Hybrid hydrogen-electricity production using spherical tokamaks: a cost-driver sensitivity study and techno-economic analysis

PAPER • OPEN ACCESS Hybrid hydrogen-electricity production using spherical tokamaks: a cost-driver sensitivity study and techno-economic analysis To cite this article: J. Hidalgo-Salaverri et al 2025 Nucl. Fusion 65 036027 View the article online for updates and enhancements. You may also like Multi-functional code for hydrogen isotopes transport analyses: verification & validation against fusion-relevant applications F. Hattab, V. Narcisi, C. Ciurluini et al. - Access and sustainment of ELMy H-mode operation for ITER pre-fusion power operation plasmas using JINTRAC E. Tholerus, L. Garzotti, V. Parail et al. - Assessment of the possibility of irradiating tungsten and Cu-alloys in IFMIF-DONES using a realistic specimens configuration Irene Álvarez, Marta Anguiano, Fernando Mota et al. - This content was downloaded from IP address 193.147.173.203 on 24/04/2025 at 10:51 International Atomic Energy Agency Nuclear Fusion Nucl. Fusion 65 (2025) 036027 (15pp) https://doi.org/10.1088/1741-4326/adaa01 Hybrid hydrogen-electricity production using spherical tokamaks: a cost-driver sensitivity study and techno-economic analysis J. Hidalgo-Salaverri1,a,∗, T. Griffiths2,a, Z. Xuereb Conti3, P. Cano-Megias4, R. Chacartegui5, M. Bluck2, J. Ayllon-Guerola1, A. Mancini6, M. Garcia-Munoz6 and E. Viezzer6 1Department of Mechanical Engineering and Manufacturing, University of Seville, Seville, Spain 2Department of Mechanical Engineering, Imperial College London, London, United Kingdom of Great Britain and Northern Ireland 3Data-Centric Engineering, The Alan Turing Institute, London, United Kingdom of Great Britain and Northern Ireland 4Max-Planck Institut für Plasmaphysik, Garching, Germany 5Department of Energy Engineering, University of Seville, Seville, Spain 6Department of Atomic, Molecular and Nuclear Physics, University of Seville, Seville, Spain E-mail: jhsala[email protected] Received 22 January 2024, revised 27 November 2024 Accepted for publication 14 January 2025 Published 18 February 2025 Abstract Hybrid fusion power plants, which produce both hydrogen and electricity, are proposed as a way to decarbonise the fossil-fuel-dominated primary energy market and improve plant economics. The main cost drivers of a fusion power plant based on a spherical tokamak have been identified using statistical analysis (Morris and Sobol methods) from a wide range of cases obtained with the systems code PROCESS. The analysis reveals the importance of plasma physics and reactor geometry on power plant economics. Three scenarios of advancing technophysical assumptions (conservative, moderate and optimistic) have been chosen to study the integration of the fusion reactor with the power block (Rankine, He-Brayton or super-critical-CO2-Feher) and with the PEM electrolyser. The super-critical-CO2cycle returns the best results for the studied temperature range (500 ◦C–800 ◦C), with an efficiency between 40%–56%. The modelled PEM is in line with current commercial models with a consumption of 51.97 kWh kg−1H2. The economic feasibility of these scenarios has been explored for a set of learning factors that consider the cheapening of the capital costs tied to experience. The LCOE of these scenarios have been compared against current price ranges of solar, wind and fission power and the LCOH against PEM prices, showing that the moderate and optimistic aEqual contribution ∗Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1741-4326/25/036027+15$33.00 Printed in the UK 1 © 2025 The Author(s). Published by IOP Publishing Ltd on behalf of the IAEA Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al scenarios could be competitive for learning factors lower than 0.5 and capacity factors larger than 0.7. An extrapolation of the optimistic scenario shows that the hybrid fusion power plant in the French and German market can improve the plant profits by 15% and 66% respectively. Keywords: PROCESS, spherical tokamaks, commercial power plants, technoeconomics, hybrid hydrogen production, power plant sensitivity study, statistical analysis (Some figures may appear in colour only in the online journal) 1. Introduction In 2019, electricity made up 20% of global primary energy consumption and is predicted to rise to 25% by 2040 [1]. This means that three quarters of the energy demand needs to be met by non-electric energy resources. The majority of these non-electric resources are thermally consumed, i.e. a fuel is used to generate heat that may be an intermediate step or the final product. It is also likely that by 2050, due to pushes for global decarbonisation, the electricity market will already be saturated with low-carbon technologies. Nuclear fusion can serve as the cornerstone of carbon-free energy generation. However, targeting the electricity market alone will not address the remaining 75% of non-electric primary energy consumption. Fusion power, owing to its thermal origin, has