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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A dataset of cyber-induced mechanical faults on buildings with network and buildings data

We have collected data of cyber-induced mechanical faults on buildings using a simulation platform. A DOE reference building model was used for running the simulation under a Rogue device attack and collected the network data as well as the physical buildings data to better understand the impacts of cyber attacks on the building and help identify the source of the mechanical fault with the network data. Alfalfa is the tool used for simulating the DOE reference buildings and acts as an interface to the model for querying the status and providing input externally. The Building Automation System (BAS) is the centralized controller providing control commands to other BACnet devices on the network based on the building status received from Alfalfa. The BACnet devices like damper will listen for the control commands from BAS on the BACnet network and implement it. The attacker is the malicious actor on the network creating disruptions by placing cyber-attacks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2016

Cyber-Threat Assessment for the Air Traffic Management System: A Network Controls Approach

Air transportation networks are being disrupted with increasing frequency by failures in their cyber- (computing, communication, control) systems. Whether these cyber- failures arise due to deliberate attacks or incidental errors, they can have far-reaching impact on the performance of the air traffic control and management systems. For instance, a computer failure in the Washington DC Air Route Traffic Control Center (ZDC) on August 15, 2015, caused nearly complete closure of the Centers airspace for several hours. This closure had a propagative impact across the United States National Airspace System, causing changed congestion patterns and requiring placement of a suite of traffic management initiatives to address the capacity reduction and congestion. A snapshot of traffic on that day clearly shows the closure of the ZDC airspace and the resulting congestion at its boundary, which required augmented traffic management at multiple locations. Cyber- events also have important ramifications for private stakeholders, particularly the airlines. During the last few months, computer-system issues have caused several airlines fleets to be grounded for significant periods of time: these include United Airlines (twice), LOT Polish Airlines, and American Airlines. Delays and regional stoppages due to cyber- events are even more common, and may have myriad causes (e.g., failure of the Department of Homeland Security systems needed for security check of passengers, see [3]). The growing frequency of cyber- disruptions in the air transportation system reflects a much broader trend in the modern society: cyber- failures and threats are becoming increasingly pervasive, varied, and impactful. In consequence, an intense effort is underway to develop secure and resilient cyber- systems that can protect against, detect, and remove threats, see e.g. and its many citations. The outcomes of this wide effort on cyber- security are applicable to the air transportation infrastructure, and indeed security solutions are being implemented in the current system. While these security solutions are important, they only provide a piecemeal solution. Particular computers or communication channels are protected from particular attacks, without a holistic view of the air transportation infrastructure. On the other hand, the above-listed incidents highlight that a holistic approach is needed, for several reasons. First, the air transportation infrastructure is a large scale cyber-physical system with multiple stakeholders and diverse legacy assets. It is impractical to protect every cyber- asset from known and unknown disruptions, and instead a strategic view of security is needed. Second, disruptions to the cyber- system can incur complex propagative impacts across the air transportation network, including its physical and human assets. Also, these implications of cyber- events are exacerbated or modulated by other disruptions and operational specifics, e.g. severe weather, operator fatigue or error, etc. These characteristics motivate a holistic and strategic perspective on protecting the air transportation infrastructure from cyber- events. The analysis of cyber- threats to the air traffic system is also inextricably tied to the integration of new autonomy into the airspace. The replacement of human operators with cyber functions leaves the network open to new cyber threats, which must be modeled and managed. Paradoxically, the mitigation of cyber events in the airspace will also likely require additional autonomy, given the fast time scale and myriad pathways of cyber-attacks which must be managed. The assessment of new vulnerabilities upon integration of new autonomy is also a key motivation for a holistic perspective on cyber threats.

