Pierre-Etienne Labeau

Dynamic reliability: towards an integrated platform for probabilistic risk assessment

Abstract Dynamic reliability methods are powerful mathematical frameworks capable of handling interactions among components and process variables explicitly. In principle, they constitute a more realistic modeling of systems for the purposes of reliability, risk and safety analysis. Although there is a growing recognition in the risk community of the potentially greater correctness of these methods, no serious effort has been undertaken to utilize them in industrial applications. User-friendly tools would help foster usage of dynamic reliability methods in the industry. This paper defines the key components of such a platform and for each component, provides a detailed review of techniques available for their implementation. This paper attempts to provide milestones in the creation of a high level design of such tools. To achieve this purpose, a modular approach is used. For each part, various existing techniques are discussed with respect to their potential achievements. Issues related to expected future developments are also considered.

Procedures of Monte Carlo transport simulation for applications in system engineering

Abstract Monte Carlo (MC) simulation is the most promising tool for performing realistic reliability and availability analysis of complex systems. Yet, the efficient use of MC simulation technique is not trivial in large scale applications. This paper considers the two commonly adopted approaches to MC simulation: the direct, component-based approach and the indirect, system-based approach. The mathematical details of the two approaches are worked out in detail, so as to show their probabilistic equivalence. The proper formulation for biasing the simulation is introduced, thus leading to the correct expressions for the statistical weights. Both approaches are applied, in an analog as well as in a biased scheme, to a simple system of the literature and comparisons are made with respect to the computing time and the goodness of the estimate, as measured by the variance of the results.

Probabilistic dynamics: Estimation of generalized unreliability through efficient Monte Carlo simulation

Abstract The dynamic behaviour of a system is generally omitted in its PRA study, though it can greatly influence the failure risks. Probabilistic dynamics is a Markovian framework for the dynamic treatment of reliability. In this model, the concept of unreliability does not only consist in a transition to a failure state, but also in the crossing of the border of a safety domain in the space of the physical variables. Monte Carlo simulation appears to be the only tool likely to cope with realistic problems. However, since it aims at estimating the risk of very rare events, an analogue game is too time-consuming or inaccurate. Therefore, simulation techniques have to be improved to be practically used. Different ways of achieving this task exist: the definition of unbiased efficient estimators, the acceleration of the integration of the equations of the dynamics and the development of biased schemes. We review these possibilities in this paper and apply them on a study case.

A level-1 probabilistic risk assessment to blackout hazard in transmission power systems

The blackout risk in power systems is difficult to estimate by actual probabilistic methods because they usually neglect, or do not properly consider, the dependencies between failures and the dynamic evolution of the grid in the course of a transient. Our purpose is therefore to develop an integrated probabilistic approach to blackout analysis, capable of handling the coupling between events in cascading failure, and the dynamic response of the grid to stochastic initiating perturbations. This approach is adapted from dynamic reliability methodologies. This paper focuses on the modeling adopted for the first phase of a blackout, ruled by thermal transients. The goal is to identify dangerous cascading scenarios and better calculate their frequency. A Monte Carlo code specifically developed for this purpose is validated on a test grid. Some dangerous scenarios are presented and their frequency calculated by this method is compared with a more classical estimation neglecting thermal effects, showing significant differences. In particular, our method can reveal dangerous scenarios neglected or underestimated by the more classical method because they do not take into account the increase of failure rates in stress conditions.

Blackout Probabilistic Risk Assessment and Thermal Effects: Impacts of Changes in Generation

Renewable energy integration and deregulation imply that the electric grid will be operated near its limits in the future, and that the variability of cross-border flows will increase. Therefore, it is becoming more and more crucial to study the impact of these changes on the risk of cascading failures leading to blackout. We propose in this paper to emphasize important factors leading to blackouts, to review methodologies which were developed to simulate cascading failure mechanisms and to study specifically the impact of thermal effects on the risk of blackout for several changes in generation (variations in cross-border flows, wind farms penetration, shut-down of power plants). This is studied by applying to a test system the first level of a dynamic probabilistic blackout risk assessment developed previously. We show that taking into account thermal effects in cascading failures is important not only to have a good estimation of the risk of blackout in different grid configurations, but also to determine if a specific change in generation has a positive or a negative impact on the blackout risk.