been suggested for diverse applications beyond electricity generation [2]. Proposals include the development of DEMO-like fusion power plants capable of ensuring energy security across a spectrum of applications. These applications span from low-temperature power needs, like district heating [3], desalination [4,5], and hydrogen production [6]. In this study, the latter is proposed. In the quest for decarbonisation, clean hydrogen emerges as a versatile solution. Its production, whether harnessed from renewable or nuclear energy sources, or derived from fossil fuels with carbon capture, presents a pathway to mitigate emissions across challenging sectors such as long-haul transport, chemicals, and the manufacturing of iron and steel [7, 8]. These sectors pose considerable emission reduction challenges. Significantly, the integration of hydrogen-powered systems in industrial vehicles and freight/shipping operations not only holds the promise of simultaneously decreasing carbon emissions and enhancing air quality but also addresses a critical limitation for shipping, where batteries might not be a feasible solution [9,10]. Furthermore, hydrogen’s role extends to facilitating the seamless integration of variable renewables within the electricity system [11], and serving as one of a few valuable options for storing energy over extended periods. In the context of providing a comprehensive technoeconomic analysis, this study evaluates fusion power as an energy source for the hybrid generation of electricity and hydrogen through electrolysis. Whilst holding a wellestablished position within the industrial landscape, electrolysis has a comparably low-carbon profile, particularly in contrast to processes such as fossil fuel reforming. Importantly, it offers a streamlined technological configuration, setting it apart from un-established and complex alternatives such as the thermo-chemical sulphur-iodine cycle. Electrolysis operates solely through electrical processes, eliminating any reliance on nuclear heat sources. This intrinsic feature opens avenues for the co-generation of hydrogen and electricity production. Such a synergy could seamlessly match peak energy demand in an energy paradigm where fusion serves as the consistent base load power, complemented by renewable sources. It can also ensure that the plant specifications are aligned with those required for electricity production, meaning that development pathways for electricity production efforts still remain valid until a choice can be made on which pathway is best for fusion to exploit. Studies from Sheffield et al and Nicholas et al further investigate this narrative through cogeneration between hydrogen and electricity [4,12,13]. The deployment time of fusion power plants is crucial for their effective integration into the energy mix. In this context, spherical tokamaks (STs) are potentially quicker to incorporate than conventional tokamaks due to their relatively smaller size, which potentially results in shorter construction times and reduced capital costs-two common challenges in the deployment of fission power plants. However, it is important to note that the smaller size of STs can also introduce increased complexity in their design and operation, which should be carefully considered in the evaluation of deployment timelines. STs are characterised by an aspect ratio (A), the ratio between the major (R) and minor (r) radius, <2. In general, lower aspect ratio tokamaks are designed with lower toroidal field (BT) than conventional tokamaks. This is due to how BTscales such that BT=BmaxRTF RP, where Bmax is the maximum field at the toroidal field coil, RTF is the inner radius of the toroidal field coil, and RPis the major radius of the plasma [14]. In spherical tokamaks The inner radius of the TF coil (RTF) is small. The major plasma radius (RP) is also small but larger relative to RTF. Together, these factors reduce the achievable BTfor a given Bmax [14]. This decreases the fusion power as Pfusion ∝B4 T. However, by leveraging high beta, compact design, and efficient current drive, STs remain competitive against conventional tokamak designs. This is why many current research efforts focus on optimising STs to improve their scalability and overall performance. Following this reasoning, multiple public and private programmes are funding ST pilot plants with the target of energy production by the 2040–2050 s [15–18]. From a physics perspective, ST plasmas can reach a higher confinement, achieving elevated values of ratio of the plasma 2 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al pressure to the magnetic pressure, β, elongation (κ), and safety factor, (q) [19]. In the context of β, it is noteworthy that ST plasmas can exceed the Troyon limit, exemplified by the START ST achieving βtvalues exceeding 30% [20]. A distinctive characteristic of STs is the balance between the magnetic fields, particularly the similarity of the poloidal field (Bp) and the toroidal field (BT) in the outer field region. This