Complex Networks↗
NASA NTRS2019

Cyber Physical Security (CPS) Extension to Air Traffic Management (ATM) Testbed

The Air Traffic Management (ATM) Testbed is being developed at NASA to enable benefit, impact, safety and cost assessments for accelerating the deployment of Concept and Technologies (C&T) in the National Airspace System (NAS). Today, C&T introduction into the NAS takes decades. The primary reason for this is an inability to assess the operational impact of the interaction between the proposed C&T and operationally deployed systems (Realistic Technologies) in terms of NAS-wide safety, traffic flow efficiency, roles and workload of controllers and traffic managers, and impact on airline fleet operations. Transition of C&T to operations requires mathematical modeling and simulation, Human-in-the-Loop (HITL) testing and shadow-mode evaluation driven by operational data. Whereas interaction with the operational system during testing and stages of deployment is not permissible due to safety concerns, it is certainly possible to create a simulation environment that closely mimics the NAS using the same operational systems/hardware for enabling such assessments. This presentation focuses on a proposed Cyber Physical Security extension to the ATM Testbed for creating a modeling and simulation architecture to study how well the Air Traffic Management system will perform and analyze effectiveness of mitigating security measures against particular cyber-attack scenarios.

Datta, Koushik↗
NASA NTRSDate not supplied

A Survey of Cyber Threat

Multiple companies are competing to develop human-crewed and unmanned aerial vehicles to provide flight in urban environments. With the growth of aerial systems and future airborne vehicle networks and the need to enable secure data exchange and service interactions within Urban Air Mobility (UAM) environments, cybersecurity has come to the forefront as a topic, highlighting the need to protect these networks from cyber-attacks. This paper will identify potential threats, vulnerabilities, and weaknesses of UAM environments, that could lead to system compromises and disruptions.

Cyber Security↗
NASA NTRSDate not supplied

NASA’s Secured Airspace for Urban Air Mobility (UAM)

The Urban Air Mobility (UAM) architecture is leveraged from the Unmanned Traffic Management (UTM) concept of operations. Within the UAM environment, UAM operators work collaboratively to manage aerial vehicles in the urban environment. Providers of Services for UAM (PSU), UAM operators, and Supplemental Data Service Providers (SDSP) provide services to support flight operations within that environment. As a recognized need, various views of UAM flight information are provided to the public and public safety entities. To accomplish this, among other goals, the Federal Aviation Administration (FAA) can coordinate flight information between the FAA controlled National Airspace System (NAS) and the UAM environments through the FAA-Industry Data Exchange Protocol (FIDXP). This concept of UAM proposes to develop short-range, point-to-point transportation systems in metropolitan areas using vertical take-off and landing (VTOL) or short take-off and landing (STOL) aircraft to overcome increasing surface congestion. To garner the support of UAM and to realize its potential, an assurance of cybersecurity is critical for public acceptance. Understanding the various components communicating with one-another cybersecurity, like in other industries, has come to the forefront highlighting the need to protect these networks and systems from cyberattacks. With the planned growth and reach of UAM systems, it’s clear that the associated data exchange and service interactions will be at risk due to numerous types of cybersecurity attacks. Consequently, as these threats evolve, the UAM cybersecurity capabilities must adapt to these changes as well. While learning is always the goal, the overall intent of this workshop is to make recommendations on the following: (1) how future UAM environments can be protected against cyber-attacks, and (2) what mechanisms should be put in place to detect attacks against UAM environments.

UAM↗
DOE OSTI2022

OPERATIONAL TECHNOLOGY BEHAVIORAL ANALYTICS (OTBA) – A DATA-CENTRIC APPROACH FOR REDUCING CYBERSECURITY RISK

This paper provides a summary of the methodology, findings, lessons learned, and insights from an investigation into the feasibility of the Operational Technology Behavioral Analytics (OTBA) cybersecurity approach. The concept was evaluated with data from the National Carbon Capture Center (NCCC) – a U.S. Department of Energy (DOE) funded facility that is managed and operated by Southern Company at Alabama Power’s E. C. Gaston generating power plant in Wilsonville, Alabama. Appropriate data sources for the post-combustion carbon capture system were identified. Infrastructure was deployed to monitor, capture and archive data for the system. Critical parameters for each subsystem were identified and analyzed. Machine-learning algorithms were used to establish and characterize normal operations and subsequently identify anomalies. This effort yielded valuable insights and formed the basis of a data-centric strategy for detecting cyber-attacks along with a coordinated response philosophy. A significant takeaway is that the OTBA cybersecurity approach is quite portable; it can be applied to other critical infrastructure beyond fossil power generation.

