Stochastic Optimization for Grid Resilience. FY18 Final Technical Report

The electric power system is one of the most important critical infrastructures of a country. Recently, the number of natural and man‐made disasters is increased, which can impose extensive damages and costs to the power system. A resilient power system can withstand against, adapt to and recover from these disasters. Power system resilience is quantified by mathematical tools which are called “resilience metrics”. Currently, a lot of resilience metrics are proposed in the power system literature. In this paper, based on the extensive research in the critical infrastructure resilience literature which specifically concentrates on the “area‐based” resilience metrics, a new area‐based resilience metric is proposed which can measure the power system resilience considering the government policymaker criteria, which are rarely noticed before. The proposed and conventional area‐based resilience metrics are evaluated based on the real data from the 2012 Superstorm Sandy in the USA, which led to significant damage to the power distribution system. The simulation results show that the proposed area‐based resilience metric is very simple, can successfully address actual power system performance curves and is more meaningful and tangible than the conventional area‐based metrics for the government policymaker. The proposed area‐based resilience metric has also a general form and can be used for other critical infrastructures.

Recently, there has been a focus on natural and man-made disasters with a high-impact low-frequency (HILF) property in electric power systems. A power system must be built with “resilience” or the ability to withstand, adapt and recover from disasters. The resilience metrics (RMs) are tools to measure the resilience level of a power system, normally employed for resilience cost–benefit in planning and operation. While numerous RMs have been presented in the power system literature; there is still a lack of comprehensive framework regarding the different types of the RMs in the electric power system, and existing frameworks have essential shortcomings. In this paper, after an extensive overview of the literature, a conceptual framework is suggested to identify the key variables, factors and ideas of RMs in power systems and define their relationships. The proposed framework is compared with the existing ones, and existing power system RMs are also allocated to the framework’s groups to validate the inclusivity and usefulness of the proposed framework, as a tool for academic and industrial researchers to choose the most appropriate RM in different power system problems and pinpoint the potential need for the future metrics.

In this work, large-scale structural optimization problems involving non-ordinal categorical design variables and continuous variables are investigated. The aim is to minimize the weight of a structure with respect to cross-section areas, with materials and stiffening principles selection. First, the problem is formulated using a bi-level decomposition involving master and slave problems. The master problem is given by a first-order-like approximation that helps to drastically reduce the combinatorial explosion raised by the categorical variables. Continuous variables are handled in a slave problem solved using a gradient-based approach, where the categorical variables are driven by the master problem. The proposed algorithm is tested on three different structural optimization test cases. A comparison to state-of-the-art algorithms emphasize efficiency of the proposed algorithm in terms of the optimum quality, the computation cost, and the scaling with respect to the problem dimension.

Intentional controlled islanding (ICI) is a crucial strategy to avert power system collapse and blackouts caused by severe disturbances. This paper introduces an innovative IoT-based ICI strategy that identifies the optimal location for system segmentation during emergencies. Initially, the algorithm transmits essential data from phasor measurement units (PMUs) to the IoT cloud. Subsequently, it calculates the coherency index among all pairs of generators. Leveraging IoT technology increases system accessibility, enabling the real-time detection of changes in network topology post-disturbance and allowing the coherency index to adapt accordingly. A novel algorithm is then employed to group coherent generators based on relative coherency index values, eliminating the need to transfer data points elsewhere. The “where to island” subproblem is formulated as a mixed integer linear programming (MILP) model that aims to boost system transient stability by minimizing power flow interruptions in disconnected lines. The model incorporates constraints on generators’ coherency, island connectivity, and node exclusivity. The subsequent layer determines the optimal generation/load actions for each island to prevent system collapse post-separation. Signals from the IoT cloud are relayed to the circuit breakers at the terminals of the optimal cut-set to establish stable isolated islands. Additionally, controllable loads and generation controllers receive signals from the cloud to execute load and/or generation adjustments. The proposed system’s performance is assessed on the IEEE 39-bus system through time-domain simulations on DIgSILENT PowerFactory connected to the ThingSpeak cloud platform. The simulation results demonstrate the effectiveness of the proposed ICI strategy in boosting power system stability.

The problem of capacitor placement on a radial distribution system is formulated and a solution algorithm is proposed. The location, type, and size of capacitors, voltage constraints, and load variations are considered. The objective of capacitor placement is peak power and energy loss reduction, taking into account the cost of the capacitors. The problem is formulated as a mixed integer programming problem. The power flows in the system are explicitly represented, and the voltage constraints are incorporated. A solution method has been implemented that decomposes the problem into a master problem and a slave problem. The master problem is used to determine the location of the capacitors. The slave problem is used by the master problem to determine the type and size of the capacitors placed on the system. In solving the slave problem, and efficient phase I-phase II algorithm is used.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The shipboard power system of an all-electric ship can be characterized as an isolated microgrid system with limited capacity and no support from external grid. Its resilience problem is more prominent when confronting some extreme events, compared to land-based power system. Currently, there are few researches concerning about the shipboard power system's resilience. It's urgent to fill the comprehensive evaluation need of ship power system's resilience. This paper proposes a comprehensive evaluation framework for all-electric ship's power system resilience. Furthermore, evaluation metrics of shipboard power system resilience comprising resistance, security, self-healing ability, environmental friendless and personnel quality are established. Based on Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation methods, a comprehensive assessment framework is performed to evaluate the resilience of shipboard power system. Numerical results demonstrate that the proposed method can provide guidance for all-electric ship's fault recovery and resilience improvement strategy.