equilibrium induces particles to follow high-pitched trajectories, resulting in reduced time spent in regions of unfavourable curvature and, consequently, featuring a better particle confinement. Moreover, STs naturally feature elongated plasma shapes, characterised by the parameter κ, which represents the ratio of the half of the plasma height to minor radius, accounting for the total vertical size of the plasma. This inherent elongation substantially diminishes the energy needed to achieve this advantageous configuration. ST plasmas are able to achieve high bootstrap currents, increasing plasma stability and performance. A high bootstrap fraction indicates that a significant portion of the required plasma current is generated internally. In turn, the plasma remains at the necessary temperature and density for fusion reactions, reducing the need for additional energy intensive external heating and current drive methods, improving the overall efficiency of the fusion reactor. Reduced reliance on external current drive systems can lower the operational costs of a fusion reactor, making it more economically viable for long-term fusion power generation [21,22]. The advantages of ST designs are not without their tradeoffs. Achieving a higher fusion gain (Q) in a more compact machine translates to a greater heat flux impacting the reactor’s first wall and, notably, the divertor, which must endure heat fluxes reaching magnitudes in the range of tens of MW m−2 [23,24]. The compact configuration also results in limited space within the central stack. This region accommodates the central solenoid, inner leg of the poloidal field coils, shielding materials, and the breeder blanket (though not all designs incorporate a breeder blanket in the high field region, a challenge when aiming for a self-sustaining tritium breeding ratio). Certain designs address this concern by minimising the central solenoid’s spatial occupancy (it is exclusively employed for startup, with external means and the bootstrap current supplying plasma current) or by its complete removal, as seen in solenoid-free startup designs such as [25,26]. The heightened volumetric fusion yield, coupled with limited central stack space, results in elevated neutron fluence rates in the poloidal field coils. This degree of fluence can potentially damage materials and induce heat fluxes incompatible with the coils’ thermomechanical integrity. 2. Scope Fusion holds a unique position in the energy future landscape, marked by recent advancements in technological demonstration and significant investment, especially in private developers. Yet, there is a noteworthy absence of strategic planning concerning its commercial application and economics. The lack of studies in the literature addressing potential non-electric commercial applications for fusion, particularly for STs, underscores the necessity of this study. We outline three techno-economic scenarios, optimistic, moderate and conservative. For each one, there are a set of important physics and engineering parameters with a given value, and a corresponding capital cost. These values are carried forward and fed into examinations of power blocks and electrolysers. Notwithstanding these challenges, commercial fusion via STs remains a promising, yet unrealised technology, still in the prototyping phase of research and development. To grasp the techno-economic implications for an ST in hybrid electricity and hydrogen production, it is necessary to envisage a future context where fusion technology has been demonstrated with an operational First of a Kind (FOAK) power plant. Consequently, thorough conceptualisation of design specifications becomes paramount. This ensures the optimisation of energy production and a deep understanding of plasma physics and engineering parameters that impact important technoeconomic indicators, such as capital cost. Leveraging systems codes can enable this approach, facilitating design optimisation. However, conceptualising an unrealised technology means that assumptions and uncertainties inevitably arise in these power plants concepts. The PROCESS systems code has been chosen to conceptualise the ST [27]. Developed by UKAEA, PROCESS is able to study the interplay between the engineering and physics aspects that comprise a fusion power plant. The code is given a study space formed by the constraints set by the user. Then, PROCESS can obtain the optimum working point (for the chosen figure of merit) using a series of 0D and 1D approximations that model all subsystems. The code achieves convergence within seconds, making it a valuable tool in cases of exploratory analysis aimed at establishing a design baseline [28]. The low computational cost of the code allows also for uncertainty studies to pinpoint the most influential parameters with respect to the chosen figure of merit. To address uncertainties and assumptions surrounding the ST concept, a two-fold sensitivity analysis approach was used. First, Morris uncertainty analysis was applied to reduce