Black, Clifton↗
DOE OSTI2021

BioSecure Digital Twin: Manufacturing Innovation and Cybersecurity Resilience

U.S. national security, prosperity, economy, and well-being require secure, flexible, and resilient Biopharmaceutical Manufacturing. The COVID-19 pandemic reaffirmed that the biomedical production value-chain is vulnerable to disruption and has been under attack from sophisticated nation-state adversaries. Current cyber defenses are inadequate, and the integrity of critical production systems and processes are inherently vulnerable to cyber-attacks, human error, and supply chain disruptions. The following chapter explores how a BioSecure Digital Twin will improve U.S. manufacturing resilience and preparedness to respond to these hazards by significantly improving monitoring, integrity, security, and agility of our manufacturing infrastructure and systems. The BioSecure Digital Twin combines a scalable manufacturing framework with a robust platform for monitoring and control to increase U.S. biopharma manufacturing resilience. Then, the chapter discusses some of the inherent vulnerabilities and challenges at the nexus of health and advanced manufacturing. Next, the chapter highlights that as the Pandemic evolves, we need agility and resilience to overcome significant obstacles. This section highlights an innovative application of Cyber Informed Engineering to developing and deploying a BioSecure Digital Twin to improve the resilience and security of the biopharma industrial supply chain and production processes. Finally, the chapter concludes with a process framework to complement the Digital Twin platform, called the Biopharma (Observe, Orient, Decide, Act) OODA Loop Framework (BOLF), a four-step approach to decision-making outputs from the Digital Twin. The BOLF will help end users leverage twin technology by distilling the available information, focusing the data on context, and rapidly making the best decision while remaining cognizant of changes that can be made as more data becomes available.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Cyber risk assessment and investment optimization using game theory and ML-based anomaly detection and mitigation for wide-area control in smart grids

The electric power grid is increasingly becoming susceptible to cyber attacks that exploit vulnerabilities in the smart grid control, information, and physical layers. Successful cyber attacks can have catastrophic impacts on the social and economic well-being of any nation all over the globe. It has, thus, become imperative to secure the smart grid against such adversarial actions to ensure stable, secure, and reliable operation of the grid. The existing research and industry practices prove to be inadequate in terms of providing pragmatic and effective defense methodologies and measures for long-term cybersecurity planning and real-time cybersecurity for grid operation. For example, existing works lack models that incorporate uncertain behavior of cyber-attackers and pragmatic defense measures for cyber risk assessment and cybersecurity investment optimization which often provide unreliable and strictly qualitative solutions to these problems. At the same time, with the growing number of cyber incidents in the grid, there still exists a need to develop attack-resilient algorithms for wide-area monitoring, protection, and control (WAMPAC) applications like the wide-area voltage control systems (WAVCS) for Flexible AC Transmissions Systems (FACTS) that lack in scalable and feasible solutions from the cybersecurity perspective. This dissertation proposes novel models and methodologies for: (1) Cybersecurity planning, and (2) Cybersecurity for system operation. The cybersecurity planning is achieved through cyber risk assessment and cybersecurity resource investment optimization for long-term cybersecurity of the grid using game theory and attack-defense trees. Cybersecurity for system operation consists of development of cyber anomaly detection and mitigation algorithms for flexible AC transmission system (FACTS) controller-based wide-area voltage control systems (WAVCS) using machine learning (ML), and software defined networking-based moving target defense network routing for achieving real-time cyber-physical security for grid operations. This is followed by hardware-in-the-loop (HIL) implementation and evaluation of these attack prevention, detection, and mitigation algorithms and methodologies showcasing their feasibility in a close to real-world environment. For cybersecurity planning, a novel approach involving a combination of game theory and attack defense trees (ADT) for optimal cybersecurity resource allocation in the smart grid is proposed. This methodology involves modeling of the cyber-physical smart grid substations as ADTs, defining attacker costs, defense costs, and attack probabilities for attack access points. Using game theoretical formulation, optimal defense strategies for the defender of the system to invest cybersecurity resources in the grid are obtained. Additionally, a game-theoretic framework is developed for quantitative cyber-physical risk assessment of the grid under a dynamically changing cyber threat space and uncertain behavior of cyber attackers which is further used to optimize investments in the smart grid's cybersecurity resources. The attacker, defender, and the smart grid system are modeled while incorporating attacker-stochasticity and federal guidelines for smart grid cybersecurity. This allows quantification of threat, vulnerabilities, and attack impact of the grid for quantitative risk assessment. The defender's budget to invest in the security resources in the grid is optimized based on the strategies leading to minimum system risk. The evaluation of the proposed solutions highlight the feasibility for practical implementation of these methodologies and algorithms in the smart grid, while taking the federal requirements and guidelines for smart grid security into consideration. For achieving cybersecurity for system operation, attack prevention, detection, and mitigation algorithms and methodologies are developed specifically for FACTS-based WAVCS. Anomaly detection and mitigation in the WAVCS are achieved using algorithms based on machine learning which involves offline training and testing of ML models with CPS datasets incorporating physics-based features that allow accurate distinction between system faults and cyber attacks. For attack prevention, a methodology based on software defined network (SDN)-based moving target defense (MTD) network routing is proposed that enables prevention of Denial of Service (DoS) type attacks on the smart grid communication system. Subsequently, these methodologies and algorithms are implemented and evaluated on an HIL testbed that allows for real-time attack prevention, detection, and mitigation of emulated cyber attacks on the WAVCS in a close to real-world environment. The results show highly accurate and efficient performance of the implemented algorithms and methodologies with the smart grid system operating within the NERC's system operation limits even in the presence of DoS and data integrity cyber attacks. This work opens up future research opportunities in other directions such as (1) Expanding cybersecurity planning methodologies to real-time cyber contingency analysis with different game formulations; and (2) Applying the cybersecurity for system operation algorithms to broader categories of wide-area control applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Emulation and Adversarial Analysis of EV Charging Networks

