In 2021, Sweden established a national competence center, the Academic-Industrial Nuclear Technology Initiative to Achieve a Sustainable Energy Future (ANItA) (Håkansson, 2024), to conduct research and development on the introduction of small modular reactors (SMRs). At the competence center, numerous research projects—both technical and non-technical—have been initiated to address various aspects of SMRs in Sweden. This work was conducted as part of a project dedicated to fuel performance studies of SMRs. The project focuses on identifying the key differences and specific features of SMRs compared to large-scale conventional reactors, on which many SMRs are based (Carlson et al., 2022), and examining their impact on fuel performance.

One of the sought-after features of SMRs is their load-following operation capability. It is anticipated that SMRs will operate under load-following conditions (Park et al., 2023; Genglei et al., 2014; Ah et al., 2023; Zhang and Jiang, 2024) to integrate with intermittent renewable energy sources. This capability enables SMRs to adjust their power output in response to fluctuating energy demands, thereby enhancing their operational flexibility and synergy with diverse energy resources. However, power cycling associated with load-following operations may affect fuel performance (Aas, 1975; Bjurenfalk, 2020; IAEA, 2021) and operational lifespan. Power cycling causes variations in the heat output of fuel rods, leading to significant variations in the temperature of the fuel and cladding, which, in turn, affect many phenomena critical to nuclear fuel performance. This is particularly concerning in load-following operation, where repeated changes in power levels may exacerbate pellet–cladding interaction (PCI) and pellet–cladding mechanical interaction (PCMI) (Videm et al., 1979; Sercombe et al., 2012;IAEA, 1987; von Jan and Hering, 1981; NEA, 2024), posing challenges to fuel integrity and safety. The scope of this work is, therefore, to study the effects of load-following operations on fuel performance. As SMR operation data and fuel histories are not yet openly available, this study utilized fuel rod data and power histories from a large pressurized water reactor (PWR).

We analyzed the impact of load-following operations on fuel performance using the TRANSURANUS fuel performance code (Lassmann, 1992; Lassmann and Blank, 1988). Real power histories from an existing PWR were used as a reference, and hypothetical load-following operations were simulated by adjusting the linear heat rate, neutron flux, and coolant flow rate. These adjustments were made according to a parameterized load-following signal, with key parameters including cycle length, power reduction, and transition rate, which are further described in the Methods section. The impact on fuel performance was then systematically evaluated. Additionally, a sensitivity study on load-following parameters was conducted using the DAKOTA toolkit (Adams et al., 2023) to assess the effects of variations in these parameters.

Hypothetical load-following operations allow controlled variations in load-following parameters, providing flexibility to explore load-following without being constrained by historical practices. Simulating these operations with fuel performance codes is a useful starting point for studying their effects. The results can guide future research, including observational studies on irradiated nuclear fuel, irradiation experiments, and further development of the models used in fuel performance codes.

In this work, we used the fuel performance code TRANSURANUS to simulate and analyze fuel performance (Van Uffelen et al., 2019; Magni et al., 2021) in a reactor. Thermal and mechanical analyses of an irradiated fuel rod can be performed using TRANSURANUS, in which a fuel rod is represented in 1.5 dimensions (Van Uffelen, 2015), where all transport processes are solved in one (radial) dimension and the axial segments/slices/nodes are coupled via balance equations. The code requires input data on fuel design (such as dimensions and material properties) and power history (irradiation conditions such as linear heat rate, neutron flux, and coolant mass flow rate). Various fuel performance parameters, such as temperatures, pressures, stresses, strains, fission gas release, and burnup, can be obtained from the output data generated by the code. For this study, we utilized power history data from a PWR, which contains irradiation parameters at different time intervals. A total of 50 different fuel rod power histories were used. Some key fuel properties and boundary conditions are given in Table 1. In the TRANSURANUS simulations, the fuel rod was divided into 12 equal sections (or nodes), each approximately 300 mm long. To simulate a hypothetical load-following operation, the operating power history was adjusted by applying a load-following signal. The methodology for generating the load-following signal is described in the next section.

