Recoverability Modeling of Power Distribution Systems Using Accelerated Life Models: Case of Power Cut due to Extreme Weather Events in Norway

Abstract

Today's societies rely on electrical power distribution systems. Recent weather events have illustrated that the loss of such service can lead to severe consequences for societies and stakeholders. Hence, in order to reduce the impact of such extreme events on infrastructure systems and to limit the associated losses, it is crucial to design infrastructure that can bounce back and recover rapidly after disruptions (i.e. to be resilient). In this regard, it is vital to have knowledge of technical, organizational, internal, and external factors that influence the infrastructure's recovery process. These factors can broadly be categorized into two different groups, namely observed and unobserved risk factors. In most studies on resilience, the effect of unobserved covariates is neglected. This may lead to erroneous model selection for analyzing the time to recovery of the disrupted infrastructure, as well as wrong conclusions and thus decisions. The aim of this paper is to identify the risk factors (observed and unobserved) affecting the recovery process of disrupted infrastructure. To this aim, the paper extends the application of accelerated failure time (AFT) models, to model the recovery time of disrupted critical infrastructures in the presence of unobserved and observed risk factors. This model can be used to analyse how important these factors are from the viewpoint of resource allocation and decision-making. The application and implications of the model are presented in a case study, from both technical and management perspectives. The case study investigated in this paper applies the developed model, analysing recovery times from 73 disruption reports on Norwegian electric power distribution grids after four major extreme weather events. The analysis indicates that failures in the regional grid, natural conditions, area affected, and failures in operational control system have a significant impact on the recovery process.

Spare-part management in a heterogeneous environment

“…In general, based on the nature of collected data, if there is an unobservable risk factor, the frailty model is appropriate; otherwise, the PHM and its extension can be used for reliability analysis. In the presence of p 1 time-independent risk factors, (z) , and p 2 time-dependent risk factors, ( z(t) ), the frailty model takes the following form [ 33 , 34 ]: where λ 0 (t) is the baseline hazard rate, the function captures the effect of observed risk factors, and α is the frailty. The α > 1 are said to be frailer for reasons left unexplained by the observed risk factors and will have an increased risk of failure, while items with α < 1 are less frail; hence, given a specific observed risk factor pattern, they tend to be more reliable.…”

“…As Eq ( 2 ) shows, frailty represents one or more unobserved risk factors’ cumulative effect. Given the relationship between the hazard rate and the reliability functions, it can be shown that the conditional reliability function, R ( t ; z ; z ( t )| α ), can be written as [ 33 , 34 ]: …”

“…The available time-dependency analysis models can be categorized into analytical and graphical approaches. Among the analytical models, the Schoenfeld Residuals test is one of the most widely used analytical tests [33][34][35]. In general, based on the nature of collected data, if there is an unobservable risk factor, the frailty model is appropriate; otherwise, the PHM and its extension can be used for reliability analysis.…”

“…In general, based on the nature of collected data, if there is an unobservable risk factor, the frailty model is appropriate; otherwise, the PHM and its extension can be used for reliability analysis. In the presence of p 1 time-independent risk factors, (z), and p 2 time-dependent risk factors, (z(t)), the frailty model takes the following form [33,34]:…”

Management of Resilience in Civil Infrastructure Systems: An Interdisciplinary Approach

“…To be more specific, these two indexes can identify which components in an infrastructure network are vulnerable to disruption in advance and thus enable taking immediate restoration actions in the aftermath of a disaster. Rød et al (2020a) acknowledged the significance of unobserved technical, organizational, internal, and external factors, which can affect the recovery process of power distribution systems. The authors developed an accelerated failure time model to consider the effect of such otherwise neglected factors along with traditionally observed ones in simulating the recovery time of disrupted power distribution systems in Norway.…”