NFC transition alternatives and assessment criteria

In our previous study, we developed a dynamic model to analyze the quantitative performance of China’s future NFC transition from existing to advanced energy systems through 2100 [31, 40-42]. The MCDM framework uses model performance to present an integrated holistic evaluation of representative NES scenarios for sustainability orientation in China. The four proposed candidate NFC transition alternatives are as follows: Alternative 1 (A1) involves a once-through (OT) fuel cycle, wherein uranium–plutonium oxide (UOX) fuels are consumed in both pressurized water reactors (PWRs) and pressurized heavy water reactors (PHWRs) without recycling the spent fuel; Alternative 2 (A2) maintains an OT fuel cycle in a PHWR. Here, the PWR spent fuel discharged from Al is reprocessed and reused in the PWR in the form of mixed uranium–plutonium oxide (MOX) fuels; Alternative 3 (A3) involves reprocessing of the MOX spent fuel discharged from A2 and multi-recycling of the resulting plutonium (Pu) in a fast reactor (FR); Alternative 4 (A4) involves reprocessing of the PWR spent fuel discharged from Al, followed by direct recycling in an FR, as shown in Figure 2.

Fig. 2Full-screen View

(Color online) NFC diagram of four candidate alternatives

We also identified six sustainability-oriented main criteria (MC) and 12 sub-criteria (SC) from the perspective of E-E-T to establish a suitable criteria system for evaluating the comprehensive sustainable performance of China’s potential NFC alternatives, as shown in Fig. 3.

Fig. 3Full-screen View

(Color online) Sustainability-oriented main criteria and sub-criteria

Weights of criteria

As a relative measurement method, AHP applies to ranking multiple alternatives while considering both qualitative and quantitative criteria and can also be used to determine criteria weights. Based on the combination of conventional AHP and fuzzy set theory, a fuzzy AHP method extends the limits of conventional AHP by converting original crisp judgments into fuzzy contexts, effectively addressing uncertainty/obscurity situations in practice. However, the existence of fuzzy sets and intricate associated operations increases the complexity of programming and calculation. The major procedures of fuzzy AHP are as follows: 1) constructing the decision-making hierarchy, 2) establishing the fuzzy pairwise comparison matrix in terms of fuzzy numbers, 3) aggregating group decisions and computing priority weights, and 4) defuzzifying fuzzy weights and verifying consistency [46]. Notably, no fixed execution sequence exists between aggregation and defuzzification; however, the calculation is simplified if the defuzzification process is performed first. Subsequently, we thoroughly review and compare various approaches for these procedures across the entire fuzzy AHP model.

Alternative ranking and evaluation

PROMETHEE is more applicable to case studies involving a limited number of alternatives than other popular MCDM techniques. It possesses the advantages of both simplicity and high specificity of outranking relationships with respect to multiple conflicting criteria. By obtaining the preorder of candidate alternatives using the preference function to aggregate leaving and entering outranking flows, PROMETHEE I provides a partial ranking, which may lead to incomparability between some alternatives, whereas PROMETHEE II updates to generate a complete ranking by computing the net outranking flow. The major procedures of PROMETHEE II are described in the SI. The net outranking flow is the balance between exiting and entering flows. This defines the complete preorder of PROMETHEE II, implying that an alternative with a higher net flow would yield a better advantageous sequence.

Although a complete preorder enables DMs to effectively compare all alternatives, some relationship information may be lost during the calculation of net outranking flow. To demonstrate the conflicts and mutual relations among the criteria and alternatives applied to the scores of unicriterion net flow (Table 2), the concept of GAIA was proposed to improve PROMETHEE II using a visually descriptive approach [48].

Table 2 presents more information than the conventional multicriteria table owing to the extra consideration of the preference degrees of DMs. ${\varphi }_j\left(a_i\right)$ is dimensionless and its value lies between $-$ 1 and 1. Each alternative can be shown as a unique point in the k-dimensional space.

GAIA employs the principal components analysis to achieve dimension reduction, which can maintain the integrity of information to the extent possible in the k-dimensional space. The GAIA plane is the best selection to translate the k-dimensional representation on a two-dimensional plane as it can retain the maximum possible quantity of information, as shown in Figure 4.

