiles of all resources, electricity, and product flows can be calculated in a reasonable way. Therefore, the annual cost of resource consumption and waste emission is computed for the OPEX. Similarly, the annual production rate of the final product can be calculated.

When employing the solid oxide electrolyzer (SOE), one difficulty of the system design is to meet the heat demand for water vaporization. The amount of electrical heating and process heat is minimized by a heat cascade calculation, where the electrical heating and the process heat are considered as hot utilities with certain limitations. For example, when a MSPT is involved as an electricity supplier, a molten-salt hot utility with an inlet/outlet temperature of 574/290°C is added to the heat cascade calculation. Once the heat cascade problem is solved, the nominal electricity capacity ( W ̇ nom ) , including electrical heating and the size of the molten-salt hot utility ( Q ̇ proc ) , is obtained. The following equation has been employed to evaluate the heat supplied. For a given capacity of the solar power tower ( W ̇ csp ) , the size of molten-salt hot utility is ( Q ̇ mshu ) ; for a given design efficiency of the Rankine power cycle (η _rc), the design efficiency of the Rankine cycle is scaled as η rc new = W ̇ csp / η rc W ̇ csp / η rc + Q ̇ mshu (3) so that the input energy of Rankine cycle is properly scaled to provide both the nominal electricity and process heat. The thermal storage, tower, and heliostat field are then automatically sized and optimized by the SAM. Particularly, this trick does not affect the cost of the power cycle, as the nominal power output of the Rankine cycle does not change. It should be noted that the cost of heat exchangers related to the molten-salt hot utility is not included in the cost of the solar power tower plant but is separately calculated via an effective heat exchanger network estimation.

For calculating the CAPEX, the reasonable estimation of the MSPT part (given in Section 3.2) is of great importance. This is because when the plant size varies, the specific cost of key components, the heliostat field, tower, storage, and power cycle varies as well. Thus, before optimizing the heliostat field, the specific cost or the cost function is first calculated or adapted depending on the plant size. Then, the heliostat field is optimized to minimize the cost of the whole solar power tower plant. The details of the CAPEX calculation of all involved subsystems are given in the Supplementary Material with the formulations of calculating the levelized product cost.

For calculating the CAPEX, the reasonable estimation of the MSPT part (given in Section 3.2) is of great importance. This is because when the plant size varies, the specific cost of key components, the heliostat field, tower, storage, and power cycle varies as well. MSPT plant design parameters should be in certain ranges as listed in and will be tuned by a genetic algorithm for each evaluation.

The System Advisor Model (SAM) developed by the National Renewable Energy Laboratory is integrated into our calculation platform. The SAM offers fast and precise simulation of renewable power generation, for example, (concentrated) PV, various concentrated solar thermal power (tower/trough/dish/linear Fresnel), and wind and geothermal power. Particularly, for the solar tower technology, the functionality of SolarPILOT in the SAM allows generating the heliostat field layouts, characterizing the optical performance of the solar field using an analytical technique derived from the Hermite polynomial approach used in DELSOL3, and more importantly, optimizing the heliostat field in terms of the capital cost. Heliostat field optimization is critical for thermo-economic evaluation and optimization of PtG/PtL technologies, since the heliostat field is typically the most cost-intensive component.

The detailed optimization procedure for the MSPT design presented in Figure 2 is further elaborated in Figure 3. For each design of the whole system, the nominal capacity and heat requirement of the SOE subsystem are obtained by simultaneous utility sizing and heat cascade calculation in OSMOSE (an analysis and optimization tool developed in the Group of Industrial Process and Energy Systems Engineering of Swiss Federal University of Technology in Lausanne). Then, given the design DNI, solar multiple, full-load storage hours, and the cycle design thermal efficiency, the capacity of thermal storage is determined together with an updated cycle design thermal efficiency by considering the process heat supply for the SOE subsystem. Then, for the given plant capacity, the cost data are updated and put into the SAM platform, based on cost functions provided by DLR (Dieckmann et al., 2016) for each involved component. Afterward, with respect to the reduction in the total cost, automatic generation of the heliostat layout and optimization of the solar field geometry is performed by SolarPILOT to obtain the optimal heliostat number and layout, receiver height and diameter, and tower height. Eventually, the cost breakdown and hourly performance of the optimal MSPT design can be obtained. The employed cost functions predicted for 2025 by DLR are summarized in Dieckmann et al. (2016).

In Italy, methane for mobility is promising due to the widespread use of compressed natural gas (35% of the transport consumption in Europe contributed by Italy). In total, the country counts 880,000 vehicles powered by natural gas on roads, and around 80% of Europe’s entire car fleet is on gas. Around 1,060 stations with 1,010 public are available for natural gas refueling. The regions with high DNI are Sardinia and Sicily (above 1900 kWh/m²), south coasts of Calabria and Puglia (1800–1900 kWh/m²), and the west coast of Lazio (close to 1700–1800 kWh/m²). However, as the targeted application is methane for mobility, injection into the gas grid for the methane transportation and distribution to various fueling stations is required; thus, the islands Sicily and Sardinia, with a high potential for MSPT, are excluded. Considering the CO₂ supply potential by a hub of industries (over 50 kton/year), the Lazio region is chosen for this case study. The emission of CO₂ is mainly from the glass industry, whose oxygen supply is usually with a purity of 90–99.5%. The methane pressure for mobility is 200–250 bar.

