Cascading-Driven Intentional Controlled Islanding for Enhancing Power Grid Operational Resilience

JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX Abstract—Power systems face significant threats from severe disturbances, often triggered by extreme weather, leading to widespread cascading power outages. Although intentional controlled islanding (ICI) is an effective last-resort operational mitigation strategy employed by system operators worldwide to prevent complete cascading blackouts, the impact of large-scale disturbances, particularly weather-induced cascading outages, on when and where to implement it is not adequately considered nor reflected in current operational decision-making standards and procedures. This paper proposes a holistic cascading-driven framework that seamlessly integrates advanced weather-related incident modelling and cascading risk quantification of highimpact low-probability (HILP, or tail-risk) events with a novel decision-making-based islanding method to enhance operational resilience. The framework provides a portfolio of mitigation actions proportional to cascading impacts, differentiating between tail-risk events and expected (“average”) events typically addressed in reliability-oriented studies and current industry practices, while being tailored to both near-real-time operations and short-term operational planning. The proposed method involves system splitting around blackstart units while forming stable and self-sufficient islands, thereby enhancing system reliability and resilience. Implemented on the IEEE 39-bus and IEEE 118-bus systems, the studies demonstrate effectiveness with a significant improvement in served demand across all simulated initiating events, including up to N-6 contingencies. Index Terms—Cascading-driven controlled islanding, decisionmaking-based mitigation strategies, operational resilience. I. INTRODUCTION ORDERN power systems are increasingly vulnerable to cascading failures driven by the rising frequency of extreme weather events. Such failures stem from dependent component outages, often initiated by severe disturbances and amplified by protection relay operations, ultimately weakening the grid and causing costly blackouts [1]. Mitigating such phenomena requires remedial actions such as controlled islanding, which complements infrastructure-based measures by enhancing operational resilience [2]. Effective ____________________________________ Manuscript received: December 21, 2024; revised: April 23, 2025; accepted: September 19, 2025. Date of CrossCheck: September 19, 2025. Date of online publication: XX XX, XXXX. This work was funded by H2020 and Horizon Europe program through the projects “HVDC-based Grid Architectures for Reliable and Resilient WideSpread Hybrid AC/DC Transmission Systems” (HVDC-WISE) (Grant ID: 101075424), “Reliability, Resilience, and Defense Technology for the Grid” (R2D2) (Grant ID: 101075714), and “EUniversal” (Grant agreement ID: 864334). application of such actions depends on detailed modeling of system responses during cascade initiation and propagation. Cascading failure analysis has been widely studied through various approaches, including topological [3], stochastic simulation [4], statistical models [5], quasi-steady state (QSS) [6], dynamic [7], and other interdependent models [8]. These methods, whether stochastic or deterministic, capture the complex mechanisms of cascades. Metrics such as the number of affected elements and operated protection relays are essential for quantifying impacts and informing mitigation strategies, including load reduction and controlled islanding. Controlled islanding, or intentional system partitioning, is a last-resort remedial action designed to confine cascading failures and limit blackout severity. By isolating the affected network section from the healthy grid, it suppresses initiating events locally and thereby enhances resilience, particularly against weather-related disturbances. Formulations of controlled islanding typically employ graph theory [9], clustering techniques [10], or linear/nonlinear programming [11], individually or in hybrid forms. Recent studies also incorporate artificial intelligence techniques such as genetic algorithms [12], grey wolf–optimized neural networks [13], particle swarm optimization [14], and ant colony methods [15]. The intentional controlled islanding (ICI) problem is inherently a constrained combinatorial optimization task, aiming to minimize power flow disruption, power imbalance, load shedding, voltage and frequency deviations. Depending on the time frame and type of mitigation strategies against the spread of anticipated or evolving events, ICI can be considered either preventive [11], [12] or corrective [16], [17]. Preventive schemes, implemented ahead of anticipated events, involve actions such as generator rescheduling and demand response. Corrective schemes are applied after disturbances and rely on rapid measures, including load curtailment and frequency reserve activation. From a resilience perspective, several studies have advanced controlled islanding methods. Ref. [18] incorporates transient stability constraints, while [19] emphasizes frequency stability. Ref [12] develops a preventive scheme for typhoon events using the Batts model and fragility S. Hashemi (corresponding author), B. V. Venkatasubramanian, and M. Panteli are with the University of Cyprus, Nicosia 1678, Cyprus (e-mail: hashemi.seyedsi[email protected]y; [email protected]; [email protected]). P. Mancarella is with the University of Melbourne, Australia and with he University of Manchester, UK (e-mail: [email protected]; [email protected]). DOI: 10.35833/2024.001371 Cascading-driven Intentional Controlled Islanding for Enhancing Power Grid Operational Resilience Sina Hashemi, Member, IEEE, Balaji V. Venkatasubramanian, Senior Member, IEEE, Pierluigi Mancarella, Fellow, IEEE, and Mathaios Panteli, Senior Member, IEEE M This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX curves. Data-driven detection based on wide-area measurements is proposed in [20], while [21] introduces a hybrid optimization approach balancing disruption