Fig. 4Full-screen View

(Color online) GAIA plane

In the GAIA plane, each point represents an alternative and the axes represent criteria. The decision axis is determined as the weighted result of all criteria axes. Alternatives with similar profiles tend to be closer to each other on the plane, reflecting their shared strengths and weaknesses. Criteria with similar attributes are presented as adjacent axes in the same direction, whereas the axes of conflicting criteria perform in the opposite direction. The length of each axis indicates the weight assigned to the corresponding criterion. When an alternative point is located close to the orientation of a certain criterion axis or several interconnected criteria axes (particularly when it aligns perfectly with an axis), this alternative performs well on those criteria or several interconnected criteria, and vice versa. The decision axis, represented by the projection of the unit vector of the weights, demonstrates the relationship between criteria and PROMETHEE rankings. If a specific criterion is provided for almost all weights, the decision axis coincides with the criteria axis in the GAIA plane. However, the decision axis does not indicate the optimal alternative. Rather, it provides information on the position of the most appropriate alternative relative to the criteria. The orientation and length of a decision axis can change as criteria weights change. This change can thus be considered an indicator to illustrate the type of compromise following multiple measures of performance across all criteria and improve weight assignment. Additionally, the shorter the decision axes in the GAIA plane, the more reliable the decisions, suggesting a significant distinction between alternatives.

Although the GAIA plane covers almost all information, some information may be lost after the projection process. Set $\delta$ as the quantity of information preserved. $\delta =\frac{{\lambda }_1+{\lambda }_2}{{\displaystyle {\sum }_{j=1}^k{\lambda }_j}}$ (3)

Let the scores of the unicriterion net flow be arranged as a matrix [M]_n×j, where ${\lambda }_1,{\lambda }_2,\cdots ,{\lambda }_j,\cdots {\lambda }_k$ is the set of positive eigenvalues of the covariance matrix $M\text{'}M$ satisfying the condition ${\lambda }_1<{\lambda }_2<,\cdots ,<{\lambda }_j<,\cdots <{\lambda }_k$. Generally, $\delta$ exceeds 60% and often 80%. A higher value of $\delta$ indicates that concrete and complete structures of MCDM problems were built considering multiple criteria explicitly. When $\delta$ decreases to lower than 50%, the reliability of the GAIA plane decreases.

Decision-making optimization

MOORA is one of the recent MCDM methods proposed by Braorers and Zavadskas [36]. Compared with other conventional techniques, MOORA significantly simplifies mathematical computations and streamlines the overall process while reinforcing the stability of the MCDM framework. The main steps are as follows:

Step 1: Define a decision matrix $F={\left[c_{ij}\right]}_{m\times n}$ with $m$ alternatives and $n$ criteria. $c_{ij}$ denotes the value of the $i_{th}$ alternative on the $j_{th}$ criterion. $F={\left[c_{ij}\right]}_{m\times n}=\left[\begin{array}{c}{c}_{11}{c}_{12}\cdots c_{1n}\\ c_{12}{c}_{22}\cdots c_{2n}\\ ⋮⋮\ddots ⋮\\ c_{m1}{c}_{m2}\cdots c_{mn}\end{array}\right]$ (4)

Step 2: Normalize the decision matrix $F={\left[c_{ij}\right]}_{m\times n}$ using Eq.5. $c_{ij}^{\ast }=\frac{c_{ij}}{\sqrt{{\displaystyle {\sum }_{j=1}^m{c}_{ij}^2}}}$ (5)

Step 3: Calculate the normalized evaluation value for each alternative by considering all existing alternatives and their weights. $y_i^{\ast }={\displaystyle \sum _{j=1}^t{w}_j{c}_{ij}^{\ast }}-{\displaystyle \sum _{j=t+1}^n{w}_j{c}_{ij}^{\ast }}$ (6) where $y_i^{\ast }$ is the final MOORA score for the i_th alternative. $j=1,2,3,\cdots ,t$ refers to the beneficial criteria, and $j=t+1,t+2,\cdots ,n$ refers to the remaining non-beneficial criteria.

