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Intentional islanding is to determine proper network splitting strategy while ensuring local power balance and transmission capacity constraints when islanding operation is unavoidable. The intentional islanding problem is very complicated in general because a combinatorial exploitation of strategy space is required. This paper apply a topology analysis and genetic algorithm combined approach for determining proper splitting strategies of large-scale power networks. Topology analysis is used to simplify the original power network into a simple equivalent network so that the splitting strategy space world be dramatically reduced; while the genetic algorithm incorporated with the breadth-first search (BFS) is employed to determine the final proper splitting strategy in the simplified power network. Two additional applications, mimicking weak connections between islands and obtaining specific pre-defined islands, of the proposed method are introduced. Simulation results on several test system show that the proposed approach can quickly provide proper splitting strategies and is effective for larger-scale power systems.

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... Based on the research trends, the references that are relevant to "Where" subsection are classified in Table 2 [53], swarm-based [56], and hybrid meta-heuristic [59] algo- MILP [41], [42], [43] MINLP [56] OBDD Two-step [44] Three-step [45] Graph-based Slow Coherency [65], [66], [67], [68], [69], [70] Multi Objective [71] Multi Level [46] Minimum Cutset [47], [12] BFS&DFS [48] Branch and Bound [49] Prim Algorithm [50], [51] Dijkstra [49] Evolutionary-based and population-based algorithms MPSO [52] GA [53] Ant Search [54] PSO [56] Modified SFLA [55] Tabu Search [35], [72] ABC [13] CLPSO [59] FL-based methods [57] Machine Learning methods PSO+SOM [58] different Objective function Minimum Load shedding [41], [60], [61] Minimum power imbalance [62] Minimum power disruption [63] Minimum dynamic coupling [64] Combined method Topology analysis +GA algorithm [53] rithms have been used. In terms of objective functions, minimum Load shedding [41,60,61], minimum power imbalance [62], minimum power disruption [63] and minimum dynamic coupling [64] are mostly considered. ...

... Based on the research trends, the references that are relevant to "Where" subsection are classified in Table 2 [53], swarm-based [56], and hybrid meta-heuristic [59] algo- MILP [41], [42], [43] MINLP [56] OBDD Two-step [44] Three-step [45] Graph-based Slow Coherency [65], [66], [67], [68], [69], [70] Multi Objective [71] Multi Level [46] Minimum Cutset [47], [12] BFS&DFS [48] Branch and Bound [49] Prim Algorithm [50], [51] Dijkstra [49] Evolutionary-based and population-based algorithms MPSO [52] GA [53] Ant Search [54] PSO [56] Modified SFLA [55] Tabu Search [35], [72] ABC [13] CLPSO [59] FL-based methods [57] Machine Learning methods PSO+SOM [58] different Objective function Minimum Load shedding [41], [60], [61] Minimum power imbalance [62] Minimum power disruption [63] Minimum dynamic coupling [64] Combined method Topology analysis +GA algorithm [53] rithms have been used. In terms of objective functions, minimum Load shedding [41,60,61], minimum power imbalance [62], minimum power disruption [63] and minimum dynamic coupling [64] are mostly considered. ...

... Based on the research trends, the references that are relevant to "Where" subsection are classified in Table 2 [53], swarm-based [56], and hybrid meta-heuristic [59] algo- MILP [41], [42], [43] MINLP [56] OBDD Two-step [44] Three-step [45] Graph-based Slow Coherency [65], [66], [67], [68], [69], [70] Multi Objective [71] Multi Level [46] Minimum Cutset [47], [12] BFS&DFS [48] Branch and Bound [49] Prim Algorithm [50], [51] Dijkstra [49] Evolutionary-based and population-based algorithms MPSO [52] GA [53] Ant Search [54] PSO [56] Modified SFLA [55] Tabu Search [35], [72] ABC [13] CLPSO [59] FL-based methods [57] Machine Learning methods PSO+SOM [58] different Objective function Minimum Load shedding [41], [60], [61] Minimum power imbalance [62] Minimum power disruption [63] Minimum dynamic coupling [64] Combined method Topology analysis +GA algorithm [53] rithms have been used. In terms of objective functions, minimum Load shedding [41,60,61], minimum power imbalance [62], minimum power disruption [63] and minimum dynamic coupling [64] are mostly considered. ...

Blackouts or cascade failures are costly events which may threaten the integrity of electrical energy systems. The Intentional Controlled Islanding (ICI) is the last measure to reduce the undesirable technical, economic and social consequences of a blackout. In case of an emergency, the ICI of Distributed Generation (DG) units is a solution to preserve reliable power supply in a smart distribution grid. In this paper, three important aspects of ICI problem, namely the proper time of ICI (When), its optimal boundary (Where), and its execution method (How) are comprehensively reviewed. After reviewing the basic algorithms and procedures, to find the best (optimal) time, boundary and execution details, the different methods of the mentioned aspects are summarized
and discussed. Finally, a discussion about current challenges and future trends
of ICI in smart power systems (in distribution and transmission levels) are provided and moreover, a generalized framework for implementation of ICI in Active Distribution Networks (ADNs) and smart microgrids are presented.

