Seismic reliability of electrical power transmission systems

The reliability of electric power transmission systems is important for the probabilistic safety assessment of nuclear power plants under a given earthquake loading as it relates to the loss of off site power to the nuclear power plants. Here, a comprehensive model to evaluate the seismic reliability of electric power transmission systems is presented. The model provides probabilistic assessments of structural damage and abnormal power flow that can lead to power interruption in a transmission system under a given earthquake. With the proposed methodology seismic capacities of electrical. equipment are determined on the basis of available test data and simple modeling from which fragility functions of specific substations are developed. Earthquake ground motions are defined as stochastic processes. Probabilities of network disconnectivity and abnormal power flow are assessed through Monte Carlo simulations. The proposed model is applied to the electric power network in San Francisco and vicinity under the 1989 Loma Prieta earthquake, and the probabilities of power interruption are contrasted with the actual power failures observed during that earthquake.     

Seismic fragilities for nuclear power plant risk studies

Seismic fragilities of critical structures and equipment are developed as families of conditional failure frequency curves plotted against peak ground acceleration. The procedure is based on available data combined with judicious extrapolation of design information on plant structures and equipment. Representative values of fragility parameters for typical modern nuclear power plants are provided. Based on the fragility evaluation for about a dozen nuclear power plants, it is proposed that unnecessary conservatism existing in current seismic design practice could be removed by properly accounting for inelastic energy absorption capabilities of structures. The paper discusses the key contributors to seismic risk and the significance of possible correlation between component failures and potential design and construction errors.     

Numerical computation of fragility curves for NPP equipment

The seismic probabilistic risk assessment (PRA) methodology is a popular approach for evaluating the risk of failure of engineering structures due to earthquake. In this framework, fragility curves express the conditional probability of failure of a structure or component for a given seismic input motion parameter A, such as peak ground acceleration (PGA) or spectral acceleration. The failure probability due to a seismic event is obtained by convolution of fragility curves with seismic hazard curves. In general, a log-normal model is used in order to estimate fragilities. In nuclear engineering practice, these fragilities are determined using safety factors with respect to design earthquake. This approach allows to determine fragility curves based on design study but largely draws on expert judgement and simplifying assumptions. When a more realistic assessment of seismic fragility is needed, simulation-based statistical estimation of fragility curves is more appropriate. In this paper, we will discuss statistical estimation of parameters of fragility curves and present results obtained for a reactor coolant system of nuclear power plant. We have performed non-linear dynamic response analyses using artificially generated strong motion time histories. Uncertainties due to seismic loads as well as model uncertainties are taken into account and propagated using Monte Carlo simulation.     

堆芯补水箱地震易损性分析

本文采用有限元软件ANSYS建立AP1000核电站堆芯补水箱（CMT）三维有限元模型,通过模态分析获得其结构特征,采用时程分析法较为真实地模拟CMT地震下响应。通过地震易损性数学模型,对CMT的各项易损性参数进行分析,获得了其抗震能力中值A_m、随机性标准差β_R以及不确定性标准差β_U,计算出其高置信度低失效概率（HCLPF）值。结果表明：CMT的HCLPF值明显高于设计安全停堆地震强度0.3g,说明其具有较高的抗震能力,且HCLPF值略高于采用确定论方法得到的值。对易损性参量误差敏感性分析发现β_R取值变化对CMT的条件失效概率和HCLPF值影响较小,可简化部分随机性误差的考虑,使得易损性分析更简洁。     