Fuzzy AHP Weights

In this study, a stochastic sampling model was developed to simulate an iterative expert survey process for estimating group decisions. This model incorporates an anonymous iteration method among a panel of simulated experts, underlying the Delphi technique. Significantly, none of the strict guidelines or absolute recommendations have yet defined the most appropriate sample size of panel participants for the Delphi survey, as many Delphi studies used between 30 and 60 panelists [49]. We further analyzed and determined a reasonable sample size for the proposed stochastic sampling model. Unlike expert judgments in practice, the simulated results of the 30-sample size contained the largest diversity with high sampling error. As the sample size increases, the resultant distribution presents a normal distribution with a low standard deviation and broad confidence interval. Finally, we determined the upper limit of the 60-sample size to simulate and collect 60 groups of expert opinions in the form of a pairwise comparison matrix in line with 6 MC and 12 SC. Each selected comparison matrix passed a consistency check because its consistency ratio was less than 0.10.

Figure 5 shows the calculated weights for the 6 MC and 12 SC. Seven sets of final criteria weights were determined using the characteristics of the different procedures used across the entire fuzzy AHP model. For the first four sets, the GM method was first employed to aggregate the fuzzy information from group decisions, followed by weight aggregation via four different methods: GM, L-M, LLS, and FPP. Finally, the TFN weights were defuzzified using the identical COG method. In the latter three sets, the GM method was applied for group decision aggregation and the IA, CFCS, and SEA methods were selected to aggregate and defuzzify the criteria weights. Significantly, the weight of SC41- Pu in nuclear system per electricity generated calculated using the SEA method is 0.000. A value of zero indicates that this criterion slightly influences the overall performance. However, its role in the entire evaluation system cannot be ignored because of its zero value.

Fig. 5Full-screen View

(Color online) Main- and sub-criteria weights under different methods combinations for fuzzy AHP processes

As shown in Fig. 5, most SC weights exhibit similarities with slight variations when different aggregation and defuzzification procedures are employed. Although the effect of individual discrepancies may be negligible in many cases, the accumulation of successive and arbitrary discrepancies can have an immeasurable effect on the final MC weights. To address this issue, we proposed an integrated fuzzy AHP weighting approach, which aggregates and averages the different calculated weighting results using the above seven methods to finally integrate criteria weights. This integrated approach can significantly improve the robustness and accuracy of the fuzzy AHP model under uncertainty, effectively eliminating decision-making bias caused by methodological pitfalls. The final criteria weights presented in Figure 6 show that MC1-Resource utilization is the most important indicator for ensuring the sustainable development of nuclear energy with a weight of 0.193, followed by MC4-Proliferation risk (0.173), MC5-Environmental Impact (0.171), MC3-Levelized Cost of Electricity (0.164), and MC6-Technological Readiness with a weight of 0.151. By contrast, MC2-Nuclear Waste Management had the lowest impact on the overall prioritization of alternatives, with a weight of 0.148. For MC1-Resource utilization, although the NU supply is not considered a restrictive factor limiting nuclear energy development in the short term as additional uranium resources are discovered, it is still becoming a prime concern for nuclear sustainability [10, 50]. This was directly reflected as a high weighting value of MC1-Resource utilization. Compared with other toxic industrial wastes, nuclear waste is neither particularly hazardous nor difficult to manage, and its amount is relatively low. Moreover, the nuclear sector takes full responsibility for the waste. Additionally, safe methods for the final disposal of nuclear waste including LILW and HLW have been technically and contrapunctally proposed in terms of radioactivity. As an international consensus approach to provide safe management of nuclear waste, geological disposal ensures that no harmful contaminants and no radioactivity can leach or migrate from waste repository into ambient environments for hundreds of years. Because future risks cannot easily be assessed, the impact of nuclear waste management criteria is always underestimated. Thus, for MC2-Nuclear waste management that gained a relatively low weight in this study, it would be also reasonable. By contrast, moderate weights for the proliferation risk criteria can be derived in response to the immediate consequences of nuclear security incidents and emergencies.

Fig. 6Full-screen View

(Color online) Proportion of the final weights of all criteria

As shown in Figure 6, no extremely high or low weighting value exists, implying that no criterion has an overwhelming importance for nuclear sustainability. This also proves that the proposed fuzzy AHP model and data are reasonable and reliable.

