Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids

IEEE POWER & ENERGY SOCIETY SECTION Received 16 July 2025, accepted 22 August 2025, date of publication 28 August 2025, date of current version 8 September 2025. Digital Object Identifier 10.1109/ACCESS.2025.3603695 Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids SINA HASHEMI , (Member, IEEE), MARKOS ASPROU , (Member, IEEE), LENOS HADJIDEMETRIOU , (Member, IEEE), AND MATHAIOS PANTELI , (Senior Member, IEEE) Department of Electrical and Computer Engineering, University of Cyprus, 1678 Nicosia, Cyprus Corresponding author: Sina Hashemi ([email protected]) This work was supported by the Horizon Europe program through the projects ‘‘HVDC-based Grid Architectures for Reliable and Resilient WideSprEad Hybrid AC/DC Transmission Systems’’ (HVDC-WISE) under Grant Agreement No. 101075424 and ‘‘Pan-European Interoperable AC-DC Hybrid Electricity Networks’’ (HYNET)under Grant Agreement No. 101172757. ABSTRACT With the increasing penetration of HVdc technologies in today’s power systems, especially for interconnecting neighboring grids—including those that are renewable-rich—there is a need to explore their contribution to system reliability and resilience in the context of cascading failures. This paper introduces a holistic framework for quantifying and mitigating cascading risks in HVdc-interconnected systems. It considers extreme events in addition to credible or expected events that threaten the resilience of interconnected systems, as evidenced by recent cascading blackouts with cross-border propagation impacts in Europe and worldwide. To achieve this, advanced dynamic cascading failure modelling is leveraged to simulate and quantify the cascading effects in HVdc-interconnected systems, particularly focusing on frequency stability and large-scale disturbances. This sheds light on the influence of HVdc on mitigating the propagation of non-local cascading events with cross-border impacts in interconnected systems, attributed to its ‘‘firewall’’ property. It also seamlessly integrates the dynamic cascading simulator with operational strategies, specifically controlled islanding, to further mitigate both local and non-local cascading impacts, especially addressing cross-border propagation, in interconnected systems. The simulation results on HVdc-interconnected test systems demonstrate the efficiency of the proposed work in significantly reducing cascade metrics, including Expected Demand-Not-Served (EDNS) and, notably, Conditional Valueat-Risk (CVaR) which captures tail risk events. INDEX TERMS Cascading failure risk, cascading impact quantification and mitigation, controlled islanding, HVdc interconnections, reliability and resilience enhancement, renewable-rich grids. I. INTRODUCTION As today’s power systems continue to develop and interconnect, the complexity of operation and control is increasing, particularly when addressing high-impact and lowprobability (HILP) events stemming from extreme weather and natural hazards. The growing integration of renewable energy sources (RES) into modern power grids necessitates a more resilient and flexible system operation to overcome weather events, natural hazards, and preserve uninterrupted power supply. Recently, there has been increased attention on establishing grid interconnections among neighboring countries through emerging HVdc links. This heightened attention The associate editor coordinating the review of this manuscript and approving it for publication was Dragan Jovcic . is attributed to the advantages offered through these links, including enhanced flexibility, controllability, interconnection of asynchronous systems, black-start capability, and mitigation of blackout risks [1]. Asynchronous interconnection of neighboring power grids through HVdc links provides a ‘‘firewall’’ property [2] that can prevent the spread of outages from one interconnected network to another. When transferring power between interconnected asynchronous systems, HVdc links function as dynamic isolation, preventing the propagation of cascading failures to the interconnected systems. The August 2003 blackout in the USA and Canada can be exemplified in this regard, where the Québec grid was not affected due to its HVdc interconnection [3]. Cascading failures, on the other hand, always pose a serious threat to current power systems, primarily triggered VOLUME 13, 2025 2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 154491 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids by extreme events, especially with the increasing frequency of extreme weather events worldwide. They originate from a series of dependent component outages and are further compounded by the operation of protective relays, progressively weakening the power system, and potentially leading to large-scale blackouts. One of the paramount considerations in cascades is their spatial characteristics, which can propagate locally or non-locally [4]. Local cascade phenomena refer to the intra-area spread of cascading events that occur within limited areas near the origin of cascade-triggering disturbances, while non-local propagation might vary from intra-area to inter-area spread of cascading failures, specifically compounded by cross-border impacts in interconnected grids. An example of non-local propagation is the blackout that occurred in the U.S. in 1996 [5]. Additionally, several major cascading failures with both local and non-local impacts, that led to cross-border propagation, occurred in Italy and Switzerland in 2003, Brazil and Paraguay in 2009, and Argentina, Paraguay, and Uruguay in 2019 [6]. Mitigating this type of non-local propagation across interconnected systems is usually more challenging when inter-area blackout risks emerge. A. LITERATURE REVIEW Cascading failure studies, encompassing modelling and analysis, have been extensively explored in the existing literatures [7],[8],[9],[10],[11], and [12]. Such investigations involve capturing relevant mechanisms and dynamic