Bazylevych Roman Petrovych, Doctor of Technical Sciences, professor Lviv Polytechnic National University, Lviv, Ukraine
ORCID: 0000-0002-7949-1353
Kliushta Oleksandr Volodymyrovych, PhD student
Lviv Polytechnic National University, Lviv, Ukraine
ORCID: 0009-0002-8701-962X
POWER SYSTEM ISLANDING USING METIS ALGORITHM
Introduction. Hierarchical decomposition of power systems is an important tool for modeling, analyzing, and managing complex networks. Modern electrical systems cover vast territories and consist of thousands of elements and interconnections, making their analysis as a whole exceedingly challenging. To effectively address these challenges, the system is often divided into subsystems that can be studied separately, taking into account the key dependencies between them [1]. This division simplifies the computational processes and enhances the ability to pinpoint critical points in the network. One approach to this decomposition relies on graph theory, where a power system can be represented as a graph. The METIS algorithm, which specializes in efficient graph partitioning, enables this division by maintaining balance between the parts and minimizing the number of connections between them. This optimization improves the efficiency of calculations and analysis, which is particularly relevant when dealing with large networks [2]. The goal of my research is to apply the METIS algorithm for hierarchical decomposition of a power system. This approach opens up new possibilities for efficient modeling, simplifying the handling of large datasets, and enhancing the accuracy of decision-making processes in the energy sector.
Relevance of the topic. The decomposition of power systems is becoming increasingly relevant due to the rapid complexity of their structure and operation. Modern power networks encompass various types of generation, transmission, and distribution, driven by the growing share of renewable energy sources and the integration of digital technologies. These changes pose new challenges for both analysis and management, as processing such systems as a whole can be excessively resource-intensive and time-consuming. Hierarchical decomposition makes it possible to divide a complex power system into simpler, interrelated components that can be analyzed independently [3]. This significantly facilitates the analysis of both normal and emergency operating conditions, while also accelerating the system's adaptation to changes. Such an approach is particularly critical for ensuring the reliability and resilience of power networks, where even local failures can have wide-reaching consequences. The need for efficient decomposition algorithms becomes even more pronounced in an environment where large volumes of data must be processed in real time [4]. The METIS algorithm, which excels at optimal graph partitioning, can greatly improve the speed and accuracy of these processes. This makes its use highly relevant in contemporary research aimed at advancing the management of power systems.
METIS algorithm is designed to handle the partitioning of large and complex graphs, making it a powerful tool for various applications in network analysis, including power systems. At its core, METIS performs what is known as graph partitioning, where the goal is to divide a network into multiple smaller subgraphs (or partitions) while optimizing certain criteria. The algorithm seeks to minimize the number of connections (or edges) between these subgraphs and ensure that each part is roughly equal in size, which is essential for maintaining balance in computational workloads [5]. In the context of power systems, representing the network as a graph helps capture the structure and relationships between different system components. Nodes in this graph correspond to important elements such as power plants, substations, or consumers, while edges represent the transmission lines or other physical connections between these components. An optimal partitioning can isolate different regions of the network, allowing engineers to analyze individual sections independently without compromising the overall system’s coherence. A major challenge in partitioning such graphs is to prevent over-segmentation or unbalanced partitions, where certain parts may become too interconnected or too large compared to others. This imbalance can lead to inefficiencies during simulations, such as uneven processing times and bottlenecks in parallel computations. METIS addresses these challenges through a series of optimization techniques that ensure the partitions are not only balanced in terms of node count but also exhibit minimal "cross-boundary" dependencies (connections between different partitions). The algorithm is particularly advantageous for large-scale systems where manual decomposition would be impractical. Power grids, which can have thousands or even millions of nodes and connections, require sophisticated partitioning strategies to support real-time simulations and analysis. For example, in cases of emergency response, such as a blackout or overload, having the network already divided into manageable subsystems can accelerate decision-making by enabling targeted analysis and localized solutions. Furthermore, METIS supports multi-objective optimization, which allows users to prioritize different aspects of the partitioning depending on the problem context. For example, in a power system, priorities might include minimizing the number of critical nodes (those with many connections to other partitions) or ensuring that key infrastructure (e.g., major power plants) is evenly distributed across partitions. Overall, the METIS algorithm provides a robust foundation for large-scale hierarchical decomposition, ensuring both scalability and efficiency in network analysis. Its effectiveness in minimizing interconnections between subgraphs while maintaining balance makes it a critical tool in modern energy system research and management. 
