metadata: authors: 0: author: Schweikert,Amy Elizabeth
1: author: Nield,Lindsey
2: author: Otto,Erica
3: author: Klemun,Magdalena
4: author: Ojanpera,Sanna Maria
5: author: Deinert,Mark Robert
count: World
docna: 0: docna: Vulnerabilities of Networked Energy
            Infrastructure : A Primer
docty: Policy Research Working Paper
subtopic: Energy Policies & Economics,Energy and Mining,Energy and Environment,Energy Demand,Transport Services,Natural Disasters,Ports & Waterways
teratopic: Energy,Transport,Environment
abstracts: cdata!: Considerable work has been done to
            understand and improve the resilience of individual
            infrastructure components. However, systems of components,
            or even systems of systems, are far less well understood.
            Cascade effects, where the loss of one infrastructure
            affects others, is a major source of vulnerability which can
            lead to catastrophic disruptions of essential services.
            Interdependencies can also lead to large-scale failures when
            even a single component is disrupted and results in
            'cascading' failures within and between networks.
            This is particularly true for power systems, as many other
            lifeline infrastructure systems rely on electricity. In this
            study we review the literature and give a primer on the
            vulnerabilities of networked energy infrastructure. Several
            recurrent themes emerge from across different systems: (1)
            Electricity is essential for many lifeline infrastructure
            systems to function; (2) Electrical distribution systems are
            particularly vulnerable to disruption from natural and
            manmade hazards; (3) Highly networked systems can be
            unstable even when their individual components are
            functioning as intended; (4) Redundancy and network density
            can increase reliability but also increase the likelihood of
            cascade effects when failures do occur; (5) Disruption of
            ports and roads can limit fuel supplies for generators and
            replacement components. Based on these insights, this study
            offers suggestions for further research and policy actions.
repnme: repnme: Vulnerabilities of Networked Energy
            Infrastructure : A Primer
display_title: Vulnerabilities of Networked Energy
            Infrastructure : A Primer
listing_relative_url: /research/2019/06/31167005/vulnerabilities-networked-energy-infrastructure-primer
topicv3: Energy and Extractives m1326595 507,Transport m1326661 135,Power and Electricity Sector m1327094 515,Ports m1327399 167,Hurricane m1503314 3179
publishtoextweb_dt: 2019-06-19T00:00:00Z
historic_topic: Energy,Transport,Environment
no_of_pages: 20
author_keys: 0: author_key: 1154780
1: author_key: 1264157
2: author_key: 1667844
model_extractions: Policy Research Working Paper 8901 Lifelines: The Resilient Infrastructure Opportunity _Background Paper_ Vulnerabilities of Networked Energy Infrastructure

# A Primer

_Amy Schweikert Lindsey Nield Erica Otto Magdalena Klemun Sanna Ojanpera Mark Deinert_ Climate Change Group Global Facility for Disaster Reduction and Recovery June 2019
Policy Research Working Paper 8901

# **Abstract**

Considerable work has been done to understand and improve the resilience of individual infrastructure components. However, systems of components, or even systems of systems, are far less well understood. Cascade effects, where the loss of one infrastructure affects others, is a major source of vulnerability which can lead to catastrophic disruptions of essential services. Interdependencies can also lead to large-scale failures when even a single component is disrupted and results in ‘cascading’ failures within and between networks. This is particularly true for power systems, as many other lifeline infrastructure systems rely on electricity. In this study we review the literature and give a primer on the vulnerabilities of networked energy infrastructure. Several recurrent themes emerge from across different systems: (1) Electricity is essential for many lifeline infrastructure systems to function; (2) Electrical distribution systems are particularly vulnerable to disruption from natural and manmade hazards; (3) Highly networked systems can be unstable even when their individual components are functioning as intended; (4) Redundancy and network density can increase reliability but also increase the likelihood of cascade effects when failures do occur; (5) Disruption of ports and roads can limit fuel supplies for generators and replacement components. Based on these insights, this study offers suggestions for further research and policy actions.