A Monte Carlo estimation of the marginal distributions in a problem of probabilistic dynamics

Modelling the effect of the dynamic behaviour of a system on its PSA study leads, in a Markovian framework, to a development at first order of the Chapman-Kolmogorov equation, whose solutions are the probability densities of the problem. Because of its size, there is no hope of solving directly these equations in realistic circumstances. We present in this paper a biased simulation giving the marginals and compare different ways of speeding up the integration of the equations of the dynamics.

Modeling PSA problems. I. The stimulus-driven theory of probabilistic dynamics

Abstract The theory of probabilistic dynamics (TPD) offers a framework capable of modeling the interaction between the physical evolution of a system in transient conditions and the succession of branchings defining a sequence of events. Nonetheless, the Chapman-Kolmogorov equation, besides being inherently Markovian, assumes instantaneous changes in the system dynamics when a setpoint is crossed. In actuality, a transition between two dynamic evolution regimes of the system is a two-phase process. First, conditions corresponding to the triggering of a transition have to be met; this phase will be referred to as the activation of a “stimulus.” Then, a time delay must elapse before the actual occurrence of the event causing the transition to take place. When this delay cannot be neglected and is a random quantity, the general TPD can no longer be used as such. Moreover, these delays are likely to influence the ordering of events in an accident sequence with competing situations, and the process of delineating sequences in the probabilistic safety analysis of a plant might therefore be affected in turn. This paper aims at presenting several extensions of the classical TPD, in which additional modeling capabilities are progressively introduced. A companion paper sketches a discretized approach of these problems.

The cell-to-boundary method in the frame of memorization-based Monte Carlo algorithms. A new computational improvement in dynamic reliability

Dynamic reliability aims at estimating failure risks associated with very rare scenarios, while accounting for the system dynamic evolution. In a Monte Carlo game devised for this purpose, the most time consuming operation consists in performing these dynamic calculations, which are repeated in thousands of histories. In order to save computer resources, the idea of memorizing information on the dynamic trajectories before the simulation was investigated. Two approaches were propounded: the cell-to-boundary (CTB) method, and algorithms based on the memorization of the most probable evolution (MPE) from each initial state. This paper presents a way to combine both methods, in order to further reduce the numerical workload of the simulation. A memorization of second-order MPEs is also propounded, to better investigate transients following the failure of a control means. These techniques are illustrated on the previously defined application of a PWR pressurizer.

A Two-Level Probabilistic Risk Assessment of Cascading Outages

Cascading outages in power systems can lead to major power disruptions and blackouts and involve a large number of different mechanisms. The typical development of a cascading outage can be split in two phases with different dominant cascading mechanisms. As a power system is usually operated in N-1 security, an initiating contingency cannot entail a fast collapse of the grid. However, it can trigger a thermal transient, increasing significantly the likelihood of additional contingencies, in a “slow cascade.” The loss of additional elements can then trigger an electrical instability. This is the origin of the subsequent “fast cascade,” where a rapid succession of events can lead to a major power disruption. Several models of probabilistic simulations exist, but they tend to focus either on the slow cascade or on the fast cascade, according to mechanisms considered, and rarely on both. We propose in this paper a decomposition of the analysis in two levels, able to combine probabilistic simulations for the slow and the fast cascades. These two levels correspond to these two typical phases of a cascading outage. Models are developed for each of these phases. A simplification of the overall methodology is applied to two test systems to illustrate the concept.

Modeling PSA problems. II. A cell-to-cell transport theory approach

Abstract In the first paper of this series, we presented an extension of the classical theory of dynamic reliability in which the actual occurrence of an event causing a change in the system dynamics is possibly delayed. The concept of stimulus activation, which triggers the realization of an event after a distributed time delay, was introduced. This gives a new understanding of competing events in the sequence delineation process. In the context of the level-2 probabilistic safety analysis (PSA), the information on stimulus activation mainly consists of regions of the process variables space where the activation can occur with a given probability. The evolution equations of the extended theory of probabilistic dynamics are therefore particularized to a transport process between discrete cells defined in phase-space on this basis. Doing so, an integrated and coherent approach to level-2 PSA problems is propounded. This amounts to including the stimulus concept and the associated stochastic delays discussed in the first paper in the frame of a cell-to-cell transport process. In addition, this discrete model provides a theoretical basis for the definition of appropriate numerical schemes for integrated level-2 PSA applications.