and stability with efficient blackstart allocation. A three-stage cutset optimization method is presented in [22], and [23] applies genetic algorithms to manage temporary overvoltages and distributed generation utilization. Finally, [24] proposes a microgrid control strategy to enhance resilience through coordinated energy sharing and frequency support. Operational standards provide guidance on managing largescale disturbances but lack explicit frameworks for controlled islanding. The ENTSO-E Operation Handbook [25], [26] emphasizes system security, incident containment, and coordinated restoration, aligning with resilience principles. IEEE Std 1547-2018 [27] specifies requirements for both unintentional and intentional islanding, focusing on stability and DER transitions. NERC EOP-011-1 and EOP-011-2 [28], [29] address emergency preparedness, while ISO New England OP-19 [30] provides transmission operation procedures during emergencies. However, none of these documents define controlled islanding strategies to prevent or mitigate cascading failures—a critical gap for resilience under extreme events. Most existing studies [18], [19] evaluate islanding under a limited set of random N-k contingencies, often neglecting the timescales of mitigation and the cascading impacts of weatherrelated events. As a result, their strategies may be inefficient under uncertain conditions. To address this gap, this paper develops a holistic framework that integrates reactive and proactive measures, tailored to event type, operating condition, and cascade severity. The framework combines quantification, detection, and mitigation of cascading failures, identifies assets vulnerable to windstorms, and evaluates their impacts to guide operational responses. By managing multiple concurrent outages, including events up to N-k, the approach systematically enhances resilience against both expected and high-impact low-probability (HILP) events. Designed for both short-term operational planning and near-real-time operation, it explicitly accounts for stochastic weather-driven disturbances. Indeed, the novelty of this work lies in integrating several key modules and submodules into a unified, practical cascadingdriven resilience enhancement framework that enables system operators to make informed decisions for mitigating cascading impacts—an increasingly critical need in light of recent largescale blackouts such as the one in the Iberian Peninsula. Central to the framework is a novel decision-making mechanism that leverages cascade quantification metrics to determine the appropriate mitigation strategy, thereby addressing the “when” aspect of ICI. Building on this, the framework introduces a newly formulated optimization problem for ICI—enhanced by an innovative search space reduction technique—to deliver optimal solutions that address the remaining ICI objectives of “where” and “how” to execute system partitioning effectively, with a particular focus on maintaining post-islanding stability. The main contributions of this work are outlined below: • Developing a holistic resilience enhancement framework by capturing cascading impacts and enabling zonal restoration through the assignment of blackstart units (BSUs) to islands. • Quantifying the risks of weather-induced cascading failures, where triggering events are spatially correlated, by employing a stochastic spatiotemporal weather event simulator and QSS cascading failure analysis. • Demonstrating and quantifying the benefits of a portfolio of mitigation actions—enabled by a fast, reliable, rule-based Decision-Making mechanism guided by cascading failure analysis—for enhancing operational resilience, tailored to timescales, operating conditions, and cascade severity. • Providing ICI solutions that address "when", "where" and “how” to island based on cascading impacts, by identifying optimal island networks around coherent generator groups, while ensuring stability after boundary lines are opened. The remainder of this paper is organized as follows: Section II presents a detailed overview of the proposed method, including the cascading-driven resilience analysis technique, the decision-making mechanism, and the controlled islanding method. Section III delves into simulation studies and results for a large set of both deterministic and stochastic contingencies. Finally, Section 4 concludes the paper. II. CASCADING-DRIVEN CONTROLLED ISLANDING A. Proposed Method Fig. 1 illustrates the proposed framework of the operational resilience enhancement strategy, applicable to both short-term operational planning and near-real-time operation. The framework addresses weatherand non-weather-related events, particularly HILP disturbances, through decision-making– based mitigation strategies that suppress cascading failures. It supports both proactive and reactive applications, as represented by the resilience trapezoid curve [31]. In operational planning, preventive controlled islanding can be implemented hours ahead using projected data, isolating vulnerable areas to limit cascade propagation and reduce demand loss. In the near-real-time application, corrective islanding mitigates evolving events based on current data. As shown in Fig. 1, corrective islanding typically results in greater degradation, since early event impacts trigger tripping and load shedding before islanding is executed. Preventive measures, by contrast, reduce degradation by allowing operators to redispatch generation, adjust topology, and implement load reduction ahead of time. Fig. 2 presents the flowchart of the proposed cascading-driven ICI method, integrating the Event Simulator, Cascading Failure Modeling, Cascading Assessment and Decision-Making, and Intentional Controlled Islanding into a unified framework. This integration is a key novelty, enabling operators to make informed decisions for mitigating cascading impacts. The process begins with resilience assessment through modeling and quantification of cascading failures. Inputs include specific initiating events for real-time operation or wind event–based scenarios for short-term operational planning. Two metrics are employed: Demand Not Served (DNS) to characterize cascade size, and the number of affected components to indicate grid integrity. Based on these metrics, the decision-making module selects the appropriate strategy. If events do not propagate under controlled load reduction, curtailment is applied proportionally across loads; otherwise, controlled islanding is executed. For cascading failure modeling, the framework employs the AC-CFM method [6], which integrates AC power flow and QSS calculations to assess system performance under This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. 