Probabilistic Safety Assessment Model Research Articles

The power of precursors: An empirical assessment of nuclear power risks

The opposition in some countries to including nuclear power in future sustainable energy portfolios—in part due to “nuclear dread”—often has limited quantitative scientific foundation of the real benefits and risks. This has been amplified by the lack of sound estimates of operational risk due to the scarcity of the relevant empirical data. In order to address this gap, we use the largest open database on accident precursors along with our in-house generic probabilistic safety assessment models to conduct a comprehensive statistical study of operational risks in the civil nuclear sector. We find that the distribution of precursor severities follows a Pareto distribution, and we observe a runaway Dragon Kings regime for the most significant events. Based on our findings, we have determined that exogenous factors account for 95% of the risk associated with nuclear power. By addressing these factors in new reactor designs, we estimate that the frequency of accidents similar to the Fukushima Daiichi level can be reduced to about one every 300 years for the global fleet. Finally, our study highlights the importance and need for international cooperation focused on constructing comprehensive blockchains of accident precursors.

International case study comparing PSA modeling approaches for nuclear digital I&C – OECD/NEA task DIGMAP

Nuclear power plants are increasingly being equipped with digital I&C systems. Although some probabilistic safety assessment (PSA) models for the digital I&C of nuclear power plants have been constructed, there is currently no specific internationally agreed guidance for their modeling. This paper presents an initiative by the OECD Nuclear Energy Agency called “Digital I&C PSA – Comparative application of DIGital I&C Modelling Approaches for PSA (DIGMAP)”, which aimed to advance the field towards practical and defendable modeling principles. The task, carried out in 2017–2021, used a simplified description of a plant focusing on the digital I&C systems important to safety, for which the participating organizations independently developed their own PSA models. Through comparison of the PSA models, sensitivity analyses as well as observations throughout the whole activity, both qualitative and quantitative lessons were learned. These include insights on failure behavior of digital I&C systems, experience from models with different levels of abstraction, benefits from benchmarking as well as major contributors to the core damage frequency and those with minor effect. The study also highlighted the challenges with modeling of large common cause component groups and the difficulties associated with estimation of key software and common cause failure parameters.

A Pragmatic Approach to Update Support Studies and Human Reliability Analyses for a PSA Model

A probabilistic safety assessment (PSA) is used to estimate potential risks associated with a nuclear power plant. Event trees (ETs) and fault trees (FTs) describe accident scenarios following initiating events. They allow for identifying and quantifying the consequence frequencies. Based on success criteria, support studies are used to determine each scenario’s consequence. They are also used to define the time available for the operators to carry out the actions involved in the scenario, and consequently, the corresponding human failure probability. In this paper, we use a dynamic PSA toolbox to optimize support studies for a classical (ET/FT) PSA model. We analyze medium-break loss-of-coolant accident (LOCA) initiating events with the possible failure of the high-pressure safety injection (HPSI) system for an internal event Level 1 PSA for a pressurized water reactor plant. In order to prevent core uncovery and subsequent core damage, operators must depressurize the primary circuit to reach the low-pressure safety injection set point. This scenario represents a significant contribution to the core damage frequency. The dominant cut sets corresponding to this scenario involve HPSI failure to run over 24 h, while the thermal-hydraulic analysis supporting the human reliability assessment (HRA) analysis for this sequence assumes the unavailability of HPSI pumps at the beginning of the accident. We update the thermal-hydraulic assumptions in the support study by performing simulations for different values of the HPSI failure time. We find that even a short HPSI operation time buys significant (from the HRA point of view) available time for operators and drives significant improvement in estimating the human error probability (HEP). We postprocessed the minimal cut-set probability by integrating the obtained HEP. This result allows for more realistic quantification of the contribution of the medium-break LOCA in the core damage frequency.

Practical modeling and quantification of a single-top fire events probabilistic safety assessment model

In general, an internal fire events probabilistic safety assessment (PSA) model is quantified by modifying the pre-existing internal event PSA model. Because many pieces of equipment or cables can be damaged by a fire, a single fire event can lead to multiple internal events PSA initiating events (IEs). Consequently, when the fire events PSA model is quantified, inappropriate minimal cut sets (MCSs), such as duplicate MCSs, may be generated. This paper shows that single quantification of a hypothetical single-top fire event PSA model may generate the following four types of inappropriate MCSs: duplicate MCSs, MCSs subsumed by other MCSs, nonsense MCSs, and MCSs with over-counted fire frequencies. Among the inappropriate MCSs, the nonsense MCSs should be addressed first because they can interfere with the right interpretation of the other MCSs and prevent the resolution of the issues related to the other inappropriate MCSs. In addition, we propose a resolution process for each of the issues caused by these inappropriate MCSs and suggest an overall procedure for resolving them. The results of this study will contribute to the understanding and resolution of the inappropriate MCSs that may appear in the quantification of fire events PSA models.