interactions among various components and integrating them into the simulation and analysis of a cascade. This facilitates understanding how a local failure or disturbance can propagate to widespread outages and disruptions. In general, as outlined in [4], cascading failure analysis models can be categorized into topological models [7], stochastic simulation models [8], high-level statistical models [9], Quasi-Steady State models (QSS) [10], dynamic simulation models [11], and other interdependent models [12]. These studies aim to develop either deterministic or stochastic models to incorporate the complex mechanisms of the cascading failure phenomenon into quantification. Furthermore, the application of HVdc systems and their impacts on power system issues have been introduced so far, mainly focusing on the restoration of blacked-out systems [13], stability [14] and resilience [15] improvement, as well as addressing HVdc commutation failure and cascading fault [16],[17]. The study on resilience improvement in [15] is based on the flexibility provided by Voltage Source Converter (VSC) HVdc links in controlling active and reactive powers. From the perspective of cascading failure analysis in AC/DC hybrid grids, a few papers [18],[19], [20] have also delved into the relevant issues. Reference [18] introduces the evolution process of cascading failures initiated by a fault on the AC side of the inverter, resulting in a prolonged commutation failure, and further leading to a DC system block, and subsequently causing cascading trips of overloaded paralleled AC lines. In [19], an analysis of cascading faults in AC/DC hybrid grids is presented, specifically the blackout that occurred in Brazil in 2018, highlighting HVdc commutation failure, DC blocking, power flow transferring, and other cascading outages. In [20], four quantitative indices are established to identify and assess the risk of cascading failure sequences. This risk is taken into account during the planning phase of AC/DC hybrid power grids. However, the influence of HVdcs on the reliability and resilience of interconnected power systems, especially from the perspectives of dynamic cascading failure modelling, quantification, and mitigation integrated with operational strategies, have not fully addressed. Existing literature on operational mitigation strategies, specifically controlled islanding, largely overlook its applications in emerging HVdc-interconnected grids. Such an operational strategy is examined for suppressing the progressive impact of cascading failures, which are mainly caused by random extreme initiating events. Various controlled islanding methods introduced in the existing literature involves different modelling and problem formulations for system splitting, such as graph theory [21], clustering techniques [22], and linear/nonlinear programming [23], either individually or in combination. For instance, a transient and a frequency stability-constrained controlled islanding approach are presented in [24] and [25], respectively, to merely enhance grid resilience against power system blackouts. However, these approaches do not address both system reliability and resilience enhancement through the mitigation of cascading impacts due to expected and HILP events, especially in AC/DC interconnected power systems. In essence, a thorough understanding of the merits and demerits of synchronous and asynchronous system interconnections is crucial, especially when considering the influence of the HVdc firewall capabilities in operational mitigation strategies against both low-impact, high probability and highimpact, low probability events. This understanding guides informed decisions in designing reliable and resilient interconnected power grid architectures through HVdc links and efficient mitigation strategies. This paper establishes a holistic framework involving novel quantification and an enhanced operational strategy for mitigation of non-local cascading propagation with cross-border impacts, as well as local propagation, within AC/DC interconnected systems for the first time. It aims to further enhance system reliability and resilience against both expected and HILP events in HVdc-interconnected systems by incorporating the HVdc firewall’s influence on preventing cross-border cascading propagation into a controlled islanding strategy. This study primarily focuses on neighboring power grids that are already interconnected asynchronously or are planned to be interconnected through HVdc links. B. MAIN CONTRIBUTIONS The contributions of this work are summarized as follows: •Developing an enhanced framework for cascading failure modeling of AC/DC interconnected systems that 154492 VOLUME 13, 2025 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids leverages time-domain RMS simulation to capture the dynamics of converter-interfaced technologies, such as HVdc links, with a focus on frequency stability and large-scale disturbances. •Introducing a novel cascading risk assessment of HVdc-interconnected power systems using cascade metrics such as Expected Demand-Not-Served (EDNS) and Conditional Value-at-Risk (CVaR), which represent expected and tail risk events, respectively, while highlighting and quantifying the influence of the HVdc link acting as a cascading firewall on mitigating crossborder impacts. •Providing an enhanced operational mitigation strategy for AC/DC interconnected power grids by refining spectral clustering for controlled islanding with constraints on coherent generator groups and HVdc connection points to ensure stable, self-sufficient islands while keeping HVdc links connected during grid partitioning, thereby confining cascading stress and enhancing reliability and resilience. C. OUTLINE The remainder of this paper is organized as follows: Section II details the proposed methodology for cascading-driven reliability and resilience assessment and enhancement of AC/DC interconnected power grids. It primarily provides a comprehensive explanation for