3 Fig. 1. Proposed framework for enhancing operational resilience. Fig. 2. Detailed flowchart of the proposed cascading-driven ICI method. disturbances. Inputs are provided either by the Event Simulator—generating anticipated weather-related and N-k contingency scenarios for short-term planning—or by observed initiating events in real-time operation. This comprehensive setup for the resilience enhancement framework enables cascade quantification and supports the selection of mitigation strategies, effectively addressing the three key objectives of ICI: when, where, and how to island. The when is determined by the Cascading Assessment and Decision-Making Module, which evaluates whether triggering events initiate a propagating cascade or remain contained. If propagation is confirmed, ICI is applied to define where boundary lines should be opened and how to maintain stability and self-sufficiency across the resulting islands. System splitting may be accompanied by generation rescheduling, frequency reserve utilization, and load reduction within islands experiencing load–generation imbalance. In this study, the objective is to minimize the total system DNS resulting from load-generation imbalances, as formulated by Eq. (1). Here, Κ is the set of controlled islands, 𝑁𝑖𝑠𝑙 is the total number of islands, 𝜁𝑘 is the total impedance-based distance in island 𝑘, 𝑃𝑙,𝑗 represents the active power of load 𝑗, and Λ𝑘 is the set of load buses in island 𝑘. 𝑃𝑔,𝑖 and 𝐹𝑅𝑅𝑔,𝑖 refer to the active power and frequency restoration reserve (FRR) of generator 𝑖, respectively. Ω𝑘 denotes the set of coherent generators in island 𝑘. 𝑍𝑚 is the shortest impedance-based distance from bus 𝑚 to coherent generator groups (CGGs) of island 𝑘 and is calculated as the smallest length of the path between two nodes using the Dijkstra algorithm [32]. The problem is constrained by two sets of constraints: structural and operational, which are further detailed in Section II-D-2-b. min{𝜁𝑘(∑𝑥𝑗𝑃𝑙,𝑗 𝑗 ∈ Λ𝑘 − ∑𝑥𝑖(𝑃𝑔,𝑖+𝐹𝑅𝑅𝑔,𝑖) 𝑖 ∈ Ω𝑘 )}𝑘 ∈ Κ (1) 𝜁𝑘= ∑ 𝑍𝑚 𝑚 ∈ 𝐵𝑖𝑠𝑙𝑘 (2) B. Cascading-driven Resilience Assessment This module assesses the resilience of a disturbed power system. The disturbances may include specific initiating events that have already occurred or anticipated weather-related events, depending on the timescales of the mitigative measures. This work utilizes the wind event modelling developed in [33] for resilience assessment purposes, extending beyond deterministic N-k (k ∈ [1, 3]) contingencies. 1) Event Simulator The Event Simulator generates N-k transmission line contingencies deterministically (k ∈ [1-3]) or stochastically (k>3). A fragility-based wind event model is employed to anticipate line outages from upcoming weather incidents. The resulting operating conditions are then analyzed using quasi– steady-state cascading failure modeling for short-term planning (see Fig. 2). Fragility curves, derived from statistical, experimental, simulation-based, or expert methods, define the probability of line failure as a function of hazard intensity. Following [33], wind-dependent fragility curves are applied to model line outages. Windstorm characteristics such as gust speed and radius are extracted from historical data [34], [35], and Monte Carlo simulations generate a large set of stochastic scenarios. By varying storm parameters, the simulator captures uncertainty and determines line outage status, with tripping decisions based on Eq. (3). 𝐿𝑆(𝑤𝑠𝑡,𝑙)={1 if 𝒫𝑙(𝑤𝑠𝑡)<𝑟 0 if 𝒫 𝑙 (𝑤 𝑠𝑡 )>𝑟 (3) where, 𝑤𝑠𝑡 is the wind intensity or wind speed at step 𝑠𝑡, 𝒫𝑙 is the wind-dependent failure probability of line 𝑙, and 𝑟 is the random number generated between 0 and 1. The concept of 𝑟 is introduced in this procedure to add more stochasticity to the model. 2) Detection of Uncontrolled Network Splitting (UNS) Depending on the severity and number of concurrent initiating events—particularly weather-related events that are spatially correlated and capable of simultaneously disrupting nearby transmission lines—early uncontrolled network splitting (UNS), including the isolation of at least one load bus, is very likely to occur, as conceptually shown in Fig. 3. Active Islands Active & Blacked-out Islands Data Cascading-driven Resilience Assessment Quantification of cascading impacts Implementation of an Operational Mitigation Strategy Power System Short-term operational planning (a few hours ahead) Near real-time operations Total Demand Served No Mitigation Strategies Pre-disturbance time With Proactive Mitigation Strategies Event Short-term operational planning Total Demand Served No Mitigation Strategies time With Reactive Mitigation Strategies Event Disturbance progress Near Real-Time Operations •Network partitioning •Load Reduction •Generation Rescheduling •Network partitioning •Load Reduction •Frequency Restoration Reserve Cascading Failure Analysis Module Intentional Controlled Islanding (ICI) - Ongoing conditions with evolving events - Deterministic Events - Stochastic Weather Events Detection of uncontrolled network splitting Cascading Failure Modelling (AC-CFM) DNS > Cascading Assessment and Decision-Making Module Are there Cascading Events? Yes No No Mitigation Strategy Module Yes No Cascading Failures and No Need for Mitigation Load Reduction Identifying CGGs Controlled Network Splitting Short-term operational planning Near-real-time operation MS0 MS2 MS1 Mitigation Strategies: - MS0: Not needed - MS1: Controlled islanding - MS2: Load reduction -------------------------------- This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX Fig. 3. Detection of UNS caused