... A probabilistic search algorithm based on linear programming was proposed in [22] to solve the ICI problem with minimising the power imbalance, which started from some randomly selected initial points; however, the number of islands was predefined. A combination of graphbased method and optimisation technique was implemented in [23,24] first to simplify the large scale network and then optimise the objective function. Genetic Algorithm was utilised in [23] to find the boundaries with minimal load shedding. ...

... A combination of graphbased method and optimisation technique was implemented in [23,24] first to simplify the large scale network and then optimise the objective function. Genetic Algorithm was utilised in [23] to find the boundaries with minimal load shedding. Angle Modulated Particle Swarm Optimisation (AMPSO) technique was employed in [25] to optimise a fitness function considering both the power balance of islands and the coherency index. ...

Intentional controlled islanding (ICI) is proposed to split the power system into a certain number of self-healing islands as the ultimate protective solution to avoid blackout after a large disturbance. Finding the separation boundaries and stabilising the created islands are two aspects of the ICI problem investigated in this paper. Most studies do not address the transient stability along with stability constraints in one framework. These studies ignore the impact of power flow disruption (PFD) on the stability of ICI. This study proposes a framework to solve the ICI problem in a timely manner by combining transient stability constraints with both frequency and voltage stability constraints. Transient stability is addressed in the first stage. A Mixed Integer Linear Programming (MILP) model of islanding is formulated to minimise the PFD caused by network splitting. In the second stage, which deals with the frequency and voltage stability of islands, a multi-stage Linear Programming (LP) algorithm determines the final generation-load adjustments necessary to be undertaken in each island after splitting to achieve acceptable voltage and frequency levels. The proposed multi-stage algorithm employs a frequency stability constraint as well as an indicator of risk of voltage instability to improve both voltage and frequency stabilities, while they meet power balance and operational limit constraints. The efficiency of the proposed algorithm is verified by using the New England 39-bus, and IEEE 118-bus systems. It is illustrated that the proposed method can create more stable islands with short computation times compared to other ICI methods with power imbalance as the primary objective.

... The ability of the power network to withstand such extraordinary events with a high impact, but a low probability, to "rapidly recover from such disruptive events, and adapt its operation and structure to prevent or mitigate the impact of similar events in the future" [4] is called resilience [5], [6]. One way to increase the network resilience is intentional islanding, which prevents cascading events by splitting the network into separated sections (islands), which are stable and self-adequate [4], [7]. By doing so, vulnerable components are isolated, while the remaining part of the grid is protected and can maintain operation. ...

... A number of publications deal with finding the best splitting strategy [7], [10]- [12]. Intentional islanding always comes at a cost, as some islands will no longer be able to supply their demand, and consequently, the load in these islands will have to be reduced. ...

... In Ref. [10], the model of distribution network is simplified, and a heuristic search strategy is adopted to determine the reasonable areas of different islands, considering controllability and levels of loads. In Ref. [11], the author treats intentional islanding as an integer nonlinear programming problem and uses the genetic algorithm to solve it, aiming at minimum power losses and unsupplied loads. In Ref. [12], the authors consider frequency and voltage stabilities in real time, and represent an ant search mechanism for optimal island separation of the distribution network. ...

... In conclusion, the existing methods mainly proceed from graph theoretic techniques, simplify the topology of power system to a tree graph with nodes and edges, model intentional islanding as a NP-hard problem [6][7][8][9][10][11][12][13][14][15], and solve it by some search algorithms. The essential attributes of distribution network, such as electrical distance and line parameters, are ignored in the solution, which may make the intentional islanding scheme inconsistent with the actual operation of the power system. ...

Intentional islanding is an effective approach to avoid large-area blackouts and minimize outage losses through making full use of renewable energy sources. This paper proposes a novel strategy based on node electrical relevance and artificial bee colony algorithm. The node electrical relevance is defined with equivalent electrical distance and traditional line weight, which can reflect the electrical characteristics of power systems, differentiating the proposed strategy from most existing strategies which are based on graph theory. The artificial bee colony (ABC) algorithm employed has fewer control parameters, strong robustness, and high accuracy; therefore, more loads can be incorporated into islands and restored. The constraints of load priority, load controllability, line capacity, and stable operation requirements of power systems are considered to tally with the actual distribution networks. The strategy is tested using the IEEE 69-bus distribution system and compared with other strategies from the literature. The simulation results demonstrate that the proposed strategy is more feasible and efficient. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

... Discrete particle swarm optimization is used to restore the CLPU by reducing the total power consumption and dividing the system into sections [5]. In [6], topology analysis and genetic algorithm are used to determine intentional islanding, keeping power balance and transmission constraint in bounds. In [7], FICO Xpress Optimizer is used to allocate the BS unit in the grid. ...

... Two important characteristics of GAs are the representation used (e.g., binary or real) and the genetic operators employed (e.g., mutation and crossover). GAs have been successfully applied to solve electrical problems [51][52][53]. ...