dynamic cascading failure modelling, quantification, and mitigation of cascading failures applicable to such grids. Section III delves into simulation studies and analyzes the results for a large set of both expected and tail-risk events. Finally, Sections IV and V present a comparative discussion of different HVdc technologies and the paper’s conclusion, respectively. II. CASCADING-DRIVEN RELIABILITY AND RESILIENCE ASSESSMENT AND ENHANCEMENT OF AC/DC INTERCONNECTED POWER SYSTEMS A. PROPOSED METHODOLOGY The framework and methodology introduced in this work are based on enhanced dynamic modeling, quantification and mitigation of cascading failures in AC/DC interconnected power systems, whether already interconnected or planned to be interconnected synchronously or asynchronously. Fig. 1 illustrates the flowchart of the proposed framework and methodology. The framework begins by setting up the test power system with the relevant controllers and protective relays. Disturbance scenarios are then defined and applied to the system as initiating events. Following the dynamic cascading failure modeling (DyCFM), the RMS time-domain simulation is initialized and executed, solving the system’s differential-algebraic equations at each time step as the dynamic simulation progresses. This is implemented in DIgSILENT PowerFactory software to analyze whether any cascades initiate and propagate in the disturbed test system. Then, the impacts of cascading failures on the system under FIGURE 1. Flowchart of the proposed framework and methodology for DyCFM in AC/DC interconnected systems. expected and tail-risk events are quantified using cascade metrics, including EDNS and CVaR, for individual interconnected power grids. By doing so, the quantified impacts on both the originating system and other interconnected systems reveal the extent of local and non-local cascading propagation. Following this cascading-driven reliability and resilience assessment, the detection of cascading propagation is performed through the identification of operating limit violations, such as overloading of lines. In the case of cascade initiation and propagation, controlled islanding is implemented to confine the progressive spread of failures to limited islanded areas. To maintain rotor angle stability during system split, coherent generator groups (CGGs) are identified to be considered in constraints of the controlled islanding problem. Therefore, islanded subnetworks are formed surrounding these identified CGGs while minimizing power flow disruption. The framework then outputs the results of the dynamic cascading failure analysis, including cascade metrics, along with detailed information on implementing controlled islanding, such as the boundary lines to be opened and the loads to be reduced in a controlled manner to maintain system stability. The overall methodology is then composed of these three main stages according to Fig. 1: AC/DC interconnected systems modelling detailed in Section II-B, cascading-driven reliability and resilience assessment presented in Section II-C, and enhanced intentional controlled islanding introduced in Section II-D. VOLUME 13, 2025 154493 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids It is worth noting that the proposed framework and methodology is applicable to both operational planning and near-real-time applications. For operational planning, timedomain RMS simulations and controlled islanding can be performed in advance to prepare defense plans or mitigation strategies for anticipated disturbances, with the number of scenarios analyzed depending on the available timescales. In near-real-time applications, the method leverages real-time data to calculate controlled islanding for specific evolving events, with computational time of just a few seconds (a maximum of three seconds across all individual cascading scenarios). This allows for timely and effective mitigation strategies during actual system operations. Moreover, since this work primarily focuses on resilience analysis during system degradation due to cascading failures triggered by HILP events, treating it as a system-level phenomenon, it leverages RMS simulations to efficiently capture transient system behaviors over timescales ranging from milliseconds to minutes [26], ensuring computational efficiency for large-scale scenario analysis. The proposed framework is tailored to VSC-HVdc systems, which have distinct operational and control characteristics compared to LCC-HVdc systems. Specifically, exploring cascaded commutation failures in LCC-HVdc systems requires EMT simulations to capture detailed device-level transient behaviors (on a much finer timescale e.g., microseconds), significantly increasing computational complexity in system resilience studies. Cascading failures typically unfold across these timescales (milliseconds to minutes), encompassing both fast and slow phases of propagation [27]. As such, RMS simulations offer an ideal balance between computational efficiency and details required to assess system-wide dynamic behavior and resilience under a variety of HILP events. B. AC/DC INTERCONNECTED SYSTEM MODELLING AND CASE STUDY APPLICATION According to Fig. 1, the methodology initiates computations with the relevant data, including AC/DC grid topology, HVdc control mode (grid-forming or following), parameters for the dynamic RMS simulation-based cascading failure modelling (e.g., AVR, governors, HVdc controller parameters), and disturbance scenarios. The generic representation of the AC/DC network topology used in this study is shown in Fig. 2, illustrating point-to-point VSCHVdc interconnected systems. It comprises two converter stations connected by DC cables. These stations are commonly known as the sending-end converter station (rectifier) and the receiving-end converter station (inverter). Each converter station, along with its controller, performs specific functions. The rectifier controller regulates the firing angle of power electronic switching devices, such