Parametric geological model update and probabilistic analysis of shield tunnel excavation: A borehole-based conditional random fields approach

Shield tunnel construction has faced considerable challenges due to the uncertain geological conditions in real scenarios. The borehole data obtained from geological investigations are often too limited to effectively evaluate uncertainties at nonsampled points. Moreover, the existing probabilistic safety assessment (PSA) frameworks that consider the uncertainties of soil properties have encountered limitations in engineering practice due to the complexity of conditional random field (CRF) theory and the operability of numerical modeling. Based on the digitization of the underground infrastructure, this study implements the object-oriented parametric modeling (PM) to address these limitations. A PM-CRF engine is first developed to automate the process of parametric geological modeling using CRFs. Then, a PM-CRF-PSA interoperability framework is proposed to automatically generate a PSA model for comprehensive safety assessment considering the uncertainties of soil properties. Finally, a case study is conducted with the proposed framework to assess the whole process of parametric modeling from CRF characterization to PSA. The results of this study highlight the clear advantages of this framework compared to traditional deterministic safety assessment (DSA) methods in terms of characterization of the uncertainty of soil properties and the efficiency of PSA modeling. Thus, the proposed framework enables the efficient and comprehensive exploration of shield tunnel design schemes by considering the uncertainties of soil properties.

A traceable process to develop Bayesian networks from scarce data and expert judgment: A human reliability analysis application

The present paper develops a Bayesian Belief Network (BBN) for quantification of aggravating actions, as outcomes of inappropriate decisions, to be integrated in probabilistic safety assessment (PSA) models (i.e., the so-called errors of commission, EOCs). The BBN connects analyst ratings on influencing factors to the error forcing impact of a specific scenario, supporting the CESA-Q method (the Quantification module of the Commission Error Search and Assessment method). While contributing to the quantification of EOCs, this paper presents a novel process for the quantification of the BBN parameters (the Conditional Probability Distributions, CPDs), striving for traceable integration of expert knowledge and (scarce) data, in the form of retrospective analyses of operational events involving EOCs. The process combines the functional interpolation method for populating CPDs and Bayesian updates to adjust the BBN response to the available evidence. A first, prior BBN is developed, then sequentially updated to adjust to two data sets. This allows some intermediate validation and puts forwards the steps for future BBN updates as new EOC events (or new analyst assessments) become available.

A New Reliability Allocation Method Based on PSA and AHP for Fusion Reactors

Reasonable and feasible reliability index allocation is significant for improving safety and reducing costs for fusion reactors. Although the reliability index is allocated when designing some key systems, reliability allocation is not implemented from the overall layer to the system and component layers for fusion reactors. In this contribution, fusion reactors are divided into different layers by applying the Analytic Hierarchy Process (AHP); these layers include the overall layer, system layer and component layer, failure mode layer, etc. Combining the Probabilistic Safety Assessment (PSA) model for fusion reactors and AHP, the reliability index is allocated from the overall layer to the system and component layer. Firstly, a new reliability index allocation method based on PSA and AHP for fusion reactors is proposed. Secondly, the PSA model for an in-vessel LOCA accident of fusion reactors is selected as a case study to demonstrate the applications of the proposed method. Lastly, the relationship between PSA, items safety classification and reliability allocation are discussed. The allocation results indicate that the proposed method provides a more systematic reliability allocation scheme and contributes to improving the safety and economy of fusion reactors.

Exhaustive simulation approach for severe accident risk in nuclear power plants: OPR-1000 full-power internal events

The estimation of severe accident risks in nuclear power plants (NPPs) is significant to confirm the safety level of NPPs and to reinforce their vulnerable points. Severe accident risks can be quantified by Level 2 probabilistic safety assessment (PSA), which traditionally applies a grouping feature to handle the tremendous numbers of accident scenarios. Accordingly, risk information is likely to be lost in the process of grouping similar scenarios and in the treatment of many scenarios with one representative scenario. To obtain more comprehensive risk information including source term behaviors and plant responses during severe accidents, this study suggests an exhaustive simulation approach with new software that helps to automatically generate a large number of input data for an accident simulation code, and performs an application study using PSA models from OPR-1000 full-power internal events. Only a three-day run time was required to simulate all the severe accident scenarios, totaling 690 scenarios, using a commercial computer. The application study revealed that the conventional grouping approach can either underestimate or overestimate overall NPP risk depending on the selection of the representative scenario.