In the effort of decarbonization and evolution of the modern electrical grid, electric vehicles (EVs) play a key part to transform the grid. However, due to the rapid adoption of EVs and the demand of the charging infrastructure required to power said EVs, risk of a cyber-attack may impose serious consequences. There is a need to analyze and protect the charging ecosystem infrastructure from cyber threats before it reaches wide-scale deployment. In an effort to secure vehicle to grid (V2G) communications, standardization is necessary for continued reliable system operation. The protocol ISO 15118 outlines controls and practices that should be implemented for secure vehicle to grid (V2G) communications. The standard is gaining momentum for American markets as the demand for EV infrastructure grows. The adoption of ISO 15118 in American markets poses several challenges: the deployment of a public key infrastructure (PKI) as outlined within the standard, interoperability of charging different EVs with chargers from different manufactures using the PKI, and scaling the ecosystem to meet the demand while managing risks. This project was created to understand potential cyber and scaling challenges of PKI for EV infrastructure through utilizing a series of emulated components mapping to what exists in the EV ecosystem today, and the components of the PKI that are under development. The key nodes within the emulation that are under development are: electric vehicle (EV), electric vehicle supply equipment (EVSE), charge network operator (CNO), certificate authority (CA), and online certificate status protocol (OCSP) that must all interact using secure and trusted communications. With these emulated components and utilizing orchestration methods to rapidly deploy and scale the components, the ability to analyze risks of the ecosystem and address gaps before the PKI ecosystem is fully deployed to production should yield a more robust and mature production charging infrastructure. Our approach will use a modular architecture of virtual machines within an orchestration platform and will target scales of 100s, 1000s, and 10,000s of entities interacting. The core research questions trying to be answered with this scope of work are: what are the impacts of a rogue CA, what are the risks of certificate revocation list (CRL) management, what is the value of OCSP stapling, what components are vulnerable to DOS attacks, and what test effective payloads may impact the components.

charging ecosystem↗
DOE OSTI2024

OT Operational Anomaly Detection (OAD) T&D + DER

The growth of utility-scale renewable energy resources, distributed energy resources (DER), and transportation electrification has increased uncertainty and cybersecurity risks in power grids. The Purdue Enterprise Reference Architecture model which is widely adopted by the utility industry is now insufficient to protect the power grid against cyber-attacks. There is a need to identify what cybersecurity model is effective on Energy Management System (EMS), Advanced Distribution Management System (ADMS), and DER Management System (DERMS) to address the fundamental cybersecurity challenges in the age of increasing renewable energy and DER share as well as consumer participation in the electric energy industry. The next generation of cybersecurity model for OT network should be able to detect inside attackers, mitigate the cybersecurity risks arising from the new grid participants including DER aggregators, electric vehicle owners, and behind-the-meter consumers outside the utility company, and develop the strategy to trust consumer measurement data. This panel will discuss the challenges and pathways for the development of an ensemble cybersecurity model based on predictive state estimation to detect cybersecurity anomalies in OT network including EMS, ADMS, and DERMS.