by initiating events. Algorithm I: Detection of uncontrolled network splitting (UNS) - Detect isolated bus(es) 𝐵𝑖𝑠𝑜 - if ∃𝐵𝑖𝑠𝑜∈Λ then - if ∃𝐵𝑖𝑠𝑜∈𝐵𝐺 then - 𝑈𝑁𝑆𝑤𝐺⊆ Minor Subnetwork - if 𝑁𝑖𝑠𝑙 𝑈𝑁𝑆≥2 (as per Eq. (4)) then - Quantify 𝐷𝑁𝑆𝑚𝑛 using CFA of the 𝑈𝑁𝑆 and 𝐼𝐷𝑀 𝑚𝑛=1 (ICI may be needed) - else - Quantify 𝐷𝑁𝑆𝑚𝑛 using CFA of the 𝑈𝑁𝑆 and 𝐼𝐷𝑀 𝑚𝑛=0 (No need for ICI but load reduction may be needed) - end if - else - Calculate 𝑃𝐿𝐼𝑠𝑜 (bus(es) with load but without a generator) - end if - else - 𝑃𝐿𝐼𝑠𝑜=0 (bus(es) with neither load nor a generator) - end if To detect UNS and integrate it into the main framework, as illustrated in Fig. 2, Algorithm I is developed. In this study, UNS refers to isolated bus(es) (𝐵𝑖𝑠𝑜), either without generation (𝑈𝑁𝑆𝑤𝑜𝐺) or with at least one generator (𝑈𝑁𝑆𝑤𝐺). As 𝑈𝑁𝑆𝑤𝑜𝐺 inevitably experiences outages, the focus is on the remaining network. Each 𝑈𝑁𝑆𝑤𝐺 is treated as a minor subnetwork, while the rest forms the major subnetwork—both potentially requiring ICI depending on size and cascading severity. If 𝐵𝑖𝑠𝑜 contains both load and generator buses, it is classified as 𝑈𝑁𝑆𝑤𝐺. Since splitting can fragment the grid into multiple generator-containing segments, each 𝑈𝑁𝑆𝑤𝐺 is analyzed individually as a minor subnetwork in Algorithm I. The decision-making indicator ( 𝐼𝐷𝑀 𝑚𝑛 ) then specifies whether controlled islanding is required (1) or not (0). The number of islands (𝑁𝑖𝑠𝑙) is calculated using Eq. (4), based on the number of Black-Start Units (𝑁𝐵𝑆𝑈) and total buses (N). The formulation ensures that each partitioned network is sufficiently large, defined as ⌊0.5∙√𝑁⌋ [36], and contains at least one BSU. If number of islands in an isolated subnetwork (𝑁𝑖𝑠𝑙 𝑈𝑁𝑆) exceeds two, controlled islanding may be applied, with the decision-making indicator (𝐼𝐷𝑀 𝑚𝑛) set to 1. Otherwise, 𝐼𝐷𝑀 𝑚𝑛 is set to 0, and stability must be preserved through load reduction, frequency reserves, or generation rescheduling. Minor subnetworks with fewer than two islands are excluded from controlled islanding, while isolated buses without generation experience blackout. The algorithm outputs include interrupted load from isolated buses ( 𝑃𝐿𝐼𝑠𝑜), minor subnetwork DNS (𝐷𝑁𝑆𝑚𝑛), and data for both minor and major subnetworks. 𝑁𝑖𝑠𝑙=min(𝑁𝐵𝑆𝑈, ⌊ 0.5∙√𝑁 ⌋ ) (4) 3) Cascading Failure Modelling and Quantification Resilience assessment is performed using QSS cascading failure modeling, specifically the AC-CFM method [6]. This fast, recursive algorithm simulates the successive activation of protection mechanisms and models cascades that may propagate within each island. It incorporates overload protection (OLP), underand over-frequency load shedding (UFLS, OFGS), under-voltage load shedding (UVLS), and generator over/under-excitation limiters (O/UXL), enabling replication of steady-state frequency and voltage responses. The model captures power flow redistribution after component failures, leading to overloads and line tripping. Cascade impacts are quantified through metrics such as (DNS and the number of affected elements. These results inform the decision-making module, which selects the appropriate mitigation strategy. C. Decision-Making Mechanism for Cascade Mitigation Building on the cascading-driven feature of the proposed framework shown in Fig. 2, this module determines when to island based on assessed cascading risks and what-if analysis. It evaluates cascade initiation and propagation using two metrics: cascade size, measured as DNS, and grid integrity, quantified by the number of tripped elements ( 𝑁𝑇𝐸). DNS reflects protection actions such as undervoltage and underfrequency load shedding, while 𝑁𝑇𝐸 captures effects of overcurrent relay operations and generator tripping. Although simple, the mechanism is robust, relying on current operating conditions and cascading failure analysis using AC power flow and QSS calculations. Decisions are made quickly through threshold rules derived from these analyses. Algorithm II defines the decision-making mechanism, which selects the most effective mitigation strategy—load isolation, controlled islanding, or load reduction—based on cascade severity. The decision-making indicator (𝐼𝐷𝑀 𝑀𝑆) takes values of 0, 1, or 2, corresponding to load isolation, controlled islanding, or load reduction, respectively. If DNS in either the major (𝐷𝑁𝑆𝑚𝑛) or minor subnetworks 𝐷𝑁𝑆𝑚𝑛 (with 𝐼𝐷𝑀 𝑚𝑛=1) exceeds zero and cascading propagation is confirmed (𝑁𝑇𝐸> 0), controlled islanding (MS1) is triggered. If no propagation occurs (𝑁𝑇𝐸=0), load reduction (MS2) suffices to alleviate stress and halt the cascade. These rule-based decisions, formulated in Eq. (5), precede the optimization-based controlled islanding process (Fig. 2). In controlled load reduction, the reduction is proportional to each load’s share of the total connected load. Otherwise, if controlled islanding is required, the corresponding optimization problem is solved. 𝐷𝑒𝑐𝑖𝑠𝑖𝑜𝑛={𝑁𝑜 𝐴𝑐𝑡𝑖𝑜𝑛 , 𝑖𝑓 𝐷𝑁𝑆<𝑃𝐿𝐼𝑠𝑜 𝐿𝑆ℎ, 𝑖𝑓 𝐷𝑁𝑆>𝑃𝐿𝐼𝑠𝑜 𝑎𝑛𝑑 𝑁𝑇𝐸=0 𝐼𝐶𝐼, 𝑖𝑓 𝐷𝑁𝑆>𝑃𝐿𝐼𝑠𝑜 𝑎𝑛𝑑 𝑁𝑇𝐸>0 (5) Algorithm II: Decisionmaking for an effective mitigation strategy - Update the data from the available network elements - Identify the minor and major subnetworks using Algorithm I - Update the total amount of 𝑃𝐿𝐼𝑠𝑜 and 𝐷𝑁𝑆𝑚𝑛 after initiating events - Quantify 𝐷𝑁𝑆𝑀𝑁 using CFA performed for the remaining active network or major subnetwork; (𝐷𝑁𝑆= 𝐷𝑁𝑆𝑀𝑁+𝐷𝑁𝑆𝑚𝑛+𝑃𝐿𝐼𝑠𝑜 ) - if 𝐷𝑁𝑆𝑀𝑁 >0 𝑜𝑟 (𝐷𝑁𝑆𝑚𝑛 >0 𝑎𝑛𝑑 𝐼𝐷𝑀 𝑚𝑛=1) then - if any subsequent cascading outages occurred (𝑁𝑇𝐸>0) then - Need to halt cascading propagation by performing ICI (MS1) 𝐼𝐷𝑀 𝑀𝑆=1 - else - Calculate load reduction per bus to control the system and satisfy operational constraints (MS2) 𝐼𝐷𝑀 𝑀𝑆=2 - end if - else - Load interruption due to bus isolation (No cascading occurred) 𝐼𝐷𝑀 𝑀𝑆=0 - end if G GG G Entire Network Major Subnetwork This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. 