	The METIS algorithm is built upon a multilevel partitioning strategy, which is designed to enhance both efficiency and accuracy when dividing large graphs. This approach involves three key stages: coarsening, initial partitioning, and uncoarsening (or refinement). Each stage serves a specific role in simplifying the partitioning problem while maintaining an optimal balance and minimizing interconnections between partitions. In the coarsening phase, METIS progressively reduces the size of the graph by merging nodes and edges. This process, called graph contraction, aggregates nodes that are closely connected, forming "super-nodes" that represent groups of original nodes. By reducing the graph size, the algorithm simplifies the structure and decreases the complexity of the partitioning task. During this phase, the algorithm carefully selects which nodes and edges to combine based on factors such as edge weights and connectivity. The goal is to preserve the overall structure and relationships of the original graph so that the partitioning results remain meaningful even after the graph is reduced. Once the graph has been coarsened to a manageable size, METIS performs an initial partitioning on this simplified graph. Since the reduced graph has far fewer nodes and edges, this step can be completed quickly using relatively simple partitioning techniques. The goal here is to generate a rough but reasonably balanced division of the graph into the desired number of partitions. While the initial partition may not be perfect, it serves as a starting point for further optimization. The algorithm uses heuristics to ensure that partitions are approximately equal in size and that cross-boundary connections are minimized as much as possible at this stage.  After the initial partitioning, the algorithm enters the uncoarsening phase, where the graph is gradually expanded back to its original size. As each level of the graph is restored, METIS refines the partitioning by adjusting node assignments to improve the overall balance and reduce inter-partition connections. This iterative process involves moving nodes between partitions if doing so decreases the number of cross-boundary edges without disrupting the balance of partition sizes. This refinement process ensures that the final partitioning is optimized both in terms of balance and connectivity. METIS uses techniques such as multi-objective optimization and greedy refinement to achieve high-quality results efficiently.
	The METIS algorithm offers several distinct advantages that make it a valuable tool for the decomposition of large, complex networks such as power systems. These benefits include its scalability, processing efficiency, and ability to maintain a balanced partitioning. These characteristics are crucial for systems that require high-performance analysis and parallel computing, where imbalanced partitions can cause bottlenecks and reduce the effectiveness of simulations. One of METIS’s greatest strengths is its ability to handle large graphs with millions of nodes and edges. By using a multilevel partitioning strategy, METIS efficiently reduces the problem size through graph coarsening, allowing it to perform partitioning operations that would otherwise be computationally prohibitive. This scalability makes it particularly suitable for modern power grids, which involve extensive networks of generators, substations, and consumers connected by thousands of transmission lines. In large-scale power systems, where multiple regions and components interact dynamically, scalable partitioning is essential to facilitate both localized and system-wide analysis. METIS ensures that these analyses can be performed on smaller, independent subsystems without compromising the integrity of the overall network structure. The efficiency of METIS stems from its ability to minimize both the number of inter-partition connections and the computational cost of partitioning. The coarsening and refinement phases significantly reduce the amount of time and resources needed to achieve high-quality partitioning. This performance optimization is critical for applications that require frequent updates or real-time analysis, such as load balancing, fault detection, and network reconfiguration in power grids. By balancing the sizes of partitions, METIS prevents overloading of individual computational nodes in parallel processing environments. This allows researchers and engineers to run multiple simulations or analyses concurrently, thereby reducing overall processing time and improving system performance. Maintaining balanced partitions is essential for efficient resource utilization in parallel and distributed computing. Imbalanced partitions, where some parts of the system contain significantly more nodes or connections than others, can lead to delays and inefficiencies in simulations. METIS addresses this by ensuring that partitions are of approximately equal size, thereby distributing workloads evenly across computational resources. In power system analysis, balanced partitioning helps avoid scenarios where certain regions of the network dominate processing time, allowing for more consistent performance across all subsystems. This is particularly beneficial when simulating power flows, demand forecasting, or system reliability under various operating conditions. The practical applications of METIS in power systems research and management are extensive. Key use cases include:
●	Simulation and modeling: Partitioned networks allow for faster simulations of power flows, fault scenarios, and system stability.