This paper is a product of the Global Facility for Disaster Reduction and Recovery, Climate Change Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/ prwp. The authors may be contacted at aschweikert@mines.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Vulnerabilities of Networked Energy Infrastructure: A Primer**

**Amy Schweikert**<sup>**1,2**</sup> **, Lindsey Nield**<sup>**2**</sup> **, Erica Otto**<sup>**2**</sup> **, Magdalena Klemun**<sup>**3**</sup> **, Sanna Ojanpera**<sup>**4**</sup> **, Mark Deinert**<sup>**1,2**</sup>

1Payne Institute for Earth Resources, Golden, Colorado, USA 2The Colorado School of Mines, Golden, Colorado, USA 3 Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 4 Oxford University and The Alan Turing Institute, London, UK

**JEL classification:** Q54, H54, O13

**Keywords** : Resilience; critical infrastructure; natural hazards
**Executive summary** .  Functional societies depend on the ability to move people, goods, and information, as well as to provide healthcare, food and access to clean water.  Doing this consistently and reliably requires functional ‘lifeline infrastructures’ that encompass the internal communication, transportation and distribution networks of a country, as well as its energy supply systems.  All of these are typically coupled to other infrastructures, such as financial markets and governmental institutions, which makes the resilience of lifeline infrastructures essential for a society’s ability to withstand shocks.

The expanse and quality of lifeline infrastructure varies widely between countries and even the regions within them. Regardless of location, lifeline infrastructure typically constitutes a major societal investment and is correlated to economic and social well-being. Discussions and analyses of infrastructure often focus on the hardware (i.e., the roads, transmission lines, pipes, communication satellites, etc). However, it is actually the services that these systems provide that are of real value to society. This link between lifeline systems and services is critical even though it is often poorly defined. However, understanding this link is essential when discussing the design and maintenance of infrastructure to ensure resilience against hazard events that are both manmade and natural.

Considerable work has been done to understand and improve the resilience of individual infrastructure components. However, systems of components, or even systems of systems, are far less well understood. Cascade effects, where the loss of one infrastructure affects others, is a major source of vulnerability is which can lead to catastrophic disruptions of essential services. It is obvious that this could occur when a large hazard event disables multiple infrastructure components simultaneously. However, interdependencies can also lead to large-scale failures when even a single component is disrupted and results in ‘cascading’ failures within and between networks. This is particularly true for power systems, as many other lifeline infrastructure systems rely on electricity. Highly networked systems can also have nonlinearities that render them subject to intrinsic instability even when all of their components are functioning correctly. In addition, highly networked systems are increasingly vulnerable to cyber attack.

Increasing the resiliency of networked systems has lagged behind work on individual components in part because of the complexity of the problem. Additional work is needed to develop a complete theoretical framework for understanding the stability of networked systems. Even if this existed, key data on network structure and infrastructure interdependencies are often missing or difficult to access.

In this study we give a primer on the vulnerabilities of networked energy infrastructure. The literature reviewed for this assessment shows that some highly networked systems, such as the electricity grids found in the United States and Western Europe, have been investigated for structure and reliability. The degree distributions for those systems fall within a consistent range and the systems have demonstrated their ability to reroute power when their components failed. However, these assessments might not apply directly to areas with sparse infrastructure or less developed grid network systems, such as those found in developing economic regions. System size and density have been shown in many studies to affect system stability. Grid infrastructure was found to be particularly susceptible to high winds, and damage to ports limiting for supply chains in isolated or island states. Several recurrent themes emerge from across different 2
# systems:

- 1) Electricity is essential for many lifeline infrastructure systems to function; 2) Electrical distribution systems are particularly vulnerable to disruption from natural and manmade hazards;

- 3) Highly networked systems can be unstable even when their individual components are functioning as intended;

- 4) Redundancy and network density can increase reliability but also increase the likelihood of cascade effects when failures do occur;

- 5) Disruption of ports and roads can limit fuel supplies for generators and replacement components.