5 D. Mitigation Strategy The mitigation strategies pointed out in Algorithm II, which involve load reduction and controlled islanding based on the impacts of initiating events and subsequent cascading events, are detailed here. 1) Load Reduction Load reduction curtails demand locally or system-wide, either through operator control or protection schemes. Beyond balancing supply and demand to maintain frequency stability, it mitigates cascading propagation by relieving stress from postevent power flow redistribution. When triggered by the decision-making module (MS2), load reduction addresses load–generation imbalance and line overloading. Depending on the timescale, it may be combined with generation rescheduling in short-term operational planning or frequency reserve utilization in near-real-time operation. Curtailment is allocated proportionally to each load’s share of total demand. For the test system, load reduction is quantified using Eq. (6), which incorporates generator contributions to the frequency restoration reserve (FRR), yielding the total reduction for island k (𝐿𝑅𝑘). In short-term operational planning, 𝐹𝑅𝑅𝑔,𝑖 is zero, but 𝑃𝑔,𝑖 may change due to generation rescheduling. In contrast, in near-real-time operations, 𝑃𝑔,𝑖 remains unchanged, while 𝐹𝑅𝑅𝑔,𝑖 varies. 𝐿𝑅𝑘=∑ 𝑃𝑙,𝑗 𝑗 ∈ Λ𝑘−∑ (𝑃𝑔,𝑖+𝐹𝑅𝑅𝑔,𝑖) 𝑖 ∈ Ω𝑘 (6) 2) Intentional Controlled Islanding (ICI) As shown in Fig. 2, this module determines where and how to island by forming stable, self-sufficient islands around BSUs. Using system data and outputs from the resilience assessment and decision-making modules, it identifies boundary buses and lines while maintaining frequency and rotor angle stability through coordinated load and generation control. • Identification of Coherent Generator Groups (CGG) To preserve rotor angle stability after controlled islanding, coherent generator groups (CGGs) must be identified. Algorithm III outlines this process using generator terminal voltage phase angles from PMUs [11]. Coherency is quantified through the Intraclass Correlation Coefficient (ICC), scaled from 0 to 1, and weighted by impedance-based electrical distances to ensure spatial proximity and avoid infeasible partitions. A K-medoids spectral clustering algorithm [37] is then applied to the distance-weighted ICC (DICC) values, using 100 samples of 10 ms each within a moving window. Electrical distance is defined as the minimum equivalent impedance between generators, computed via the Dijkstra algorithm [32]. The DICC formulation is given in Eq. (7). 𝐷𝐼𝐶𝐶𝑖,𝑗=1−(𝐼𝐵𝐷𝑖,𝑗⊙ (1−𝐼𝐶𝐶𝑖,𝑗)) ,∀ 𝑖,𝑗 ∈𝐵𝐺 (7) where 𝐼𝐵𝐷𝑖,𝑗 refers to the impedance-based distance between each pair of generators (𝑖,𝑗); 𝐼𝐶𝐶𝑖,𝑗 represents the intraclass correlation of the phase angles for each pair of generators; and 𝐷𝐼𝐶𝐶𝑖,𝑗 denotes the distance-weighted intraclass correlation of generators, ranging from 0 to 1, with values closer to 1 indicating greater coherency. 𝐵𝐺 represents generator bus set, and ⊙ denotes element-wise product operation. 𝐼𝐵𝐷𝑖,𝑗 is calculated by finding shortest length 𝕃(ℙ), where ℙ denotes the path between each pair of generators (𝑖,𝑗) in the Algorithm III: Identification of CGGs - Update the data from the available network elements - Calculate the sparse impedance matrix of the network 𝑍𝑏𝑢𝑠 - Establish impedance-weighted graph of the power system - for 𝑖 ∈ 𝐵𝐺 do - for 𝑗 ∈ 𝐵𝐺 do - if 𝑖≠𝑗 then - Calculate 𝐼𝐵𝐷𝑖,𝑗 by finding the shortest length 𝕃(ℙ) among the paths between the origin generator node 𝑖 and the destination node 𝑗 using the Dijkstra algorithm (see Eq. (8)) - Calculate the intraclass correlation (ICC) between each pair of phase angles 𝐼𝐶𝐶𝑖,𝑗 - Calculate distance-weighted ICC between each pair of phase angles 𝐷𝐼𝐶𝐶𝐺𝑖𝑗 (see Eq. (7)) - else - 𝐷𝐼𝐶𝐶𝐺𝑖𝑗 =1 - end if - end for - end for - Identify coherent groups of generators around BSUs using the K-medoids clustering algorithm based on 𝐷𝐼𝐶𝐶𝑖,𝑗 Algorithm IV: Cascading-driven ICI module - Update the data of the minor and major subnetworks - if 𝐼𝐷𝑀 𝑀𝑆=1 then - Identify the marginal buses - Run the subroutine of Algorithm III to identify CGGs - while stopping criterion is unmet do - Solve the optimization problem subject to all constraints (find a set of decision variables that minimizes the objective function while satisfying all constraints) - end while - end if - Identify all islands and update their corresponding networks - Calculate the total value of DNS for the entire network 𝐷𝑁𝑆=∑𝐷𝑁𝑆𝑘𝐼𝑠𝑙 𝑘∈𝛫 + 𝑃𝐿𝐼𝑠𝑜 - return DNS, the boundary lines, the set of buses pertaining to each island, load and generation values at each bus impedance-weighted graph of power system 𝔾=(𝕍,𝔼,𝕎), with 𝕍 representing the set of vertices, 𝔼 the set of edges, and 𝕎 the weights associated with the edges in the graph 𝔾. 𝐼𝐵𝐷𝑖,𝑗=min𝕃(ℙ𝑖,𝑗:𝑖 →𝑗), ∀ 𝑖,𝑗∈𝐵𝐺 (8) This calculation is updated dynamically after cascade quantification, assessment, and decision-making, capturing near-real-time changes such as outages or impedance variations for use in ICI optimization. To ensure BSU presence, they serve as central cores in CGG identification, and availability is rechecked within the ICI algorithm. The number of CGGs, equivalent to the required islands for cascading-driven partitioning, is determined by Eq. (4) (Section II-B-2). The resulting set of CGGs is expressed in Eq. (9). 𝐶𝐺𝐺={𝐺𝐺𝐺𝛾 | 𝛾∈𝛫} (9) • Controlled Network Splitting The proposed controlled islanding method reduces computational burden by limiting search space using electrical distance. As outlined in Algorithm IV, buses close to a CGG are directly assigned to that island and excluded, while marginal buses—those nearly equidistant or located at boundaries— define the reduced search space. The solver then operates on this subset to identify optimal boundary buses for islanding. a) Search Space Reduction (SSR) The search space reduction (SSR) technique, introduced here for the first time in controlled islanding, applies impedancebased electrical distance to limit possible solutions. Since This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX assigning buses far from reactive power sources can risk voltage instability, subnetworks are first formed around CGGs using shortest-path distances. Buses near island boundaries are then identified as marginal buses, determined by their maximum impedance-based distance to CGGs. These marginal buses define the problem’s search space (SS), which is explored by an optimization algorithm to minimize load–generation imbalance. The process is conceptually illustrated in Fig. 4. After initiating events, system integrity is first assessed. If unintentional splitting occurs, the isolated minor subnetwork is excluded from the islanding study, with its decision variables set to zero. For the remaining major subnetwork, bus decision variables take integer values from 1 to 𝑁𝑖𝑠𝑙, representing island assignments. As formulated in Eq. (10), buses are allocated to islands based on their shortest distance to the corresponding CGG, while marginal buses at boundaries may take any island value from the set 𝛫={1,2,…,𝑘,…,𝑁𝑖𝑠𝑙}. Here, 𝐵𝑖𝑠𝑙𝑘 denotes the set of buses in island 𝑘 such that 𝐵𝑖𝑠𝑙𝑘⊂𝐵𝑀𝑚𝑁, and 𝐵𝑀𝑎𝑟𝑔 is the set of marginal buses with 𝐵𝑀𝑎𝑟𝑔⊂𝐵𝑀𝑚𝑁; 𝐵𝑀𝑚𝑁 denotes the set of buses for the major and minor subnetworks. 