dimensionality and streamline parameter selection (section 3.1). Next, an in-depth Sobol analysis was performed (section 3.2), evaluating first-order (S1), second-order (S2), and total interaction effects (Stot). These methods identified key parameters and their interrelationships, improving the understanding of factors influencing capital cost. From this analysis, three distinct reactor scenarios-optimistic, moderate, and conservativewere identified. These scenarios informed the subsequent thermodynamic power block modelling (section 4), electrolyser modelling for hydrogen production (section 5), and economic modelling for levelised cost of electricity and hydrogen calculations (section 6). This approach allows for exploring diverse operating conditions and design parameters, providing insights into potential energy generation and hydrogen production capabilities. 3 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al 3. Sensitivity methods In this section, two statistical methods (Morris and Sobol) will be used to determine their effect on the capital cost of a ST. The methodology here presented is similar to the followed in [29], where PROCESS was used to determine the main capital cost drivers for a DEMO-like fusion power plant. Thus, allowing for the direct comparison of the cost drivers found for a conventional tokamak and a spherical one. The identification of the cost drivers allows for the definition of three scenarios (conservative, moderate and optimistic) in the next section that will be used to analyse their thermoeconomic behaviour (power block, electrolyser and their respective costs). The studied ST model here presented is modelled after the work presented by Menard et al in [14], that was successfully reproduced in PROCESS by Muldrew et al [30]. Menard’s model, from now on referred as Menard-2016 baseline, is an ST pilot power plant with a fusion power output of 500 MW and solenoid-free operation achieved thanks to a high bootstrap current fraction (∼70%–80%, consistent with the fractions obtained in other modelling [31,32] and theoretical studies [33]) and 50 MW of NBI power. This has motivated research lines on solenoid-free startup [34,35], solenoid-free operation [18,31]. In Bock et al [36], an advanced scenario was experimentally explored in the conventional tokamak ASDEX Upgrade where just a small fraction of the current drive was provided from inductive means, while the rest was provided by a substantial bootstrap current and external means (NBI, ECCD). For this work, the electric output of the reactor has been constrained to 500 MWe. This is in line with the DEMO design presented in [29] allowing for a more direct comparison. Table 1shows all the parameters that will be studied in this statistical study together with their upper and lower limits. A few of these parameters include the superindex max or min, these correspond to iteration variables that PROCESS vary between some given limits in order to achieve the optimum result with the given constraints. For example, Bmax Tmeans that PROCESS can vary BTup to this value, but the optimum scenario may feature a lower value. Several parameters in the investigation overlap with those in Pearce et al [29], while some have been introduced or removed in accordance with their relevance to compact STs. Parameters like ρcore and fWare within the ranges used in Pearce et al’s work. Adjustments have been made to the limits for Ato reflect those seen in STs. Parameters such as fmax GW, fHe,fmin LH ,CBS,ηiso,q95,fCD,Pmax inj ,σmax CS , and Bmax Tshare the same range widths as Pearce et al but are centred around the Menard-2016 baseline. The rest of the parameters limits are set around existing/projected technophysical values or limits. i.e. ∆Tin varies between normal power plant temperature and achievable turbine temperatures in supercritical carbon dioxide plant [37], or βthat varies between the minimum converged value obtained in [14] and 20% that is the maximum stable and economically feasible value despite larger βof up to 50% have been achieved in START [38]. This list does not Figure 1. Absolute mean, µ∗, and variance, σi, of the elementary effects of screen PROCESS parameters. X in the units represent the units of the varied quantity (i.e. M$ T−1for Bmax T). There is a significant accumulation of unimportant parameters close to the (0,0) position, these parameters are: ηiso,qmin 95 ,Pmax inj ,σlimit CS ,ηhtp. intend to collect all the possible parameters and their ranges, future contributions should help expand this study to improve the generality of the findings. The Morris method was used first as it is computationally more efficient than Sobol, making it advantageous in high dimensionality problems to filter out less influential variables. However, the Morris method provides less detailed information and does not capture the interplay between different variables as comprehensively as the Sobol method. 