as Insulated Gate Bipolar Transistors (IGBTs), to control the voltage of the DC link. The inverter controller, on the other hand, drives IGBTs to regulate the AC voltage and frequency of the conFIGURE 2. A schematic representation of a generic VSC-HVdc link model. nected network or active and reactive power feed-in. This model, incorporating the selective control mode, enables the switching between Grid-Following (GFL) and Grid-Forming (GFM) control strategies [28]. During disturbances, converters in the GFL control mode maintain their output power nearly constant at the setting value, unless they incorporate additional virtual inertia, frequency droop, or voltage droop strategies in their closed-loop feedback controller. In the GFM mode, converters regulate the frequency and voltage of the node connected to the AC network through droop control, thereby indirectly adjusting the infeed active and reactive power. It is worth noting that the methodology fully emphasizes the impact assessment of HVdc links in interconnected systems. Nevertheless, it can also consider distributed energy resource (DER) capacity, and their associated controllers related to Fault Ride Through (FRT), voltage, and frequency support. In this work, protective relays and controllers associated with devices in the test system, including the VSC-HVdc link with GFL or GFM control functionality, are simulated using built-in DSL and composite models from the DIgSILENT software library. The analysis conducted for various disturbance scenarios includes 100 random N-3 contingencies of lines, extending beyond the N-1 and N2 reliability-oriented analysis to also address resilience applications. C. CASCADE-DRIVEN RELIABILITY AND RESILIENCE ASSESSMENT 1) DYNAMIC MODELLING AND ANALYSIS OF CASCADING FAILURES Dynamic modelling of cascading failures thoroughly involves system dynamics capturing transient responses of all incorporated elements in terms of voltage, angle, and frequency at each time instant. All relevant controllers and protective relays are considered, including the generator’s AVR and governor, voltageand frequency-related controllers for the VSC-HVdc link, over/under frequency generator tripping, undervoltage and underfrequency load shedding relays, as well as thermal or overcurrent relays for lines [26]. Fig. 3shows the detailed flowchart of the cascading failure modelling, capturing all relevant dynamic mechanisms through time-domain RMS simulation implemented within 154494 VOLUME 13, 2025 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids FIGURE 3. Conceptual representation of dynamic cascading failure modelling through time-domain RMS simulation. the DIgSILENT software. These mechanisms involve a complex sequence of events and actions triggered by controllers and protective relays in response to any deviation from setpoints or violations of operating limits, aiming to alleviate frequency and voltage violations, as well as line overloading. This may result in uncontrolled extensive asset tripping, system-wide instability, and blackouts [3]. System controllers, which include governors for regulating system frequency, AVR for adjusting voltage, and HVdc for either regulating network frequency and voltage in GFM mode or controlling active and reactive power in GFL mode (as illustrated in Fig. 2)[29],[30], detect deviations by comparing measured signals with their setpoints. Upon detecting a deviation, controllers send control signals to connected devices to regulate the relevant voltage and frequency at their respective points of contact. Depending on the type and severity of events, a power system might experience disturbances in its voltage, frequency, and line flow differently. When operating limits, such as the maximum allowable deviations in voltage magnitude, frequency, and loading, are exceeded, and the system operates outside its designed parameters, protective relays are activated by sending trip signals to breakers to restore the system to a stable and secure state. The relays necessary for dynamic cascading failure modelling include line overload protection, under-frequency and undervoltage load shedding relays, as well as overand under-frequency generator tripping relays [26]. In this work, protective relays and controllers associated with devices in the test system, including the VSC-HVdc link, are simulated using built-in DSL and composite models from the DIgSILENT software library. The entire model for cascading failure studies is developed in DIgSILENT using the Python API (application programming interface), which facilitates the automation of simulation-related tasks, particularly for a large set of scenarios (see Fig. 23 in the Appendix). This is achieved by setting up the test power system with relevant controllers and protective relays. Following the cascading failure modeling, the methodology defines and applies initiating events to the system, then proceeds with the initialization and execution of the time-domain RMS simulation. 2) LOCAL AND NON-LOCAL CASCADE QUANTIFICATION Quantifying cascading failures involves evaluating the potential consequences and impacts of initiating events, as well as determining the extent and severity of subsequent cascading event propagation within a power system. According to existing literatures [31],[32], and [33], different cascade quantification metrics can be considered depending on the study, including cascade size, grid integrity, cascade speed, cascade spatiality, and the operation of protective relays. In this study, the metrics of Demand-Not-Served (DNS) and the number of tripped elements are utilized to quantify cascade severity and assess grid integrity, respectively, with the latter also reflecting the cascade spread across all individual interconnected grids. This work refines these metrics to tailor them specifically for AC/DC interconnected grids, aiming to quantify the cascading impacts in all individual grids that are synchronously or asynchronously interconnected. The study considers both the average or expected value of all DNSs for a large set of contingencies (EDNS) and their Conditional-Value-at-Risk (CVaR)..