PROMETHEE GAIA

In this study, we intend to incorporate currently available modeling techniques into a novel hybrid MCDM framework to evaluate the sustainability of four candidate NFC alternatives using a specific E-E-T criteria system. After the identification of the 6 relevant MC and 12 SC, all quantitative performance indicators were linked with the output data of the four reference fuel cycle scenarios simulated to build a system evaluation metric of the MCDM framework. Notably, the specifics of the first stage for structuring the decision-making problem of the proposed MCDM framework (as shown in Figure 1) were elaborated in a separate study [40]. Table 3 presents the performance metrics of the criteria system for the four fuel cycle alternatives. In addition, the details of the material and energy flow modeling (e.g., the design specifications and parameters of the reference nuclear reactors, time factor assumption, and deployment rate of nuclear facilities) and the related performance analysis can be found in our previous studies [31, 40-42]. A weighted decision matrix can be derived by combining the fuzzy AHP weights and performance data. Because all the criteria have been unified into cost-type attributes, where lower values yield better performance, the weighted decision matrix was directly normalized using the linear min-max normalization method. Subsequently, an alternative screening and ranking process was performed using PROMETHEE GAIA.

3.2.1

Screening and ranking results

For PROMETHEE GAIA, an outranking model was first built using the PROMETHEE II method to calculate the net flow. In this model, we selected a level preference function to evaluate the quantitative criteria of MC1–5 (including their subcriteria) and a V-shaped function for the qualitative criteria of MC6. Figure 7 shows the overall net ranking flow results for the four selected NFC alternatives. This indicates that the alternative ranking of prioritization, from highest to lowest, is as follows: A4, A1, A2, and A3. For A4, which involves direct spent fuel recycling in FRs, a compelling advantage to balancing its leaving and entering flows for net flow maximization is achieved.

Fig. 7Full-screen View

(Color online) Net ranking flows of four alternatives

Figure 8 shows a GAIA plane with a quality of 97.2%, maintaining the most integrated information via a two-dimensional representation comprising both U and V, where U and V are the first and second principal components with the most valid information, respectively, and V possesses the maximum additional information orthogonal to U. As shown in Figure 8, the clubs and diamonds linked with black axes drawn from the center of the GAIA plane represent alternatives and criteria, respectively. The shades of the clubs are related to the performances of the corresponding alternative; the darker the shade the better the performance of the club. The thick red axis represents the decision axis.

Fig. 8Full-screen View

(Color online) GAIA plane of four alternatives and six main criteria (CM)

The length of each axis indicates the relative importance of each criterion. For example, the axis of MC5-Environmental impact was the shortest because of its least assigned weight. The orientation of the axis can be applied to compare the effects of the criteria on the alternative evaluation. If the axes point in a parallel direction, their relevant criteria will have properties similar to those of the alternatives. For instance, both axes of MC1-Resource utilization and MC2-Nuclear waste management point in similar directions, implying that they could similarly influence the alternative evaluation. However, the resultant change caused by MC1-Resource utilization is slightly more significant than that of MC2-Nuclear waste management because the axis of the former is slightly longer. The dispersion of some axes in opposite directions indicates the presence of conflicting criteria such as MC1-Resource utilization and MC3-Economics, MC5-Envrionmental impact, and MC6-Technological readiness. Additionally, Figure 8 shows that A4 can be identified as the best compromise alternative because it is located within the area of decision axis points. This may be attributed to the relatively high performance of each conflict criterion.

Further, we analyzed the alternative performances of the different criteria separately through alternative positions with respect to the criteria axes. Figure 9 shows the U-V GAIA planes for the six MC cases, where the blue axis represents a certain criterion. When the projection of a certain alternative on the criteria axis close to the thick red decision axis is relatively long, the performance of this alternative is better than that of the others. For MC1-Resource utilization, A4 was the preferred choice, while A1 was the worst. MC2-Nuclear waste management shares the same ranking results as MC1-Resource utilization, indicating that A4 performs the best in terms of both resource utilization and nuclear waste management. However, from an economic perspective (MC3-Economics), A1 is ranked first and A4 last. Furthermore, A1 adopts a favorable position under MC4-Proliferatrion risk and MC6-Technological readiness. Because the overall process of an NFC system is more complex and involves various species of nuclear fuels than others, A3 must address additional technological barriers while exiting higher nuclear proliferation risks. Therefore, A3 is the least competitive because of the importance of MC4-Proliferation and MC6-Technological readiness. However, when considering MC5-Environmental impact, the ranking result becomes the opposite: A3 is the best and A1 the worst.

