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This paper proposes a modeling approach for characterizing the probability of wildfire ignition caused by faults on power distribution systems. The proposed model serves as a starting point in research literature to illustrate, from an analytical perspective, the many factors that influence wildfire ignitions in power distribution systems. This paper presents the series of events that leads to power-system-related wildfire ignitions, and characterizes the wildfire ignition probability as a combination of the probability that a fault occurs along a power distribution line segment, and the probability that the fault results in the sustained ignition of a vegetation fuel bed surrounding the line. The proposed model integrates a variety of data including environmental conditions, power system protection settings, and power system line flows. A case study is performed on the IEEE 33-bus distribution system using observed historical weather data from a high-threat fire district in California. The California case study is utilized to investigate the effects of three primary factors (wind speed, line congestion, and relay protection) on wildfire ignition probability.

A challenging problem facing AC-Quasi-Steady-State (AC-QSS) cascading failure models of power system is the divergence issue primarily stemming from voltage collapse phenomena. In reality, there are undervoltage load shedding (UVLS) relays, which aim to prevent such a collapse by shedding a pre-specified fraction of load at buses where the corresponding voltages fall below a threshold. However, capturing the UVLS action in QSS models is very difficult, because most of the time the model cannot generate an equilibrium below the voltage threshold due to divergence. To address this problem, current models have applied different variants of uniform load shedding (ULS) till convergence is achieved, which differ from the ground truth. In order to solve this, we propose a methodology that leverages the post-ULS load flow as a starting point when divergence occurs. In this condition, a sensitivity index coupled with the voltage magnitudes of buses is used to recognize the buses that are most prone to voltage collapse. The UVLS scheme is then applied to these buses. To verify the accuracy of the results, we also present a suitable dynamic cascade model with appropriate limits and protection details that can selectively capture UVLS action, thereby revealing the proximate ground truth. Predictions of the proposed model are validated against those of the dynamic model for representative cases in IEEE 118-bus system. In addition, results of the proposed model are contrasted with two ULS schemes on the 2383-bus Polish system.

The allocation of fault current limiters (FCLs) is increasingly challenging in transmission systems these days. Specifically, the utilized deterministic expected short-circuit fault (SCF) scenarios are prone to cause over-configuration of FCLs. Moreover, the well-established local switching framework (LSF) renders inappropriate FCL switching and may further harm the system safe operation. Aiming at the above deficiencies, a novel 5G-based centralized switch FCL (CSF) framework as well as a method to allocate such flexible FCLs optimally is proposed in this paper. In the proposed CSF, the FCLs are switched by a FCL dispatching (FD) model considering system security constraints of both fault current and voltage sags. By exploiting the fast communication capability of 5G network as well as an off-line fault scanning strategy, the FD model is enabled to give online FCL switching schemes to meet the fast requirement of power system protection. Moreover, considering the probabilistic characteristic of SCFs, a bi-level FCL allocation model is established, in which the upper-level model sites and sizes FCLs considering the installation and expected switching costs while the lower-level model determines the optimal switched FCLs under each specific SCF scenario. Finally, numerical results are provided to verify the proposed allocation model, including its defending effect against SCFs in terms of fault current limiting, voltage sags relieving, as well as its cost-effectiveness. This work was supported in part by the China NSFC under Grant 51807173.

Symmetrical components theory, presented by Fortescue in 1918, and the analysis of the time-domain presented by Lyon in 1954, have been widely used in fault analysis and power system protection algorithms. In recent times, applications in time-domain have been deeply studied given their potential for getting a quicker failure detection. There are two main techniques which apply signal processing methods in the time-domain: Travel-wave and incremental quantities. This article presents a new algorithm that allows detecting direction and gives an indication for a fault location based on the calculation of the symmetrical components and processing them as incremental quantities. The algorithm is tested in a simulation study case and on the data provided by a relay for a real-world fault.

Power system cascading failures become more time variant and complex because of the increasing network interconnection and higher renewable energy penetration. High computational cost is the main obstacle for a more frequent online cascading failure search, which is essential to improve system security. We propose a more efficient search framework with the aid of a graph convolutional network (GCN) to identify as many critical cascading failures as possible with limited attempts. The complex mechanism of cascading failures can be well captured by training a GCN offline. Subsequently, the search for critical cascading failures can be significantly accelerated with the aid of the trained GCN model. We further enable the interpretability of the GCN model by a layerwise relevance propagation algorithm. The proposed method is tested on both the IEEE RTS-79 test system and China's Henan Province power system. The results show that the GCN-guided method can not only accelerate the search of critical cascading failures, but also reveal the reasons for predicting the potential cascading failures.

Contingencies such as faults, loss of generation or load may produce undesirable relay operations which can lead to cascade tripping causing system catastrophic failure. Thus, security of power system protection is a major concern for utilities. In this article, an approach based on system integrity protection scheme is proposed for enhancing the security of protection functions. Synchronous data measurements from strategic portions in the system are utilized for separating fault from stressed conditions. Determining the vulnerable relays (VR) which may maloperate during a stressed condition and incorporation of remedial strategy are proposed. It includes two algorithms; the first of which computes the relay margin to form a look-up table containing VR at different fault scenario and operating condition, in offline studies. Then, in accordance with the real-time system conditions, the relay characteristics are set for VRs based on the local information to avoid maloperation. The second is activated during critical heavy loading condition that may lead to voltage collapse and determines the load to be shed based upon sensitivity calculations of relay operation margin. The proposed method is tested for an IEEE-39 bus New England system as well as validated on real-time digital simulator (RTDS) platform for various operating scenarios and found to be robust. Thus, improvement in security of protection operation is achieved without compromising the dependability factor.