𝑥𝑖 is the decision variable for bus 𝑖 that takes the value of the island number 𝑘 if it has the shortest distance to the CGG of island 𝑘. The decision variables for the marginal buses around the boundary of the islands can take integer values from the set 𝐾 representing the island numbers (see Fig. 4). 𝑥𝑖={𝑘, 𝑖𝑓 𝑖 ∈ 𝐵𝑖𝑠𝑙𝑘 ∈𝐾, 𝑖𝑓 𝑖∈𝐵𝑀𝑎𝑟𝑔 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (10) As a result of the proposed SSR method, two vectors for the lower and upper bounds of the decision variables are calculated, as formulated in Eq. (11). 𝑋={𝑥𝑖 | 𝑥𝑖≤𝑥𝑖≤𝑥𝑖 ,𝑖∈𝐵𝑀𝑚𝑁} 𝑋∈[𝑋 ,𝑋] (11) The problem solver only needs to search the space within these bounds to find an optimal solution for the boundary buses and the lines connecting each pair of islands. As illustrated in Fig. 4, and assuming three islands, the decision variable matrix 𝑋 lies within bounds 𝑋 and 𝑋, taking integer values from 0 to 3. A value of 0 denotes an isolated bus, while other integers assign buses to the corresponding island based on shortest distance (e.g., 2 for Island 2). Marginal bus assignments, boundary line identification, and the optimal post-islanding operating point are determined by solving the optimization problem in Eq. (1). The resulting subnetworks are then updated to reflect the optimal ICI solution. 𝑋∈ [ 012310⋮12 ⋮⋮⋮⋮⋮⋮⋮⋮ 032310⋮23 ] →𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑑 𝑏𝑢𝑠 →𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑏𝑢𝑠 →𝑖𝑠𝑙𝑎𝑛𝑑 2 →𝑖𝑠𝑙𝑎𝑛𝑑 3 →𝑖𝑠𝑙𝑎𝑛𝑑 1 →𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑑 𝑏𝑢𝑠 ⋮ →𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑏𝑢𝑠 →𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑏𝑢𝑠 Fig. 4. Proposed search space reduction concept involving marginal or distant buses. b) Constraints • Structural Constraints These constraints ensure network connectivity and the assignment of at least one BSU to each island, facilitating the restoration of a blacked-out island after a controlled islanding failure. Eq. (12) ensures that every bus 𝑖 with a non-zero decision variable 𝑥𝑖≠0 in the combined major and minor subnetwork bus set 𝐵𝑀𝑚𝑁 is assigned to a specific island, thereby maintaining connectivity within the subnetwork of islands without isolated buses after controlled islanding. |𝐵𝑀𝑚𝑁| denotes the cardinality (or size) of the set 𝐵𝑀𝑚𝑁. Eq. (13) ensures that for each 𝛾∈𝛫, there is at least one 𝐵𝑆𝑈𝑖 in 𝐺𝐺𝐺𝛾. The binary variable 𝑢𝑖,𝛾 takes the value 1 if 𝐵𝑆𝑈𝑖 is in 𝐺𝐺𝐺𝛾, and 0 otherwise. ∑ 𝑥𝑖/𝑥𝑖 𝑖 ∈ 𝐵𝑀𝑚𝑁 =|𝐵𝑀𝑚𝑁| 𝑖𝑓 𝑥𝑖≠0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖∈ 𝐵𝑀𝑚𝑁 (12) ∑ 𝑢𝑖,𝛾 𝑖 ∈ 𝐵𝑆𝑈 ≥1 ∀ 𝛾∈𝛫 , 𝑤ℎ𝑒𝑟𝑒 𝑢𝑖,𝛾= {1, 𝑖𝑓 𝐵𝑆𝑈𝑖∈𝐺𝐺𝐺𝛾 0 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (13) • Operational Constraints Operational constraints ensure that all operating limits are met, including line power flow (Eqs. (14)-(19)), generator active and reactive power (Eqs. (17)-(18)), and bus voltage (Eq. (19)). During optimization, if a constraint is violated, load reduction and generation redispatching are implemented to find a feasible and optimal solution. 𝑃𝑖𝑗(𝑉,𝜃)=𝑦𝑖𝑗[𝐺𝑖𝑗𝑉𝑖2−𝑉𝑖𝑉𝑗(𝐺𝑖𝑗𝑐𝑜𝑠𝜃𝑖𝑗+ 𝐵 𝑖𝑗 𝑠𝑖𝑛𝜃 𝑖𝑗 )] ∀ (𝑖,𝑗)∈ 𝐵𝑙𝑛𝑒 (14) 𝑄𝑖𝑗(𝑉,𝜃)=𝑦𝑖𝑗[𝑉𝑖𝑉𝑗(𝐺𝑖𝑗𝑠𝑖𝑛𝜃𝑖𝑗−𝐵𝑖𝑗𝑐𝑜𝑠𝜃𝑖𝑗) −𝐺 𝑖𝑗 𝑉𝑖2 ] ∀ (𝑖,𝑗)∈ 𝐵𝑙𝑛𝑒 (15) (𝑃𝑖𝑗 2+𝑄𝑖𝑗 2)1/2≤𝑆𝑖𝑗 ∀ (𝑖,𝑗)∈ 𝐵𝑙𝑛𝑒 (16) 𝑃𝐺𝑖≤𝑃𝐺𝑖≤𝑃𝐺𝑖 ∀ 𝑖 ∈ 𝐵𝐺 (17) 𝑄𝐺𝑖≤𝑄𝐺𝑖≤𝑄𝐺𝑖 ∀ 𝑖 ∈ 𝐵𝐺 (18) 𝑉≤𝑉𝑖≤𝑉 ∀ 𝑖 ∈ 𝐵 (19) where 𝑃𝑖𝑗, 𝑄𝑖𝑗, and 𝑆𝑖𝑗 denotes the active, reactive, and maximum apparent power flow of line 𝑖𝑗, respectively, and 𝐵𝑙𝑛𝑒 refers to the set of two-end pair buses of lines. The voltage and reactive power constraints accommodate voltage deviations within permissible operating limits at postislanding operating points, while the objective function— minimizing load-generation imbalance—helps mitigate frequency deviations. Together, these elements significantly contribute to ensuring post-islanding stability and align with the how objective of the proposed cascading-driven ICI method. III. RESULTS AND DISCUSSION The IEEE 39-bus system (345 kV, 6254.2 MW total load) is used to evaluate the proposed approach. The optimization problem is solved with MATLAB’s mixed-integer nonlinear toolbox [38] and MATPOWER [39]. Simulations are performed on a PC with an Intel Core i7 (2.8 GHz, 16 GB RAM), yielding an average computation time of around 15 seconds across all scenarios for the test system. Generators are assumed to provide up to 5% of capacity as frequency EntireNetwork Marginal buses or Search Space (SS) This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. 7 restoration reserves [40], and all transmission lines are considered available for de-energization to enable islanding. BSUs are located at buses 32, 36, 37, and 39. The framework is tested for both near-real-time operation, addressing evolving events, and short-term operational planning, covering weatherand non-weather-related scenarios. A. Near real-time operation under evolving events In this case, three lines (1-39, 2-3, and 3-4) are removed as initiating events, representing an N-3 contingency. This outage set does not cause early bus isolation or minor subnetworks (𝑃𝐿𝐼𝑠𝑜=0 𝑎𝑛𝑑 𝐼𝐷𝑀 𝑚𝑛=0). Cascading failure analysis shows propagation with 13 additional line outages from overload protection (Fig. 5a), resulting in 2348.2 MW unserved demand, including the disconnection of buses 3, 12, 18, and 27, and partial load shedding elsewhere ( 𝐷𝑁𝑆𝑀𝑁 =2348.2). The cascade is visualized in Fig. 5b using a tree-like graph, where connected and blacked-out