Network connectivity is a key to understanding these aspects of a system, but data is lacking in many developing regions. A lack of appropriate independent redundancies is also consistently shown to limit network resiliency and interdependencies were found to increase the likelihood of cascade effects. Another theme that is consistent among the literature reviewed is that interdependencies within lifeline infrastructure are poorly quantified.

**Recommendations** .  In the above context, several areas emerge as deserving particular nearterm attention to help guide the allocation of funds for lifeline infrastructure development:

- a) Develop data on the connectivity of lifeline infrastructure systems to determine key interdependencies and how these vary geographically or with other parameters such as per capita GDP or HDI;

- b) Use data on ports of entry and transportation infrastructure to identify regions where supply chain bottlenecks could impact lifeline infrastructure;

- c) Use high spatial and temporal resolution global historical data on wind velocities to determine where electricity grids would be particularly susceptible to damage;

- d) Develop a methodology to identify lifeline infrastructure systems that lack important redundancies.

The above might, at first glance, appear difficult to achieve. However, if the focus is narrowed to electrical distribution and power system supply chains (essential for other lifeline infrastructure) data exist with which to move forward on these goals. Considerable data exists from agencies within the United States with which to construct initial databases to address the first three. This includes data on several island states whose infrastructure can be used as a proxy for that found in many developing regions.

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(Helbing 2013). The most famous of these occurred on 6 May 2010 when the Dow Jones Industrial Average dropped by 998.5 points in twenty minutes– the largest intraday point drop in history at that time – and then recovered 600 points. The cause of the sudden swing was attributed in part to a spoofing scheme by Navinder Sarao, a London based equity trader. Sarao is alleged to have manipulated the price of near-month E-mini S&P 500 futures contract by layering the sell side of the order book with large quantities of non-executable orders at nonmarketable prices. Recent analysis suggest instead that the 2010 flash crash was instead a form of self-organized criticality driven by systemic structures that were vulnerable to feedback loops with automated trading systems (e.g. Aldrich, et al. 2016). Additionally, some speculate that because of these issues underlying the system, future crashes were inevitable, and in fact seen with rapid fluctuations that have occurred since. Findings after the event include that many of the mechanisms of the system are not well understood (Madhavan 2012). An extensive analysis can be found in Kirilenko et al. (2017).

Self-organized criticality can also be particularly important in the study of failure in interdependent infrastructures. In systems such as these, large catastrophic events can occur as a consequence of the same dynamics that produce small ordinary events. Examples of this have been seen in power grids which operate with a dynamic a balance between production and load. If the balance is not quickly reestablished after disturbances (planned and otherwise) generator and load breakers will trip to keep from damaging components. This process can evolve to cause cascading outages that can last for varying degrees of time. Exactly this was seen in a 2009 blackout in Brazil that the Itaipu hydroelectric facility to shutdown (e.g. Carlotto and Grzybowski 2014). Analyses of grid blackouts from several countries show that the frequency of large events follows a power-law distribution (e.g. Dobson et al. 2007) which is consistent with self-organized criticality (Helbing 2013). If such situations are to be avoided in lifeline infrastructures, steps must be taken during the design phase, or mitigation procedures put in place to address a failure before it cascades out of control (Perrow 1999; Bak and Paczuski 1995).

