Planning resilient networks against natural hazards: Understanding the importance of correlated failures and the value of flexible transmission assets
Introduction
Network security is paramount for the well-functioning of power systems and for delivering reliable energy supply to consumers. A power outage can have catastrophic effects in the economy due to lost output, delayed production, and damaged infrastructure [1]. In addition, power outages can lead to human deaths [2]. For these reasons, power systems are normally planned and operated following strict standards of security and reliability [3].
Today, extreme weather events, natural hazards such as earthquakes and tsunamis, and physical attacks are the most common causes of major failures of power grids [4], [5]. These exogenous events can cause simultaneous failures of multiple components of a power grid, increasing the likelihood of outages that affect broad geographical regions.
According to a recent report by the Oak Ridge National Laboratory, more than 95% of electric disturbance events affecting at least 50,000 customers between 2000 and 2016 in the US were triggered by some climate-related event, including severe winter storms, hurricanes, tornadoes, heavy rain, heat waves, and lightning [6]. In Puerto Rico, Hurricane Maria in 2017 caused so much damage to the grid that some people lost power for more than ten months [7].
Power grids in earthquake-prone areas can also be vulnerable to correlated component failures. For example, on February 27, 2010, a major earthquake affected some of the most populated areas in Chile and caused simultaneous failures of generation, transmission, and distribution assets, resulting in the curtailment of an equivalent of 75% of the annual peak demand for power in the system [8]. In 2011, Japan experienced the fourth strongest earthquake ever recorded in history, followed by a tsunami. The event triggered the disconnection of nearly 23 GW of generation and caused multiple failures both in transmission and distribution systems [9].
As expected, these major outages due to natural disasters can be very costly for the economy. A study by the US President’s Council of Economic Advisers and the US Department of Electricity Delivery and Energy Reliability reports that weather-related power outages between 2003 and 2012 have cost the US economy an average of $18 billion to $33 billion, but this number can increase up to $75 billion in a year with major weather events [10]. Consequently, investment and operation strategies that are effective at reducing the impact of natural disasters and physical attacks on the power grid can result in relatively large economic savings.
Historically, power networks have been designed and operated by using the so-called security criterion (e.g., or ), meaning that power systems must withstand the outage of one () or two () elements without shedding (significant volumes of) demand and without violating the operating limits established in security standards [3]. This security criterion, however, has been questioned for years because it does not properly acknowledge the probabilistic nature of power outages and the cost of curtailing demand [11]. For example, the criterion does not recognize that long power lines may be more prone to fail than short lines or transformers in substations that are closely monitored. In addition, the criterion does not necessarily prevent power outages that result from correlated component failures, which are more likely to occur than independent failures when a power grid is exposed to natural disasters or extreme weather events [12].
To cope with these limitations, there is a body of work that recommends replacing deterministic standards with probabilistic (or stochastic) approaches to ensure a secure design and operation of power networks [3], [11], [12], [13], [14], [15], [16], [17], [18], [19]. Under a probabilistic approach, outage risks can be appropriately measured and balanced against the costs of designing and operating the grid in a manner that could reduce such risks [13].
In spite or their benefits, probabilistic models present a number of challenges in order to be successfully applied in practice. For example, probabilistic models are more complex and harder to solve and scale up than deterministic models with minimum security standards, such as an requirement. The number of possible contingent states of the network grows exponentially with the number of network elements, which increases the computational complexity of probabilistic models as number of elements in the system goes up. Reliability data is not always available, especially dependencies and correlations among network outages that are hardly ever observed; hence outage dependencies are usually ignored in order to make models tractable. Also, information and communication technologies (ICT), protection and control systems are usually assumed 100% reliable.
Part of the computational challenges that result from the use of probabilistic models can be addressed through model simplifications or decomposition algorithms. In terms of simplifications, the authors in [20] show different alternatives to simplify network models with security constraints. In terms of computational algorithms to solve optimization problems, one alternative is to rely on the concept of the so-called “umbrella” outages and constraints that seek to identify, prior to running the mathematical program, a subset of relevant network outages that result in the exact same solution as considering the entire set of outages [19], [21]. Another alternative is the application of Benders decomposition, which has been successfully used in security analysis for network [19], [22] and generation investment planning [23], [24]. Other modern solution algorithms and heuristics, such as optimization via simulation, have also been utilized recently [[25], [53]].
In terms of the reliability of corrective control actions, there are a few references associated with modeling malfunctions of ICT, protection and control systems. Reference [26] utilizes the concept of the so-called hidden outages to model failures corresponding to malfunctions that are hidden, unrevealed until these are exposed by abnormal system conditions, transforming an initially benign outage into a major incident. Interestingly, such failures can be hedged by making appropriate decisions through probabilistic optimization models [27], [28].