cybersecurity↗
DOE OSTI2023

Development of A Hardware-In-the-Loop (HIL) Testbed for Cyber-Physical Security in Smart Buildings

As smart buildings move towards open communication technologies, providing access to the Building Automation System (BAS) through the building's intranet, or even remotely through the Internet, has become a common practice. However, BAS was historically developed as a closed environment and designed with limited cyber-security considerations. Thus, smart buildings are vulnerable to cyber-attacks with the increased accessibility. This study introduces the development and capability of a Hardware-in-the-Loop (HIT) testbed for testing and evaluating the cyber-physical security of typical BASs in smart buildings. The testbed consists of three subsystems: (1) a real-time HIL emulator simulating the behavior of a virtual building as well as the Heating, Ventilation, and Air Conditioning (HVAC) equipment via a dynamic simulation in Modelica; (2) a set of real HVAC controllers monitoring the virtual building operation and providing local control signals to control HVAC equipment in the HIL emulator; and (3) a BAS server along with a web-based service for users to fully access the schedule, setpoints, trends, alarms, and other control functions of the HVAC controllers remotely through the BACnet network. The server generates rule-based setpoints to local HVAC controllers. Based on these three subsystems, the HIL testbed supports attack/fault-free and attack/fault-injection experiments at various levels of the building system. The resulting test data can be used to inform the building community and support the cyber-physical security technology transfer to the building industry.

Li, Guowen↗
DOE OSTI2023

Maximum-impact Adversary Design for Network-based Control System: A Case Study on Grid-interactive Efficient Buildings

The Internet of Things (IoT) technology has dramatically improved the efficiency of today's building operation and management. By connecting controllable devices into a communication network, control signals can be easily passed to the devices, and operating status can be acquired from measurable ends with minimal effort. However, this all-connected configuration could also expose the network-based control system (NBCS) to malicious actions, such as cyberattacks. One of the common NBCSs is the building automation system. With the promotion of grid-interactive efficient buildings (GEBs), there has been increasing attention on securing the buildings from the network perspective. This research proposes a maximum-impact adversary design framework so that the adversary can provide the most adversarial impact on the controlled system while remaining stealthy. The proposed framework is numerically demonstrated on a network-based building energy and control system. The building energy system is built in a Modelica-based simulation environment and controlled by the state-of-the-art ASHRAE Guideline 36 control sequences. The control commands at the supervisory level, generated from the Guideline 36 controller, are assumed to be sent to local devices through communication networks using the BACnet protocol. Simulation results show that the proposed maximum-impact adversary on such a system can stealthily affect the building system's performance to its maximum extent. It is anticipated that results can be used by researchers and practitioners in the building automation industry to design efficient and robust cyber-attack detection algorithms, especially for stealthy attacks.

Chu, Mengyuan↗
DOE OSTI2023

Robust and cybersecure coordinated unintentional island detection for microgrids

Unintentional islanding (UI) of a circuit of distributed energy resources (DERs) may leave area electrical power systems (EPS), external to the DER circuit, energized. Thus, UI detection methods have been developed to detect unintentional islanding and trigger a UI response. However, individual UI detection methods have various deficiencies. Thus, a consensus-based UI detection process is disclosed that builds a consensus from multiple UI detection sources, optionally implementing different UI detection methods. The redundancy in this consensus-based UI detection process provides robust, sensitive, selective, and cybersecure UI detection for the entire DER circuit. For example, the consensus-based UI detection process may eliminate or reduce non-detection zones, avoid false positives, thwart cyber-attacks, and/or the like.

