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We propose a computationally efficient approach to detect severe multiple contingencies. We pose a contingency analysis problem using a nonlinear optimization framework, which enables us to detect the fewest possible transmission line outages resulting in a system failure of specified severity, and to identify the most severe system failure caused...
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... clarity, the relevant (fourth) quadrant of Fig. 3 is redrawn in Fig. 4. The arrow represents the movement of the operating point from to . Its projection onto the axis corresponds to the amount of load that is shed at bus 3. Note in Table I that due to the distributed slack bus mechanism, the generators have been redispatched in a constant proportion to their nominal values so as to accommodate the ...
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Citations
... In Ref. [44], the minimum load shedding problem based on DC power flow was taken as the lower model, and the Karush Kuhn Tucher (KKT) condition and duality theory were further used to transform the double-layer model into a single-layer mixed integer linear programming, which could accurately screen the random fault events that cause the maximum load loss. Ref. [45] considered the constraints of reactive power and voltage in the lower operation model and proposed a random fault screening algorithm based on mixed integer nonlinear programming. In Ref. [46], the loss and probability of random fault events were considered in the upper model, and a mixed integer linear programming model with risk as the goal was proposed, which could realize the rapid risk ranking of high-order fault events in transmission system. ...
In the context of large-scale wind power access to the power system, it is urgent to explore new probabilistic supply–demand analysis methods. This paper proposes a wind power stochastic and extreme scenario generation method considering wind power–temperature correlations and carries out probabilistic supply–demand balance analysis based on it. Firstly, the influence of temperature on wind power output is analyzed via Pearson coefficient to obtain the correlation between wind power and temperature. Secondly, based on the historical wind power curve, a large number of wind power output scenarios are randomly generated while fully preserving its characteristics, and probabilistic supply–demand analysis is carried out. Thirdly, for the extreme case of continuous multi-day extreme heat without wind, extreme scenarios are selected from the generated scenarios for supply–demand balance analysis. Finally, a practical example in a province in central-eastern China is used to verify the effectiveness of the proposed method. The results indicate that the scenario generation method can effectively capture the historical wind power characteristics and can be better applied to the diversified supply and demand balance analysis to obtain more accurate analysis results.
... To be specific, some researchers propose rigorous mathematical formulations for exploring vulnerable elements or contingencies in power grids [6,7], while others focus on the practical modeling of cascading failures [5,8]. Thus, the identification approaches are developed to search for critical branches or initial malicious disturbances that cause the large-scale disruptions [9][10][11][12][13][14][15][16]. For instance, some schemes are proposed to identify the collections of n − k contingencies via the event trees [10], line outage distribution factor [11] and other optimization techniques [12][13][14]. ...
... Thus, the identification approaches are developed to search for critical branches or initial malicious disturbances that cause the large-scale disruptions [9][10][11][12][13][14][15][16]. For instance, some schemes are proposed to identify the collections of n − k contingencies via the event trees [10], line outage distribution factor [11] and other optimization techniques [12][13][14]. Nevertheless, these approaches are not efficient to identify the large collections of n − k contingencies that result in cascading blackouts. ...
The identification of disruptive initial events on vulnerable components is crucial to the protection and reliability enhancement of critical infrastructure systems. Due to the evolving nature of system parameters and the complicated coupling relationship of different components, it has been a great challenge to identify the contingencies that could trigger cascading blackouts of power systems. This chapter aims to develop a generic approach for identifying the initial disruptive contingencies on vulnerable branches that can result in catastrophic cascading failures of power systems. Essentially, the problem of contingency identification is formulated in the mathematical framework of hybrid differential-algebraic system, and it can be solved by the Jacobian-Free Newton-Krylov (JFNK) method in order to circumvent the Jacobian matrix and relieve the computational burden. Moreover, an efficient numerical algorithm for contingency identification is developed to search for the disruptive disturbances that lead to catastrophic cascading failures with guaranteed convergence accuracy in theory. Finally, a case study is presented to demonstrate the efficacy of the proposed identification approach on the IEEE test systems.