Symmetry is a key concept in the study of power systems, not only because the admittance and Jacobian matrices used in power flow analysis are symmetrical, but because some previous studies have shown that in some real-world power grids there are complex symmetries. In order to investigate the topological characteristics of power grids, this paper proposes the use of evolutionary algorithms for community detection using modularity density measures on networks representing supergrids in order to discover densely connected structures. Two evolutionary approaches (generational genetic algorithm, GGA+, and modularity and improved genetic algorithm, MIGA) were applied. The results obtained in two large networks representing supergrids (European grid and North American grid) provide insights on both the structure of the supergrid and the topological differences between different regions. Numerical and graphical results show how these evolutionary approaches clearly outperform to the well-known Louvain modularity method. In particular, the average value of modularity obtained by GGA+ in the European grid was 0.815, while an average of 0.827 was reached in the North American grid. These results outperform those obtained by MIGA and Louvain methods (0.801 and 0.766 in the European grid and 0.813 and 0.798 in the North American grid, respectively).

... As the community detection problem is highly complex, researchers have applied heuristics and meta-heuristics to obtain high quality solutions with a reduced runtime. In particular, GAs are selected because they have been used to solve many electrical problems [6,33,34,39,42]. In this study, two genetic algorithms have been adapted to solve community detection problems in power grids. ...

The large-scale interconnection of electricity networks has been one of the most important investments made by electric companies, and this trend is expected to continue in the future. One of the research topics in this field is the application of graph-based analysis to identify the characteristics of power grids. In particular, the application of community detection techniques allows for the identification of network elements that share valuable properties by partitioning a network into some loosely coupled sub-networks (communities) of similar scale, such that nodes within a community are densely linked, while connections between different communities are sparser. This paper proposes the use of competitive genetic algorithms to rapidly detect any number of community structures in complex grid networks. Results obtained in several national- scale high voltage transmission networks, including Italy, Germany, France, the Iberian peninsula (Spain and Portugal), Texas (US), and the IEEE 118 bus test case that represents a portion of the American Electric Power System (in the Midwestern US), show the good performance of genetic algorithms to detect communities in power grids. In addition to the topological analysis of power grids, the implications of these results from an engineering point of view are discussed, as well as how they could be used to analyze the vulnerability risk of power grids to avoid large-scale cascade failures.

... In [1][2], the one-machine-infinite-bus system (OMIB) and the extended equal area criterion (EEAC) are implemented to determine whether to split. The problem "where to split" is still a research hotspot in controlled splitting, and several methods have been presented in existing publications and can be generally divided into three categories: methods based on slow-coherency [3][4], methods based on artificial intelligence algorithms [5][6], and methods based on the graph theory [7][8][9]. However, existing methods for searching splitting sections are mainly based on the static power flow information before splitting without considering the dynamic process, so the impact of splitting time has not yet been taken into account. ...

... Moreover, the calculation time required for finding a candidate islanding solution is approximately 0.1 second. It is found that the presented stochastic controlled islanding strategy is computationally efficient and fast in comparison with other comparative algorithms such as OBDD, 19 ant search mechanism, 13 spanning tree-based breadth first search, 15 angle modulated particle swarm optimization, 11 and Bender's decomposition technique based 2-stage mixed integer linear programming. 6 In addition, Figure 13 illustrates total expected values of 3 objectives for 5 various values of β. ...

Nowadays, occurrence of severe contingencies may cause an interconnected power system to lose stability and lead to the partial or wide-spread cascading failures. Hence, intentional islanding is the last countermeasure to mitigate the system vulnerability and avoid the catastrophic wide area blackout. This paper proposes a novel probabilistic splitting strategy for generating all possible islanding solutions and evaluating different static and dynamic constraints in reduced power system graph. The proposed stochastic scenario generation algorithm investigates the steady-state stability of all partitions in each generated solution taking into account the uncertainties of loads and wind farms. Multi-objective binary imperialistic competitive algorithm is then developed to find the optimum line switching points that minimizes load-generation mismatch and probability of islands' partial blackout, maximizes voltage stability security margin, and satisfies the slow coherency, connectivity, voltage, and the transmission capacity constraints. Monte Carlo simulation and point estimation method are applied in the stochastic programming model to investigate the islands' stability, calculate the optimization error, and determine the critical stressed transmission lines and PQ-busses under uncertain operating condition. The validity and speed of the proposed approach are revealed using simulation on IEEE 39-bus standard system.

... The presented model can give the system operator an efficient and optimal way to properly respond to outages. Wu, Tang, Han, and Ni (2015) apply a topology analysis and genetic algorithm combined approach for determining proper splitting strategies of large-scale power networks. Topology analysis is used to simplify the original power network into a simple equivalent network so that the splitting strategy space world be dramatically reduced; while the genetic algorithm incorporated with the breadth-first search (BFS) is employed to determine the final proper splitting strategy in the simplified power network. ...