In this paper, a coupled interaction matrix is proposed to describe the interactions between line outages and the load shed at buses. The coupled interaction matrix is effectively estimated by the Expectation Maximization algorithm. A highly probabilistic coupled interaction model is further proposed to efficiently generate cascades with both line outages and the load shed based on the coupled interaction matrix and the distribution of initial outages. To mitigate cascading failures, critical links are identified based on the coupled interaction matrix by calculating a comprehensive severity index that considers the consequences of both line outages and the load shed. Simulation results on the IEEE 300-bus system verify the effectiveness of the proposed approach. The cascades generated from the coupled interaction model match the statistics of the original cascades very well. The identified critical links based on the comprehensive severity index enable a proper tradeoff between reducing line outages and reducing the load shed, leading to a better mitigation effect than only considering either line outages or the load shed.

Transmission line failure in power systems prop-agate non-locally, making the control of the resulting outages extremely difficult. In Part II of this paper, we continue the study of line failure localizability in transmission networks and characterize the impact of cut set outages. We establish a Simple Path Criterion, showing that the propagation pattern due to bridge outages, a special case of cut set failures, are fully determined by the positions in the network of the buses that participate in load balancing. We then extend our results to general cut set outages. In contrast to non-cut outages discussed in Part I whose subsequent line failures are contained within the original blocks, cut set outages typically impact the whole network, affecting the power flows on all remaining lines. We corroborate our analytical results in both parts using the IEEE 118-bus test system, in which the failure propagation patterns exhibit a clear block-diagonal structure predicted by our theory, even when using full AC power flow equations.

Most of today's smart grids are highly vulnerable to cascading failure attacks in which the failure of one or more critical components may trigger the sequential failure of other components, resulting in the eventual breakdown of the whole system. Existing works design different ranking methods for critical node or link identifications that fail to identify potential cascading failure attacks. In this work, we first consider the system from the attacker's point of view with a limited attack budget to study the smart grid vulnerability, referred to as Maximum-Impact through Critical-Line with Limited Budget (MICLLB) problem. We propose an efficient algorithm by considering the interdependency property of the system, called Greedy Based Partition Algorithm (GBPA) to solve the MICLLB problem. In addition, we design an algorithm, namely Homogeneous-Equality Based Defense Algorithm (HEBDA) to help reduce damages in case the system is suffering from the cascading failure attacks. Through rigorous theoretical analysis and experimentation, we demonstrate that the investigated problem is NP-complete problem and our proposed methods perform well within reasonable bounds of computational complexity.

Geomagnetic Disturbances (GMDs) are the result of solar storms or a high-altitude nuclear detonation. On the power systems, they might lead to the flow of quasi-DC currents referred as Geomagnetically Induced Currents (GICs). These currents cause the AC current offset that may drive the power transformers into saturation. This leads to large draw of reactive power, causes transformer internal heating and increased noise level, damage to shunt capacitors, harmonic filters and maloperation of power system protection equipment. This paper reviews the state-of-the-art of the GIC mitigation and elimination strategies and their respective limitations. It also introduces converter-based strategies as a new avenue of power system protection against GICs by presenting novel strategies that involve the integration of the proposed schemes between the neutral and ground of power transformers. One of the proposed schemes is a contribution to the approaches solely focused towards GIC mitigation, whereas, the other provides a variety of grid-support functions in addition to GIC elimination. The simulations performed in a Controller Hardware-in-the-Loop (C-HIL) environment verify the proposed schemes as a promising alternative to the current GIC mitigation approaches.

Accounts of extreme power outages of transmission systems suggest the acceleration of cascading outage propagation over time and the splitting of the cascade into a slow phase and a subsequent fast phase. This is significant to network operators, as mitigation actions, such as load shedding, can only be effectively applied during the slow phase. During the fast phase, the network disintegrates too quickly for any manual intervention. To supplement the accounts of extreme outages, we describe the observed acceleration of smaller and more common cascading outages by analyzing transmission outage data published by one North American utility. Our results show that these common cascades accelerate much less than the extreme cascades. This justifies ongoing research in mitigation strategies.

The protection of power system is an essential trait in a huge network to efficiently detect and isolate the sections undergoing faults or abnormal behaviour. The key components of a protection scheme include circuit breakers, relays, switchgears and fuses which employ communication from one station to another to achieve high-speed tripping. The automation of these components at the laboratory level using programmable logic controller (PLC) along with supervisory control and data acquisition (SCADA) system owns paramount importance for intelligent decision making, sensing, actuating, monitoring and maintaining the record in the host server. This paper discusses such a technique for conventional power system protection laboratory at a new level of development to promote a control system through PLC and SCADA. The control system has indication of over and under values of voltage, load and frequency, which can trigger malfunctioning of equipment and must be rectified. Furthermore, ground fault and inverse current indication are added to the system for monitoring and controlling purposes. The proposed system enhances the efficiency and safety of the expensive equipment and the personnel to the next level and also introduces new standards of automated protection schemes for modern technical institutes.