The study of resiliency has its roots in the study of ecological systems and their ability to ‘bounce back’ after a disturbance or at least maintain a certain level of function (e.g. May 1971) Although widely recognized as a serious concern, how to mitigate the risks posed by infrastructure interdependency and complexity remains a nascent area of research (Turner et al. 2003; Bocchini Paolo et al. 2014; Schweikert, Espinet, and Chinowsky 2018). With few exceptions, even quantifying the linkages between infrastructures, their interdependencies, or failure mechanisms, has rarely been done (World Economic Forum 2011; Helbing 2013; Little 2002). This paper, commissioned by the World Bank’s Global Facility for Disaster Reduction and Recovery division, provides a primer on the vulnerabilities of networked energy infrastructure. This work reviews literature related to these subjects and how they may vary geographically. The work is broken into a discussion of electricity transmission and supply chains with subsequent conclusions and recommendations for areas of near-term research to address ongoing work in this field.

# **ELECTRICITY TRANSMISSION**

There are multiple components to understanding whether a power grid will be resilient to a 6
specific type of hazard event. These include the initiating event(s), the components contributing to system stability/instability, the ability to address or adapt to perturbations in the system, the lack of robust data sets to analyze the problem as well as the role that policy and organizational structure play in each of these layers. For example, initiating events could range from a tree falling on a power line to a targeted cyber attack on network stability. In both cases, the outcome of a blackout and power loss is caused by propagation through the system, but each event causes a unique stress on the system.

Grid systems in the US, Europe and China have been studied extensively to see if their connectivity impacts their stability. This type of complex network approach is common when including the graph structure of systems in an analysis (Pagani and Aiello 2012). The results show that the grids investigated, all large, have inherent redundancy which makes rerouting power because of a line failure relatively easy (Pagani and Aiello 2012). However, redundant systems increase cost due to construction, maintenance and operation of additional infrastructure assets. Redundancies can also increase the likelihood of cascading failures. One response to this is to use ‘defensive islanding’ to isolate grid failures. This effectively creates sub-regions within a larger grid that can operate, or fail, independently of the larger system of which they are a part.

The tradeoffs between highly integrated systems and ones that are independent, or can be run that way, are worth deeper analysis (Blumsack 2018). A particularly relevant example is given by the recent hurricane events in Puerto Rico. The island was hit by Categories 4 and 5 Hurricanes, Maria and Irma respectively, in 2017, resulting in devastation of much of the island’s infrastructure, including the power grid.

Figure 3 shows a map of the island including key generation facilities, and transmission infrastructure. Unlike the grids investigated by Pagani and Aiello (2012), the one in Puerto Rico was both sparse (many regions having only one power line to them) and isolated (i.e. no connections to the mainland, or other islands). As a result of the former, parts of the island were still without power a year after the hurricanes because of damaged transmission lines. Because of the latter, interruptions to fuel supply chains would have caused power outages after the storms even if the grid had not been interrupted.

One of the biggest vulnerabilities in large power grids comes from the complex interactions between the physical infrastructure (generation stations, transmission lines) and the systems connected to it. This includes fluctuating demand, diverse generating sources including intermittent renewables, public policy and cost incentives and weather.

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even if the power grid is taken offline - one definition of being ‘un-resilient’ - the supply of power to a facility is not interrupted because of the backup generators. Therefore, the definition of a 'resilient system' depends upon whether the supply (the power grid) or demand (availability of electricity) component of the system is being modeled. The perspective of which definition of resilience is being targeted also affects the policy and preparation of decision makers.

A recent paper (Hines, Dobson, and Rezaei 2016) investigated the propagation of power transmission outages using influence graph modeling. A finding from this paper is that the propagation of outages (that is, the subsequent failure of a component due to the prior failure of another) does not follow proximal geographic or topological patterns one may expect when applying models such as contagions used for infectious diseases. The simulations presented are tested against a large historical outage in the United States and result in similar distributions. The findings of this method focus on quick identification of critical components that can be targeted for reduction of large, cascading blackout events.

The approach most used in modeling failure propagation of power networks is graph theory and network analysis in conjunction with the ‘Swing equations’ or some other dynamical model. The identification of ‘nodes’ connected by ‘edges’ that can be directional and have different weights allows for the simulation of power transmission. The Swing equations can be used to model the effect of loads and generators on phase shifts when a system asset is perturbed.