(..) [34], using the cumulative distribution function (CDF) curve as illustrated in Fig. 4. This aims to investigate the impacts of expected events as well as unexpected tail risk events, respectively. Moreover, a 95% confidence level of DNS (CVaR95%) is considered in this study for the average DNS among the 5% worse events. In the case of two interconnected neighboring systems, depicted in Fig. 5, quantifying both local and nonlocal cascades, while considering cross-border impacts, can be formulated using (1). DNS ="DNS1 1DNS2 1 DNS1 2DNS2 2# DNSj i=XkLSk,∀k∈Sj,∀i,j∈NS(1) where NSis the set of interconnected systems (here, it is [1], [2]);]). Sjis the set of all buses within system j; kis the bus number involved in load shedding (LSk);). LSkcan take values from 0 up to the maximum load at bus k.iis the system number where initiating events originate; and jrepresents the system number for which the unserved load is calculated. For instance, DNS1 2measures the demand-not-served in system 1 while the origin of initiating events is in system 2. DNSj i can take values from 0 up to the maximum load of system j. In the case of j=T, with Tdenoting the total impact, DNS represents the total value of unserved load for the whole system. The local cascade phenomenon, referring to the intra-area spread of cascading events that occur within limited areas near the origin of cascade-triggering disturbances, VOLUME 13, 2025 154495 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids FIGURE 4. Risk measures, mean, var, and CVaR for demand-not-served (DNS). FIGURE 5. Simple illustration of two interconnected systems. is quantified by DNS1 1and DNS2 2. On the other hand, nonlocal propagation, specifically compounded by cross-border impacts in interconnected grids, is quantified by DNS2 1and DNS1 2. In addition, the metric for grid integrity, represented by the number of tripped elements (TE) and reflecting the cascade spread across all individual interconnected grids, is similarly formulated as follows: GIj i=dim TEj i,∀i,j∈NS(2) where TEj iis the vector of tripped elements in system jfollowing initiating events in system i; and GIj irefers to the metric of grid integrity, quantifying cascading outages in system j due to the occurrence of initiating events in system i. It is determined by the dimension or length of the vector of tripped elements, representing the total number of cascading outages. D. CONTROLLED ISLANDING IN AC/DC INTERCONNECTED SYSTEMS The intentional controlled islanding (ICI) method developed in this study employs constrained spectral clustering, selected for its low computational time [35], rendering it suitable for near-real-time network splitting applications. In this context, the ICI problem is constrained by identified coherent generator groups within the interconnected system where initiating events occur and subsequent cascading failures initiate. This aims to maintain the rotor angle stability of generators after system splitting. The methodology begins the controlled islanding upon detecting the initiation of cascading failures due to major disturbances in the system, such as multiple line outages or out-of-step operation of big generators. This is particularly crucial for systems that are highly susceptible to cascading failures with rapid propagation, as demonstrated in the simulation results. Using the data of available network elements after the occurrence of initiating events and conducting the dynamic cascading failure analysis through RMS simulation, the ICI problem is solved to identify the optimal island subnetwork while ensuring stability and self-sufficiency of each island. Then, boundary lines between each pair of islands and controlled load reduction at each bus in islands, as determined by the controlled islanding results, are applied to the AC/DC interconnected grids. 1) IDENTIFICATION OF COHERENT GENERATOR GROUP (CGG) To maintain rotor angle stability following controlled islanding, it is crucial to cluster coherent generators together in the same group within the interconnected grid where cascading failures initiate and are intended to be mitigated. Due to data availability and similarity to rotor angle behavior, phase angles of terminal voltage from generators, as measured by PMUs, are utilized for CGG identification [23]. This work employs the Intraclass Correlation Coefficient (ICC) and the K-medoids clustering algorithm [36] to develop a CGG identification method. The method is further enhanced through the associated formulation to be tailored and applicable to HVdc-interconnected systems, accounting for the differing dynamic responses of generators in asynchronously interconnected systems. The ICC measures the coherency between each pair of generators on a scale from 0 to 1, where values closer to 1 indicate higher coherency. Moreover, the K-medoids clustering algorithm is employed to partition the calculated ICC values into k-distinct clusters of coherent generators by identifying medoids that minimize the sum of dissimilarities between data points and their nearest medoid. The ICC matrix is defined as: ICC =ICCi,ji,j∈Gε(3) where: ICCi,j=σ2 b σ2 b+σ2 w ,i,j∈Gε Gεdenotes the set of generators in the interconnected grid ε. εis the identifier for the interconnected grid where initiating events occur. σ2 bis the between-generator variance, quantifying variability of dynamic responses between generators iand j;σ2 wis the within-generator variance, quantifying variability of dynamic responses for each generator. Using the coherency matrix ICC, the K-medoids clustering algorithm is employed to partition Gεinto kclusters {CGG1,CGG2, . . . , CGGk}. The clustering process is defined as follows: CGGε γ= {g∈Gε|g belongs to cluster m}(4) Equivalently, using medoids Mm, we express the clusters as: CGGε γ={g∈Gε|Mm=arg min Mk d(g,Mm)}m=1,2, . . . , k (5) where: d(g,Mm)=1−ICCg,Mm 154496 VOLUME 