Fig. 9Full-screen View

U-V GAIA plane of six MC

3.2.2

Sensitivity analysis

Using the relationship between criteria and alternatives shown in Figure 8, we conducted a sensitivity analysis of criteria weights to prove the effectiveness and robustness of the chosen preference relations and to validate the reliability of the overall MCDM framework. As shown in Figure 10, when the weight of a single criterion changes within a specially limited range and the weights of the other criteria are reassigned accordingly based on their previously specified proportions, as shown in Figure 6, the net ranking flows of the four alternatives can make a difference with no ranking reversals. The specifically limited range is termed the stability intervals of the criteria. Figure 11 shows the stability intervals of the six MC. The broader the stability range, the more stable the corresponding criteria are against external interference.

Fig. 10Full-screen View

(Color online) Trajectory of GAIA decision axis in the four alternatives influenced by indicator weights

Fig. 11Full-screen View

(Color online) Weight stability interval of MC

The decision axis, which is an exclusive and flexible tool in PROMETHEE GAIA, is the visual pointing axis of the criteria weights located in the k-dimensional space of the GAIA plane. Its length, position, and orientation on the U-V plane depend only on its projection in a two-dimensional space. Its orientation can be used to determine only the optimal alternative; its length has no specific meaning because of the uncertainty and diversity of the projection angle. The decision loses its effectiveness only when the length is extremely short. The decision axis is similar to the weighted average of the criteria axes; thus, a position change in the decision axis reflects the variance of the criteria weights intuitively. This is significant for detecting underweight or overweight criteria. When the criteria weight increases from zero, the decision axis begins to rotate toward the corresponding criteria axis with a length change until both axes coincide when the weight reaches 100%, as shown in Figure 10. The red shaded area indicates the stability interval of the designated criterion.

From the perspective of alternatives, the results show that A1 and A3 are sensitive to criteria weight changes, namely, larger uncertainties exist in assessing these two candidate NFC alternatives. On the contrary, A4 is the most insensitive candidate because its net outranking flow can always be the largest, regardless of the variances in the criteria weight.

For a certain criterion, when its weight changes within a range of 0-100%, a wide trajectory of the decision axis implies that it is less sensitive. As the weight of MC1-Resource utilization or MC2-Nuclear waste management increases, the decision axis turns in the same clockwise direction in the U-V GAIA plane, indicating that MC1-Resource utilization and MC2-Nuclear waste management can similarly influence these four alternatives. However, if the weight of MC1-Resource utilization or MC2-Nuclear waste management accounts for more than 50%, no changes in their final ranks are observed, with only a slight change in the outranking flow.

When strengthening the importance of MC3-Economics, the decision axis rotates counterclockwise in the two-dimensional U-V GAIA plane. This indicates that as DMs focus on economic issues, A1, which currently has an incomparable economic advantage, becomes the most optimal alternative rather than A4. However, when the weight of MC3-Economics increases to 47%, the length of the decision axis becomes the shortest, with a high uncertainty. This is a consequence of the internal interactions of conflicting criteria with an impact on alternatives. In such extreme circumstances, the credibility of the ranking results is compromised, and it is challenging to determine the best alternative.

When DMs focus on MC4-Proliferation risk, as shown in Figure 10, A1 still maintains the first rank among all the alternatives, its decision axis rotates in a counter-clockwise direction, and its length increases significantly with the largest weight stability interval (16.49-58.59%) compared with those of the other criteria. A broad stability interval indicates that proliferation risk cannot easily alter the overall ranking results of NFC alternatives. However, when the weight of MC4 decreased from 16.49% to zero, A4 was the best option. Notably, its decision axis length became extremely small as the weight approached zero, leading to unreliable results. This in turn proves that the public cannot completely disregard nuclear security. Similarly, as the weight of MC6 increases, Figure 10 shows a similar trajectory of the decision axis as that of the MC4 case. However, the decision axis in the MC6 case was stable, and its length showed no noticeable change. This is mainly because of the differences in inherent characteristics and sensitivity to external disturbances between different criteria.