Increased electricity demands and economic operation of large power systems in a deregulated environment with a limited investment in transmission expansion planning causes interconnected power grids to be operated closer to their stability limits. Meanwhile, the loads uncertainty will affect the static and dynamic stabilities. Therefore, if there is no emergency corrective control in time, occurrence of wide area contingency may lead to the catastrophic cascading outages. Studies show that many wide area blackouts which led to massive economic losses may have been prevented by a fast feasible controlled islanding decision making. This chapter introduces a novel computationally efficient approach for separating of bulk power system into several stable sections following a severe disturbance. The splitting strategy reduces the large initial search space to an interface boundary network considering coherency of synchronous generators and network graph simplification. Then, a novel islanding scenario generator algorithm denoted as BEM (Backward Elimination Method) based on PMEAs (Primary Maximum Expansion Areas) has been applied to generate all proper islanding solutions in the simplified network graph. The PPF (Probabilistic Power Flow) based on Newton-Raphson method and Q-V modal analysis has been used to evaluate the steady-state stability of created islands in each generated scenario. BICA (Binary Imperialistic Competitive Algorithm) has then been applied to minimize total load-generation mismatch considering integrity, voltage permitted range and steady-state voltage stability constraints. The best solution has then been applied to split the entire power network. A novel stochastic contingency analysis of islands based on PSVI (Probability of Static Voltage Instability) using MCS (Monte Carlo Simulation) and k-PEM (k-Point Estimate Method) have been proposed to identify the critical PQ buses and severe contingencies. In these approaches, the ITM (Inverse Transform Method) has been used to model uncertain loads with normal probability distribution function in optimal islanded power system. The robustness, effectiveness and capability of the proposed approaches have been validated on the New England 39-bus standard power system. Full Text Preview Introduction Power industry restructuring and competition in the deregulated electricity markets to provide increased demand causes operation of large power systems close to their stability boundaries. Although an interconnected power system may be stable against small disturbances, if there is no emergency corrective control to resynchronize all generators and prevent from fault spreading into the entire network, occurrence of large contingency may cause the system to lose stability and even lead to wide area blackout. Studies show that many wide area blackouts such as 2012 India blackout which led to massive economic losses may have been prevented by a fast feasible controlled splitting decision making (Wang, Shao, & Vittal, 2005). Hence, power system islanding is the last defense line to protect power grids from incidence of wide-area blackout. In other words, controlled system islanding also known as controlled system splitting provides the final remedial action against power system major incidence following a severe disturbance. If there is no proper remedial action in time, immediately after occurrence of large disturbance, it may lead to a catastrophic failures and power system blackout. If a system is encountered with severe instability problem, and emergency control fail to bring the faulted system back to the normal state, an islanding strategy executes by splitting the interconnected power network into several islands by disconnecting proper selected transmission lines. Achieving the proper islanding strategy which satisfies all steady-state and dynamic constraints within islands is a complicated scenario. Major efforts are needed to determine a splitting scheme with two following important characteristics (Ibrahim, 2011): • When to Split: Islanding starts exactly after separating detection. There are many different techniques to detect the interconnected power system islanding. • Where to Split: Many wide area blackouts may have been prevented and load-generation mismatch could have been reduced by fast, accurate, feasible controlled splitting strategies (Andersson et al, 2005; Yang, Vittal & Heydt, 2006). Controlled intentional islanding separates a bulk power system into a number of stable islands by tripping selected transmission lines according to the minimum load-generation mismatch (L. Liu, W. Liu, Cartes & Chung, 2009). Hence, once separation is detected, the most important step is to find the optimal splitting points. In the literature, several approaches have been proposed to split a large power system into a number of stable sections following a wide area contingency. These procedures can be divided into two general categories. The first one is based on the coherent generators clustering and the second one is based on the network graph theory (Najafi, Hosseinian & Abedi, 2010). Continue Reading

Frequent typhoon rainstorm events often trigger transmission lines outage, which are prone to cause cascading events and even worse blackouts. This paper proposed a risk prediction based preventive islanding scheme to ensure safe operation of power system under typhoon rainstorm events. First, the outage probability of lines is fairly assessed under typhoon rainstorm occurring simultaneously using the finite element method. Then, the risk prediction and grading are detailed to depict the emergency degree of risk induced by typhoon rainstorm and provide decision-making for the preventive islanding scheme. Next, a preventive control strategy based on islanding scheme is proposed. Specifically, the lines vulnerable to typhoon rainstorm are respectively separated into different islands by the proposed preventive islanding scheme to disperse the impacts of these vulnerable lines on power system, which can effectively alleviate cascading effects and reduce the risk of the system. Finally, a real power system in southeast part of China is used as the test system, and the real data of typhoon ever hit the system are used to verify the proposed preventive islanding scheme.

Distributed generation (DG) has not only electricity value, but also capacity value. The capacity value can be represented by the credible capacity (CC) based on the equal power supply reliability criterion. The evaluation of reliability on distribution network (DN) is the core of CC calculation. Under a fault state, DGs can continue to supply power to some load by the island operating mode, and the DN reliability can be improved. Therefore, it is necessary to utilize the power supply restoration potential of DG and formulate an island partition scheme accurately in the reliability calculation of DN. A DG CC evaluation method based on island partition is proposed in the paper. The power supply reliability of an active distribution network is evaluated based on an island partition model, to realize the accurate evaluation of DG CC. The main work is as follows: First, an island partition model under a random fault state of DN is established. The fluctuation of DGs and load, interconnection switch, load priority, secondary outage constraint and other factors are fully considered in reliability assessment. A heuristic prospective greedy algorithm and the Prim algorithm are used to solve the island partition model accurately. Second, a reliability evaluation method of DN based on sequential Monte Carlo simulation (SMCS) is proposed. The system reliability level can be accurately analyzed under a fault state. Then, a CC evaluation method based on hypothesis testing is proposed. The convergence of the CC searching process can be scientifically judged by checking the conspicuousness of the reliability indices distribution obtained by the SMCS. Finally, a case study of the PG&E 69-bus system is analyzed. The topology of the DN, permeability of the DG and island partition strategy are known to have a significant impact on the DG CC.