Generic and adaptive probabilistic safety assessment models: Precursor analysis and multi-purpose utilization

Motivated by learning from experience and exploiting existing knowledge in civil nuclear operations, we have developed in-house generic Probabilistic Safety Assessment (PSA) models for pressurized and boiling water reactors. The models are computationally light, handy, transparent, user-friendly, and easily adaptable to account for major plant-specific differences. They cover the common internal initiating events, frontline and support systems reliability and dependencies, human-factors, common-cause failures, and account for new factors typically overlooked in many PSAs. For quantification, the models use generic US reliability data, precursor analysis reports, the ETHZ Curated Nuclear Events Database, and experts’ opinions. Moreover, uncertainties in the most influential basic events are addressed. The generated results show good agreement with assessments available in the literature with detailed PSAs. We envision the models as an unbiased framework to measure nuclear operational risk with the same “ruler”, and hence support inter-plant risk comparisons that are usually not possible due to differences in plant-specific PSA assumptions and scopes. The models can be used for initial risk screening, order-of-magnitude precursor analysis, and other research/pedagogic applications especially when no plant-specific PSAs are available. Finally, we are using the generic models for large-scale precursor analysis that will generate big picture trends, lessons, and insights.

Insights gained from applying negate-down during quantification for seismic probabilistic safety assessment

Approximations such as the delete-term approximation, rare event approximation, and minimal cutset upper bound (MCUB) need to be prudently applied for the quantification of a seismic probabilistic safety assessment (PSA) model. Important characteristics of seismic PSA models indicate that preserving the success branches in a primary seismic event tree is necessary. Based on the authors' experience in modeling and quantifying plant-level seismic PSA models, the effects of applying negate-down to the success branches in primary seismic event trees on the quantification results are summarized along with the following three insights gained: (1) there are two competing effects on the MCUB-based quantification results: one tending to increase and the other tending to decrease; (2) the binary decision diagram does not always provide exact quantification results; and (3) it is identified when the exact results will be obtained, and which combination provides more conservative results compared to the others. Complicated interactions occur in Boolean variable manipulation, approximation, and the quantification of a seismic PSA model. The insights presented herein can assist PSA analysts to better understand the important theoretical principles associated with the quantification of seismic PSA models.

Risk-informed based comprehensive path-planning method for radioactive materials road transportation

The optimization of transportation routes of radioactive materials (RADMAT) is recognized as one of the most important measures to reduce the radioactive risks and costs during transportation. However, the route optimization indicators have not been fully considered and quantified in current researches. Here, we propose a Risk-Informed based Comprehensive Path-Planning method (RICPP) for RADMAT Road Transportation (RMRT) route optimization by considering radiological risk cost, time cost, and economical cost. Among which, the ET/FT based Probabilistic Safety Assessment (PSA) model is established to quantitatively assess the accident occurrence probability, and then the PEHR (personnel, environment, hazard target, and rescue force) comprehensive severity indexes considering vulnerability and resilience are established and quantified to characterize the accident radiological consequence. Finally, the gray relation analysis (GRA) model is employed to select an optimal path considering the multi-objective route planning indicators. The case study results show that the obtained path could reasonably reduce risks and costs during the transportation process, which demonstrates the effectiveness of the proposed method. The proposed RICPP methodology is beneficial for selecting a safer and more economical route for radioactive materials road transportation.

Framework to model severe accident management guidelines into Level 2 probabilistic safety assessment of a nuclear power plant

Severe accident management guidelines (SAMG) play a significant role in mitigating severe accidents in nuclear power plants (NPPs), and thus the modeling of SAMG into Level 2 probabilistic safety assessment (PSA) has become essential to more realistically quantify the safety of NPPs and the effectiveness of SAMG. This study developed a systematic framework to model SAMG into Level 2 PSA, in which SAMG event trees and fault trees are modeled to formulate SAMG in a probabilistic manner. Application results to the internal events of a real plant, the OPR-1000, showed that the inclusion of SAMG in the Level 2 PSA model led to not only a significant increase in the conditional containment intact probability, from 37 to 70%, but also a considerable decrease in NPP risk, namely by 44% compared to the case without SAMG. The method can be used for the estimation of the effectiveness of each mitigation strategy, as well as for the identification of the risk-significant factors regarding SAMG.

