Deterministic Analyses

Analytical improvements represent activities performed mainly for the safety analysis reports (SAR), including conservative deterministic analyses and probabilistic best estimate analyses (LPS PSA). 

At present a project is being carried out to summarize all needs for deterministic analyses in shutdown modes, to evaluate the applicability of existing models and methods to the specified conditions, and to create a basis for systematic evaluation of Bohunice NPP safety in shutdown modes. As a result, an upgraded SAR will be provided, reflecting also results of relevant LPS PSA-PHARE 2.09/95, Boron dilution-PHARE2.08, etc. 

The methods of calculation employed are those which are used as well for deterministic analyses. The difference is that stochastic boundary conditions, which are closer to reality, are used for the calculations. For example, instead of a fixed leak size a whole spectrum of leak sizes is treated with pertinent expected frequencies of occurrence being assigned to the different leak sizes. Instead of calculating the dispersion of a toxic substance based on a specific weather situation, different possible weather situations with their corresponding probabilities of occurrence are accounted for. This is reasonable, since the instant in time of the accident and the weather condition, which then prevails, are not known beforehand. 

The analyses outlined above cannot be performed without fixing certain parameter values and making simplifications. This is in reality a specific characteristic of deterministic analyses. However, the assumptions and simplifications made in probabilistic analyses are generally closer to reality than in deterministic assessments. Their extent depends on the focus and degree of detail specified for the analysis. 

The deterministic approach studies the behaviour of the plant in operational states and under specific accident conditions originally identified on the basis of evaluations of prudent engineering or for compliance with the chosen criteria. Today, probabilistic techniques are sometimes used to aid decisions concerning the deterministic approach, for example if a new candidate appears (e.g. from research or operating experience) for inclusion in the list of Design Basis Accidents (DBAs), the decision on inclusion or not can be aided by a probabilistic comparison with other situations already inserted in the DBA list. Usually the deterministic analyses are performed using conservative assumptions on input data, intermediate parameters for the analyses and on the behaviour of plant systems (single failure, etc.). Consequently, the behaviour of the plant as evaluated could be rather different from the most... 

The deterministic analyses have been used for a longer time and, therefore, they are based on a well-consolidated basis, at least for the rare events included among the DBAs. 

Severe accidents are now also part of the deterministic analyses. However, because of then-very low probability, the conservative assumptions used for DBAs are not used. A best estimate treatment of the phenomena is preferred in this case. 

Since early nineties of the last century, PSA methods have been used as a complementary approach to common deterministic analyses within the process of ensuring acceptable level of nuclear power plant operation safety in Czech Republic. More recently, PSA concept has become a fi eestanding decision-making tool for controlling both instantaneous and permanent plant risk level. Since human factor has been playing a fairly significant role in plant risk profile, special HRA methods had to be adopted as a part of worldwide know-how transfer and used to address human related specifics of Czech NPPs operation, in order to keep the corresponding PSA models as realistic as possible. 

Detailed proposals for the implementation of corrective actions and/or safety improvements should be prepared after receiving the feedback from the regulatory body on the submitted reports. Tiis should include the outcome of discussions with the regulatory body regarding the scope and adequacy of the outline proposals of corrective actions and/or safety improvements. In addition, the corrective actions and/or safety improvements should be prioritized. Different approaches exist for the prioritization of corrective actions and/or safety improvements on the basis of deterministic analyses, PSA and engineering judgement. 

In addition to deterministic analyses, and simulations performed with thermal-hydraulic computer codes, a level 1 PSA study has been performed for the BWR 90. It was adapted to the off-site electrical power grid in Finland and to recent data on common cause failures obtained from research work sponsored by the Swedish Nuclear Power Inspectorate (SKI). The PSA study addresses internal events only since previous studies have demonstrated that external events do not contribute significantly to the core damage probability. The PSA shows that LOCA events leading to core melt are extremely unlikely which is typical for BWRs with internal recirculation pumps. 

In addition to the deterministic analyses, and the simulations performed with thermal-hydraulic computer codes, a preliminary Level 1 PSA study has been completed in a joint effort by ABB Atom and the Italian oitities ENEA-DISP/ENEL (ENEA-DISP is the state regulator and ENEL is the (former) state utility) The study represents a first comprehensive review of the PIUS plant design, based on ultra-conservative assumptions - the failure fi-equency for the prestressed concrete vessel ended up as somewhat higher than for a steel vessel, and a number of transients were just postulated to yield core damage even though calculations showed that they would not Still, the resulting "core damage" frequency is below 10 ... 