3.1. Morris method The Morris Method [39], also known as the method of elementary effects, is a sensitivity analysis technique used to explore the qualitative behaviour of a model’s output in response to changes in input parameters. Unlike traditional sensitivity analyses that focus on quantifying the impact of each parameter individually, the Morris Method assesses the influence and interactions of multiple parameters simultaneously. It achieves this by systematically varying each parameter across a range of values while keeping others constant, allowing for the identification of influential factors and coupling effects on the model’s output. In the context of this study, the Morris Method was employed to analyse the sensitivity of capital cost to changes in input parameters, providing insights into the relative importance and interdependencies of these parameters in shaping the economic viability of the proposed fusion power plant design. In figure 1, a scatter plot of the absolute mean and standard deviation of the elementary effects for each parameter is presented. The absolute mean, µ∗, shown in equation (1) can be seen as providing a ranking of the effect of such an input on the capital cost, and this allows for easy identification of negligible inputs, whereas the standard deviation σi, provides an estimation of the linearity of the input and its interaction 4 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al with other variables: µ∗ i=1 N N X j=1 |EEij|(1) σi=v u u t 1 N−1 N X j=1 (|EEij| − µ∗ i)2(2) where: µ∗is the calculated absolute mean for parameter Xi. σiis the standard deviation of the elementary effects for parameter Xi.Nis the total number of samples. EEij is the jth elementary effect of parameter Xi. The EEij measures the change in the output of a model due to a small, incremental change in one of its input parameters. It is a sensitivity measure used in sensitivity analysis to understand the influence of individual parameters on the model output. The units of elementary effects depend on the units of the model output and the corresponding input parameter. For example, for the model output is capital cost, (with units of dollars) and the input parameter is Bmax T(with units of T), the EEij will be in dollars/T. Therefore, µ∗and σwill share the same units. Fusion parameters in the upper right quadrant (high µ∗ and high σi), such as β, indicate parameters that strongly effect to the capital cost, and are strongly correlated to other variables. Concerning β, its influence on capital cost can be attributed to the necessity of achieving high plasma β, which demands robust plasma control systems. Alternatively, instead of achieving high plasma β, there is a solution that uses high-temperature superconducting magnets (HTS magnets) to achieve a stronger magnetic field, thereby mitigating the requirement for high plasma β. In the case of certain proposed HTS tapes, such as rare-earth barium copper oxide (ReBCO), challenges emerge due to the scarcity of some constituent minerals in the Earth’s crust. This scarcity can lead to elevated material costs. Furthermore, the novelty of the technology increases final prices due to limited industrial infrastructure for large-scale production. Data points in the upper left quadrant (high σi, low µ∗), such as Psep/R, represent parameters with a notable average effect on the capital cost but relatively low inter-dependence. These parameters could consistently affect the capital cost, making them important and stable contributors. The fusion parameter Psep/Rimpacts the capital cost of a fusion machine by indicating the efficiency of plasma confinement and power losses. A high Psep/Rsuggests less efficient confinement and increased power losses due to plasma transport. To mitigate these losses and sustain a viable fusion reaction, advanced and costly technologies for supplementary heating (to maintain plasma temperature and thus sustain fusion reactions), confinement, plasma stability, and materials are required. Efficient heating systems and current drive methods, such as neutral beam injectors employed in this ST concept play a crucial role in contributing to the capital cost. Other methods include cyclotron resonance heating. Data points in the lower right quadrant (low σiand high µ∗) indicate parameters that exhibit substantial inter-dependency, but have a modest average effect on the capital cost. The absence of fusion parameters in the lower right quadrant (low σiand high µ∗) is context-dependent and reflects the unique conditions and parameters in the study, rather than a limitation. Data points in the lower left quadrant (low µ∗and low σi) represent parameters with both a low average effect and low variability, such as Pmax inj ,fmin LH ,σmax TF ,ηhtp, and q95. These parameters show minimal impact on the capital cost and are relatively stable in their behaviour. The same upper and lower limits, as shown in table 1, were used, and the nine most influential parameters were carried forward for variance-based analysis of Sobol indices. These were: fmax GW,fW,Psep/R,fCD,A,Bmax T, ∆Tin,β, and ηNBI. Comparing Morris sensitivity analysis results with Pearce et al highlights similarities and differences in parameter importance [29]. Parameters like CBS,Bmax T, and fWexhibit consistent high influence. In contrast, Psep/R,fmax GW, and Ashow distinct variations in influence, with greater prominence in this study. Parameters such as σmax CS ,ρcore, and Pmax inj exhibit reduced influence and coupling compared to [29]. 