In complex networks, the identification of influential nodes is very important to study the transmission and control of viruses, the location of key points of network attacks, the spread of public opinion, and the marketing promotion of markets. Therefore, based on analysis of the existing algorithms for the identification of influential nodes in complex networks, this paper proposes a new method to identify influential nodes by aggregating local structure information (ALSI). This method considers two factors: the influence of the node itself and the influence contributed by the neighbor node. The degree and K-shell value of the node are introduced when calculating the influence of the node itself, and the degree and K-shell value of the neighbor node are introduced in the calculation of the influence contributed by the neighbor node. Different calculation methods are adopted according to the comparison result of the K-shell value with the node. The greater the K-shell value and the node degree are, the more important the node is. To evaluate the performance of the algorithm, the susceptible-infected-recovered (SIR) model is used to analyze and compare the running results of 9 algorithms on 8 different networks. The experimental results show that the proposed algorithm can effectively detect the influence of nodes and outperforms many state-of-the-art algorithms.

To improve electrical energy system resilience under catastrophic events, an efficient intentional controlled islanding (ICI) model is proposed in this article. The proposed remedial action relies on a new mixed integer linear programming (MILP) model which aims at minimizing the overall energy curtailment, power flow disruption, and generation and demand re‐dispatches through a cost‐based objective function. Another innovative characteristic of this model is demand response (DR) inclusion in the proposed ICI. To improve the balance between demand and supply of electricity, DR can be employed as an effective strategy in the ICI problem. In addition, another main original feature of the proposed model is considering energy storage units (ESUs) in each resulted island after the splitting process. To provide enough time for the system operator to re‐dispatch the islands and to improve frequency stability of islands, a charging/discharging scheme is proposed for ESUs during ICI. Moreover, a new time decomposition is proposed to accurately model the fast and slow corrective actions considering their interactions. Using this time decomposition, energy curtailments, considering their period durations, are treated as decision variables in the ICI problem to minimize involuntary load shedding as the most expensive corrective action. The results of scrutinizing the proposed ICI framework on the IEEE 118‐bus test system illustrate its performance. In addition, the results of the proposed ICI approach are compared with the results of other ICI models to illustrate the effectiveness of the new features of the proposed approach.

An effective strategy for intentional islanding of a transmission system is proposed in this paper to boost its resilience under low-probability high-impact events such as man-made attacks and natural disasters, which can cause catastrophic blackouts. This strategy considers two main aspects of islanding, i.e. time and scheme. To realize the appropriate time that the system need to be intentionally islanded, a new algorithm based on analysis of the rotor angles of its generators is first presented to distinguish coherent groups of the generators. The main advantage of this algorithm is its independence to the predefined degree of coherency and number of the groups. The information obtained by grouping the generators is then used to compute a new defined indicator, whose sign change specifies the islanding time. To decide about the lines that must be disconnected for fulfillment of the islanding scheme, the initial islands are first formed by tracing the active power produced by the generators. Then, the intended scheme is devised by solving a binary linear programming (BLP) problem that minimizes the disruption of the power transferred between these islands. Comparing the proposed scheme with some existing ones shows that the proposed strategy splits two IEEE test systems into stable islands with a better voltage profile and lower imbalance between the active power generation and demand by disconnecting fewer lines, which have smaller amounts of the power flows.

This chapter provides a detailed introduction of the graph‐theory and ordered binary decision diagram (OBDD)‐based methods. It discusses what constraints or criteria the separation points for controlled system separation (CSS) should meet. The chapter introduces two ways of formulating this problem in mathematics. When generators start to oscillate under disturbances, a general observation is that generators are clustered as two or more groups. The ways in which generators tend to group under disturbances are critical to the success of CSS. Separation strategies satisfying the generation coherency and power balance constraints can be solved as k cuts of the graph model. Each k‐cut solution can easily be translated back into separation points on the original power network. For some power systems with more uncertainties in generator coherency and dynamics, the pattern of generator grouping may have to be judged by real‐time measurements on the actual system dynamics or even post‐disturbance system condition.