Power system protection and asset management have drawn the attention of researchers for several decades; but they still suffer from unresolved and challenging technical issues. The situation has been recently exacerbated in the wake of the ever-changing landscape of power systems driven by the growing uncertainty and volatility subsequent to the vast renewable energy integration, more frequent natural extreme events due to climate changes, increasing malicious cyberattacks, and more constrained transmission systems as the result of load growth and limited investments. On the opposite side, the proliferation of advanced measuring devices such as phasor measurement units, emerging electric and non-electric sensors, and Internet of Thing (IoT)-enabled data gathering platforms continually expand/nourish the databases; they hence offer unprecedented opportunities to take the advantage of data-driven techniques. Machine learning (ML) as a principal class of artificial intelligence is the perfect match solution to this need and has newly revoked many researchers’ interests to tackle the problems excluding their exact/detailed models. This paper aims to provide an overview on applications of ML techniques in power system protection and asset management. This paper elaborates on issues pertaining to (1) synchronous generators, (2) power transformers, (3) transmission lines, and (4) special and system-integrity protection schemes. In addition to the opportunities offered by the ML techniques, this paper discourses on the barriers and challenges to the wide-spread application of ML techniques in real-world practices.

Cascading failure simulation data contain many fault chains (FCs), which can present cascading failure propagation paths. In cascading failure process, some component outages play dominating roles in propagation, indicating the common characteristics among different FCs. The commonness is embodied as combinations of components which are vulnerable to trip and cause serious blackout consequences. In addition, a component outage will increase the outage probability of relevant components and induce dependent outage in subsequent stage. Such relevance between two components can be called component outage causality. A combination of sequential component outages with outage causalities, which exists in different FCs and leads to system load loss, can be regarded as a cascading failure pattern (CFP). Statistical characteristics of FCs indicate that CFPs are variously distributed in different FCs, can present propagation paths and cause different impacts on system blackouts. This paper proposes a cascading failure pattern (CFP) identification method based on sequential pattern mining approach. The proposed method focuses on mining CFPs from massive FCs, quantifies the influence of CFP on system blackout and identifies the critical ones. The proposed method is verified with FCs data on IEEE 39-bus and 118-bus test systems.

The protection of the electric power system (EPS) components such as synchronous generators, transformers, transmission lines, and substations is important because it allows having continuity in the electricity service when disturbances are present. It also avoids a possible permanent damage to the elements of the EPS. The relays monitor variables as voltages, currents, harmonics, frequency, active and reactive power. The function of the relay is to detect an abnormal operating condition, and with the aid of breakers a faulted equipment can be isolated by disconnecting only a small portion of the EPS, so that a small number of consumers are affected. The relay setting adjustment is important because it must operate in a safe, reliable and coordinated way. The above can be achieved by teaching to students the philosophy, theory, adjustments, and coordination of relays in an electrical network, and by using computer simulations a more effective teaching and learning can be achieved. However, to have a more complete contribution in learning the relay coordination philosophy, the usage of a laboratory is highly recommended. In this paper, a hybrid approach for teaching electric network protection is presented. It is aimed at undergraduate students of electric engineering and it is based on the use of computer simulation of mathematical models and laboratory experiments. To demonstrate the proposed teaching approach, computer simulations and lab experiments of an overcurrent inverse time relay were carried out in radial and parallel electrical networks where different case studies were successfully tested.

Given the decisive modernization of power systems and the evolution of protective relaying, it is imperative to merge traditional protection systems with innovative approaches that allow flexibility and time-domain protection. Time-domain approaches for power system protection must be tested in realistic and flexible platforms prior to their actual implementation. Inexpensive and flexible testing platforms are needed to fill this gap; consequently, a hardware-in-the-loop (HIL) testing platform for a distance relay for feeder protection is presented in this article. The relay is tested in an HIL simulation of a single-machine infinite-bus system simulated in PSCAD software, and the distance protection function is implemented in a commercially available LAUNCHXL-F28379D microcontroller. One-phase-to-ground, two-phase-to-ground, two-phase, and three-phase faults are tested in the simulation system, showing the feasibility of the proposed approach for protection system testing.

The success of a power system protection scheme so much depends upon the optimal coordination of its different units, which are protective relays. The task of finding the optimal set of relay parameters or settings can be achieved by solving a nonlinear and highly constrained optimization problem. This paper develops a new variable neighborhood search (VNS) algorithm as a potent tool for coordinating the controlling parameters of directional overcurrent relays (DOCRs), particularly the current settings and tripping times. VNS is an optimization algorithm which works based on a systematic change of neighborhood while searching the optimal solution of a given problem in both descent and perturbation phases. The performance of the proposed VNS-based algorithm is demonstrated on the 8-bus, 9-bus and 15-bus power system networks with diverse scenarios. The obtained outcomes are compared with other competitive customary algorithms. Thus, the superiority of the proposed technique is validated in coordinating the DOCRs for better protection of the power system.