Realistic evaluation of source terms for steam generator tube rupture accidents

In the existing Probabilistic Safety Assessment (PSA) model, all the Steam Generator Tube Rupture (SGTR) sequences have been assumed to have identical fission product release characteristics without considering the sequences of no source term release resulting in a conservative evaluation. Since the Korean Nuclear Safety Act was revised in 2016, a realistic method that can reasonably evaluate the risk became needed to satisfy the PSA targets. Therefore, a new method is proposed to improve the Level 2 PSA model (decomposition event tree, containment event tree, source term category logic diagram) that can identify the SGTR sequences without fission product release to the environment. The sequences are classified by dividing the Source Term Category (STC) of SGTRs into SGTR_CON (containment) and SGTR_ENV (environment). If fission product is trapped inside the containment building and not released to the environment, it is classified as SGTR_CON. Otherwise it is classified as SGTR_ENV. About 72% of the existing STC for SGTR is treated as SGTR_CON, which does not release fission product to the environment. If SGTR STCs are divided into SGTR-CON and SGTR-ENV, then a more reasonable source term evaluation of SGTR sequences is expected.

A Method to Avoid Underestimated Risks in Seismic SUPSA and MUPSA for Nuclear Power Plants Caused by Partitioning Events

Seismic probabilistic safety assessment (PSA) models for nuclear power plants (NPPs) have many non-rare events whose failure probabilities are proportional to the seismic ground acceleration. It has been widely accepted that minimal cut sets (MCSs) that are calculated from the seismic PSA fault tree should be converted into exact solutions, such as binary decision diagrams (BDDs), and that the accurate seismic core damage frequency (CDF) should be calculated from the exact solutions. If the seismic CDF is calculated directly from seismic MCSs, it is drastically overestimated. Seismic single-unit PSA (SUPSA) models have random failures of alternating operation systems that are combined with seismic failures of components and structures. Similarly, seismic multi-unit PSA (MUPSA) models have failures of NPPs that undergo alternating operations between full power and low power and shutdown (LPSD). Their failures for alternating operations are modeled using fraction or partitioning events in seismic SUPSA and MUPSA fault trees. Since partitioning events for one system are mutually exclusive, their combinations should be excluded in exact solutions. However, it is difficult to eliminate the combinations of mutually exclusive events without modifying PSA tools for generating MCSs from a fault tree and converting MCSs into exact solutions. If the combinations of mutually exclusive events are not deleted, seismic CDF is underestimated. To avoid CDF underestimation in seismic SUPSAs and MUPSAs, this paper introduces a process of converting partitioning events into conditional events, and conditional events are then inserted explicitly inside a fault tree. With this conversion, accurate CDF can be calculated without modifying PSA tools. That is, this process does not require any other special operations or tools. It is strongly recommended that the method in this paper be employed for avoiding CDF underestimation in seismic SUPSAs and MUPSAs.

Development of a Software Tool for Seismic Probabilistic Safety Assessment Quantification with a Sufficiently Large Number of Bins for Enhanced Accuracy

Quantification in seismic probabilistic safety assessment (PSA) includes the convolution of hazard and fragility curves. Because it is difficult to find the closed-form integration for the convolution of two curves, numerical methods are widely used in practice. In practical applications, the number of ground motion level bins in numerical methods is limited, and it is not clear whether the limited number of bins leads to conservative or optimistic results. In this study, the effect of the number of bins on the quantification results with simplified assumptions is investigated. It is found that the quantification results mostly decrease as the number of bins increases. To enhance accuracy in the quantification results of seismic PSA, a method and a software tool that enable a sufficiently large number of bins to be used for the quantification of seismic PSA models are developed. The application of the developed software tool to an example seismic PSA model demonstrates how the quantification results approach accurate results as the number of bins increases. The software tool developed in this study is expected to enhance the accuracy of seismic PSA quantification results.