MOORA and optimization suggestions

The MOORA analysis provides a comparative evaluation to validate the above-mentioned screen results, ranking the four NFC alternatives in descending order of the final MOORA score $y_i^{\ast }$. The calculated results of the MOORA method are presented in Table 4. As aforementioned, A4 is the most suitable alternative, whereas the ranking of the other three alternatives has differences: A3 and A1 are ranked second and third, respectively, and A2 is considered the least preferred because it exhibits the weakest performance. Moreover, A4 gains a good ranking considering the benefits of NU conservation, nuclear waste management, and environmental impact reduction. However, the promising A4 cannot continuously assume the dominant position in all aspects because of its present performance. Combined with the MOORA results, we further analyzed the system optimization potential and provided some policy suggestions following the national strategy of nuclear energy.

Although progress has been made toward environmental sustainability, environmental issues have become a major concern in China. NU mining and milling activities have caused a significant impact on the environment, particularly in the processes of open-pit mining and open-air waste disposal, which use most of the land over the entire fuel cycle. The second contributor to land occupation is NPP construction and operation, and the final geological repository for nuclear waste contributes slightly[51]. Currently, China has become self-sufficient in most aspects of the fuel cycle. However, it still relies mostly on foreign uranium supply. Regarding the rapid expansion of nuclear power, the Chinese government has declared a future development plan for self-sufficient uranium production in cooperation with foreign suppliers. This plan includes at least one-third of domestic uranium production and two-thirds of Chinese equity in foreign mines and open uranium markets. Therefore, along with the growth in domestic uranium supply, the environmental impact caused by land use will increase accordingly. Compared with OT alternatives, A4 and other NFC paths with reprocessing and recycling processes can significantly reduce NU consumption, thus giving prominence to the future of small land occupations over time.

In recent years, decarbonization has gradually become a global imperative for climate change mitigation, as the European Union has implemented a plan to render the entire community block free of CO₂ emissions by 2050 [6, 52]. The Chinese government has proposed carbon peak and neutrality goals in close alignment with several countries, and the long-awaited carbon tax policy is also on the agenda [53]. In the 14th Five-Year Plan, energy and climate were central policy priorities, and the National Energy Administration has proposed realistic plans for carbon reduction by the end of 2021 [54]. Recently, the Ministry of Ecology and Environment has deliberated and approved a series of administrative measures to promote the development of the national carbon emissions trading market, maximize the role of market mechanisms in addressing climate change, and encourage low-carbon technology innovation under green economic development [55-57]. As presented in Table 4, A4, which involves direct spent fuel recycling in fast reactors, has a comparative advantage in terms of reducing the life-cycle carbon emissions of the system. The active enforcement of emission–reduction policies and strategies, as well as the upcoming carbon tax, would provide potential incentives for all emitters to be responsible for increasingly expensive environmental costs, and the upcoming carbon tax could monetize environmental superiority. Although this inevitable trend is progressing, NFC innovation in the pursuit of a low-carbon development transition is urgently needed. However, solely relying on the low-carbon profit and NU conservation endowment of A4 is still insufficient to compensate for its overall low economic performance at the current stage. Normally, LRC accounts for more than 75–80% of the system’s LCOE, whereas LFCC only contributes to the remaining 20–25%. Because of the high capital investment for NPP construction, especially for extremely expensive Gen-IV reactors with some major technological obstacles, the LRC in A4 and other advanced NFC systems may not easily be changed in a short time. In addition, the LFCC considerably influences the overall economic competitiveness of nuclear energy for different fuel cycle strategic priorities. The back-end fuel cycle costs in A2–4 are generally higher than those in A1 of the OT fuel cycle [41]. This might be partially attributed to the costly investment in complex facilities and technologies subject to reprocessing, including when offsets from decreased waste disposal costs are considered. Although advanced NESs are required to address multiple barriers, future nuclear energy will become technically feasible and economically attractive with innovation-driven development in China regarding domestic policy and market environments. Notably, an excessive pursuit of a new technology might be unnecessary and cost-expensive. An understanding of the near-term viability and long-term potential of advanced nuclear technologies, as well as their economic and technical contributions to the future energy market, should be established among DMs. “What's next for nuclear energy in China” should maintain flexibility and autonomy for future uncertainties through strategy, collaboration, and innovation while being complementary with variable renewables for securing a clean, affordable, reliable, and sustainable future energy system. An optimal transition alternative for NFC might not be a potential solution, as it leads to a continuous improvement in dynamic compliance with time.