3.2. Sobol method Sobol analysis, a variance decomposition method, stands apart from the Morris method in its rigorous approach to sensitivity assessment. While Morris evaluates parameter importance through direct evaluations, Sobol analysis delves deeper by utilising Sobol sampling methods, uncovering the individual and interactive contributions of parameters to overall output variance. This method offers a more comprehensive perspective on sensitivity and influential factors, especially beneficial for models with numerous input parameters. Employing sensitivity indices like S1(first-order sensitivity index), Sobol analysis quantifies the proportion of output variance attributed to each parameter individually, providing insights into their isolated effects on the output variability. Specifically, S1answers the question: ‘How much does changing this parameter alone impact the variability in the output?’ This index is calculated as the ratio of the variance of the conditional expectation of the output given the variation in a single parameter to the overall output variance: S1(Xi) = V[E(Y|Xi)] V(Y)(3) where: V[E(Y|Xi)] is the variance of the conditional expectation of Ygiven only Xivaries. V(Y) is the variance of the output Y. Sobol analysis also extends to higher-order sensitivity indices to provide a more detailed understanding of parameter interactions. Second-order sensitivity indices (S2) assess the joint effects of pairs of parameters. They evaluate how two 5 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al Table 1. Parameters predicted to impact power plant economics, with their corresponding upper and lower limits. Parameter Lower limit Upper limit fmax GW Greenwald fraction 0.85 1.15 H98,y2Radiation corrected H-Factor 1.47 1.67 fHe Helium impurity fraction 0.085 0.115 fWTungsten impurity fraction 1.00e−5 1.00e−4 Psep/R(MW m−1) 20.0 45.0 fmin LH Lower bound LH threshold 0.85 1.15 CBS Bootstrap current fraction 0.08 0.80 fCD Current drive efficiency [A W−1] 0.03 3.00 ηiso Isentropic efficiency of blanket coolant pumps 0.75 0.95 qmin 95 Safety factor near plasma edge 3.0 3.5 Pmax inj Maximum allowable value for injected power (MW) 45.0 55.0 σlimit CS Allowable hoop stress in central solenoid structure (MPa) 340 460 σlimit TF Allowable maximum shear stress in TF coil case (Tresca criterion) (MPa) 640 760 AAspect ratio 1.8 2.0 Bmax TToroidal field on axis (T) 3.5 4.5 ρcore Normalised radius defining the core region 0.45 0.75 ∆Tin Turbine inlet temperature (◦C) 519.85 824.9 βTotal plasma beta 0.04 0.2 ηNBI NBI plug efficiency 0.2 0.6 ηhtp Electric efficiency of primary pumps 0.75 0.95 parameters, when varied together, influence the capital cost variability beyond their individual impacts. Third-order and higher-order sensitivity indices (S3,S4, and so on) further expand the analysis to consider the joint effects of three or more parameters simultaneously. They help in uncovering intricate relationships that might not be evident when analysing parameters individually or in pairs. In addition to lower order indices, Stot (total-order sensitivity index) takes a broader view. This index quantifies the entire influence of a parameter on capital cost variability, encompassing its direct impact and its collaborative effects with other inputs. The total-order sensitivity index Stot is expressed algebraically as the sum of all the lower-order sensitivity indices. In essence, Stot answers the question: ‘When considering all possible interactions, how much does this parameter contribute to the capital cost variability?’: Stot (Xi) = 1−V[E(Y|X∼i)] V(Y)=1− n X i=1 Si(4) where: V[E(Y|X∼i)] is the variance of the conditional expectation of Ygiven all input parameters except Xivary. V(Y) is the variance of the output Y. Here, nrepresents the total number of parameters or factors being considered in the sensitivity analysis. Non-zero values for all indices suggest that the parameter has both direct influence on the capital cost and contributes to the overall variability through interactions with other parameters. In the equations provided, the arguments of Vare defined as follows: V[E(Y|X∼i)]: This represents the variance of the conditional expectation of the output Y, given that all input parameters except Xivary. In other words, it quantifies the variability in the expected value of Ywhen all parameters except Xi are considered to vary. V(Y): this denotes the variance of the output Y, which measures the degree of dispersion or spread of the output values around their mean. fCD,Bmax T,β, and ηNBI have non-zero S1indices, thus indicating that the parameters in