Catastrophic power blackouts can cause tremendous losses and influence up to tens of millions of people. Since the 1965 Northeast Blackout, many efforts have been made by power industry, but cascading power outages continued to happen. Some recent blackout events are such as the east and west coast blackouts in North America in 2003 and 2011, respectively, the 2006 European blackout and the 2012 Indian blackout events [1, 2, 3, 4, 5]. Blackouts are usually caused by cascading failures initiated by, e.g., natural disasters and mis-operations, which are long chains of dependent equipment failures or outages successively weakening the transmission network [6]. If not prevented or mitigated, cascading failures can break the stability and integrity of the system and result in large-area power outages. When cascading failures occur, it is hard for grid operators to manually take a real-time remedial action in a matter of tens of seconds, so automatic system-wide protection and control schemes are vitally important to stop propagation of failures towards wide areas. At present, most existing protection systems lack adaptability and system-wide coordination. Their mechanism is prone to trip equipment under a predefined fault or abnormal condition, which, however, further weakens the transmission network and may speed up propagation of failures. Therefore, effective mitigation of cascading failures requires smart grid be armed with an adaptive, system-wide protection, and control scheme.

In order to evaluate the influence of nodes in complex networks, a new method is advanced of evaluating key nodes in complex networks, in combination with the “structural hole” theory and closeness centrality of nodes, through defining and applying the influence matrix of nodes’ “structural holes” in response to the limitations of existing methods. The “structural hole” theory gives a comprehensive consideration of the node degree as well as information about topological relations with its neighbors, whereas the closeness centrality of nodes is a reflection of the node's global information. The “structural holes” influence matrix in degree reflects the node's local and global information. So a more proper evaluation standard is established for influence of nodes and a simulation analysis is made of different-scale networks. The results of such analyses show that the method can not only make an exact assessment of the influence of nodes, but also obtain ideal evaluation results from actual complex networks of different scale.

Genetic algorithm is a well known bio-inspired algorithm, which has been widely used to solve practical problems in real-life. The performance of the algorithm heavily depends on the convergence related to the values of parameters involved. It is formulated as a hard problem to select suitable values of mutation and crossover rates to achieve fast or slow convergence for unknown problems. As a new study of system framework inspired by cell model, membrane computing models is with a membrane structure having region segmentation, intrinsic discrete, non-deterministic, programmable and transparent features. In this paper, a hybrid “fast-slow” convergent framework for genetic algorithm inspired by membrane computing is proposed and applied to search optimal solution of 41 benchmark functions. It is obtained by the data experimental results that our method performs well in solving benchmark functions by achieving accuracy rate about 96%.

When interconnected power system out of step occurs, it is imperative to detect it rapidly, and islanding should be taken to prevent widespread blackout. This paper presents a review of the main aspects on power system islanding. Out of step detection methods are classified to six categories. Islanding schemes are outlined according to graph partitioning, minimal cutset enumeration and generator grouping. In addition, four types of load shedding schemes after islanding operation are discussed. Synchronized phasor measurements and AI technologies facilitates the out of step detection, and makes the adaptive islanding and load shedding scheme

System splitting is that the dispatching center controls the splitting of a power network to form designed islands when loss of synchronism occurs. This paper describes and compares three possible ways to realize real-time decision-making of system splitting, and shows that online pre-analysis & real-time matching (ONPARM) is a recommendable way under current technological conditions. An ONPARM system-splitting scheme is presented, and related techniques are described. Simulations on the IEEE 118-bus system show that the scheme can meet the requirement of real-time decision-making. The scheme can be combined with existent emergency control (non-system-splitting) schemes to form a unified real-time security control scheme containing system splitting

The Dommel-Tinney approach to the calculation of optimal power-system load flows has proved to be very powerful and general. This paper extends the problem formulation and solution scheme by incorporating exact outage-contingency constraints into the method, to give an optimal steady-state-secure system operating point. The controllable system quantities in the base-case problem (e.g. generated MW, controlled voltage magnitudes, transformer taps) are optimised within their limits according to some defined objective, so that no limit-violations on other quantities (e. g. generator MVAR and current loadings, transmission-circuit loadings, load-bus voltage magnitudes, angular displacements) occur in either the base-case or contingency-case system operating conditions.

System splitting problem, also known as controlled system separation problem, is to determine the proper splitting points for splitting the entire power network into islands when island operation of system is unavoidable. By "proper" we mean that the splitting strategies should guarantee both the power balance and satisfaction to capacity constraints of transmission lines and other facilities in each island. The system splitting problem is very hard because the strategy space is huge for even middle-scale power networks. This paper proposes a two-phase method to search for proper splitting strategies in real-time. The method narrows down the strategy space using highly efficient OBDD-based algorithm in the first phase, then finds proper splitting strategies using power-flow analysis in the reduced strategy space in the second phase. Simulation with symbolic model checking tool SMV indicates that this method is very promising.

This paper concerns the critical role enhanced control will play in the operating of future electric power systems reliably and efficiently. The nonstandard control problems are due to a large variety of controllers, presently acting in a multirate mode at various levels of the system. Today's monitoring and control logic is largely effective during normal conditions. This paper concerns its possible enhancements which might enable the system to operate reliably over broader ranges of loading and equipment status. In particular, it is suggested that major benefits could come from providing computer tools to assist human operators with their decision making when the system is under stress. A multilayered approach is introduced to support:1) on-line adjustment of available resources; 2) monitoring the interconnection based on qualitative indices (QIs) essential for deciding the severity of the operating mode; and 3) using the QIs to adjust structure of control as the system evolves from one mode to the next. An equivalenced model of the Northeast Power Coordinating Council (NPCC) interconnection is used to illustrate the potential of enhanced control in scenarios that resemble the blackout of August 2003. Also, the potential for efficient use of the resources during normal conditions is illustrated using this multilayered monitoring and control architecture.