One significant challenge in modeling the power grid is the size of large, interconnected networks such as the United States: The Eastern Interconnect (one of three main grids operating in the USA) required approximately a month of simulation time on a 7 petaflop machine to model the addition or subtraction of generation (Personal Communication, NREL). Small grids, intrinsically requiring less components and interactions, are therefore easier to model and optimize.

# **SUPPLY CHAINS AND CASCADE FAILURES**

Understanding the interdependencies of different infrastructures is a necessary component of designing resilient lifeline systems. This includes supply chains where the operation of one system is necessary for the operation of the another. In power systems this can be differentiated into three general categories: the supply of fuel to generation facilities, the supply of resources required for the operation of facilities (such as water used for cooling), and the supply of electricity to other critical infrastructure that rely on it for operation (such as hospitals). Because the latter two issues are addressed in an earlier white paper (Schweikert et al. 2018), this section focuses on the first category.

The importance of supply chains to private organizations is well recognized. The development of ‘smarter energy supply chains’ breaks down the fuel supply chain for electricity production into five distinct processes: upstream, in-bound, out-bound, remote worker, and emergency supply chains (Harrington 2014.). The first four processes correspond to the actual extraction of fuel from a location. The fifth process focuses on supporting organizations when the supply chain is perturbed or interrupted by non-normal events, including natural hazard events. The extraction and transportation of fuel for electricity consumption is a known vulnerability in the reliability of the power grid system (Schweikert et al. 2018). As global energy consumption 10
shifts towards emerging economies, projected to account for more than 90% of net energy growth by 2035, understanding supply chain and critical points of failure become increasingly valuable (International Energy Agency 2013).

The 2011 floods in Thailand provide an important case study for cascade effects from supply chain failures. Thailand experienced severe and prolonged flooding in 2011, especially in the Central region of the country including areas of the City of Bangkok and Ayutthaya Province. A large amount of the manufacturing in the country is centralized in these regions. Disruption from heavy rains to manufacturing facilities, workers’ homes, transportation and other infrastructure caused a sharp decline in production and exports. This included significant impacts to the automotive, electronics, and optical equipment industries, as well as many others. The automotive industry saw the sharpest impact with over 85% decline in production index in November 2011. Together, this decline in the fourth quarter of 2011 resulted in national GDP projection revisions of 2.6% down to 1.0%. The event highlighted the vulnerability of just-intime supply chain networks.

Supply chain risk management encompassing low-probability, high-risk events is a relatively nascent field. This may be due to fewer events occurring and less information with which to predict future events, particularly in an era of climate change. In many ways, redundancy in inventory and/or suppliers can act as shock absorbers and diversify risk from single suppliers but reduces the extreme efficiency and cost reductions from normal operating conditions. In Thailand, this included geographic clustering of industrial facilities, lean operations to enhance efficiency and economies-of-scale centralized production (Chongvilaivan 2012). The heavy impacts in a few regions resulted in closures and delays of production for technology organizations with global supply chains including Seagate, Microsemi, ON Semiconductor, Hutchinson Technology, Western Digital and more (Savitz 2011). Notably, these disruptions may be best characterized with complex systems methods including network analysis: Chongvilaivan (2012) states that this flooding event has made it “increasingly evident” that supply chain disruptions from natural hazards and other events can “endanger the just-in-time approach to procurement and production because any disruptions to a single node of production may lead to a breakdown of the entire production chain”. A thorough examination of the implications of the impacts on upstream and downstream supply chain management, specific to the automotive industry, can be found in Heinecke (2013).