question have both individual and interaction effects on the capital cost variance. The colour map in figure 2(a) represents the S2indices obtained from the analysis. Positive values in second-order Sobol analysis indicate the degree to which two input variables, interact with each other to influence the capital cost. A higher positive value suggests a stronger interaction between the two factors, meaning that they jointly explain a larger portion of the capital cost variance. As shown, βshows strong coupling with Bmax T(0.15), ∆Tin (0.15) and ηNBI (0.16). Zero values imply that there is no significant interaction between the two factors in explaining the capital cost variance, as shown between Aand Bmax T. In other words, the direct combination of these two parameters do not have an effect on the capital cost. In this study β,A, and Bmax Thave the highest Stot indices, and therefore demonstrate that they interact strongly with other parameters, and have a strong influence on capital cost. fmax GW,Psep/R,A, and ∆Tin exhibit zero S1indices, but notable Stot, see figure 2(b). This indicates that these parameters have strong interactions and their effects on the output variance are 6 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al Figure 2. (a) Second order Sobol results. Each square shows how strong is the interplay between two variables. Only the top half is shown as the matrix is symmetric and the diagonal (each parameter to itself) is equivalent to S1(shown in (b)). (b) showing S1and Stot indices of screened PROCESS parameters. predominantly driven by higher-order interactions rather than their individual contributions. High Stot indices suggest that these parameters, when combined with other inputs, have a significant impact on the capital cost variability. The influence of Bmax Ton capital cost is explained by its strong effect on the fusion power: Pfusion ∝ B4 T. Whilst high fusion power is desirable, it can also lead to increased costs, driven by the need for advanced technologies, materials, safety measures, and infrastructure to support the increased power output. The ∆Tin influences the efficiency of the thermal management system. A larger temperature difference would require advanced cooling systems and materials to handle the heat load, therefore impacting the capital cost. fmax GW is related to the maximum allowable plasma density. Achieving and maintaining high plasma density requires enhanced fuelling and divertor systems and could be more expensive. It is important to note that the currently implemented model for STs in PROCESS considers δand κas a function of the aspect ratio; thus, they cannot be controlled as independent parameters. This explains why these two parameters, the top contributors to the capital cost in the DEMO-like study presented by Pearce et al are not considered in this study. The influence of Aon the plasma’s increased proximity to the central stack together with its control on δand κresults on the third highest Stot factor for the studied ST case. 3.3. Scenario identification Identifying the main cost drivers for the presented ST configuration led to the design of three scenarios with increasing techno-physical complexity: conservative, moderate, and optimistic. These scenarios, detailed in table 2, were defined using the parameters studied with the Sobol method. Figure 3 presents a histogram of the capital cost for all cases examined Table 2. Input and output parameters that compose the optimistic, moderate and conservative scenarios. Conservative Moderate Optimistic Inputs fW4.5·10−55·10−510−4 Psep/R[MW m−1] 25 33 42 fmax GW 1.0 1.0 1.0 fCD 0.8 1.0 0.8 A2.0 2.0 2.0 Bmax T[T] 3.8 4.0 4.5 β0.081 0.11 0.18 ηNBI 0.3 0.4 0.5 ∆Tin [◦C] 500 650 800 Outputs Ip[MA] 18.5 15.3 13.9 R[m] 4.75 3.10 2.78 Capital cost [1990 M$] 9827.76 5124.62 4551.47 Qreactor [MWt] 1916.9 1466.8 1231.5 Consumptions [MWe] 241.0 180.1 151.6 in the Sobol studies. Here, the optimistic case lies the bottom 10% of cases, moderate at 50%, and conservative at 90%. The Sobol analysis identified the parameter βas highly influential on the capital cost. Even small changes in βcan lead to significant fluctuations in capital cost, highlighting the potential for targeted refinements to substantially reduce costs within the scope of this study. fW, effectively a proxy of the plasma impurities, is playing an interesting role in these scenarios. The first order effect of this parameter is that the plasma radiation increases which dampers the reactor efficiency. But a higher plasma radiation means a lower heat flux on the divertor which is known to 7 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al Figure 3. Histogram with the distribution of all capital cost values estimated by the Sobol analysis with optimistic, moderate and conservative FOAK scenarios referenced respectively. be a bottleneck for STs. For the short range here expressed a higher impurity fraction was found to relax sufficiently the divertor heat flux to allow for a cheaper design as this limit