Modeling PSA Problems—I: The Stimulus-Driven Theory of Probabilistic Dynamics

Labeau, Pierre-Etienne; Izquierdo, José María

doi:10.13182/nse05-a2506

Cited by 22 publications

(29 citation statements)

References 14 publications

(16 reference statements)

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“…Subsection 4 introduces then the concept of stimulus and develops the mathematical model of the SDTPD. This overall Section is mainly based on (Labeau et al, 2005) and (Izquierdo et al,2004). The Theory of Probabilistic Dynamics…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The interpretation of equation (4) In order to extent the integral form of the Chapman-Kolmogorov equation to semi-Markovian systems, we have to introduce ingoing densities (Labeau et al, 2005). We denote by ( ̅ ) ̅ the probability to enter state with electrical variables in ̅ about ̅ during the time interval about .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…However, the algebraic variables can endure an instantaneous change which can be modeled by a shock for a transition from state to state as ̅ ̅ ( ̅ ̅ ) {12} where ̅ and ̅ are the value of the algebraic variables after and before the transition, respectively. The Chapman-Kolmogorov equation under the formulation {7} can be slightly modified to consider these shocks (Labeau et al, 2005): e Congrès de Maîtrise des Risques et Sûreté de Fonctionnement -Dijon 21-23 octobre 2014…”

Section: Extension To Random Shocksmentioning

confidence: 99%

“…Such a hypothesis is not relevant for the analysis of electrical transients in transmission power e Congrès de Maîtrise des Risques et Sûreté de Fonctionnement -Dijon 21-23 octobre 2014 systems, as a significant delay exists between the crossing of the set point and the actual transition. An extension of the classical TPD has been proposed to be able to consider such time-delays, called Stimulus-Driven TPD (SDTPD) (Labeau et al, 2005). The aim of this paper is to adapt the SDTPD to the Probabilistic Risk Assessment (PRA) of electrical transients in transmission power systems.…”

Section: Introductionmentioning

confidence: 99%

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The Stimulus-Driven Theory of Probabilistic Dynamics for electrical transients in transmission power systems

Henneaux¹,

Labeau²

2015

Congrès Lambda Mu 19 De Maîtrise Des Risques Et Sûreté De Fonctionnement

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SummaryDynamic reliability, also known as the Theory of Probabilistic Dynamics (TPD), is a framework capable of considering the mutual interaction between the continuous process variables of a system in transient conditions and the transitions of the system between several successive discrete states visited during this transient. However, modellings developed in this framework usually assume implicitly that a set point-based transition occurs as soon as soon as the corresponding set point is crossed. Such a hypothesis is not relevant for the analysis of electrical transients in transmission power systems. In this case, transitions between system states are due to the action of protection systems. The general aim of protection systems is to disconnect elements operating in unacceptable conditions, in order to protect them. A delay (partly intentional or not) exists between the crossing of the set point and the actual disconnection of the element. This delay is obviously not compatible with the implicit assumption of immediate changes in the system dynamics. An extension of the classical TPD has been proposed to be able to consider such time delays, called Stimulus-Driven TPD (SDTPD). However, this extension has been developed mainly with the nuclear sector in mind. Its actual form is not completely adapted to the Probabilistic Risk Assessment (PRA) of electrical transients in transmission power system. The aim of this paper is therefore the adaptation and extension of the SDTPD to this context. The developed modelling will be applied to small-size examples for a better understanding of the stochastic behavior of electrical transients. RésuméLa fiabilité dynamique, aussi appelée théorie de la dynamique probabiliste (TPD), est un cadre méthodologique capable de considérer l'interaction mutuelle entre les variables dynamiques continues d'un système en conditions transitoires et les transitions du système entre différents états successifs discrets visités lors de ce transitoire. Cependant, les modélisations développées dans ce cadre se basent sur l'hypothèse implicite qu'une transition basée sur un seuil intervient aussitôt que le seuil correspondant est franchi. Une telle hypothèse n'est pas pertinente pour l'analyse des transitoires électriques dans les réseaux de transport. Dans ce cas, les transitions entre les états du système sont dues à l'action des systèmes de protection. La fonction globale des systèmes de protection est de déconnecter les éléments opérants dans des conditions inacceptables, pour les protéger. Un temps mort (partiellement intentionnel ou non) existe entre le franchissement du seuil et la déconnection réelle de l'élément. Ce temps mort n'est évidemment pas compatible avec l'hypothèse implicite de changements immédiats dans la dynamique du système. Une extension de la théorie de la dynamique probabiliste, appelée la théorie des stimuli (SDTPD), a été proposée pour permettre de considérer de tels temps morts. Cependant, cette extension a été développée principalement pour le secteur nucléaire. ...

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Section: Extension To Random Shocksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Stimulus-Driven Theory of Probabilistic Dynamics for electrical transients in transmission power systems

Henneaux¹,

Labeau²

2015

Congrès Lambda Mu 19 De Maîtrise Des Risques Et Sûreté De Fonctionnement

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“…This approach captures the interrelation between the hardware/software with operator actions by using an integral equation, which can be solved by Monte Carlo simulation techniques. To account for the shortcomings of the CET method, continuous cell-to-cell mapping (CCMT) (Tombuyes and Aldemir, 1996) and stimulus-driven theory of probabilistic dynamics (Labeau and Izquierdo, 2005) were developed and implemented. Since continuous time based methods are very computationally intensive, they could not be applied successfully to highly complex problems of real world.…”

Section: Frontiers In Energy Research | Nuclear Energymentioning

confidence: 99%

A review: passive system reliability analysis – accomplishments and unresolved issues

2014

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Damage domains of chemically reacting industrial facilities. An adequate identification model for Bhopal‐like scenarios

Benikhlef

Benazzouz

Izquierdo

et al. 2011

Asia-Pacific J Chem Eng

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This paper focuses on the improvement of solutions to some of the problems that arise in chemical and petrochemical risk assessment studies, namely those associated with potentially undue grouping in sequences of events, caused by different time evolutions. It provides an adequate work‐horse simulation model of risky scenarios able to explore a large amount of transients at a reasonable and viable cost. It is specifically suitable for the transfer of modern dynamic reliability techniques, originated in the nuclear domain, to the chemical engineering environment. As an application, it presents results of a case study to analyse Bhopal‐like scenarios. We found the model adequate to discriminate and filter out the myriad of success scenarios expected in well‐protected installations, screening necessary to focus the risk studies on damage situations. © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

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Modeling PSA Problems—I: The Stimulus-Driven Theory of Probabilistic Dynamics

Cited by 22 publications

References 14 publications

The Stimulus-Driven Theory of Probabilistic Dynamics for electrical transients in transmission power systems

The Stimulus-Driven Theory of Probabilistic Dynamics for electrical transients in transmission power systems

A review: passive system reliability analysis – accomplishments and unresolved issues

Damage domains of chemically reacting industrial facilities. An adequate identification model for Bhopal‐like scenarios

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