The seismic reliability of VVER-1000 NPP prestressed containment building

The failure probability assessment of the containment building is an essential feature of the Level 2 PSA studies of nuclear power plants. The primary purpose of this paper is to demonstrate the methodology of evaluating containment seismic induced probability of failure without containment pressurization. The Loviisa, Finland site is one of the most seismically stable in the world and the numerically evaluated seismic induced failure probabilities are not representative for other sites. In addition, the containment concept described in this paper is not the typical Russian design which uses helical tendons in the cylindrical part of the structure and has a ring girder at the spring line of the structure. So the conclusions reached are applicable only to the containment configuration described in the paper. The geometry of the containment was determined by its preliminary design. The seismic hazard of the plant site was assessed during Level 1 PSA of the Loviisa plant. The initial information for seismic fragility analysis of the containment is the seismic response of the structure. The structural model for response analysis was the stick model. The stress analysis of the containment was carried out using the shell element model. The fragility evaluation of the containment was performed with the PROSAN-program. The structure was modeled as a parallel system consisting of the most heavily stressed elements. The resulting fragility curve gives the conditional probability of failure as a function of peak ground acceleration. The seismic hazard and the fragility were convolved to obtain the annual nonexceedance probability distribution for the collapse frequency of the structure.     

重要厂用水系统地震情况下可靠性分析

重要厂用水系统是核电厂重要的安全系统之一,其失效概率通常由系统可靠性分析获得。而地震情况下设备的失效概率是地震动峰值加速度的函数,且地震的发生又具有随机性,目前概率安全评价中传统的故障树分析方法对此种情况缺乏足够的处理能力。本文采用蒙特卡罗模拟方法解决条件概率的问题,针对地震情况系统可靠性分析,提出了评价模型,并对核电厂重要厂用水系统进行了分析计算,得到地震情况下重要厂用水系统的年失效概率为1.46×10^-4。计算结果与设备抗震性能数据符合,验证了分析模型的合理性。     

Component probabilistic seismic analysis — What could be done now?

General outline on the direction of a probabilistic analysis of the seismic risk for nuclear power plants, including as far as possible the statistics of the seismic events, and of the structural or functional failures.     

Reliability assessment of emergency exhaust system in a pool-type research reactor

The reliability of an extract system in a swimming-pool-type research reactor has been assessed. A global fault-tree analysis technique has been utilized. The basic event reliability data is based on both generic and reactor specific informations.The unavailability of the extract system is quantified in terms of the unavailability of the various functional requirements of the system. The unavailability is expressed as the probability of failure on demand. The computer system unavailability is determined from the minimal cutsets of the system. It is found that only three events have a major contribution to the top event, i.e., failures of compressed air supply, electric power supply and solenoid valve. A sensitivity analysis is performed to show the effects of variations in the data values of the dominant cutsets. An uncertainty analysis was also performed on the fault tree. The evaluations show that the reactor extract system lacks diversity and redundancy in most of its components. It is tolerant of most minor degradations, as these are taken care of by the operating policies and procedures. However, it can not tolerate common cause failures, e.g., simultaneous compressed air and electric power supply failure. Based upon the results obtained some recommendations are made.     

Dependent failure analysis of NPP data bases

A technical approach for analyzing plant-specific data bases for vulnerabilities to dependent failures has been developed and applied. Since the focus of this work is to aid in the formulation of defenses to dependent failures, rather than to quantify dependent failure probabilities, the approach of this analysis is critically different. For instance, the determination of component failure dependencies has been based upon identical failure mechanisms related to component piecepart failures, rather than failure modes. Also, component failures involving all types of component function loss (e.g., catastrophic, degraded, incipient) are equally important to the predictive purposes of dependent failure defense development. Consequently, dependent component failures are identified with a different dependent failure definition which uses a component failure mechanism categorization scheme in this study. In this context, clusters of component failures which satisfy the revised dependent failure definition are termed common failure mechanism (CFM) events.Motor-operated valves (MOVs) in two nuclear power plant data bases have been analyzed with this approach. The analysis results include seven different failure mechanism categories; identified potential CFM events; an assessment of the risk-significance of the potential CFM events using existing probabilistic risk assessments (PRAs); and postulated defenses to the identified potential CFM events.     