was met later on the optimisation process. Nonetheless, it is clear that this tendency will be overturned for a sufficiently larger impurity range. Future contributions should address this point by studying wider ranges under different scenarios to understand the viable design space. Through distinction of the scenarios, parameter values are able to be carried forward into the technological part of the techno-economic investigation, as outlined in the scope. The utilisation of these parameters inform the modelling of thermodynamic cycles, electrolyser performance, and economic assessments. In section 4, thermodynamic modelling will incorporate parameters Qreactor (the thermal power output by the reactor), ∆Tin (the turbine inlet temperature as defined in table 1) and Consumptions (the overall electrical consumptions of the reactor). In the final section 6, the output variable Capital cost will be analysed to determine the economic viability of each scenario. 4. Power blocks In this section, the integration of three power blocks (namely Rankine water cycle, Brayton helium cycle, and Feher supercritical carbon dioxide cycle) on the three scenarios previously exposed will be presented. This methodology, thus, highlights the importance of knowing the main cost drivers of a fusion power plant before its design as they will end up determining the main characteristics of the power block. As previously mentioned, the key parameters for the power block selection are Qreactor,∆Tin, and the plant Consumptions (see table 2). More advanced scenarios will feature lower consumptions and higher inlet temperatures, leading to higher electric efficiencies of the cycle. Therefore, these parameters are pivotal in the selection process. Here, the efficiency of the cycle is defined as: ηcycle =˙ Welec, turbines −˙ Wcons, cycle −consumptions ˙ Qreactor (5) Where ˙ Welec, turbines represents the electric power generated in the turbines. ˙ Wcons, cycle denotes the inner consumptions within the cycle, such as pumps. Consumptions correspond to the plant consumptions, as indicated in table 2.˙ Qreactor signifies the heat flux produced in the reactor, also sourced from table 2. Here, ˙ Qreactor comprises the heat flux coming from the blanket, divertor, shield and first wall, thus, it is supposed that all of them can reach the same temperature levels. 4.1. Rankine steam cycle This cycle is based on the work developed in [3,40] and is illustrated in figure 4. This is a layout with three steam turbines where the high pressure (HPT) and medium pressure (MPT) turbines feature two bleedings to heat up the low pressure stream. The HPT outlet stream is reheated with the reactor heat to avoid the formation of liquid water. This is a standard Rankine cycle, thus, the inlet turbine temperature limit has been set at 600 ◦C to not become supercritical. This marks a limit for the moderate and optimistic scenarios that could reach temperatures of 650 ◦C and 800 ◦C respectively. 4.2. Brayton helium cycle The proposed cycle, shown in figure 5, is based on [3,41]. Helium compression is an energy-intensive process, to reduce its power consumption, the compression process has been interrupted by two intercooling steps. After the compression (point 9 in figure 5), the cold stream is heated with the turbine outlet stream before passing through the reactor heat exchanger. As in [3], the compression relation in both compressors is defined by equation (6): rci =n qrct/Σ(rct/Σ(1−∆Picj)(6) where rci is the compression relation in each compressor; n, the number of compression stages; rct, the total compression relation, and ∆Picj is the pressure jump. 4.3. Feher super-critical-CO2cycle Super-critical-CO2cycles are renowned for their exceptional regenerative capabilities, achieved by retaining elevated temperatures at the turbine outlet. Additionally, these cycles exhibit a high compressibility close to the critical point allowing an inexpensive compression of the fluid. The chosen layout is a modified version (shown in figure 6) of the HLC.LDS version of [37]. This layout features two regenerators, a high temperature one to take advantage of the high-temperature at the turbine outlet and an mass-unbalanced low-temperature heat exchanger to control the pitch point inside the regenerator. For further explanation refer to [37]. 8 Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Salaverri et al [49] Galambos J. 1990 Unpubl Intern Oak Ridge Doc [50] IEA 2023 Evolution of solar PV module cost by data source, 1970–2020, (IEA) (available at: https://www.iea.org/dataand-statistics/charts/evolution-ofsolar-pv-module-cost-bydata-source-1970-2020) (Accessed 28 July 2023) [51] Lovering J.R., Yip A. and Nordhaus T. 2016 Historical construction costs of global nuclear power reactors Energy Policy 91 371–82 [52] Mulder R.A., Melese Y.G. and Cardozo N.J.L. 2021 Plant efficiency: a sensitivity analysis of the capacity factor for fusion power plants with high recirculated power Nucl. 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