The vertex analysis solves the deterministic model for all combinations of minima and maxima of the uncertain parameters. For this model with 5 uncertainties, 32 (2 ) deterministic analysis are required at each Q -level, except for a-level 1.0, where only 1 deterministic analysis is required. In total, 161 deterministic analyses are required. 

The top graph of Fig. 8 shows the upper bound on the FRF at a-level 0.0, calculated using the MRE and vertex method. Additionally, all vertex samples are plotted. Using the vertex method, 32 deterministic analyses were needed to calculate this upper bound using the MRE method and the response surface based optimisation technique, 41 deterministic analyses were needed. The bottom graph shows the relative difference between the MRE and vertex results. These results prove that the MRE method using the response surface based optimisation method is able to calculate the bounds on the FRF accurately. 

Probabilistic safety assessment can be seen as an extension of deterministic analyses by systematically considering accident sequences and events which go beyond the design basis of a nuclear power plant. PSA applications are evolving and are useful in complementing the deterministic approach as long as the PSA used has an adequate quality for the intended applications and die staff carrying out the probabilistic assessment include experienced personnel who know the capabilities and limitations of the PSA and of the plant design and operation. 

The two main tools for establishing the loads on instrumentation and equipment are the scenario characterization (e.g., stuck-open relief valves, interfacing system pipe ruptures) and the deterministic analyses (in this case the aforementioned three-dimensional finite element analysis and MELCOR analysis). The conditions of interest are humidity, static and dynamic pressure, temperature, and radiation. All of these except radiation are readily calculated by MELCOR, though dynamic temperature and pressure estimation requires additional investigation using separate... 

Probabilistic Safety Assessment (PSA) represents an important tool in both design and operation of NPPs (e.g., IAEA-TECDOC-1200 and SSR 2/1). In fact, the probabilistic tools extend traditional deterministic analyses providing a better understanding of accidental sequences characterized by combined failures. Additionally, in parallel to deterministic safety assessment, PSA helps identifying plant vulnerabilities and dependencies between systems, examining different design options and prioritizing improvement areas. 

In this section of the SAR all the deterministic analyses performed to evaluate and justify plant safety should be considered. Deterministic safety analysis predicts the plant response to PIEs in specific predetermined operational states. It applies specific rules and uses specific acceptance criteria. The analyses typically focus on neutronics and thermal-hydraulic, structural and radiological aspects that are analysed with different computational tools. As is stated in para. 4.19 of Ref. [4] In general, the deterministic analysis for design purposes should be conservative. The analysis of beyond design basis accidents is generally less conservative than that of design basis accidents. It is acceptable that best estimate codes are used for deterministic analyses provided that they are either combined with a reasonably conservative... 

Deterministic analysis is usually performed by means of the calculation of plant parameters using complex computer codes. The models and the computer codes used for the deterministic analyses as well as the general assumptions made concerning plant parameters, the operability of systems, including control systems, and the operators actions (if any) in the events should be described. Important simphfications made should be justified. The set of limiting assumptions for safety analysis used in the deterministic safety analyses performed for the different types of PIEs should be described in this section. The methods used to ensure that these assumptions demonstrate that sufficient safety margins are achieved for PIEs of each type should also be described. 

Independent of reactor class, existing modem safety analyses are based on the twin directions of (1) assessing potential event initiators and quantifying estimates of the sequence evolution and responses using PSA/PRA and (2) Deterministic Analyses (DA) in which postulated events are analyzed largely independent of their likelihood. Combinations of many events, transients, and failures are considered, from simple upsets to loss of power, earthquakes, fires, and floods. 

The major advantage of Monte Carlo simulation is that it can deal with almost any type of nonlinearity, maybe using the same commercially available packages that are used for the deterministic analyses. Its only disadvantage is that it is time-consuming, as many analyses are requested in order to have reliable estimates of the statistical properties of the response. 

LBB evaluation at SRS included both probabilistic and deterministic analyses to demonstrate that the likelihood of a significant pipe break is acceptably low. Although deterministic methods cannot be used to directly obtain failure probability, reasonable component failure probabilities were established using applicable historical data. Allowances were made for uncertainties and the... 

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