Several important issues have been identified with the electricity and fuel supply chain (e.g. Harrington, 2014). First, the recognition that safety is a critical aspect for organizations and businesses when considering the operation of a supply chain. Second, the complex nature of operations due to required management of multiple stakeholders, parallel operations, and a variety of personnel and goods that interact at some point along a supply chain. The multiple actors within a supply chain also require consideration of accountability processes that are transparent and interlinked. A third area of recognized concern is the management of multiple data sources and the logistics required to manage safety, efficiency and productivity within a complex supply chain operation (Harrington, 2014).

**INFRASTRUCTURE INTERDEPENDENCIES** . Given the importance of lifeline infrastructure interdependencies, considering the supply chain is only one aspect of

11
understanding the value of a reliable and resilient power grid system. This is a key area for future work specific to the context of natural hazards, unpredictable disruptions and the interdependencies with other planning considerations related to the power grid.

While widely recognized as important, infrastructure interdependencies are poorly quantified, as are the cascade effects that that can result from them (World Economic Forum 2011; Helbing 2013; Little 2002). However, past hazard events can be informative about the scale of the potential problem. Comes and Van de Walle (2014) identify several key findings related to the impact of the Hurricane Sandy on individual infrastructure systems and the interconnected impacts they have on each other:

- The electrical grid was found to be most vulnerable in the transmission and distribution components, with storm winds damaging overhead power lines and requiring substantial rebuilding efforts. Additional damages were seen to substations (flooding and storm surge);

- The Subway transportation system within Metropolitan New York City was damaged due to flooding within the subway tunnels and damage and debris covering the tracks;

- Damages to the transmission and distribution grid caused feedback effects to power plant infrastructure operation and grid stability;

- Repairs to the electrical grid were hampered due to inaccessibility of sites caused by the closure of roads due to flooding and debris;

- The Subway transportation system within Metropolitan New York City was seen to have a slower pace of recovery because of its dependence on the availability of commercial power to operate;

- Oil and gas infrastructure saw damages due to storm surges and salt water intrusion, but the major impacts were from their interdependency on the power grid;

- Power outages impacted the operation of oil and gas supply. Specifically, pipelines, oil terminals, storage tanks and filling stations were not fully operational. Delivery bottlenecks were identified as a key detrimental impact to the system, including a limited supply of backup generators and storage of gasoline fuel onsite;

- Information and communication infrastructure were damaged due to flooding and saw slower recovery due to a lack of access to sites for repair. The operation of this infrastructure relies on power supply for operation, but in the case of Hurricane Sandy, mobile trailers and other backup supply options were deployed and limited the overall impact to system operation.

- The transportation systems, including rail, roads, subway and other infrastructure were damaged due to direct impacts of the hurricane. This includes saltwater damage, debris, and flooding. The largest impacts of the recovery of the transportation system were seen because of interdependencies. The operation of the metropolitan transportation networks relies on commercial power, oil and gas supply, and functioning information and communication systems. This cascading failure effect included the extended restoration times because of limited road access to repair damages to the electric and these systems.

An important finding from research on Hurricane Sandy has been that the immediate priorities, disruptions and consequences of lifeline systems failures can evolve as a hazard situation 12
unfolds. With Sandy, interdependencies between the power grid and other systems included immediate information and communication outages, disruption of oil and gas distribution, and shutdown of transportation systems. These consequences of the storm then evolved to include feedback effects such as a lack of fuel availability impacting the backup power system operability, shutdown of data and control centers that effected the power grid, etc. Prolonged restoration times for information and communication infrastructure, as well as damaged transmission and distribution infrastructure because of road blockages and damage then followed. Another example of how interconnected infrastructure can affect hazard response was evident during and after Typhoon Haiyan (Typhoon Haiyan struck The Philippines in 2013; see Schweikert et al. (2018) for more information). Specifically, it was found that the response efforts were delayed by damages and disruptions to the communications infrastructure, transportation systems and loss of power (Comes and de Walle 2014). These temporal aspects of impacts and recovery have subsequently been underscored as important considerations in the design of resilient infrastructure systems (Comes and de Walle 2014).