●	Real-time monitoring: Large-scale networks can be broken into manageable segments for localized analysis and faster response to operational changes or emergencies.
●	Planning and optimization: By reducing the complexity of the system, METIS helps optimize network expansion, maintenance schedules, and resource allocation.
Overall, METIS provides the tools necessary to simplify complex networks while preserving their essential characteristics. Its scalability, efficiency, and balanced partitioning capabilities make it an indispensable resource for improving the performance of modern power systems. Through effective decomposition, METIS supports both theoretical research and practical decision-making in the energy sector, enhancing system reliability and adaptability in an increasingly complex energy landscape.
Novelty of the application. The novelty of applying the METIS algorithm in my research lies in its adaptation for hierarchical decomposition of power systems, which enhances the efficiency of analyzing complex network structures. Traditional approaches to power system decomposition are often based on physical or geographical characteristics, which may not always provide optimal results for control and simulation tasks [4]. My approach involves utilizing the multilevel strategy of METIS to build a hierarchical structure of subsystems that supports better management of computational processes. This enables parallel analysis of individual subsystems without significant losses in accuracy or complex synchronization requirements. Moreover, the algorithm minimizes the number of critical connections between parts of the system, contributing to increased resilience against local failures. This allows the application of advanced data processing methods for modeling and forecasting in large-scale networks, opening new opportunities to improve power system management.
Expected results. The application of the METIS algorithm for hierarchical decomposition of power systems is expected to significantly improve the efficiency of network analysis and management. Dividing the system into subsystems will reduce the computational load during modeling and monitoring. This should enhance the system's ability to respond quickly to changes or emergency situations, which is crucial for maintaining reliability. Another important outcome is the possibility of using parallel computing to analyze different parts of the network. This will accelerate calculations in large systems and allow more efficient use of computational resources. By maintaining balance between subsystems, the risk of overloading individual components is minimized, ensuring a more even distribution of loads. Additionally, minimizing interconnections between subsystems will enhance system resilience. In the event of a local failure, the issue can be isolated within a single subsystem, reducing the risk of cascading effects across the network. This is particularly important in modern power systems, which increasingly face challenges related to structural complexity and the integration of diverse energy sources. Thus, the application of METIS not only improves system analysis and modeling but also lays the groundwork for enhanced reliability, resilience, and management efficiency in an ever-evolving network environment.
Conclusions. The application of the METIS algorithm for hierarchical decomposition of power systems offers new possibilities for efficient analysis and management of complex networks. By enabling the division of the system into balanced subsystems with minimal interconnections, the algorithm simplifies computational processes and enhances data processing speed. This capability allows for timely responses to operational changes and failures, which are key factors in ensuring system reliability. The novelty of this approach lies in using METIS's multilevel strategy to optimize the decomposition structure not just by geographical or functional criteria, but by the graph parameters of the system. This provides additional advantages in resource management and supports the integration of new monitoring and forecasting methods in large-scale energy networks. The expected results confirm the feasibility of implementing METIS in power system decomposition tasks. Improvements in calculation accuracy, the ability to perform parallel subsystem analysis, and enhanced network resilience form a strong foundation for further research and the development of modern power management systems. Consequently, algorithmic methods like METIS are becoming essential tools for ensuring stability and efficiency in the face of rapid changes and increasing complexity in power systems.

References
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