13, 2025 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids Mmdenotes the medoid of cluster m and d(g,Mm)represents the dissimilarity of generator gfrom medoid Mm. The objective is to find k medoids {M1,M2, . . . , Mm⊆Gε}, such that the sum of dissimilarities within all clusters is minimized. Therefore, the set of identified CGGs can be expressed as: CGG = {CGGε γ|γ∈0}(6) where, γis the identifier for the CGG set. 0denotes the set of identified numbers of CGGs. 2) SPECTRAL CLUSTERING APPLIED TO INTERCONNECTED GRIDS In essence, the spectral clustering method utilizes the graph-cut of an undirected edge-weighted graph that is built according to (7) by ignoring the direction of power flow [37]. In this study, the mean of the absolute values of the active power across a transmission line connecting nodes iand jserves as the edge weight (wij). The dynamic weighting of edges, based on power flow, incorporates the effects of changes in actual operating conditions on controlled islanding. wij =wji =(Pij+Pji)2 (7) As mentioned earlier, the aim of system splitting is to suppress cascading propagation within limited areas of the interconnected grid where the initiating events occur. The objective function, which focuses on minimizing the power flow disruption, represented by the summation of the absolute value of the active power flow across the splitting boundary branches in the interconnected system where initiating events occur, is expressed in (8). In the proposed methodology, the formulation of spectral clustering is refined and enhanced to be applicable to HVdc-interconnected grids by introducing two types of pairwise constraints: Must Link (ML) and Cannot Link (CL) [38]. An ML constraint between two vertices ensures that these vertices will belong to the same cluster, while a CL constraint guarantees that the vertices will be assigned to different clusters. min Xi,j∈Sε B (Pε ij+Pε ji).2 Subject to: ML =n(i,j)|i,j∈SHVdc POC o CL = {(i,j)|∃l= k∈0such that i∈CGGε land j ∈CGGε k}(8) where, Sε Bis the set of buses at both ends of the splitting boundary branches in the interconnected grid ε.SHVdc POC is the set of bus pairs connected to the HVdc link. This ML constraint ensures that the HVdc link remains connected during controlled islanding. The CL constraint also ensures that buses iand j, which belong to different coherent generator groups CGGε land CGGε k(with l= k), must not be assigned to the same island. It should be noted that distinct controlled islanding configurations—featuring different boundary lines and post-splitting operating conditions—can be obtained under varying operating conditions and initiating events. This is because the dynamic weighting of edges, based on measurement data or power flows, incorporates changes in actual operating conditions into the islanding process via Eq. (8). Consequently, different disturbances and operating scenarios can result in different optimal islanding configurations. Given the objective of mitigating the progressive impact of cascading outages by splitting the system into limited islanded areas under stable operation, the identified coherent generator groups are applied to the constrained controlled islanding problem through the pairwise constraints. During the computations of controlled islanding, the sending and receiving buses of the HVdc connection points in interconnected grids are considered generation buses with nearly equal negative and positive active power, respectively. In the proposed controlled islanding algorithm, two types of controlled load reduction are determined and applied in the dynamic simulation study: 1) Frequency control load reduction (FCLR) due to load-generation imbalance of an island after controlled splitting; and 2) Line overload relief load reduction (LOLR) due to overloading of lines in an island after controlled splitting. It is worth mentioning that, although the objective function of the problem focuses on minimizing power flow disruption, controlled load reduction is implemented in cases of insufficient generation due to load-generation imbalances or line overloading in one or more islanded subnetworks. Subsequently, the calculated details of the ICI problem are applied in the dynamic simulation study in order to open boundary lines and reduce loads, ensuring stable and self-sufficient islanded operation of the interconnected grids following initiating events. III. RESULTS AND DISCUSSION A. SYSTEM MODELLING AND CASE STUDY APPLICATION In order to model interconnected neighboring power grids, IEEE 39-bus and 14-bus systems are employed in this work, as shown in Fig. 6. The interconnection of a larger system, such as the IEEE 39-bus system, with a smaller system like the IEEE 14-bus system, serves as a simplified case study and prototype, reflecting real HVdc-interconnected systems. For example, the Estlink interconnector between Estonia and Finland, the Skagerrak4 link between Norway and Denmark, the NordLink between Norway and Germany, the ALEGrO link between Germany and Belgium, and the Nemo Link between the UK and Belgium exemplify a similar paradigm, where a smaller system is linked to a larger one through VSCHVdc technology. The reason for choosing the VSC-HVdc link in this work is to explore the influence of emerging converter technologies, particularly those with advanced control capabilities such as grid-supporting voltage source converters (VSCs). Compared to traditional LCC-HVdc systems, VSC-HVdc systems offer distinct operational advantages that enhance system resilience during extreme disturbances. While both technologies support long-distance power transfer, VSC-HVdc systems outperform LCC-HVdc in their VOLUME 13, 2025 154497 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids TABLE 1. Systems’ load and HVdc connection points. ability to provide fast and flexible voltage and frequency support in grid-forming mode, as well as enabling blackstart in islanded conditions. More critically, VSC-HVdc systems possess inherent cascade firewall