Uranium oxide fuel pellets and Zircaloy cladding have different thermal expansion coefficients, causing differential responses to changes in heat output. This disparity can lead to mechanical interactions between the two, potentially compromising cladding integrity. TRANSURANUS provides various important parameters to assess the behavior of nuclear fuel under different operating conditions. We have obtained key parameters and compared them under both normal and load-following operating conditions. Some of the key parameters extracted and compared for slice/node 6 (located at the middle of the fuel rod) between normal and load-following operation cases include cladding hoop stress, permanent tangential cladding strain, fuel centerline temperature, and fractional fission gas release. These parameters were plotted against rod average burnup for both cases and are presented in Figure 3.

The rod average burnup is lower in the load-following operation case as the reactor operates at low power for a prolonged duration. Comparison of fuel performance parameters shows that the maximum values during load-following operation were either comparable to or lower than those observed under normal operation, with all values remaining well within the defined safety margins (NRC, 1987). However, for the load-following operation case, TRANSURANUS also outputs cracks in the cladding, the lengths of which are calculated using the SPAKOR subroutine. These cracks are initiated as a result of pellet–cladding interaction–stress corrosion cracking (PCI–SCC). In the subroutine, crack initiation and growth are calculated based on the model proposed by Jernkvist (2005), but with an improved correlation for the critical stress intensity factor, as proposed by Jernkvist (2005). According to Mattas et al. (1979), crack initiation results from the chemical attack of iodine and progresses independently of applied stress, as described in Equation 1a, until a critical stress intensity factor, K ISCC , is reached (as given in Equation 1b). Beyond this point, crack growth follows the relationship described in Equation 2. In the code, specific threshold conditions (as stated in Box 1) are defined for crack initiation and growth. Once these conditions are met, the crack length is calculated using Equation 1a, b, Equation 2. Figure 4 shows crack growth as a function of the linear heat rate. a t = B ⁡ ln A 0 B Δ t + e a t − Δ t B , (1a) K ISCC = 2.2742 × 1 0 2 − 6.6881 × 1 0 − 1 T tip + 4.9617 × 1 0 − 4 T tip 2 , (1b) a t = a t − Δ t C C − a t − Δ t σ 4 y 4 Δ t , (2) where a t :  crack length at time  t , a t − Δ t :  crack length at previous time  t − Δ t , B :  rate constant,  3.3 × 1 0 − 5 m , A 0 : 3.55 × 1 0 10 e − 2.013 × 1 0 4 T avg  m h 1 , where  T avg  is the average cladding temperature in K. T tip :  temperature at crack tip, in  K , C : 1.15 × 1 0 − 3 e 1.409 × 1 0 4 T avg MPa 4 m h , where  T avg  is the average cladding temperature in K. σ :  applied stress, in  MPa y : 2 ,  geometric factor .

The same load-following signal was applied to 50 different power histories. A few parameters from each case of load-following operation and the corresponding normal operation were compared to assess whether the same trend persists across all cases or if there are any deviations. In Figure 5, the maximum cladding hoop stress (left) and the maximum fuel centerline temperature (right) are shown for both the load-following and corresponding normal operation cases across all 50 power histories, plotted at a rod average burnup level of 42 MWd/kgU. No deviation appears in any of the cases. Additionally, PCI–SCC crack propagation is observed in all 50 cases, as shown in Figure 6. In some cases, the maximum crack length is equal to the cladding thickness.

Results from the sensitivity study on load-following signal parameters are presented in Figures 7–10. In both batches of the sensitivity study, comprising two different ranges of t high and t low , the maximum values of different fuel performance parameters were extracted. The fuel centerline temperature was not included as an output since it remained almost constant in both batches of simulations. Figure 7 presents a scatterplot of the input parameters for the load-following signal against two fuel performance parameters. The circles in the plot are color-coded according to burnup levels. Although fission gas (Xe + Kr) release exhibits a clear dependence on both burnup and the load-following signal input parameters, the cladding hoop stress shows no significant dependence on burnup.

