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A Modeling and Simulation Framework for the Reliability/Availability A modeling and simulation framework for the reliability/availability assessment of a power transmission grid subject to cascading failures under extreme weather conditions Francesco Cadini, Gian Agliardi, Enrico Zio To cite this version: Francesco Cadini, Gian Agliardi, Enrico Zio. A modeling and simulation framework for the reliability/availability assessment of a power transmission grid subject to cascading failures un- der extreme weather conditions. Applied Energy, Elsevier, 2017, 185, Part 1, pp.267-279. 10.1016/j.apenergy.2016.10.086. hal-01652288 HAL Id: hal-01652288 https://hal.archives-ouvertes.fr/hal-01652288 Submitted on 30 Nov 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Applied Energy 185 (2017) 267–279 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy A modeling and simulation framework for the reliability/availability assessment of a power transmission grid subject to cascading failures under extreme weather conditions ⇑ Francesco Cadini a, , Gian Luca Agliardi a, Enrico Zio a,b a Dipartimento di Energia, Politecnico di Milano, Via La Masa 34, 20156, Italy b Chair System Science and the Energy Challenge, Fondation Electricite’ de France (EDF), CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92290 Chatenay-Malabry, France highlights We combine stochastic extreme weather model and realistic power grid fault dynamics. We introduce a novel restoration model accounting for the weather conditions. The complete model is quantified by means of a customized sequential Monte Carlo. Reliability/availability indicators show importance of rare extreme weather events. article info abstract Article history: Electrical power transmission networks of many developed countries are undergoing deep transforma- Received 20 January 2016 tions aimed at (i) facing the challenge offered by the stochastically fluctuating power contributions Received in revised form 15 September due to the continuously growing connections of renewable power generating units and (ii) decreasing 2016 their vulnerability to failures or malicious attacks and improving their resilience, in order to provide more Accepted 24 October 2016 reliable services, thus increasing both safety and profits. In this complex context, one of the major con- Available online 7 November 2016 cerns is that related to the potentially catastrophic consequences of cascading failures triggered by rare and difficult to predict extreme weather events. In this work, we originally propose to combine an Keywords: extreme weather stochastic model of literature to a realistic cascading failure simulator based on a direct Power grids Cascading failures current (DC) power flow approximation and a proportional re-dispatch strategy. The description of the Extreme weather dynamics of the network is completed by the introduction of a novel restoration model accounting for Wind storm the operating conditions that a repair crew may encounter during an extreme weather event. The result- Lightning ing model is solved by a customized sequential Monte Carlo scheme in order to quantify the impact of Monte Carlo simulation extreme weather events on the reliability/availability performances of the power grid. The approach is Reliability demonstrated with reference to the test case of the IEEE14 power transmission network. Availability Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction and the study of strategies for the mitigation of the consequences have gained increased attention. However, these tasks are difficult Electric energy has an impact on all modern life activities. because of the inherent complexities of the power transmission Consequently, the public expectation for reliable electric energy networks, the complex physical laws governing the power flow delivery has significantly grown in the past decades. For this, the dynamics and the uncertainties affecting the boundary conditions so-called power grids, i.e., the interconnected systems that trans- (operational and environmental) in which they operate. Additional mit electric power from where it is generated to where it is con- difficulties come from the evolution of society and energy markets, sumed, play a fundamental role. Thus, it comes with no surprise that demand changes and adaptations of the large-scale power that the assessment of the risk of failures of these infrastructures transmission infrastructures for continuing to satisfy the require- ments of reliability/availability under the continuous increase in ⇑ Corresponding author. electric power demand, avoiding congestions and overloads, so as E-mail address: [email protected] (F. Cadini). to improve safety and increase economic margins. In addition, http://dx.doi.org/10.1016/j.apenergy.2016.10.086 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved. 268 F. Cadini et al. / Applied Energy 185 (2017) 267–279 power transmission systems can no longer be considered solely as network performances in presence of failures triggered by the a means for energy delivery; rather, they are operated as an elec- extreme weather events. tricity market trading platform for shifting power volumes across With regards to extreme weather event modeling for power different regions or even different countries, for economic reasons. grids reliability/availability estimation, the common approach is Furthermore, in recent years we have witnessed an exponential that of resorting to the ‘‘two-state” model [9], or to its improved, growth in the connection of renewable power generating units ‘‘three-state” version [10], where the weather conditions are (photovoltaic power plants, wind farms, biomass plants, etc.) and divided into two or three classes, normal, adverse and, in case of poly-generation systems (electrical power, heat and cooling), three state models, major disaster, and the stochastic transitions which add even more complexity to the system. In fact, such con- among the different classes are modeled as homogeneous Poisson nections were obviously not planned in the initial design of the processes with constant transition rates, to be estimated from power networks, which now need to adapt to accommodate their weather data. fluctuating power contributions, difficult to predict and geograph- The major drawbacks of these approaches are that (i) they are ically distributed [1]. not flexible enough to represent the wide range of possible In this new setting, concerns come for the protection from fail- weather events types and intensity levels and (ii) their rates of ures and attacks, and their possible cascading effects, i.e., the prop- occurrence are, in general, dependent on time, due to their typi- agation of disconnections of components from the grid due to the cally seasonal behaviors. Significant advances towards a more real- power flows redistribution (manually or automatically) following istic modeling of the impact of weather events on power networks the initial failure or attack. Cascading failures may lead to catas- reliability/availability is proposed in [11] and further extended in trophic disconnections of wide portions of the power transmission [16]. In those works, non-homogeneous Poisson distributions of networks, as epitomized by several large-scale blackouts occurred the occurrence times and suitable distributions of the events inten- in developed countries in the recent years, such as for example the sities are derived on the basis of available weather statistics; fur- blackout in Italy on September, 28 2003 [2], that in the United thermore, the failure rates of the networks’ lines are States and Canada on August 14, 2003 [3] or that in Europe on mathematically related to the times of occurrence and the intensi- November, 6 2006 [4]. ties of the weather events considered, following the approaches Normally, a power transmission network is designed and oper- proposed in previous works of literature. In fact, it is recognized ated so that a single component disconnection does not give rise to that the failure rates of the grid’s components, typically taken con- any load shedding, so that cascading failures do not occur (N À 1 stant, are actually significantly increased by the occurrence of sev- criterion [2]); however, rare combinations of circumstances, ere weather events. For example, quadratic and exponential uncommon events or inadequate countermeasures may result in models are introduced in [12] and [13], respectively, to describe further line disconnections, eventually leading to disruptive conse- the overhead line failure rates as functions of the wind speed; a lin- quences. In fact, the operative conditions at a given time are deter- ear model is presented in [14] to model the relationship between mined by many, usually correlated factors, such as power demand, the number of line interruptions and that of lightning flashes; generating capacity, economic optimizations, technical limits and the combined effect of high winds and lightning, possibly occurring environmental conditions. Some of these factors
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