Brissette, Alex↗
DOE OSTI2024

Does practice make perfect? Lessons learned from full-scale power system incident response exercise

While threats to the energy sector occur daily, few utilities get the opportunity to fully test out their detection and response mechanisms to advanced threats in the real world. With the high demand for reliability, few grid operators would allow execution of simulated cyber-attacks on their live systems. The DOE-funded Liberty Eclipse project offers a unique opportunity for small and large utilities and coops to practice their combined IT/OT responses to a live red team executing attacks against an isolated power system on an island in New York. Both cyber teams and power operations teams must work together to detect and respond to attacks, even restoring the power system against extreme impacts. Lessons learned from these exercises reveal key takeaways for understanding what a real attack against the electric sector will look like, gaps in execution of the best-laid plans when the pressure of a real event is bearing down, and how organizations can better prepare for advanced attacks by optimizing participation in exercises. This presentation will discuss successes and opportunities for improvement both in how utilities can prepare for and respond to events, as well as how full-scale IT/OT exercises can be coordinated.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Software defined networking moving target defense honeypot

Disclosed herein are systems, methods, and storage media for thwarting cyber-attacks and data theft. A computing system receives packets and compares with a configuration resource. The computing system determines that the packet does not match the configuration resource and transmits a packet to a decoy environment via an SDN switch. The decoy environment is configured to generate time-out, service unavailable, or restricted access messages. In some embodiments, the computing system determines the packet does match the configuration and transmits the packet to a production network via an SDN switch. The SDN switch is communicatively connected to the decoy environment through a first channel and communicatively connected to a production environment through a separate second channel. The computing system is further configured to create and transmit to the SDN switch, rules to manage transmitting the packet to either the decoy environment or the production environment.

Lyle, Joshua A.↗
DOE OSTI2025

Internship Presentation: Integrating Safety and Cybersecurity: Security-by-Design with SOWT Analysis for Reactor Testing

This study covers leveraging reactor testing facilities that are primarily designed with a focus on safety to enhance cybersecurity testing. By incorporating reactor security-by-design with reactor safety-by-design principles and adopting defense-in-depth strategies that emphasize both safety and security, the research evaluates applicable cyber tools, models, and solutions. This includes simulating specific cyber-attack scenarios using reactor simulators and performing SWOT (Strengths, Weaknesses, Opportunities, Threats) analysis to improve the cybersecurity of reactor systems.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2026

Smart Inverters, Dumb Risk: Taking Control of IBR Security in the Digital Age

This presentation addresses the security challenges posed by Inverter-Based Resources (IBRs) in the modern energy landscape. The presentation highlights the vulnerabilities and risks associated with IBRs, including the potential for cyber-attacks, the impact of insecure defaults, and the systemic risks posed by supply chain dependencies. Key topics covered include: 1) The increasing digital transformation in energy systems and the associated security risks. 2) Specific vulnerabilities in IBRs, including weak passwords, hardcoded credentials, and insecure web application interfaces. 3) The implications of persistent connectivity and the strategic risks posed by foreign-manufactured components. 4) The role of regulatory frameworks, such as NERC CIP, in addressing these challenges and the limitations of current oversight. 5) Practical solutions for mitigating risks, including secure design practices, vendor risk assessments, and the importance of strong passwords and role-based access control. The presentation underscores the necessity of a comprehensive, system-of-systems approach to securing IBRs, emphasizing the need for collaboration across various stakeholders, including operators, developers, and regulators, to ensure the resilience and security of the energy grid.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Losing Control of Your Linear Network? Try Resilience Theory

Resilience of cyber-physical networks to unexpected failures is a critical need widely recognized across domains. For instance, power grids, telecommunication networks, transportation infrastructures, and water treatment systems have all been subject to disruptive malfunctions and catastrophic cyberattacks. Following such adverse events, we investigate scenarios where a node of a linear network suffers a loss of control authority over some of its actuators. These actuators are not following the controller's commands and are instead producing undesirable outputs. The repercussions of such a loss of control can propagate and destabilize the whole network despite the malfunction occurring at a single node. To assess system vulnerability, we establish resilience conditions for networks with a subsystem enduring a loss of control authority over some of its actuators. Furthermore, we quantify the destabilizing impact on the overall network when such a malfunction perturbs a nonresilient subsystem. We illustrate our resilience conditions on two academic examples, on an islanded microgrid and on the linearized IEEE 39-bus system.

97 MATHEMATICS AND COMPUTING↗