Seismic probabilistic risk analysis based on stochastic simulation of accelerograms for nuclear power plants in the UK

This article presents an approach to probabilistically assess the seismic risk of nuclear power plants (NPPs) in the UK. The approach proposed is based on direct stochastic simulation of the seismic input to conduct nonlinear dynamic analysis of a structural model of the NPP analysed. Therefore, it does not require the use of ground motion prediction equations and scaling/matching procedures to define suitable accelerograms as is done in conventional approaches. Additionally, as the structural response is directly calculated, it does not require the use of Monte Carlo-type algorithms to simulate the damage state of the NPP analysed. However, it demands longer use of computer resources as a relatively large number of nonlinear dynamic analyses are needed to perform. The approach is illustrated using an example of a 1000 MW Pressurised Water Reactor building located in a representative UK nuclear site. A comparison of risk assessment is made between the conventional and proposed approaches. Results obtained are reasonable and well constrained by conventional procedures; hence, it can confidently be used by the UK New Build Programme in the next two decades to generate 16 GWe of new nuclear capacity.     

储液容器地震易损性参数计算

本文介绍了核电厂设备的易损性分析方法以及易损性模型的参数化计算方法。对核电厂中的典型储液容器应急补水箱（ASG水箱）使用Housner质量-弹簧简化模型进行了分析。对ASG水箱的各项易损性参数进行了计算,绘制出其易损性曲线,并得出高置信度低失效概率（HCLPF）值。结果表明：ASG水箱的HCLPF值低于安全停堆地震（SSE）水平,属于抗震能力较低的设备,需在结构上进行加强。     

核电站环形吊车抗震计算分析

应用有限元分析软件ANSYS建立了核电站环形吊车结构的三维计算模型,在模态分析的基础上,以环形吊车所在的安全壳标高40.0 m处的地震反应谱作为输入,对环形吊车结构进行了地震响应分析计算.计算结果表明,地震动作用下环形吊车的垂直位移和应力响应比较小,但水平位移和应力响应比较大,原因是环形吊车水平方向1阶弯曲振动固有频率位于水平地震反应谱最大值频率区间附近;环形吊车结构在地震动作用下能满足抗震设计强度要求,应力集中处的最大应力小于材料屈服极限.     

Seismic response of reactor vessel internals for Korean standard nuclear power plant

This paper presents the development of seismic design criteria for the reactor vessel internals as a part of the standardization programme for the nuclear power plant in Korea. The seismic design loads of the reactor vessel internals are calculated using the reference input motions of reactor vessels taken from Yonggwang nuclear power plant units 3 and 4 which are being constructed in Korea. An overview of analysis related to the basic parameters and methodologies is presented. Also, the response of internal components to the reactor vessel motions is carefully investigated.     

Plant Risk Effect Analysis Focusing on Digital I&C Equipment Failures

Safety-critical digital systems have been installed in nuclear power plants and thus their safety effect evaluation has become an emerging issue. The multi-tasking feature of digital instrumentation and control (I&C) equipment could increase the risk factor because the I&C equipment affects the actuation of the safety functions in several mechanisms. In this study, we quantify the safety of the digital plant protection system in Korean nuclear power plants based on probabilistic safety assessment (PSA) technology. Fifteen fault-tree models for the digital reactor-trip system and seven for the safety-feature actuation system are constructed and integrated into the plant safety assessment model. The result of the sensitivity study shows the boundaries of a plant risk and the effect of the digital equipment failures on the total plant risk.     

应用Jeffreys方法计算可靠性参数和始发事件频率的无信息先验

在核电厂概率安全评价（PSA）分析中,有些始发事件频率或设备失效记录在工业界几乎无历史数据。为了计算这些无信息先验的可靠性参数和始发事件频率,可采用Bayesian统计学中的Jeffreys方法。本文阐述了Jeffreys先验和简化的受限无信息先验分布（SCNID）的数学原理,分别导出了Gamma-Poisson模型和Beta-Binomial模型的Jeffreys无信息先验公式和不确定性区间。结合反应堆冷却剂小破口失水事故(SLOCA)实例介绍了如何应用Jeffreys先验计算始发事件频率。结果表明,Jeffreys方法是一种计算无信息先验的有效方法。     