The frequent occurrences of cascading failures in power grids have been receiving continuous attention in recent years. An urgent task for us is to assess the vulnerability of power grids against various kinds of attacks, which trigger cascading failures. In this brief, we formulate a cost-constrained hybrid attack in power grids, where both nodes and links are targeted with a limited total attack cost. Based on the consequence and cost of removing a component (node or link), we propose an attack centrality metric for components, which can be either local or global depending on the depth of cascading failures. We further propose a greedy hybrid attack and another optimal hybrid attack by applying the attack centrality. Simulation results on IEEE bus test data demonstrate that the optimal attack is more efficient than the greedy one. Furthermore, we find, counterintuitively, that the local centrality based attack algorithms perform better than the global centrality based ones when attack cost is a concern. Our work can help in the robustness optimization of power systems by revealing the worst-case attack vulnerability and most vulnerable components.

Electric power systems are prone to disturbances and contingencies, which can trigger cascading failures with severe consequences for society. These undesirable events could disintegrate the electrical infrastructure in areas with disconnected elements. In this article, we propose a novel procedure to restore a collapsed power grid composed of multiple islands and isolated assets. The framework developed identifies the power lines to be closed during the electrical network recovery stages. In the latter, link overload limits and generation thresholds are taken into account. Two disintegrated networks based on the well-known IEEE 57-bus test system are built to demonstrate the performance of our proposal. In summary, this methodology provides a solution to recover the power system optimally and reliably.

In coupled networks, a small number of node failures will cause large-scale cascading failures of the whole networks, so coupled networks are more fragile than the general networks. We find that there are some fragile dependency links with high centrality nodes at both ends between coupled sub-networks. Once damaged, it will cause serious cascading failures. Therefore, we propose a method to enhance the robustness of coupled networks by removing key fragile dependency links. First, based on the node centrality, we propose the dependency link centrality product index, analyze the potential destructiveness of fragile dependency links and find the key fragile dependency links. Second, based on removing key fragile dependency links, the risk of cascading collapse after network failures is reduced and the robustness of coupled networks is improved. Compared with the existing removing random dependency links strategy, removing key fragile dependency links strategy proposed in this brief can make coupled networks more robust via removing fewer dependency links, thereby retaining most of the dependency links and better maintaining the network integrity and functionality. The numerical simulation results on three interdependent networks show the effectiveness of this strategy.

This article provides a framework for modeling and analysis of spatial cyber-physical power systems (CPPSs). Previous studies on structural vulnerability analysis of CPPS mainly focused on network topology without any spatial information. In this article, we first propose a hierarchical information system evolution model for spatial power grids. Then, a spatial CPPS model is established by combining power and information systems that accounts for overlapped power and information lines. Finally, the structural vulnerability under global and localized failures is investigated based on direct current (dc) power flow. Under global failures, different types of components have distinguishing effects, and the power-node failure is the most serious case. For localized failures, key zones can be identified by the cascading failure scale, and similarly, different failure modes affect different areas. Furthermore, considering power system scenarios with only defenders and those with both attackers and defenders, we investigate two resource allocation situations. For defenders, increased resources and appropriately dispersed allocation can work effectively. However, in the attack–defense scenario, the perfect subgame equilibrium suggests that both attackers and defenders must concentrate all their resources on the most vulnerable zone. These findings may establish a foundation for future efforts to model and protect spatial CPPSs.

Integration of Distributed Generation (DG) on distribution networks has a positive impact which includes the following: low power losses, improved utility system reliability and voltage improvement at buses. A real distribution network is radial in which energy flow is unidirectional from generation to transmission and from distribution to the load. However, when a DG is connected to it, the power flow becomes bidirectional, and the protection setting of the network may be affected. Therefore, the aim of this research work is to investigate the impact of distributed generation DG on power system protection. The test distribution network is first subjected to load flow analysis to determine its healthiness with and without DG connection. The load flow results confirm that the integration of the DG into the distribution network reduces the active power load loss by 92.68% and improves voltage profiles at each bus of the network by 90.72%. Thereafter, the impact of DG on the protection setting of the existing test network was investigated. Integrating DGs to the network, from our result, shows an increase in the fault currents, which in turn caused false tripping, nuisance tripping, and blinding of protection relay compared with when DGs are not connected. The protection relays were reset at the point of common coupling (PCC) to prevent any abnormal tripping. This is the major contribution of the research work

The highly intricate inter-connectivity and ever expanding scale of modern power grids have raised serious concerns on security and vulnerability of power grids. Much of the recent study on the vulnerability of power grids to cascading failure has focused on the structural changes or functional damage of the system, and results from previous studies often draw inconsistent and even contradictory conclusions. In this paper, the causes of these diverse and inconsistent results relating to structural and functional damages have been identified. In addition, the system’s vulnerability to cascading failure is studied from an attacker’s perspective, and a node attack strategy maximizing structural and functional damage is considered. Specifically, the problem of finding the optimal node attack strategy is formulated as a multi-objective optimization problem, and evolutionary algorithms are used to generate optimal solutions. Simulation results on four benchmark test systems show significant advantages of the proposed algorithms over heuristic and single-objective methods, and give important insights on identifying the critical nodes affecting vulnerability of power grids.

Current research on cascading failures of wireless sensor networks (WSNs) mainly focuses on single-sink networks and rarely involves multisink networks. To this end, this article proposes a realistic cascading model for multisink WSNs based on a new load metric “multioriented link betweenness.” On this basis, a memetic algorithm MA-MSP is proposed to help WSNs resist cascading failures via multisink placement optimization, in which the local search operator is designed based on a new network balancing metric “multioriented network entropy.” Extensive simulations have shown that the proposed cascading model can properly characterize the cascading process of multisink WSNs. Link capacity is a key factor in determining network robustness. MA-MSP can obtain a more robust placement scheme with less time compared to existing algorithms. The network communication efficiency is positively related to network robustness, and the average shortest path length is negatively related to network robustness.