Catastrophic failures of power systems are phenomena which occur with some regularity throughout the world. It is recognized that these cannot be prevented, although with the use of newer developments in power engineering, in communication systems, and in computer engineering it would be possible to reduce their frequency and their impact on society. Analyses of many blackouts point to some salient features which are common to most such events: power systems under stress because of high load levels or outages of important facilities, some initiating event-usually a fault, often followed by cascading effects due to unwanted operation of some protection systems. In particular, the role of hidden failures (HFs) in protection systems in propagating power system disturbances has become clearer with some of the recent research reported in the literature. This paper explores further the issue of HFs of protection systems and possible countermeasures. Regarding the countermeasures, adapting the protection systems so that they would change their operational logic from OR to a VOTING protocol has been discussed in the literature, and is well within the capability of present technology. Other hardware solutions, such as "Hidden Failure Monitoring and Protection Systems," have also been discussed in the literature. Most of these countermeasures will require intensive use of communication networks. Communication infrastructure will be utilized for real-time data transfer, as well as for slower speed data gathering tasks related to the condition of the power system. In this paper, we concentrate on the communication facilities and their applications for providing countermeasures against catastrophic failures of power systems.

On July 30 and 31, 2012, two widespread blackouts occurred in India. The blackouts affected the largest number of people so far. The two successive blackouts were both caused by the trip of a certain 400 kV line of inter-regional corridors between northern and western grids. Subsequent faults resulted in breaking down of the power grids. The blackouts influenced the power supply of northern, eastern, and northeast grids. The pre-fault situation of Indian power grid, cause, spread, and restoration of the blackouts were described. Furthermore, the reasons of the blackouts were analyzed in detail from the aspects of technology, management and structure. Finally, certain suggestions to ensure the security and stability of China power grid and prevent the occurrence of blackout in China were proposed.

A power grid island is a self-sufficient subnetwork in a large-scale power system. In weakly connected islands, limited inter-island power flows are allowed. Intentional islanding of a power grid is helpful for the analysis of distributed generation systems connected to a power grid, and valuable for power system reliability of extreme emergency states. In this paper, we use graph partitioning methods to form islands in a power grid and formulate these problems as mixed integer programs. Our models are based the optimal power flow model to minimize the load shedding cost. With these mathematical programming models, optimal formation of islands can be obtained and the different approaches can be compared. Through experiment on IEEE-30-Bus system, computational results are analyzed and compared to provide insight for power grid intentional islanding.

The results of an investigation of methods which might be employed for the on-line stability analysis of electric power systems are presented. On-line analysis in this instance does not refer to real-time or faster than real-time analysis, but to the analysis of data supplied primarily from the electric power system by continuous or periodic sensing of state variables. On-line stability analysis will enable the power system dispatcher to be appraised quickly of potentially unstable conditions by utilizing a preselected set of system contingencies and disturbances based on the existing power network configuration and loading. He can then quickly make decisions concerning possible system changes, such as in scheduling generator loading, line or bus switching, equipment shutdowns, etc. Modern control theory techniques, such as the use of Liapunov functions, pattern recognition, and perturbation, were tried and the results of this research are described. Communication rates needed for data to be supplied the On-Line Stability Analysis Program via the state estimator were investigated. The system state estimator and the software package required for on-line stability analysis are discussed, and the use of computer driven CRT's for displaying results is recommended. A follow-on effort for implementing on-line stability analysis is proposed.

The problem of partitioning a graph into two or more subgraphs that satisfies certain conditions is encountered in many different domains. Accordingly, graph partitioning problem has been studied extensively in the last 50 years. The most celebrated result among this class of problems is the max flow = min cut theorem due to Ford and Fulkerson. Utilizing the modifications suggested by Edmonds and Karp, it is well known that the minimum capacity cut in the directed graph with edge weights can be computed in polynomial time. If the partition divides the node set V into subsets V1 and V2, where V1 contains one of the specified nodes s and V2 contains the other specified node t, the capacity of a cut is defined as the sum of the edge weights going from V1 to V2. In electrical power distribution networks, a slow-coherency-based islanding strategy is used as a prevention against the cascading failures. In this paper, we concentrate on the graph partition problems which are encountered in electric power distribution networks. In this environment, two different definitions of capacity of a cut are used. In the first definition, capacity of a cut is taken to be the difference of the edge weights going from V1 to V2 and from V2 to V1. In the second definition, the capacity of a cut is taken to be the maximum of sum of the edge weights going from V1 to V2 and from V2 to V1. Surprisingly, with slight change of the definition of the capacity of a cut, the computational complexity of the problem changes significantly. In this paper, we show that with the new definitions of the capacity of a cut, the minimum cut computation problem becomes NP-complete. We provide an optimal solution to the problems using mathematical programming techniques. In addition, we also provide heuristic solutions and compare the performance with that of the optimal solution. Copyright © 2008 John Wiley & Sons, Ltd.