buses are marked in green and red, respectively. Protection mechanisms (OL, UFLS, UFGS, OFGS) are shown between cascade stages. Two blacked-out and three uncontrolled islands emerge. Since 𝐷𝑁𝑆𝑀𝑁 >0 with 13 cascading outages, the decision-making module sets 𝐼𝐷𝑀 𝑀𝑆= 1, requiring controlled islanding (MS1). Upon receiving realtime data, the algorithm computes an optimal solution in under 20 seconds, demonstrating feasibility for near-real-time operation [41]. Following ICI, three islands are created by deenergizing lines 14-15 and 26-27 (Fig. 6a). As shown in Fig. 6b, the cascade is contained, with controlled load reduction of 1287.4 MW and no blacked-out buses, confirming that controlled islanding effectively halts propagation and mitigates widespread failures. Fig. 7a shows time-domain RMS results for generator terminal voltage angles before islanding, where stable and unstable subnetworks appear, indicating generator instability. After islanding (Fig. 7b), cascading is prevented, and all generators remain stable due to effective CGG identification. Another instance of initiating events, representing an extreme weather-related case, considers outages of lines 1-2, 1-39, 2-3, 2-25, 17-18, and 17-27, creating a minor isolated subnetwork. Fig. 5. CFA before ICI, considering the outage of three lines. Fig. 6. CFA after ICI, considering the outage of three lines. Fig. 7. Phase angle of generators before ICI (a) and after ICI (b). Generated by the wind event simulator with stochastic N-k contingencies (k ∈ [1, 6]), this event forms isolated buses 1, 2, 30 and a minor subnetwork (with buses 25–29, 37, 38). As detailed in Section II-B-2, since 𝑁𝑖𝑠𝑙<2, this subnetwork is excluded from controlled islanding and mitigated with load reduction only. The initial interruption of load due to the Bus 1 isolation and the system DNS before ICI implementation are 𝑃𝐿𝐼𝑠𝑜=97.6 MW and 𝐷𝑁𝑆=2170.35 MW, respectively. The major subnetwork is then split by opening line 14-15, reducing DNS to 726.5 MW (66.5% improvement), as shown in Fig. 8b. B. Short-term operational planning for non-weatherand weather-related initiating events The proposed framework is evaluated under extreme < 39> < 1> < 2> < 30> G8 G9 G6 G7 G4G5 G3 G2 < 4> < 5> < 6> < 7> < 8> < 9> < 31> < 11> < 12> < 10> < 13> < 32> < 34> < 33> < 19> < 20> < 36> < 35> < 23> < 22> < 21> < 14> < 15> < 16> < 24> < 38> < 27> < 17> < 18> < 3> < 25> < 26> < 28> < 29> < BUS #> < 37> BS Unit G1 G10 Initiating Events Cascading Failures Initiating Events: Lines 1-39, 2-3, and 3-4 Load Isolation and Reduction (%) 100 50 0 Cascading Propagation Node colors: initial network status operating status blacked-out status Tree-Like Graph for Visualizing Cascading Failures UFLS OFGS OFGS UFLS EV OL OL OL OL ISL (IEEE 39-bus network) < 39> < 1> < 2> < 30> G8 G9 G6 G7 G4G5 G3 G2 < 4> < 5> < 6> < 7> < 8> < 9> < 31> < 11> < 12> < 10> < 13> < 32> < 34> < 33> < 19> < 20> < 36> < 35> < 23> < 22>< 21> < 14> < 15> < 16> < 24> < 38> < 27> < 17> < 18> < 3> < 25> < 26> < 28> < 29> < 37> BS Unit G10 Initiating Events Boundary Lines < BUS #> G1 Initiating Events: Lines 1-39, 2-3, and 3-4 Load Isolation and Reduction (%) 100 50 0 Cascading Propagation Node colors: initial network status operating status blacked-out status Tree-Like Graph for Visualizing Cascading Failures (IEEE 39-bus network) EV ISL UFLS OFGS (a) (b) (a) (b) (b) ( a ) This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX Fig. 8. CFA before ICI (a) and after ICI (b), with the outage of three lines. uncertain conditions, including severe weatherand nonweather-related events. In short-term operational planning studies for a few hours ahead, operators can assess the system under potential and anticipated events, such as deterministic N1, N-2, and N-3 contingencies of transmission lines, along with a set of stochastic scenarios involving wind events. This part of the study involves analyzing N-k contingencies of transmission lines (with k ∈ [1, 3]) deterministically and N-k contingencies (with k ∈ [1, 6]) stochastically, based on 1000 wind-related stochastic events. These stochastic events include 91, 60, and 53 distinct contingency sets for N-4, N-5, and N-6, respectively. In this phase of the study, operators can reschedule system generation during controlled islanding due to sufficient time before events, reducing reliance on load curtailment. Applying the same outage scenario as in Section III-A, Table I compares proactive strategies (generation rescheduling and load reduction implemented 1 and 2 hours ahead) with reactive ones (FRR and load reduction). The results show that proactive measures achieve greater resilience, as illustrated in Fig. 1. Based on generator ramp rates [42], generation rescheduling increases from 696 MW to 1392 MW, while load reduction decreases from 708.9 MW to 12.9 MW when implemented 1 and 2 hours ahead, respectively. As events approach, load reduction requirements rise, but overall remain lower under proactive strategies due to simultaneous generation rescheduling. The remaining simulations assume a 1-hourahead horizon, with further analysis of mitigation strategies (MS) for specific extreme wind-driven events. Table II compares mitigation strategies (MS0, MS1, MS2) for stochastic initiating events involving the loss of 4 to 6 lines (N-k, k ∈ [4, 6]). The decision-making module selects strategies based on DNS and the number of tripped elements. When DNS=0 (first row), no mitigation is required (MS0). For the second case (lines 13-14, 15-16, 16-21, 16-24), load reduction of 1673.4 MW (MS2) alleviates stress, preventing cascading and reducing DNS from 50.2% to 26.8%. In contrast, outages of lines 5-8, 67, 7-8, and 8-9 trigger cascading and severe outages (67.5%), but with ICI (MS1), DNS improves by 81.8%. Fig. 9 illustrates these outcomes with a heatmap comparing DNS across strategies. Furthermore, system reliability and resilience are quantified using the expected value of DNS (EDNS) and Conditional Value-at-Risk (CVaR) at the 95% confidence level [43]. This analysis aims to demonstrate the effectiveness of controlled islanding in mitigating the impact of both expected events (thereby