To understand the correlation between input and output variables, correlation heatmaps were generated for both batches and are shown in Figure 8. The overall trend is similar in both batches. The transition rate has a small influence on the output variables in both cases; however, compared to Batch-1 (which has a shorter load-following cycle length), its influence on hoop stress is negligible in Batch-2 (which has a longer load-following cycle length). A 3D plot, as shown in Figure 9, illustrates the influence of t high and t low on the cladding hoop stress. The plot clearly indicates that hoop stress is higher for low values of t high and high values of t low in both batches. This is presumably due to cladding contraction (deconditioning) caused by the extended low-power operation, followed by higher hoop stress from pellet–cladding mechanical interaction. Additionally, the reduced fission gas release, which occurs during prolonged low-power operation, results in lower internal rod pressure, thereby reducing the ability to counteract hoop stress.

Figure 10 shows the kernel density estimate (KDE) plots for both batches, displaying all the extracted fuel performance parameters, including maximum cladding outer oxide thickness, maximum hydrogen absorption in the cladding, and maximum cladding deformation. The output quantities are plotted in the first three rows from the top, while the bottom rows display cycle length and duty cycle. The cycle length has an average value of 35 h for Batch-1 and 155 h for Batch-2.

In this study, we have attempted to assess the effects of hypothetically implemented load-following operation on PWR fuel performance using the fuel performance code TRANSURANUS. The primary objective was to evaluate the fuel performance of near-deployment SMRs, anticipating their participation in extensive load-following operations. However, conventional PWR fuel operating history was used in the study as it closely resembles some of the upcoming SMR designs, and no SMR operating history data were available. A parameterization of the load-following schemes was developed and applied to multiple PWR power operating histories. Variations in the load-following scheme were simulated by modifying these parameters, and fuel performance was assessed. Previous studies (Videm et al., 1979; von Jan and Hering, 1981; Sercombe et al., 2012; Billaux and Haas, 1982; Fischer et al., 1988; Aas, 1975) have extensively examined the effects of power cycling on fuel performance, but typically over shorter durations. However, the impact of prolonged power cycling throughout the power history, along with variations in the load-following scheme, has not been thoroughly investigated. In addition, it is not practical to experimentally test fuel behavior under a wide range of different load-following operating conditions. Therefore, studying these effects using fuel performance codes becomes essential, making our work particularly relevant in this context.

Based on the simulation results from the TRANSURANUS code, we conclude that, apart from the cladding cracks discussed below, load-following operation does not have any adverse effects on fuel behavior, as indicated by the evaluated fuel performance parameters. Similar observations have also been made in Lokhov (2011), and nuclear power plants in Germany and France operate in load-following mode (Lokhov, 2011) with strong operational flexibility. However, many phenomena, either individually or in combination, influence fuel rod behavior, and some may be probabilistic in nature. The sensitivity study reveals that variations in the parameters of the load-following signal have distinct impacts on fuel performance. Although certain parameters, such as t high , t low , and transition rate, exhibit more pronounced effects, specific combinations can significantly increase cladding stress. For instance, extended operation at lower power followed by brief periods of high (nominal) power operation can result in elevated cladding hoop stress, which may have detrimental consequences.

No abnormal fuel behavior was observed in simulated load-following operation cases, apart from the occurrence of cladding cracks, which appeared in nearly all cases. However, the PCI–SCC model, SPAKOR, implemented in TRANSURANUS is highly questionable and cannot be relied upon to draw any firm conclusions. The model functions as a stand-alone component and neither receives nor provides feedback to other models within TRANSURANUS. In the past (Pastore et al., 2009; Rozzia et al., 2011), its predictions have been compared with data from ramp experiments, with cladding failure correctly predicted in only 50% of the cases. Therefore, further development and improvements of the PCI–SCC model are essential for reliable predictions of cladding cracks and failures in load-following operation. There is thus an identified need to improve and validate the models for PCI–SCC, which is of importance for the wider utilization of load-following operation.