Csaba Fazekas

Verification of a primary-to-secondary leaking safety procedure in a nuclear power plant using coloured Petri nets

This paper deals with formal and simulation-based verification methods of a PRImary-to-SEcondary leaking (abbreviated as PRISE) safety procedure. The PRISE safety procedure controls the draining of the contaminated water in a faulty steam generator when a non-compensable leaking from the primary to the secondary circuit occurs. Because of the discrete nature of the verification, a Coloured Petri Net (CPN) representation is proposed for both the procedure and the plant model. We have proved by using a non-model-based strategy that the PRISE safety procedure is safe, there are no dead markings in the state space, and all transitions are live; being either impartial or fair. Further analysis results have been obtained using a model-based verification approach. We created a simple, low dimensional, nonlinear dynamic model of the primary circuit in a VVER-type pressurized water nuclear power plant for the purpose of the model-based verification. This is in contrast to the widely used safety analysis that requires an accurate detailed model. Our model also describes the relevant safety procedures, as well as all of the major leaking-type faults. We propose a novel method to transform this model to a CPN form by discretization. The composed plant and PRISE safety procedure system has also been analysed by simulation using CPN analysis tools. We found by the model-based analysis-using both single and multiple faults-that the PRISE safety procedure initiates the draining when the PRISE event occurs, and no false alarm will be initiated.

Parameter Estimation of a Simple Primary Circuit Model of a VVER Plant

A simple dynamic model in physical coordinates (an improved version of our model reported in ) and the corresponding parameter estimation procedure for the primary circuit dynamics of VVER-type pressurized water reactors is presented in this paper. The primary uses of the model are control oriented dynamic model analysis and high level controller design. The most important requirements of the simple physical model are that it should contain the possible minimal number of differential equations and it should be capable of describing important dynamic phenomena such as load change transients between day and night periods. Furthermore, the estimated parameter values should fall into physically meaningful ranges. The parameter estimation method is based on the decomposition of the overall system model into separably identifiable subsystems. The identification of the subsystems is followed by the fine-tuning of the model parameters with the parameter estimation of the entire system model. The constructed model satisfies the predefined requirements and its response shows good fit to the measurement data that were obtained from three units of the Paks Nuclear Power Plant in Hungary.

Multiscale Modeling and Time-Scale Analysis of a Human Limb

A multiscale modeling approach is proposed in this paper that assists the user in constructing musculoskeletal system models from submodels describing various mechanisms on different levels on the length scale. In addition, dynamic time-scale analysis has been performed on the developed multiscale models of various parts of a human limb: the wrist, elbow, and shoulder have been characterized by different maximal muscle and skeletal length properties. The time-scale analysis results have been represented on a scale map that can be used effectively to direct the simplification of multiscale models for control-related application purposes.

Modeling and identification of a nuclear reactor with temperature effects and xenon poisoning

This paper presents the modeling and identification procedure for a VVER-type pressurized water reactor. The modeling goal is to produce a mathematical description in nonlinear state-space form that is suitable for control-oriented model analysis and preliminary controller design experiments. The proposed model takes temperature effects and xenon poisoning into consideration and thus it is an extension of formerly published simpler model structures. Real transient measurement data from the plant has been used for the identification that is based on standard prediction error minimization. It is shown that the model is fairly well identifiable and the newly inserted model components significantly improve the quality of fit between the measured and computed model outputs. Furthermore, the estimated parameter values fall into physically meaningful ranges.

Identification of the primary circuit dynamics in a pressurized water nuclear power plant

Abstract This paper presents the results of the parameter estimation procedure for the primary circuit dynamics of a VVER-type nuclear power plant. The model structure is a low dimensional lumped nonlinear model published previously in Fazekas et al. [2007a]. The parameter estimation method uses the modular decomposition of the system model for obtaining physically meaningful initial parameter estimates. The final parameter estimates are computed using the integrated model.

Modeling and identification of a nuclear reactor with temperature effects and Xenon poisoning

This paper presents the modeling and identification procedure for a VVER-type pressurized water reactor. The modeling goal is to produce a mathematical description in nonlinear state-space form that is suitable for control-oriented model analysis and preliminary controller design experiments. The proposed model takes temperature effects and Xenon poisoning into consideration and thus it is an extension of formerly published simpler model structures. Real transient measurement data from the plant has been used for the identification that is based on standard prediction error minimization. It is shown that the model is fairly well identifiable and the newly inserted model components significantly improve the quality of fit between the measured and computed model outputs. Furthermore, the estimated parameter values fall into physically meaningful ranges.

Hierarchical modelling in biology: Systematic building of limb models

Abstract A multi-level model, that provides a hierarchically structured description of a complex, multi-scale limb system is proposed in this paper for predicting and analyzing movement patters generated by various activation signals. The levels, the sub-models on each level and their interconnections are developed and described following a systematic modelling procedure. The computational properties (degree of freedom and differential index) of the developed model have been analyzed and a sub-model has been transformed to meet the index-one requirement for solving the resulting differential algebraic equation (DAE) model by standard methods implemented in MATLAB. The model is extensively verified against engineering expectations using parameter values found in the literature, and a good agreement was found. Parameter sensitivity analysis has also been performed.

Final Comments by the Authors

E-mail: fazekas@scl.sztaki.hu Figure 2 contains a simulation of the nuclear reactor with input output linearisation, where τ is set to 20min. The response to a step change of the set-pointN is shown. One can see from the top diagram that N has the desired linear behaviour and reaches the new steady state after about 2 hours. However, the internal states are far from stationary at that time, as is illustrated by the lowest diagram (note the different time scales in the diagrams). The zero dynamics is stable but slow. It needs a very long time to settle after a step change. This may be explained by the large time constants 1/λI and 1/λX of the iodine and the xenon concentration, which are between 10 h and 13 h.

Design and Implementation of an Improved and Reliable Pressurizer Controller at the Paks NPP

Abstract This paper presents the design and implementation of a pressure controller for the pressurizer of the primary circuit in the Paks Nuclear Power Plant (NPP) in Hungary. The controlled process is part of a highly safety-critical environment, therefore strict reliability requirements are imposed on both the hardware and the software of the controller. The implemented controller provides robust performance and it has a redundant and distributed architecture in order to meet these demands. The control system includes measurement and control PLCs, a continuous power controller and a special supervisor module. The pressure controller has been implemented and is in use in all the four units of the Paks NPP.