capabilities, allowing them to isolate and contain cascading failures within the local region where disturbances originate. This containment prevents the propagation of outages to adjacent interconnected systems (based on asynchronous interconnection)—an advantage that LCC-HVdc systems, due to their dependence on strong synchronous sources and limited controllability, inherently lack. These attributes position VSC-HVdc as a superior choice for enhancing the operational resilience of hybrid AC/DC grids. The test systems are analyzed under peak load conditions, replicating high stress with minimal security margin, particularly when accompanied by N-k contingencies. However, the framework can be broadly applied to diverse system conditions, including varying load levels and generation patterns. The IEEE 39-bus system serves as a source or sending system, supplying 50 MW of power to the 14-bus system, which functions as a sink or receiving system, through either the AC or HVdc link. The feed-in power across the interconnection link constitutes 19.3% of the total load in the IEEE 14-bus system. The receiving-end converter of the HVdc link in the IEEE 14-bus system operates in GFM control mode, while the sending-end converter, operating in GFL mode, supports the voltages of the DC link and the connection point. In this study, the contribution of RES, particularly at high penetration levels, is also considered in the simulation analysis. This allows for an assessment of the cascading failure impacts in renewable-rich power grids, extending beyond the primary focus on grids interconnected by VSC-HVdc as converterinterfaced technologies. Table 1outlines the total load of the interconnected systems, as well as the load for each individual system. It also includes information about the names and voltage levels of the buses within the two systems connected to the interconnectors. The study initiates dynamic cascading failure modeling and quantification for both synchronous and asynchronous interconnections, showcasing system performance with a point-to-point VSC-HVdc link compared to an AC link by examining the effectiveness of the asynchronous interconnection in halting the cross-border propagation of non-local cascading failures. Subsequently, a reactive operational mitigation strategy, specifically controlled islanding employed here, is implemented in cases of detected cascading propagation to demonstrate how it can improve the system reliability and resilience in the face of both expected and FIGURE 6. Conceptual representation of the test AC/DC system. tail-risk events. This is achieved by recalculating the RMS simulation and comparing the corresponding results. In the following subsections, Sections III-B and III-C, comparative studies are thoroughly performed for the AC/DC interconnected power grids under a specific outage scenario, as well as different outage scenarios outlined below. These studies extend from interconnected grids with the AC link to those with the HVdc link, first without ICI and then with ICI. •N-1 contingencies of lines including 53 scenarios of single line/transformer outages, including 18 from the 14-bus system, 34 from the 39-bus system, and one for the interconnected link. •N-2 contingencies of lines including 100 random scenarios of two concurrent line outages (22 scenarios from the 14-bus system, and 78 scenarios from the 39-bus system). •N-3 contingencies of lines including 100 random scenarios of three concurrent line outages (24 scenarios from the 14-bus system, and 76 scenarios from the 39-bus system). It should be noted that the present study goes beyond traditional N-1 and N-2 reliability-oriented contingency analyses by considering N-3 contingencies, which represent very severe disturbances for networks of the test system’s size. 154498 VOLUME 13, 2025 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids FIGURE 7. Systems’ frequency in the presence of the AC link. B. ILLUSTRATIVE CASCADING SCENARIO This part of the study involves an in-depth analysis of cascading failures in the test system under a specific outage scenario, highlighting the mitigation of cross-border propagation of non-local cascading failures, particularly through the cascade firewall capability of the VSC-HVdc interconnector, along with further operational mitigation provided by controlled islanding. The scenario selected for this study consists of two concurrent outages of lines 13-14 and 16-24 from the IEEE 39-bus system at 2 seconds of the simulation, representing a HILP event for this case study application that may lead to a complete blackout. The study then explores the response of the two systems during cascade initiation and propagation, comparing synchronous interconnection through the AC link and asynchronous interconnection through the HVdc link. Figs. 7to 9represent the frequency of all buses within the two interconnected systems under the aforementioned outage scenario, first with the AC and HVdc links without controlled islanding, and then during controlled islanding in the presence of the HVdc link. Accordingly, Tables 2to 4provide details on the sequence of cascading events, including the timestamps and types of events, affected systems, and cumulative DNS, in the presence of the AC and HVdc links without ICI, as well as during ICI with the HVdc link, respectively. The number in braces, like {1}, seen in Figs. 7to 9corresponds to the sequence number of events in the cascading failures, as indicated in Tables 2to 4. Following the initiating events within the 39-bus system in the presence of the AC link, the cascade non-locally propagates to the other interconnected system (the 14-bus) through the outage of lines 6-13, 6-12, 12-13, and 9-14, as well as the tripping of generators G1 and G2, in addition to local propagation, as shown in Table 2. This occurs due to the transfer of stress from one system to another, leading to the activation of overcurrent (OC) relays of the corresponding lines and over-frequency tripping