In France, Fos-sur-Mer (PACA region) is selected due to high DNI of around 1800–1900 kWh/m² and a hub of carbon-emitting industries. The region has become the largest CO₂ emitter (over 50 kton/year) ahead of Nord Pas de Calais and Lorraine regions. The company highlighted is world-leading steel and iron company, ArcelorMittal, located in Fos-sur-Mer (PACA), which emits around 7,990 kton/year. Approximately, 60–100 Nm³ of O₂ per ton of steel is necessary with a purity between 90% and 99.5% (depending on the relevant manufacturing steps). The quality of methane produced for grid injection is defined by the French standards of a higher heating value, Wobbe index, and purity level. The methane pressure varies between 4 and 16 bar for the distribution grid and 40–70 bar for the national grid.

Methanol or gasoline (via methanol-to-gasoline process) is a promising value-added product for mobility in Spain. Oil industries utilize methanol directly to blend gasoline or to produce methyl tertbutyl ether, the most widely used octane booster for reformulated gasoline. Except for northern regions such as Galicia, Asturias, Cantabria, Basque country, Navarra, and the coast of Catalonia, the minimum required rate of 1900 kWh/m² for CSP is reached in Spain. Considering the large-scale carbon-emitting oil-refining company, Compañía Española de Petróleos, S.A., emitting around 1,520 kt/year CO₂, Andalucia is chosen for this case study. The choice of a refinery can establish a circular economy for this oil industry: CO₂ emitted by the refinery is used to produce methanol or gasoline, which can be used, in turn, by the refinery. According to fuel blending regulations in Europe, the maximum allowed methanol volume is 3%vol./vol. of gasoline and 10%vol./vol. of diesel. Methanol used should have a minimum purity of 99.7%wt (and water content <0.1%wt). If used in methyl tertbutyl ether synthesis, methanol should have a minimum purity of 99% and may require to be compressed to 10–15 bar (operating conditions of MTBE synthesis). Gasoline yield produced by the methanol-to-gasoline process is high, and usually, gasoline purity (around 86%wt.) meets or exceeds existing gasoline specifications.

The trade-off between the annual power contribution of CSP and LCO of methane for cases 1 and 2 is illustrated in Figure 4. Each scattered line stands for the minimum levelized cost of methane for a given annual power contribution of CSP. The area above each scattered line is the feasible design region for each specific case study. Overall, the trade-off tends to be in a linear trend, indicating that improving the annual power share of CSP will not significantly increase the levelized methane cost. For case 1 (Italy, methane for mobility), the levelized methane cost increases from 7 €/kg with 70% CSP power contribution to 9 €/kg with approximately 100% CSP power contribution.

The plant size has a significant impact on the levelized methane cost. For case 1, the levelized methane cost at 4,000 and 20,000 kg/day H₂ are 7.2–8.7 and 5.7–6.7 €/kg, respectively. For case 2, the values are 4.5–5.3 and 5.8–6.4 €/kg. By increasing the plant size from 4,000 to 20,000 kg/day H₂, the levelized cost significantly drops by around 1.2 €/kg under the same CSP power contribution in both cases 1 and 2.

Moreover, the levelized methane cost is highly dependent on the location, that is, natural resource endowment of solar radiation. For a location with a larger annual capacity factor, the MSPT size can be smaller for a specified application. This can be revealed by Figure 5: for case 2, by the syngas pathway, with the same amount of hydrogen produced, the total power consumption, in fact, should be significantly higher than that of case 1. However, the fact that the CSP annual capacity factor (Figure 5A) in the PACA region (France) is much larger than that in the chosen location in Italy leads to a significant difference in the MSPT capacity, as illustrated in Figure 5B. As a result, compared with case 1, case 2 with a smaller MSPT size and MSPT CAPEX produced a larger amount of methane, leading to a significantly lower levelized methane cost.

The trade-off between annual power contribution of CSP and the levelized cost of methanol and gasoline is shown in Figure 10. Overall, the effect of CSP annual power contribution on the levelized methanol cost is much weaker than that on the levelized gasoline cost. In general, the levelized methanol cost is within the range of 1.5–2 €/kg, while for gasoline, the levelized cost is around 4–6 €/kg. This is because methanol is produced in larger amounts than gasoline using the same amount of H₂ for the synthesis (simply because of the molecule formulation). In order to produce gasoline, methanol is first dehydrated to create DME, and then DME should be transformed into gasoline, which ultimately results in the considerable difference in mass production. The yield of the chemical influences the variation of the levelized cost under different annual power contribution, that is, the slope of the levelized cost with regard to annual power contribution.