In this paper, real outage data from utilities are analyzed to gain better understanding of cascading outage propagation. In order to accurately estimate the interactions between component outages, two mechanisms are introduced: the evolution of interactions over generations and the memory between consecutive generations. A metric, the expected number of outages following one component outage, is calculated based on the estimated interaction networks by solving a set of carefully formulated linear equations, considering loops due to the complex component interactions. Existence of unique positive solution for the linear equations is mathematically proved. Components that are critical for outage propagation are further identified based on the developed metric. Besides, the outage propagation properties are revealed by the interaction networks estimated from real outage data. Further, the cascades simulated from a highly probabilistic generation-dependent interaction model using the estimated interactions well capture the properties of the original outage data in terms of the distribution of the number of line outages, the offspring mean of the branching process, the distribution of the component metrics, and the identified critical components. Cascading failure risks are greatly mitigated by reducing the probability that the identified critical components fail.

Inverter-Based Resources (IBRs), including Wind turbine generators (WTGs), exhibit substantially different negative-sequence fault current characteristics compared to synchronous generators (SGs). These differences may cause misoperation of customary negative-sequence-based protective elements set under the assumption of a conventional SG dominated power system. The amplitude of the negative-sequence fault current of a WTG is smaller than that of an SG. This may lead to misoperation of the negative-sequence overcurrent elements 50Q/51Q. Moreover, the angular relation of the negative-sequence current and voltage is different under WTGs, which may result in the misoperation of directional negative-sequence overcurrent element 67Q. This paper first studies the key differences between the WTGs and SG by comparing their equivalent negative-sequence impedances with SG's. Then, simulation case studies are presented showing the misoperation of 50Q and 67Q due to wind generation and the corresponding impact on communication-assisted protection and fault identification scheme (FID). The impact on directional element is also experimentally validated in a hardware-in-the-loop real-time simulation set up using a physical relay. Finally, the paper studies the impact of various factors such as WTG type (Type-III/Type-IV) and Type-IV WTG control scheme (coupled/decoupled sequence) to determine the key features that need to be considered in practical protection studies. The objective is to show potential protection misoperation issues, identify the cause, and propose potential solutions.

Distance and directional elements are widely used in power system protection. One of the used essential signals, having a substantial impact on proper operation, is polarizing voltage. During faults close to a protection relay, memory filters can be used to ensure the availability of this voltage. A basic assumption of these memory filters is that during a fault only an amplitude of a measured voltage changes rapidly and other parameters change very slow. The assumption is correct in power systems with an overwhelming share of traditional rotating generators. However, today, more and more energy sources are connected to power systems through inverters. Algorithms implemented in inverters can control parameters of output voltage so that they can be changed rapidly without any inertia. Therefore, a source of robust polarizing voltage is needed to ensure proper operation of distance and directional elements. The paper presents a method of a reference signal generation based on phase-locked loop (PLL). The algorithm consists of PLL with an adaptive notch filter, and elements adding inertia to the generated signal. The reference signal can be used as a polarizing voltage in protection elements. The paper describes all elements of the algorithm and presets operational tests.

In some conditions, the flux in the core of current transformers (CT) increases. If this increase in flux leads to saturation of the protective core, it can create a lot of problems in power system protection. One of the hardware solutions to prevent the occurrence of core saturation in CT is the fixed switched resistor demagnetization method. Due to disadvantages such as dependence on CT parameters and inefficiencies in severe core saturation, the use of this method has not been expanded. This paper proposes a new method to improve the fixed switched resistor demagnetization method. In the proposed method, instead of using a fixed resistor in the circuit topology, an adjustable resistor with an auxiliary transformer is used. In the previous method, the control process is based on flux estimation from the secondary terminal voltage. The control process in the proposed method is based on the second derivative of CT secondary current. To verify the effectiveness of the suggested method, first simulation is done using COMSOL and MATLAB softwares and then all necessary electronic and control circuitry are designed and built. Experimental test is carried out on a 20 kV- 500/5 A CT. The simulation and experimental results show that this method prevents the CT from saturation in case of short circuit faults. The main advantages of this method are independent to CT parameters and efficient in severe core saturation.

Cascading failure on complex networks has been extensively studied over the past decade. However, restoration of networks from cascading failure is still relatively unexplored. In this paper, we consider cascading failure in conjunction with the restoration process involving repairing the failed nodes in a sequential fashion. Depending on the availability of resources, we tackle the sequential recovery problem from two distinct approaches, namely, result-oriented and resource-oriented restoration approaches. In the result-oriented approach, we aim to restore the network to the largest extent and within the shortest time. Heuristic network restoration strategies based on node load or degree are proposed. For resource-oriented restoration, we aim to maximize the increase of network size with a given number of nodes to be repaired, and we propose a novel iterative strategy to improve performance. Simulation results on the Barabasi–Albert scale-free network, Internet autonomous system-level network, and IEEE 300 bus power system have demonstrated the effectiveness of the proposed sequential recovery strategies.