Outage dependencies and correlations have been recently gaining increased attention in network analysis and design. In communication networks, for example, various works have recognized outage dependencies and correlations for reliable operation and design [29], [30], [31], [32], [33]. In power systems, outage dependencies and correlations are also gaining attention because system operators have become more aware of the risks associated with natural hazards [12]. The current literature usually models simultaneous outages like a series of outages that cascade very rapidly across the system. This is the case of models such as those explained in [34], [35], [36], in which several power flow simulations are undertaken after triggering an initial network outage that can overload other parts of the network and so cascade into a major event. A stochastic optimization model for network investment, however, requires encapsulation of the above mentioned series of outages into a scenario tree [37]. Such scenario tree should describe the final state of the system after outages occur. In this vein, a series of cascading outages can be represented by a single contingent state of the system where multiple elements failed simultaneously. As failures in a cascading event are clearly not independent, dependent probabilities must be used correlating the outage probabilities of multiple elements after a given triggering event happened.
In this context, this paper studies the effects of including simultaneous system failures with dependencies in probabilistic network planning models to design resilient power networks. We refer to resilient networks as we focus on hedging against the impacts of exogenous high impact and low probability events (i.e., natural hazards) on the power system. To do so, we use a two-stage stochastic transmission expansion planning model, where, in the first stage, network investments and pre-contingency dispatch decisions are made and, in a second stage, re-dispatch decisions and demand curtailments occur as recourse decisions. The two-stage scenario tree is built using a Monte Carlo simulation process that, first, simulates the occurrence of an earthquake event and, then, simulates the following potential network outages. We compare the results of this model against two other models: a deterministic planning model and a stochastic planning model that ignores dependencies. Finally, we use the model to quantify the value of a portfolio of hybrid AC and DC power lines, attempting to further understand the benefits of utilizing flexible HVDC technologies to mitigate risks against correlated simultaneous outages. To our knowledge, this is the first study of this kind.
We structure the rest of the paper as follows. In Section 2 we provide a qualitative description of the methodology used to simulate earthquakes and a general description of the deterministic and probabilistic models used for optimal network design. In Section 3 our case study, which consists of a 14-bus network located in Northern Chile, and our main results. Finally, in Section 4 we conclude.
Section snippets
Overview
We propose a stochastic mathematical program to design power transmission networks with probabilistic outage scenarios. This program decides on new network infrastructure (i.e. lines and transformers) and its corresponding system operation, by minimizing the sum of the investment cost, operational or generation cost (pre-fault cost and post-fault expected cost), and the expected cost of the energy not supplied. We use this mathematical program to evaluate three different design criteria,
Case study and results
Instance We use the IEEE 14-busbar network presented in [42], considering 8 new candidate transmission lines as potential investments. Fig. 3 shows the original IEEE 14-busbar network, with the 8 new candidate transmission investment alternatives in yellow. Detailed data about demand, generation and transmission characteristics (including line capacities, reactances and costs) are presented in Appendix B. We also consider HVDC investment alternatives available for the same 8 new candidate
Conclusions
Natural hazards pose major threats to the secure operation of power grids. Earthquakes, hurricanes, and extreme weather events increase the likelihood of spatially-correlated failures of grid components and often result in major power outages [4], [5], [6], [7]. Recent studies in the US conclude that the economic impact of grid outages due to natural disasters can be as high as $75 billion in a single year [10]. Consequently, new planning methods for power grids that reduce the risks of major
CRediT authorship contribution statement
Javiera Barrera: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Supervision, Project administration. Pauline Beaupuits: Methodology, Investigation, Software, Validation, Visualization. Eduardo Moreno: Methodology, Validation, Formal analysis, Data curation, Visualization. Rodrigo Moreno: Conceptualization, Methodology, Formal analysis, Writing - original draft. Francisco D. Muñoz: Formal analysis, Writing - original draft.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors acknowledge the financial support of the Chilean National Agency for Research and Development (ANID) through FONDECYT grants 1161064 (E.M, J.B.), 1190228 (F.M.), and 1181928 (R.M.), ANILLO grant ACT192094 (E.M., F.M., J.B.), Programa Iniciativa Científica Milenio NC120062 (J.B., P.B.), Program Math Amsud 19-MATH-03 (J.B.), ANID-Basal Project FB0008 (F.M.), Puente 2020 VRA-Universidad Adolfo Ibáñez (J.B.), and the Complex Engineering Systems Institute ANID PIA/APOYO AFB180003 (R.M.,
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