Many of the above issues were also seen in Puerto Rico following the 2017 Hurricane season (see Schweikert et al. (2018) for more information). In a comprehensive recovery strategy (Rossello 2017), Governor Rossello proposed over $15 billion to rebuild the power grid to a more resilient standard. The suggested improvements would be designed to withstand similar Category 4 impacts (155 mph/250kph sustained winds) and would reduce ongoing maintenance costs. Additionally, the proposal included small, distributed systems that would ensure ongoing operation of key water, sanitation and health facilities if a disruption to the central grid was experienced. The latter is a key concern as the operation of health facilities months after the storm was reduced: an estimated 72 of 107 clinics were operational and 33 of those were operating on generator power inciting higher costs and environmental impacts. The recovery efforts following the event were heavily hindered by the damage to roads and bridges throughout the island. Public transit (as of 3 months following the event) had not been restored, with lack of available power cited as the primary reason. The damage to transportation also caused impacts to the humanitarian response include delivery of medical care, food and water to impacted communities and is cited as a driver for future economic recovery and growth.

A unified approach for quantifying the connectivity of lifeline infrastructures can be developed by modifying the approach of Klemun, Ojanpera and Schweikert (2018) for determining the linkages between progress on Sustainable Development Goals and energy technology interventions, Fig. 5. Here the connectivity of hazards events, lifeline infrastructures and societal impacts can be determined using an inverse network analysis. Case studies for hazard events constitute the input data for hazard, infrastructure damaged, and impact.

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large scale natural disaster) is also potential area for future modeling. Next, a deeper analysis of the tradeoffs between efficiency, connectedness, islanding and other grid structures, particularly in the broader context of resilient electricity provision during and after a natural hazard event, may provide useful insights into the planning process.

- 3) A finding across the literature reviewed on the impacts of natural hazards on the power system  is that transmission networks are the most vulnerable component of the system (Schweikert et al. 2018).  Several research areas specific to natural hazards and resiliency can be framed in this context.  The deeper analysis of smaller systems, such as Puerto Rico or other geographically isolated regions, may provide valuable insights into the operation and topological considerations that increase or reduce resiliency.  This could include different measures of intermittent generation technologies, redundant transmission networks, and others.  A final consideration in this context is a multiplecriterion assessment of transmission reliability that includes a techno-economic analysis of performance during a hazard situation, the cost of redundant transmission lines and the consideration of above or below-ground transmission lines.

# **CONCLUSIONS**

A functioning and reliable power system is important for the operation of many societal functions, including lifeline infrastructure systems. In hazard situations, damage to the electrical grid, or supply chains, can result in cascading failures throughout a society and impact response and recovery work. This was seen in the impacts of recent hurricanes in both Puerto Rico and the Northeastern United States (see: Schweikert et al. 2018 and Comes and Van de Walle 2014).

This paper provides a primer on the vulnerabilities of networked energy infrastructure. Notably, much of the work reviewed shows that these types of systems, including the electricity grid, can exhibit non-linear and unpredictable behavior. Metrics including density of networked components, the redundancy and interconnectedness of sub-systems within the electricity grid – as well as linkages to other lifeline networks – are identified as providing insight into system behavior. However, these metrics are not particularly well understood or quantified, especially in smaller systems or those existing in developing economic regions.

Future work in this area, aimed at enhancing decision making and investment for more resilient infrastructure, can focus on the following areas:

- a) Develop data on the connectivity of lifeline infrastructure systems to determine key interdependencies and how these vary geographically or with other parameters such as per capita GDP or HDI;

- b) Use data on ports of entry and transportation infrastructure to identify regions where supply chain bottlenecks could impact lifeline infrastructure;

- c) Use high spatial and temporal resolution global historical data on wind velocities to determine where electricity grids would be particularly susceptible to damage;

- d) Develop a methodology to identify lifeline infrastructure systems that lack important redundancies.

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