Severe weather events can trigger cascading power outages and lead to significant losses. In this work, we investigate cascading outage mitigation under severe weather conditions. Given day-ahead weather forecasts and component failure models, we aim to identify a set of power lines that can be hardened to minimize the expected impact of potential cascading outages. Since the expected load shedding cannot be expressed as an explicit function of line hardening decisions and system states, we developed a cascading outage simulator to estimate the expected value of load shedding under various initial weather-related disruption scenarios generated using a weather forecast. To avoid massive enumeration of all possible combinations of line hardening decisions and reduce the simulation efforts, we employed an efficient simulation-based optimization approach that quickly identifies the (near) optimal line hardening decisions in the presence of both large simulation noises due to the highly variable initial disturbances and system states, and significant randomness in the subsequent cascades. The algorithm is also able to utilize parallel computing to dramatically reduce computation time to support decision making in preparation for severe weather conditions. We performed a case study on the Northeast Power Coordinating Council (NPCC) 140-bus system model to demonstrate that our approach can significantly improve power grid resilience to adverse weather events.

Cascading failure inevitably emerges in complex power grids that can cause enormous economic losses. Over the past few decades, a great deal of effort has been devoted to failure cascade modeling, with the aim of understanding and preventing this complex process. Significant achievements include reproducing the uneven cascade propagation profiles and the power-law distribution of the size of the cascades. At the same time, power grids keep evolving, as driven by technology advancements and practical needs. Wide deployment of information technologies and high penetration of power electronics devices are two important features of future grids. These developments have profound influences on the cascading failure characteristics in future grids, which cannot be well addressed by existing models. In this tutorial, we provide an overview of the state-of-art approaches in studying cascading failure and discuss the strengths and weaknesses of these methods. The explicit changes brought by the new features to the failure cascade processes are analyzed and the limitations of existing approaches are identified. Challenges in the modeling and analysis of cascading failure and possible research directions targeting the future power grids in the next research phase are presented.

After major disturbances, power system behavior is governed by the dynamic characteristics of its assets and protection schemes. Therefore, modeling protection devices is essential for performing accurate stability studies. Modeling all the protection devices in a bulk power system is an intractable task due to the limitations of current stability software, and the difficulty in updating the setting data for thousands of protection devices. One of the critical protection schemes that is not adequately modeled in stability studies is distance relaying. Therefore, this paper proposes an iterative algorithm that uses two methods to identify the critical distance relays to be modeled in stability studies: (i) apparent impedance monitoring, and (ii) the minimum voltage evaluation (MVE). The algorithm is implemented in Python 3.6 and uses the GE positive sequence load flow analysis (PSLF) software for performing stability studies. The performance of the algorithm is evaluated on the Western Electricity Coordinating Council (WECC) system data representing the 2018 summer-peak load. The results of the case studies representing various types of contingencies show that to have an accurate assessment of system behavior, modeling the critical distance relays identified by the algorithm suffices, and there is no need for modeling all the distance relays.

Urban rail transit has become an important traffic mode in large cities and has brought great conveniences to urban residents, however traffic accidents often occur in daily operations, therefore the safety and robustness must be paid more attention. In this paper, the network utilization of urban rail transit networks (URTNs) is expressed by the travel time difference between user equilibrium and optimal system, and the travel time difference is considered as the assessment indicator of robustness. Meanwhile, Shanghai metro network is taken as the example to analyze the robustness of URTNs under different disturbances, such as node attack, link-demand attack and overall-demand attack. The results show that URTNs have better robustness subjected to the random link-demand attack than node attack, and the robustness decreases with the increase of the attack intensity when the network suffers overall-demand attack. Moreover, we find that the critical stations and links can be identified, and URTNs can be paralyzed when the attack intensity exceeds the critical threshold.

Many real-world networks have scale-free characteristics and can be abstracted into scale-free networks. Aiming at the problem that scale-free networks have low fault tolerance in the face of malicious attacks, we focus on the selective forwarding attack behavior that exists widely in the networks, and build a selective forwarding attack model based on node importance. Moreover, according to the neighbor node’s malicious and non-malicious behavior, a load redistribution strategy for failed node is proposed. Then, the network’s damage degree is given to evaluate the comprehensive impact of cascading failure phenomenon on network connectivity and information integrity under selective forwarding attack. Finally, a cascading failure model of scale-free networks considering selective forwarding attack behavior is obtained. Based on this model, the propagation condition without triggering network cascading failure, the selective forwarding attack intensity threshold and the load loss ratio are obtained. By simulation on the classical BA scale-free network model, the results show that multiple nodes’ random failure occurs in scale-free networks, selective forwarding attack behavior is helpful to improve the connectivity of the network. Besides, the network exists selective forwarding attack intensity threshold, when attack intensity is greater than the intensity threshold, the malicious nodes will not fail because of the failure of the neighbor nodes. But, selective forwarding attack behavior can destroy the information integrity, and there is a negative correlation between the attack intensity and the information integrity. These results have certain guiding significance for cascade failure analysis and prevention method research and design in real life.