Slow coherency has effectively proved its capability in determining sets of generator groups among weak connections in any given power system. In this paper, we provide two comprehensive approaches to deal with islanding the actual system based on the grouping information, by using the minimal cutsets technique in graph theory. The issue of minimal cutsets has been widely discussed in areas related to network topology determination, reliability analysis, etc. The results of this paper also show potential in application to power system islanding. The verification of the islanding scheme is provided based on a WECC 179-bus, 29-generator test system.

Area partitioning that splits a power network into self-sufficient islands is an emergency control to stop the propagation of disturbances and avoid cascading failures. This paper provides a survey of the state-of-the-art of power system islanding techniques and proposes the application of a multilevel graph area partitioning algorithm that are applicable to very large power grids. As an emergency control, network partitioning enhances the capability of a power system to withstand extreme and vulnerable operating conditions. The proposed algorithm has been simulated on two test systems, one with 200 buses and the other with 22,000 buses. The results indicate that the proposed algorithm is highly efficient.

Undervoltage load shedding is an economical solution (or partial
solution) to the voltage stability challenges facing electric utilities.
Simulations for an equivalent system and for large-scale representation
of the Puget Sound (Seattle) area of the Pacific northwest led to
several concepts for an undervoltage load-shedding program. Application
factors such as undervoltage relay settings and time delay are
discussed. Pacific northwest utilities are implementing undervoltage
load shedding for the 1991-2 winter operation period

This paper demonstrates the use of a slow-coherency-based generator grouping algorithm and a graph theoretic approach to form controlled islands as a last resort to prevent cascading outages following large disturbances. The proposed technique is applied to a 30 000-bus, 5000-generator, 2004 summer peak load, Eastern Interconnection data and demonstrated on the August 14, 2003 blackout scenario. Adaptive rate of frequency decline-based load shedding schemes are used in the load rich islands to control frequency. The simulation results presented show the advantage of the proposed method in containing the impact of the disturbance within the islands formed and in preventing the impact of the disturbance from propagating to the rest of the system. This is demonstrated by the significant reduction in line flows in the rest of the system and by improved voltage and relative angle characteristics. Based on the suggestion in the joint U.S.-Canadian task force final report on the blackout, load shedding without any islanding is also performed, and results obtained are compared with the proposed controlled islanding method. The islanding method outperforms the load shedding-only method in reducing the transmission line flows, but both methods have similar effects on voltage and relative angle behavior

Controlled islanding refers to the controlled separation of an interconnected power system into electrically isolated regions. The objective of this paper is to develop adaptive controlled islanding as a component of an emergency power system control strategy. There are two primary aspects of controlled islanding: 1) where to island and 2) when to island? Assisted by a decision tree (DT) approach, this paper seeks to address the "when to island" aspect. A decision tree based tool is proposed to recognize conditions existing in the system that warrant controlled islanding. A 29-generator, 179-bus system is employed to demonstrate the tool. Simulation data are used to train DTs, and the online performance of DTs is then evaluated as part of a controlled islanding strategy

This paper reviews the events of an incident, which occurred on
June 20, 1997, that resulted in the islanding of a major load area in
downtown Washington DC, USA, and the subsequent power outage to that
load area. It discusses the investigation and analysis of the incident
and lessons learned

This paper presents a systematic approach to predict the
structural characteristics of power systems following large
disturbances. Specifically, this paper uses the normal form of vector
fields to predict the onset of the interarea separation in power systems
following large disturbances. The normal form method is well established
in the dynamical systems theory literature. The paper develops an
analytically based index which identifies the onset of the interarea
separation. The proposed approach has been applied to the 50-generator
IEEE test system. The results obtained indicate that the proposed index
effectively captures the structural characteristics of the system
dynamic behavior and accurately predicts the nature of the system
dynamic performance following large disturbances

Tens and hundreds of thousands of disturbances occur annually in modern power systems. The overwhelming majority of them are eliminated by relay protection devices and other automatic systems and by the actions of the dispatching personnel. A small fraction of the emergencies (tens of cases in such large power interconnections as those in the United States and Canada, Europe, and the United Power System (UPS) of Russia) result in significant system failures, sometimes of a cascading nature. They are consequences of unusual primary disturbances, failures of automatic emergency control systems, protection device malfunctions, and errors by personnel, but do not cause extreme consequences for the power system and the consumers. Of these, only some rare failures-blackouts-become catastrophes with severe long-term consequences for the national economies and population. Recent blackouts in North America, Europe, Russia, and other countries require specialists once again to pay closer attention to the blackout phenomenon. It is often believed that the philosophy of preventing blackouts should be based on dispatching personnel training, wide-area system visibility,and better computer models for the analysis of the stability and security of power systems. The authors of this paper also think that in emergency situations of a cascading nature, automatic emergency control systems should play a major role. A confirmation for this statement is the fact that from 1975 to 2005 there were no blackouts in the UPS of Russia (where automatic emergency control systems are widely used). At the same time, the Moscow blackout demonstrated that the growing problems in the Russia's UPS (such as aging equipment and load growth) made it also vulnerable to major blackouts. This stresses again that the electrical power industry faces common global problems and that a global effort, cooperation, and exchange of the best practices are needed to prevent blackouts. This paper describes the Russian