Power systems are being reshaped by decarbonization, digitalization, and high shares of renewables. At the same time, increasingly severe extreme conditions expose the limits of traditional reliability frameworks, calling for risk-aware, resilience-oriented approaches to address high-impact, low-probability (HILP) events. In this context, this paper presents a comprehensive overview of the foundations of power system resilience. It revisits the transition from reliability to resilience, formalizes key concepts and metrics, and introduces advanced approaches for resilience assessment, including fragility-based modeling, cascading failure analysis, and tail-risk indicators. The paper further examines resilience-oriented investment planning, operational strategies across all event phases, and the role of distributed energy resources, microgrids, and cybersecurity. The analysis highlights that resilience extends reliability by focusing on extreme conditions, fundamentally reshaping decision-making and requiring coordinated strategies across infrastructure, operation, and governance.
We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delay: a transmission delay accounting for information exchange between agents, and a reaction delay representing the processing time before agents adjust their states. For a simplified linear two-agent system, we analyze how these delays affect asymptotic stability. We then derive sufficient conditions for asymptotic consensus and flocking in the general multi-agent setting with a nonlinear, globally positive influence function. These conditions require the delays to be sufficiently small relative to the initial data and the decay rate of the influence function. The analysis is based on a Lyapunov functional approach combined with a Grönwall–Halanay-type inequality. Our results establish rigorous sufficient conditions under which collective behavior emerges in delayed multi-agent systems where both communication and reaction lags are non-negligible, with applications to biological, social, and engineered systems.
Large-scale airspace disruptions can reorganize civil aviation traffic far beyond the directly affected airspace, yet their operational consequences are difficult to characterize using traffic volume alone. This study examines the 28 February 2026 Middle East airspace disruption to understand the operational conditions within neighboring sectors by analyzing traffic observations in a period of about two weeks time around the event. It first establishes a multi-scale empirical picture of the disruption, from intercontinental route detours to corridor redistribution across the Middle East and traffic changes within the neighboring Jeddah Flight Information Region. Building on this evidence, a trajectory-computable framework is developed to identify temporal changes in regional traffic structure and characterize sector-level operational responses. The results show that the regional traffic structure departs rapidly from its baseline configuration during the initial disruption period and subsequently settles into a distinct and comparatively stable post-event regime with limited day-to-day variation. Within the Jeddah Flight Information Region, the redistribution is spatially uneven. Northeastern sectors largely lose their former transit function, while southeastern sectors increasingly absorb traffic associated with the southern alternative routing structure. Detailed analysis of a representative southeastern sector further shows that this changing role is not captured by traffic volume alone. Although instantaneous occupancy and weekly throughput remain broadly comparable with baseline levels, boundary-crossing activity becomes more spatially distributed, some crossing bands assume different downstream directional roles, trajectories become less direct and more maneuver-intensive, and locally proximate traffic interactions shift spatially.These findings show that major airspace disruptions are better understood as structural reorganizations of traffic rather than simple regional traffic losses, providing empirical insight into the operational challenges that air traffic management may face as traffic patterns reorganize after a disruption.
The coupled effects of radical chemistry, preferential diffusion, flame curvature, and local mixture inhomogeneity on NO and N₂O distribution in lean turbulent premixed NH₃/H₂ flames are investigated using direct numerical simulation (DNS). Statistically planar NH₃–air, 60%NH₃/25%H₂/15%N₂–air, and 40%NH₃/45%H₂/15%N₂–air flames at an equivalence ratio of 0.81 are considered, all operating in the thin reaction zones regime at comparable conditions on the Borghi–Peters diagram. NO concentration increases monotonically with H₂ blending, despite similar burned gas temperatures, due to enhanced H, O, and OH radical availability that accelerates NH₃ decomposition, promotes fuel-N oxidation pathways (NH → NO and HNO → NO), and shifts NO formation towards earlier flame stages, thereby limiting NO reduction. As a result, the ratio of the volume-integrated NO mass to the volume-integrated total mass in the flame increases systematically with H₂ addition. In contrast, the increase in the ratio of the volume-integrated N2O mass to the volume-integrated total mass within the flame seems to exhibit a tendency towards saturation. Statistical correlations reveal a transition from formation- to destruction-controlled N₂O chemistry, with preferential diffusion effects becoming increasingly important at higher H₂ blending. These results demonstrate that nitrogen oxide emissions in NH₃/H₂/N2 flames are governed by coupled chemistry–transport interactions rather than temperature alone, with important implications for emission mitigation strategies. Novelty and significance statement: This work provides a DNS-based mechanistic assessment of NO and N₂O formation in lean turbulent premixed NH₃ and NH₃/H₂/N2 flames under comparable thermal conditions and identical turbulence–chemistry interaction regimes. It is shown that the monotonic increase in NO formation with H₂ blending is not governed by flame temperature but by enhanced radical production and preferential diffusion, which accelerate NH₃ decomposition and shift fuel-N oxidation toward earlier flame stages. In contrast, N₂O formation exhibits a saturation with H₂ blending. Correlation analyses further reveal the increasing influence of flame curvature and local mixture inhomogeneity on nitrogen chemistry with H₂ addition. These findings provide new insight for emission control in ammonia-fuelled combustion.
The decarbonization of power systems requires managing intermittent renewable generation and climate variability while ensuring social welfare and reliability. However, incorporating extensive climate datasets into optimization models to capture variability compromises tractability, uncertainty traceability, or reliability. We propose a novel framework for climate-reliable power system design that integrates a bi-criteria a posteriori aggregation technique with a stochastic program that incorporates operational scenarios with a non-uniform number of representative days. This scenario construction enables efficient representation of extreme weather events while maintaining computational feasibility. To benchmark the framework, capacity portfolios are optimized separately for each climate dataset, distinguishing between climate scenario and climate model uncertainty. The approach is demonstrated using 47 climate projections for Saudi Arabia by 2050 under two policy settings: a 100 million tonnes of CO2 emissions target and a fully renewable system. Results indicate substantial cost dispersion across climate models within the same emissions scenario, reaching up to 40% in the fully renewable system under the RCP4.5 climate scenario. Strong economic incentives for climate change mitigation are identified, primarily driven by the high sensitivity of electricity demand to rising temperatures. Uncertainty-aware designs with the proposed approach yield 3–6% higher design costs than single-climate designs. However, cross-scenario assessment reveals substantial supply shortfalls and excess emissions for single-climate designs, with potential additional costs that are at least 2.6 times the additional investment required by the proposed framework. Compared with stochastic programs having a uniform number of representative days, the proposed approach achieves lower unserved energy and lower worst-case evaluation costs with comparable total computational effort, demonstrating its value for climate-aware power system planning.