Harmonic phasor estimation can be used both in power system protection and monitoring applications, such as islanding detection, high-impedance fault location, and harmonic state estimation. A key challenge for harmonic phasor estimation is that different harmonics have different harmonic frequency bandwidths. As a result, a harmonic phasor estimator (HPE) that can adapt to such variations is needed. Although the sinc interpolation function-based estimator (SIFE) has such ability, it has disadvantages that: 1) it needs numerous simulations to select the model parameter and 2) it cannot obtain zero-error results under nominal frequency condition. In this article, a novel HPE is proposed based on the frequency-domain sampling theorem, where the harmonic phasor is modeled based on several imaginary exponential functions. The proposed HPE is compared with the SIFE in frequency response, model parameter selection scheme, and simulation tests. The results show that the proposed HPE has the following three advantages: 1) it has an easier scheme for model parameter selection; 2) it has zero-error results under nominal frequency condition; and 3) it has higher accuracy under harmonic frequency deviation and harmonic modulation conditions.

Metro network is the important lifeline in modern cities. Its stability and reliability are critical for guaranteeing the urban residents' efficient commuting and continuous operation of urban functions. A series of disruptions show the vulnerability of metro network, and even the breakdown of a single node is sufficient to collapse the entire network due to cascading failure. However, the vulnerability assessments of metro network in the previous studies neglect the impact of cascading failure on the drop of network service performance. This paper measures the vulnerability of metro network by capturing the demand loss and travel delay under cascading failure. First, a load-capacity based model is developed to describe the dynamic process of cascading failures. Then, a weighted composite index composed of demand loss and travel time delay under cascading failure is used to measure metro network vulnerability. Finally, taking Shanghai metro network as an example, five attack scenarios are simulated to investigate cascading failure process and network vulnerability. The results reveal that cascading failures result in severe consequences in the metro network. The vulnerability of metro network without considering cascading failure is underestimated. The decrease in the tolerance parameter leads to the increase in metro network vulnerability. Random attack on one node is the most sensitive to the tolerance parameter. Node betweenness, cascading failure path and the initial load on the overloaded nodes also affect metro network vulnerability. This study provides a new perspective for understanding vulnerability of metro network, and also provides insights for improving operation reliability and stability of the network, as well as for designing emergency strategies to protect the network.

The collapse of circuits is usually a cascading failure rather than a simple failure event. It is usually difficult to model this kind of failure due to the complex structural and functional coupling. In this article, the impedance network is introduced as a prototypical model for characterizing the cascading failure of the circuit. A current-flow redistribution approach is proposed to analyze the cascading failure mechanisms of the circuits. Specific current-flow redistribution factors for two typical failure modes, i.e., the open circuit and short circuit, are put forward to determine the effect of the failed component on the remaining components. A health confidence value is further introduced to assess the health status of the impedance network. Then, a simulation framework for cascading failure propagation is proposed to capture the dynamic failure process. Finally, an example is presented to show the cascading failure behavior. The proposed model is also validated by comparing the obtained results with those of the SPICE software simulation.

Cascading overload failures occurred in power systems due to higher penetration of renewable energy resources (RERs), which causes uncertainty in a grid. To overcome these cascading overload failures, proper assessment in the form of load flow balancing and transients stability is required in renewable integrated power grids (RIPGs). This problem becomes more critical in the occurrence of multiple intervals faults in multiple interconnected RIPGs, which causes the tripping of several RERs. Due to which outages occurred in various transmission lines, which lead the power system to cascading overload failures. To tackle this problem, hybrid probabilistic modeling is proposed in this paper for balancing load flow and an assessment of transients stability in multiple interconnected RIPGs. For balancing of load flow, a smart node transmission network topology is utilized along with integrating a unified power flow controller (UPFC), while transients instabilities are assessed through a UPFC alone. Contrary to the previously proposed algorithms, which are only suitable to compensate network instabilities in case of only a single interval fault, this work is supported by probabilistic modeling to compensate network instabilities under the occurrence of not only a single interval fault but also in case of more severe multiple intervals faults in multiple interconnected RIPGs that will lead the network to cascading failure outages. Simulation results verify that our proposed probabilistic algorithm achieved near an optimal performance by outperforming the existing proposed methodologies, which are only confined to mitigate the effect of network instabilities only in case of single interval fault and fails to address these network instabilities under the occurrence of severe multiple interval faults, which leads the network to cascading failure outages. These simulation results are also validated through an industrial case study performed on a western Denmark transmission network to show the superiority of our proposed algorithm.

A novel passive method based on Permutation Entropy (PE) is proposed for fast, efficient, and differential detection of islanding from other disturbance events in power system. The extremely remark...

Power systems are subjected to various types of faults as well as ferroresonance overvoltages. These results in the interruption of the normal operation of the power grid, failure of equipment, electrical fires, etc. To tackle these issues, this study proposes a dual function limiter to control the fault current and ferroresonance phenomenon in power systems. This compound device is a solid-state series transformer-based limiter that includes IGBT switches, capacitors, rectifiers, and a DC reactor. During the grid normal operation, the proposed limiter is not active and therefore is invisible and it operates in the instant of fault inception or ferroresonance overvoltage occurrences. Analytical studies in all operation modes are presented and assessments on the performance of the proposed ferroresonance and fault current limiter (FFCL) are conducted in Matlab. Simulation results confirm the reported analytical studies and FFCL's performance.