The smart grid paradigm promises dramatic improvements in reliability, resiliency and efficiency of power systems while addressing environmental concerns. Yet, the extensive reliance of these smart power systems on communication and information technologies increases the cyberattack surface opening up a new class of vulnerabilities to disturb power system operation. In this paper, we study the aurora attack class of assaults specifically against a microgrid point of common coupling (PCC). In contrast to the aurora attack on synchronous generator breakers, it is shown that the microgrid load level, storage and distributed generation characteristics play a key role in determining attack success. Moreover, a mitigation method based on distributed control is proposed and investigated. A co-simulation platform based on OPAL-RT real-time power system simulator and OPNET communication network simulator using the System-in-the-loop feature is employed to validate the analytical results and discussions.

This paper presents a spreadsheet-based decision support system (DSS) for any parameter optimization problem, in the small- and medium-sized enterprises to help the managers to make better decisions. Microsoft Excel is used as a DSS development platform. The DSS application requires the quality characteristics and the level of parameters affecting the problem. The proposed system considers three multi-criteria decision-making methods: TOPSIS, VIKOR and GRA. These methods are integrated into the Taguchi method to convert the multi-response optimization problem to a single-response problem. The DSS suggests proper Taguchi experimental designs and provides the decision maker with an opportunity to use different metrics and to validate the experimental results. Several issues and an application are provided for illustrative purposes. The proposed DSS is tested on a case study (the performance of the mixed integer programming (MIP) formulation solver) and the results highlight that the system is capable of offering satisfactory outcomes. Using such a quick and flexible DSS might help to reduce the daily workload of the decision makers. The different metrics used for the response variables which results with the different parameter combination. Using the optimal parameter combination of TOPSIS (come to the fore in case MinBest metric used), the MIP formulation solver gives the best integer objective function value of 609 and a GAP value of 1.93%, both of which are less than the values obtained using the other methods. Using the optimal parameter combination of GRA (come to the fore in case OptBest metric used), the MIP formulation gives a best integer objective function value of 632 and a GAP value of 6.52%, both of which are less than the values obtained by using the other methods.

The random and intermittent nature of renewable energy creates challenges for power systems to cope with sudden disturbances and extreme events. This study establishes a system network model and cascading failure model that consider the power flow relationship between different power sources, and then the impact of renewable energy on power system resilience is analyzed based on complex network theory. Furthermore, several resilience evaluation indexes are proposed from structural and functional perspectives. Using the system model, a resilience curve suitable for renewable energy power systems is proposed. The electrical degree centrality is used as the index to identify key nodes and simulate random attack and deliberate attack modes. The effectiveness of the evaluation method is verified on the IEEE 118-bus system using the typical time, different access ratios, and distribution characteristics of renewable energy. The results indicate that with high penetration of renewable energy, power systems’ resilience may decline by more than 20% in most cases.

Various fault ride-through (FRT) strategies have been proposed to constrain the maximum current during faults to levels below predefined thresholds for grid-forming (GFM) inverters, as current limiting is the primarily required FRT capability due to its direct impact on the security of inverter semiconductors and the resilience of power systems. Additionally, the latest IEEE standards and grid codes also mandate other FRT capabilities in terms of voltages, currents, and powers to further enhance the safety, stability, and resilience of power systems. However, few existing studies have comprehensively summarized these FRT capabilities and proposed effective quantification metrics to assess them. To address these gaps, this paper presents a thorough summary of the FRT capabilities of GFM inverters and introduces a set of quantification metrics to completely evaluate these capabilities, which can also indirectly quantify the FRT capabilities' impacts on power system resilience. These metrics not only enable real-time tracking but also provide a quantitative basis for comparing distinct FRT capabilities across various FRT control strategies. Furthermore, this paper also proposes a comprehensive metric that integrates the weighted contributions of all proposed quantification measures to guide the selection of the most appropriate FRT strategy. Finally, experiments in a single GFM inverter system and simulations in large-scale power systems involving four FRT strategies demonstrate the effectiveness of the proposed quantification metrics in assessing the FRT capabilities and identifying the most suitable FRT strategy of GFM inverters under grid fault conditions.