decreasing the mean value of DNS) and the effects of unexpected tail-risk events (resulting in a reduction of the conditional values of DNS). For this purpose, a 95% confidence level of DNS (CVaR95%) is considered for the average DNS among the worst 5% of events. Table III compares EDNS and CVaR before and after mitigation for deterministic N-k (k ∈ [1, 3]) contingencies, showing at least 45.6% improvement in EDNS and 32.9% in CVaR for N-3 cases. A similar analysis of 1000 stochastic wind-related scenarios up to N-6 demonstrates further benefits. As illustrated in Fig. 10, controlled islanding shifts the DNS probability distribution leftward, reducing EDNS from 1249.83 MW to 650.98 MW and CVaR from 4426.86 MW to 3241.87 MW, thereby lowering blackout risk TABLE I PREVENTIVE ICI COMPARED TO CORRECTIVE ICI Type of Strategy Proactive (Preventive ICI) Reactive (Corrective ICI) Hours ahead 1 2 Remedial actions Gen. Resch. LR Gen. Resch. LR FRR LR P (MW) 696 708.9 1392 12.9 117.5 1287.4 TABLE II RESULTS OF DIFFERENT MITIGATION STRATEGIES Sc. k in (N-k) Lines DNS in MW (%) Imp. MS Before ICI After ICI % 1 4 14-15, 16-17, 17-18, 17-27 0 0 MS0 2 13-14, 15-16, 16-21, 16-24 3140.8 (50.2) 1673.4 (26.8) 0 MS2 3 5-8, 6-7, 7-8, 8-9 4223.6 (67.5) 767 (12.3) 81.8 MS1 4 5 4-5, 6-11, 7-8, 8-9, 13-14 3298.9 (52.7) 1444.7 (23.1) 56.2 MS1 5 3-4, 5-6, 14-15, 15-16, 22-23 320 (5.1) 0 MS0 6 6 2-3, 3-4, 3-18, 17-18, 17-27, 26-27 761 (12.2) 0 MS0 7 4-14, 6-11, 10-11, 10-13, 13-14, 14-15 2171.2 (34.7) 894.3 (14.3) 58.8 MS1 Fig. 9. Comparison of cascading impacts across various scenarios using different mitigation strategies. < 39> < 1> < 2> < 30> G8 G9 G6 G7 G4G5 G3 G2 < 4> < 5> < 6> < 7> < 8> < 9> < 31> < 11> < 12> < 10> < 13> < 32> < 34> < 33> < 19> < 20> < 36> < 35> < 23> < 22>< 21> < 14> < 15> < 16> < 24> < 38> < 27> < 17> < 18> < 3> < 25> < 26> < 28> < 29> < 37> G1 G10 Minor Subnetwork : BS Unit : Initiating Events : Cascading Failures < BUS #> : Isolated Bus(es) : Wind Trajectory Minor Subnetwork < 39> < 1> < 2> < 30> G8 G9 G6 G7 G4G5 G3 G2 < 4> < 5> < 6> < 7> < 8> < 9> < 31> < 11> < 12> < 10> < 13> < 32> < 34> < 33> < 19> < 20> < 36> < 35> < 23> < 22>< 21> < 14> < 15> < 16> < 24> < 38> < 27> < 17> < 18> < 3> < 25> < 26> < 28> < 29> < 37> G1 G10 : BS Unit : Initiating Events : Boundary Lines : Isolated Bus(es) < BUS #> : Wind Trajectory Before MS After MS 1 2 3 4 5 6 7 Scenario No. Cascading Impacts under Different Scenarios and Mitigation Strategies 26.8 12.3 23.1 14.3 50.2 67.5 52.7 34.7 0 20 40 60 80 100 0 5.1 12.2 Cascading Severity (%) MS0 MS2 MS1 MS1 MS0 MS0 MS1 (b) ( a ) This article has been accepted for publication in a future issue of this journal, but has not been edited. Content will change prior to final publication. 9 TABLE III EXPECTED DNS AND CVAR FOR DETERMINISTIC EVENTS Con. DNS before mitigation (MW) DNS after mitigation (MW) Improvement (%) EDNS CVaR EDNS CVaR EDNS CVaR N-1 753.11 4736.68 320.48 1975.3 57.45 58.3 N-2 1317.49 4407.28 654.1 2860.3 50.35 35.1 N-3 1745.98 4669.37 948.85 3133.24 45.65 32.9 Fig. 10. PDF curves of DNS for stochastic contingencies. Fig. 11. Cascading failure analysis of the IEEE 118-bus system under initiating events without controlled islanding. and enhancing resilience. To demonstrate scalability, the proposed method is applied to the IEEE 118-bus system under concurrent outages of lines 4954, 59-60, 59-61, and 59-63. As shown in Fig. 11, these events trigger widespread cascading and severe blackouts. Figs. 12 and 13 plot system frequency and voltage against cascade generation numbers, where each generation represents a stage of propagation involving tripping, load shedding, or generator disconnection. Results show voltage and frequency collapse in blacked-out islands, while surviving islands stabilize near nominal values. Fig. 14 further illustrates cascading impacts through a node-branch graph, where purple dashed lines indicate windstorm-exposed elements, red solid lines represent initiating outages, and red dashed lines show subsequent cascading failures. Furthermore, system performance improves markedly with the proposed controlled islanding method. As shown in Figs. 15–18, cascading impacts are greatly reduced, and all islands stabilize with voltage and frequency near nominal values. The total computational time, including cascading failure analysis, decision-making, and islanding computation, is 16.4 seconds. Fig. 19 compares system resilience using the trapezoid curve, showing served load rising from 121.4 MW to 3960.6 MW—a 90.5% improvement. C. Comparative analysis and validation of ICI To benchmark performance, the proposed controlled islanding method is compared with the classical spectral clustering method (SCICI) [44], which models the grid as a weighted graph. While computationally efficient, SCICI Fig. 12. System frequency for the IEEE 118-bus system under initiating events without controlled islanding. Fig. 13. Voltage profile of the IEEE 118-bus system under initiating events without controlled islanding. Fig. 14. Visualizing cascading impacts on the IEEE 118-bus system under initiating events without controlled islanding. Fig. 15. Cascading failure analysis of the IEEE 118-bus system under initiating events with controlled islanding implemented. ascading ail re nalysis s syste it t ntr lled slanding nder nitiating vents : initial network status with k bus : the system with k buses during cascading propagation : the system with k active buses after CFA #k #k #k : the system with k blacked-out buses after CFA #k Cascading Failure Analysis of IEEE 118-bus system without Controlled Islanding under Initiating Events Cascading generation no. 0 10 20 30 40 50 60 70 80 90 100 Wind Trajectory : initial network status with k bus : the system with k buses during cascading propagation : the system with k active buses after CFA #k #k #k Cascading Failure Analysis of IEEE 118-bus system with Controlled Islanding under Initiating Events 0 10 20 30 40 50 60 70 80 90 100 Cascading generation no. This article has been accepted for publication in a future issue of this journal, but has not been edited. 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