Identification of Risk-Significant Components in Nuclear Power Plants to Reduce Cs-137 Radioactive Risk

The amount and frequency of Cs-137 release in a nuclear accident are regulated to enhance environmental radiation protection. While significant improvements have been accomplished, including the preparation of severe accident mitigation equipment and systems to satisfy Cs-137 regulations, no attempt has yet been made along these lines to manage the structures, systems and components (SSCs) in nuclear power plants. Therefore, this paper proposes a new approach to identify the significant SSCs by quantifying related risk importance measures using release frequency and Cs-137 radioactivity. The new approach includes a Level 1 and Level 2 probabilistic safety assessment (PSA) linked model to obtain the frequency and Cs-137 radioactivity in all accident scenarios. The developed approach was applied to an OPR-1000 full-power internal events PSA model, and as a result, the top 20 SSCs were identified based on Fussell–Vesely importance, risk reduction worth, and risk achievement worth measures. The new approach can support risk-informed management for not only Cs-137 regulations but also public risk by using early and latent cancer fatalities.

Risk monitor implementation for the LVR-15 research reactor

This paper presents the implementation of a Phoenix Risk Monitor (RM) for the Light Water Reactor-15 (LVR-15), a nuclear research reactor installed in the Czech Republic. The aim of the work was to introduce dynamic capabilities in the previously developed Probabilistic Safety Assessment (PSA) model. The paper includes a description of the main characteristics of the PSA of LVR-15 and a particular focus is assigned to the developed risk monitor interface, obtained starting from scratch, and to the methodology adopted in its implementation. The interface is conceived to visualize in a meaningful way the safety level of the reactor, suggesting possible interventions to the operator to improve it whenever needed. The risk monitor has been tested with reference to specific conditions of interest, considering, in particular, the effect of external events on the safety status of the reactor, also including the specific weather conditions occurring on a seasonal basis on the reactor site.

Probability subtraction method for accurate quantification of seismic multi-unit probabilistic safety assessment

Single-unit probabilistic safety assessment (SUPSA) has complex Boolean logic equations for accident sequences. Multi-unit probabilistic safety assessment (MUPSA) model is developed by revising and combining SUPSA models in order to reflect plant state combinations (PSCs). These PSCs represent combinations of core damage and non-core damage states of nuclear power plants (NPPs). Since all these Boolean logic equations have complemented gates (not gates), it is not easy to generate exact Boolean solutions.Delete-term approximation method (DTAM) has been widely applied for generating approximate minimal cut sets (MCSs) from the complex Boolean logic equations with complemented gates. By applying DTAM, approximate conditional core damage probability (CCDP) has been calculated in SUPSA and MUPSA. It was found that CCDP calculated by DTAM was overestimated when complemented gates have non-rare events. Especially, the CCDP overestimation drastically increases if seismic SUPSA or MUPSA has complemented gates with many non-rare events.The objective of this study is to suggest a new quantification method named probability subtraction method (PSM) that replaces DTAM. The PSM calculates accurate CCDP even when SUPSA or MUPSA has complemented gates with many non-rare events. In this paper, the PSM is explained, and the accuracy of the PSM is validated by its applications to a few MUPSAs.

A rapid modeling method and accuracy criteria for common-cause failures in Risk Monitor PSA model

In the development of a Risk Monitor probabilistic safety assessment (PSA) model from the basic PSA model of a nuclear power plant, the modeling of common-cause failure (CCF) is very important. At present, some approximate modeling methods are widely used, but there lacks criterion of modeling accuracy and error analysis. In this paper, aiming at ensuring the accuracy of risk assessment and minimizing the Risk Monitor PSA models size, we present three basic issues of CCF model resulted from the changes of a nuclear power plant configuration, put forward corresponding modeling methods, and derive accuracy criteria of CCF modeling based on minimum cut sets and risk indicators according to the requirements of risk monitoring. Finally, a nuclear power plant Risk Monitor PSA model is taken as an example to demonstrate the effectiveness of the proposed modeling method and accuracy criteria, and the application scope of the idea of this paper is also discussed.

A plant-specific HRA sensitivity analysis considering dynamic operator actions and accident management actions

The human reliability analysis is a method by which, in general terms, the human impact to the safety and risk of a nuclear power plant operation can be modelled, quantified and analysed. It is an indispensable element of the PSA process within the nuclear industry nowadays. The paper herein presents a sensitivity study of the human reliability analysis performed on a real nuclear power plant–specific probabilistic safety assessment model. The analysis is performed on a pre-selected set of post-initiator operator actions. The purpose of the study is to investigate the impact of these operator actions on the plant risk by altering their corresponding human error probabilities in a wide spectrum. The results direct the fact that the future effort should be focused on maintaining the current human reliability level, i.e. not letting it worsen, rather than improving it.