Power systems and microgrids resilience enhancement strategies: A review

Power system resilience, defined as its readiness to fulfill society’s electricity needs, is analyzed by examining differing approaches to its assessment in peaceful and wartime conditions. It is noted that periodic massive attacks on power systems lead to their gradual degradation and eventual collapse. The circumstances influencing the scale of power system bombings during 20th-century wars are examined, and the current vulnerability of power systems in Eastern European countries is highlighted. The consequences of systematic missile and drone attacks on Ukraine’s power system in 2024 are assessed, and the destroyed facilities are categorized by the extent of their damage. Restoration efforts are characterized by the duration of repair works. The characteristics of power facility destruction and the duration of repair work are incorporated into an equation modeling the dynamics of generating units available for use in the current period. To assess the resilience of Ukraine’s power system, a cluster model for load modes of power facilities was applied. In this model, similar power facilities were grouped into clusters, and instead of traditional binary variables, integer variables were used to describe discrete states of startup, loading, and shutdown. Using the proposed cluster model enabled the reproduction of hourly load modes of the main types of generating equipment in Ukraine’s power system throughout 2024 and the evaluation of its resilience on a monthly basis. The presented modeling results demonstrate the adequacy of the cluster model of Ukraine’s power system when compared to actual data obtained from open publications. Key challenges in assessing the resilience of power systems functioning under systematic large-scale attacks are outlined, including anticipated attack strategies—their periodicity, scale, and targeting—dynamics of air defense system effectiveness in protecting power facilities, scheduled commissioning of protective structures with varying levels of protection, dynamics of the effectiveness of backup mechanisms, and the sufficiency of resources for repair work. The proposed cluster model is capable of addressing these pressing challenges.

The frequency of extreme events (e.g., hurricanes, earthquakes, and floods) and man-made attacks (cyber and physical attacks) has increased dramatically in recent years. These events have severely impacted power systems ranging from long outage times to major equipment (e.g., substations, transmission lines, and power plants) destructions. This calls for developing control and operation methods and planning strategies to improve grid resilience against such events. The first step toward this goal is to develop resilience metrics and evaluation methods to compare planning and operation alternatives and to provide techno-economic justifications for resilience enhancement. Although several power system resilience definitions, metrics, and evaluation methods have been proposed in the literature, they have not been universally accepted or standardized. This paper provides a comprehensive and critical review of current practices of power system resilience metrics and evaluation methods and discusses future directions and recommendations to contribute to the development of universally accepted and standardized definitions, metrics, evaluation methods, and enhancement strategies. This paper thoroughly examines the consensus on the power system resilience concept provided by different organizations and scholars and existing and currently practiced resilience enhancement methods. Research gaps, associated challenges, and potential solutions to existing limitations are also provided.

Power systems are susceptible to natural threats including hurricanes and\nfloods. Modern power grids are also increasingly threatened by cyber attacks.\nExisting approaches that help improve power system security and resilience may\nnot be sufficient; this is evidenced by the continued challenge to supply\nenergy to all customers during severe events. This paper presents an approach\nto address this challenge through bio-inspired power system network design to\nimprove system reliability and resilience against disturbances. Inspired by\nnaturally robust ecosystems, this paper considers the optimal ecological\nrobustness that recognizes a unique balance between pathway efficiency and\nredundancy to ensure the survivability against disruptive events for given\nnetworks. This paper presents an approach that maximizes ecological robustness\nin transmission network design by formulating a mixed-integer nonlinear\nprogramming optimization problem with power system constraints. The results\nshow the increase of the optimized power system's robustness and the improved\nreliability with less violations under N-x contingencies.\n

The Unit Commitment Problem (UCP) is a critical component of power market decision-making and is typically formulated as Mixed Integer Programming (MIP). Given the complexity of solving MIPs, efficiently solving large-scale UCPs remains a significant challenge. This paper presents a hybrid Graph Neural Network (GNN)–Linear Programming (LP) framework to accelerate the solution of large-scale Unit Commitment Problems (UCPs) while maintaining the quality of solutions. By analyzing variable stability through historical branch-and-bound (B&amp;B) trajectories, we classify MIP variables into dynamically adjustable stable and unstable groups. We adopt an MIP formulation that includes multiple types of binary variables—such as commitment, startup, and shutdown variables—and extract additional information from these auxiliary binary variables. This enriched representation provides more candidates for stable variable fixation, helping to improve variable refinement, mitigate suboptimality, and enhance computational efficiency. A bipartite GNN is trained offline to predict stable variables based on system topology and historical operational patterns. During online optimization, instance-specific root LP solutions refine these predictions, enabling adaptive variable fixation via a dual-threshold mechanism that integrates GNN confidence and LP relaxations. To mitigate suboptimality risks, we introduce temporally flexible fixation strategies—hard fixation for variables with persistent stability and soft fixation allowing limited temporal adjustments—alongside a GNN-guided branching rule to prioritize unstable variables. Numerical experiments demonstrate that jointly fixing commitment, startup, and shutdown variables yields better performance compared to fixing only commitment variables. Ablation studies further validate the importance of hard fixation and customized branching strategies, especially for large-scale systems.