relays of generators (OFGT). In this case, for instance, the cascade metrics GI14 39 and DNS14 39 become 6 and 259 MW, respectively. FIGURE 8. Systems’ frequency in the presence of the HVdc link. FIGURE 9. Systems’ frequency in the presence of the HVdc link while controlled islanding implemented. FIGURE 10. Total load of both interconnected systems during cascading failures. Consequently, the entire system undergoes severe cascading power outages, resulting in a total DNST 39 of 6453.7 MW. In the presence of the HVdc link, the event is spread to some parts of the 39-bus system (the same system where the VOLUME 13, 2025 154499 S. Hashemi et al.: Quantifying and Mitigating Cascading Impacts in HVdc-Interconnected Power Grids FIGURE 23. Flow diagram of data and commands for the DyCFM tool. TABLE 8. HVdc control parameters. failures to the limited area within the interconnected grid where the initiating events originate. Thus, the consequences of cascading failures with various impacts, ranging from local to non-local blackouts, specifically compounded by cross-border cascading propagation in interconnected systems, can be alleviated through mitigation provided by the HVdc firewall property in preventing the cross-border spread of cascading failures and a controlled islanding strategy by suppressing cascading propagation within limited areas of the interconnected grid where the initiating events occur. Notably, the integration of a hybrid RMS-EMT simulation framework into cascading failure modeling and analysis for AC/DC power grids—enabling efficient device-level to system-level investigations of transient phenomena (e.g., cascaded commutation failure in LCC-HVdc) on finer timescales (e.g., microseconds), even for larger IBR-dominated grids— will be explored as an extension of this paper in future work. Additionally, incorporating a practical approach for identifying plausible and impactful N-k contingencies into cascading failure analysis represents another promising direction for future research. APPENDIX A Fig. 23 depicts the flow diagram of data and commands interchanged between the integrated parts of the DyCFM tool, including Python, DIgSILENT, and MATLAB. The flows of commands and data represent how the software interacts through codes and exchanges test system data and results, respectively. Python scripts, integrated with the DIgSILENT API, automate simulation tasks, particularly for large-scale scenario analyses. MATLAB can also be integrated with Python to perform controlled islanding calculations using MATPOWER data [39]. Moreover, Table 8outlines the parameters of the HVdc controllers. REFERENCES [1] M. 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Kezunovic, ‘‘Prevention of power grid blackouts using intentional islanding scheme,’’ IEEE Trans. Ind. Appl., vol. 53, no. 1, pp. 622–629, Jan. 2017. [38] X. Wang, B. Qian, and I. Davidson, ‘‘On constrained spectral clustering and its applications,’’ Data Mining Knowl. Discovery, vol. 28, no. 1, pp. 1–30, Jan. 2014. [39] R. D. Zimmerman, C. E. Murillo-Sánchez, and R. J. Thomas, ‘‘MATPOWER: Steady-state operations, systems research and education,’’ IEEE Trans. Power Syst., vol. 26, no. 1, pp. 12–19, 2011. SINA HASHEMI (Member, IEEE) received the Ph.D. degree from the University of Tehran, Iran, in 2022, specializing in power system stability and control. Currently, he is a Senior Research Associate with the Department of Electrical and Computer Engineering, University of Cyprus. His research interests include assessing, mitigating, and restoring power systems to enhance resilience and stability, particularly against cascading blackouts. His expertise includes cascading failure modeling and analysis, cyberattack-induced cascading failure mitigation, and the cost-benefit analysis of hybrid ac/dc power grids. MARKOS ASPROU (Member, IEEE) received the B.Sc. and Ph.D. degrees in electrical engineering from the University of Cyprus, in 2009 and 2015, respectively. Currently, he is a Research Lecturer with the KIOS Research and Innovation Center of Excellence, University of Cyprus. His research interests include wide area monitoring and state estimation of power systems, the estimation of transmission line parameters, the wide area control of power systems, power systems flexibility, and the cybersecurity of power systems. LENOS HADJIDEMETRIOU (Member, IEEE) received the Diploma degree in electrical and computer engineering from the National Technical University of Athens, Greece, in 2010, and the Ph.D. degree in electrical engineering from the University of Cyprus, Cyprus, in 2016. He is currently a Research Lecturer with the KIOS Research and Innovation Center of Excellence, University of Cyprus. His research interests include smart grids, the grid integration of renewable energy systems, energy storage systems, the control of power electronics, micro-grids, smart buildings, digital twins, and cybersecurity aspects in smart grids. MATHAIOS PANTELI (Senior Member, IEEE) received the M.Eng. degree in electrical and computer engineering from the Aristotle University of Thessaloniki, Greece, in 2009, and the Ph.D. degree in electrical power engineering from The University of Manchester, U.K., in 2013. He is currently an Assistant Professor with the Department of Electrical and Computer Engineering, University of Cyprus; a Faculty Member of the KIOS Research and Innovation Center of Excellence; and an Honorary Lecturer with the Department of Electrical and Electronic Engineering, Imperial College London. His research interests include techno-economic reliability, resilience, and flexibility assessment of future low-carbon energy systems, the grid integration of renewable energy sources, and integrated modeling and analysis of co-dependent critical infrastructures. He is an IET Chartered Engineer (C.Eng.), the Chair of the CIGRE Working Group C4.47 ‘‘Power System Resilience’’ and the CIGRE Cyprus National Committee, and an active member of multiple IEEE working groups. VOLUME 13, 2025 154507