The dependency links in interdependent networks can lead to serious cascading failures when some of the network nodes are damaged. We find that the imbalance between nodes at both ends of the dependency links is one of the important reasons for a cascade of failures, which can be reduced as a whole to improve the robustness of the networks. Therefore, we propose a method to improve the robustness of interdependent networks by reducing key unbalanced dependency links. Firstly, we propose the dependency link imbalance index ( DLI ), which denotes the degree difference between nodes at both ends of a dependency link. And then we sort the dependency links in descending order according to the index value. The small number of the dependency links whose index values are in the forefront are called key unbalanced dependency links. By removing the key unbalanced dependency links, the imbalance of dependency links in interdependent networks is reduced in the mass, and the robustness of the networks is improved. Compared with the present random dependency links reduction strategy ( RRS ), key unbalanced dependency links reduction strategy ( KURS ) proposed in this brief can maintain the integrity and functionality of interdependent networks and improve more robustness while reducing fewer dependency links. Numerical simulations on three interdependent networks verify the effectiveness of key unbalanced dependency links reduction strategy proposed in this brief.

Conversation and assurance issues play a crucial function when talking regarding to the wise grid. This particular paper presents opportunities of testing power framework assurance transfers and correspondence standards for smart supply. A depiction in the Smart Grid lab hardware and the key protection devices is usually presented in the paper. Further employ cases and uses offered by the Labrador equipment are referred to and the possibilities by dynamically setting up devices and program interaction are demonstrated. Ideas for the mix of checked and controllable decentralized vitality sources are demonstrated the network capacity and Quality of Services (QoS) are tested and evaluated. By implementing adaptive modulation scheme, the served users were increased by 10% at heavy Traffic Load (TL).

This study presents a new index for fast and reliable protection of the synchronous generator (SG) against loss of field (LOF) incidence, focusing on the operation time, reliability in clustering LOF, power system disturbance (PSD), and practical application. To this end, all allowable electrical parameters at SG output are acquired and thoroughly analysed. Analytical analysis of the parameters indicates that reactive power (Q SG) and load angle (δ SG) parameters have better conditions to improve the mentioned factors. Hence, based on the δ SG increment and Q SG decrement during LOF events, a new index based on the ratio of deviations of the δ SG over Q SG (Δδ SG /ΔQ SG) is proposed as a suitable criterion owing to remarkable fast sensitivity to LOF and PSD events. In the proposed algorithm, analysis of the events by the proposed Δδ SG /ΔQ SG index is dependent on ΔV SG

Load redistribution (LR) attacks represent a major cyber threat to the power grid that can result in branch overloads and even cascading failures in the transmission network by injecting false data to load bus power injection and line power flow measurements. While the mechanism and defense strategies have been well studied for single-occurrence (i.e., discrete) LR attacks, this paper focuses on a yet unexplored category of LR attacks, namely, the continuous LR (CLR) attack, which continuously injects time-varying false data to one or more bus and branch measurements within the system for a certain period of time. To cope with the potentially ever-changing targeted branches (i.e., the branches under attack) and system vulnerability features caused by CLR attacks, this paper takes a different route from the traditional LR defense and mitigation approaches. We propose a novel correlation chain model to capture the vulnerability correlations among branches under the CLR attack. Then, a dynamic sequential-mining algorithm (DSMA) with top-k structure is proposed based on the specific nature of the CLR attack, to mine the historical SCADA measurement database, extract vulnerable branch sequences, and identify the most suitable branches to defend preventively. Simulation studies are conducted on IEEE RTS-96 system to evaluate the effectiveness of the proposed approach in terms of increasing attack costs for the attackers and reducing the potential impacts of CLR attacks.

Power system protection has become an essential challenge with the development of the power system. This study presents a new method in detecting a power swing based on compressed sensing. The proposed method is tested on the IEEE 39-bus network using MATLAB and DIgSILENT software. The simulation results show that the presented method is able to detect and differentiate between different types of power system conditions: stable, unstable, and multi-mode power swings. In addition, this method has a high speed in detecting the simultaneous fault with the power swing phenomenon. Moreover, the proposed method is capable of operating correctly despite noise signal in the system. This study has proven that the suggested method outperforms most of the existing methods as shown in the comparison section.

Many methods are available to analyze the process of the travelling-wave propagation. Among these methods, the Finite Difference Time Domain (FDTD) method has a distinct advantage in calculating dynamic process of the travelling wave propagation in the time domain and is thus applied to the field of power system protection for researching transient fault induced travelling-wave propagation. The novelty of this paper is that the attenuation law of the traveling wave signal affected by the fork junction in the multi-branch distribution network is summarized and the cause of failure in the fault location based on the incipient travelling wave front method in distribution networks is found.

The Electrical power system has become vast and more complex, so it is subjected to sudden changes in load levels. Stability is an important concept which determines the stable operation of the power system. Transient stability analysis has become one of the significant studies in the power system to ensure the system stability to withstand a considerable disturbance. The effect of temporary occurrence can lead to malfunction of electronic control equipment. The application of flexible AC transmission systems (FACTS) devices in the transmission system have introduced several changes in the power system. These changes have a significant impact on the power system protection, due to differences inline impedance, line current and voltage. On the distance relaying protection system to identify essential issues that protection engineers need to consider during the stages of design and operation of the protection system. Transient analysis can be conducted using a simulation software package. One of the commercial simulation software package used by industry worldwide is Siemens Power System Simulation for Engineering (PSS/E). The object of this work is to improve the Transient stability and to clear critical fault times of the Kurdistan Region Government (KRG) network by using optimal FACTS devices in different optimal locations under fault conditions.