质量-弹簧模型在储液容器抗震分析中的应用

核电厂有很多储液容器,对这些储液容器进行抗震分析时,液体的晃动可明显改变容器的质心和转动惯量等一些力学参数,因此,液体晃动对设备造成的载荷是不可忽略的。质量-弹簧模型是Housner理论和ASCE-4-98规范中对储液容器在地震作用下承受的液动压力给出的简化计算模型。本工作依据Housner理论和ASCE-4-98规范,对储液容器和容器内液体建立了三维质量 弹簧有限元模型,并据此计算了核电厂的储液容器在承受水平地震载荷时液体的作用力。将计算得到的液体频率结果及对流液体对容器的作用结果与应用公式计算的结果进行比较表明,三维有限元模型的计算结果是合理、可靠的。与ASCE-4-98规范相比,将质量 弹簧模型应用到三维有限元模型中,可直接从地震输入的模型中得到板壳元或三维实体有限元上位移和应力分布结果,这样更为直观方便。     

Seismic response and fragility analysis of a water storage structure

Stress analysis of a water storage structure has been carried out for static and seismic loading. Based on the stress analyses results, assessment of most likely failure modes for the structure caused by seismic event has been carried out. An attempt has been made to quantify the initial leakage rate and average emptying time for the structure during seismic event after evaluating the various crack parameters, viz., crack-width and crack-spacing at the locations of interest. Finally, the seismic fragility of the structure is developed as families of conditional probability curves plotted against peak ground acceleration (PGA) parameter at the location of interest considering the randomness and uncertainty associated with various parameters that could affect the seismic structural response.     

Seismic re-evaluation of nuclear facilities worldwide: overview and status

Existing nuclear facilities throughout the world are being subjected to severe scrutiny of their safety in the event of an earthquake. In the United States, there have been several licensing and safety review issues for which industry and regulatory agencies have cooperated to develop rational and economically feasible criteria for resolving the issues. Currently, all operating nuclear power plants in the United States are conducting an Individual Plant Examination of External Events, including earthquakes beyond the design basis. About two-thirds of the operating plants are conducting parallel programs for verifying the seismic adequacy of equipment for the design basis earthquake. The U.S. Department of Energy is also beginning to perform detailed evaluations of their facilities, many of which had little or no seismic design. Western European countries also have been re-evaluating their older nuclear power plants for seismic events often adapting the criteria developed in the United States. With the change in the political systems in Eastern Europe, there is a strong emphasis from their Western European neighbors to evaluate and upgrade the safety of their operating nuclear power plants. Finally, nuclear facilities in Asia are also being evaluated for seismic vulnerabilities. This paper focuses on the methodologies that have been developed for re-evaluation of existing nuclear power plants and presents examples of the application of these methodologies to nuclear facilities worldwide.     

Seismic individual plant examination of external events of US nuclear power plants: insights and implications

As part of the implementation of the severe accident policy, nuclear power plants in the US are conducting the individual plant examination of external events (IPEEE). Seismic events are treated in these IPEEEs by either a seismic probabilistic risk assessment (PRA) or a seismic margin assessment. The major elements of a seismic PRA are the seismic hazard analysis, seismic fragility evaluation of structures and equipment and systems analysis using event tree and fault tree analysis techniques to develop accident sequences and calculate their frequencies of occurrence. The seismic margin assessment is a deterministic evaluation of the seismic margin of the plant beyond the design basis earthquake. A review level earthquake is selected and some of the components that are on the success paths are screened out as exceeding the review level earthquake; the remaining ones are evaluated for their seismic capacity using information from the original plant design criteria, test data and plant walkdown. The IPEEEs of over 100 operating nuclear power plants are nearing completion. This paper summarizes the lessons learned in conducting the IPEEEs and their applicability to nuclear power plants outside of the United States.