... This phenomenon was also proven in recent blackout events, such as those in India and Turkey [4], where blackouts of whole electrical grids were caused due to operational failures, and the South Australian Transmission Grid failure which was due to insufficient analysis of vulnerabilities as a result of extreme weather conditions [5]. Any critical component failure may have negative impacts on system operational costs due to the ramp-up/down of generators or unserved energy penalties [6][7][8][9]. In practice, PS planners design the grid to be sufficient to cope with contingencies by allocating adequate reserves in generator production and transmission lines to provide a certain level of redundancy in case of preestimated critical contingencies [10,11]. ...
... However, in these approaches there is a risk that the worst blackouts will not be detected and that high impact, small subsets will not be covered. In [7,8], the proposed methods are dependent on identifying over-limits and loss of loads but do not cover the complete process of disturbances. In [29], the impact of random line failures on grid vulnerability is studied, and it is concluded that small and large failures can induce similar performance loss in robustness. ...
... The type of load (critical or uncritical) is one of the most common approaches in selection of the first group of loads to be separated from the system. If the power system operator has a bunch of loads to be selected, one of the proper shedding sequence methods is defined according to the load participation matrix [7]. For a predefined amount of load separation, those which alleviate branch flows the most are selected for decreasing the stress level of the transmission system. ...
Early detection of cascading failures phenomena is a vital process for the sustainable operation of power systems. Within the scope of this work, a preventive control approach implementing an algorithm for selecting critical contingencies by a dynamic vulnerability analysis and predictive stability evaluation is presented. The analysis was carried out using a decision tree with a multi-parameter knowledge base. After the occurrence of an initial contingency, probable future contingencies are foreseen according to several vulnerability perspectives created by an adaptive vulnerability search module. Then, for cases identified as critical, a secure operational system state is proposed through a vulnerability-based, security-constrained, optimal power flow algorithm. The modular structure of the proposed algorithm enables the evaluation of possible vulnerable scenarios and proposes a strategy to alleviate the technical and economic impacts due to prospective cascading failures. The presented optimization methodology was tested using the IEEE-39 bus test network and a benchmark was performed between the proposed approach and a time domain analysis software model (EMTP). The obtained results indicate the potential of analysis approach in evaluating low-risk but high-impact vulnerabilities in power systems.
... Two bi-level programming approaches were presented and discussed in [15] and two methods were used to convert each formulation into an equivalent single-level mixed-integer linear programming problem. Nonlinear optimization was used in [16] for identifying the fewest possible transmission line outages resulting in system failures in which severity of failures determined by lost load. A combination of classical Deterministic Network Interdiction Problem (DNIP) and Multi-objective Optimization Evolutionary Algorithms (MOEA) for finding minimum contingencies with maximum load shedding was proposed in [17]. ...
Recent large blackouts in power systems showed that common reliability criteria are not efficient anymore. Since cascading outages are the prevalent cause of more blackouts, and there is enormous interaction among different elements, determining the sequence of events before occurring blackouts is very challenging. Contingency screening methods are used to overcome some difficulties and identification of bottlenecks in power systems. However, risky contingencies are those with high probability, high consequences, or both. In this paper, a challenging work of seeking multiple events which potentially may result in cascades is addressed. Severe contingency identification, which is known as N-k problem in the literature, is difficult to deal with even for small values of k. A modified Binary Particle Swarm Optimization (BPSO), which proposed in this paper, could help power system planners and operators to upgrade the network resiliency by finding critical contingences that may initiate cascading outages. Severe contingencies are detected by computer simulations in the IEEE 39-bus test system and a real-sized network. The results are compared to the results of the IEEE 24-bus test system, which shows the method is more effective.
... In ref. [13], the extension of the problem in ref. [12] is proposed that uses Benders decomposition to solve the larger instance of network interdiction model to identify the most critical components in the power grid. The research work in ref. [14] and [15] presents vulnerability assessment in the power system which is formulated as a bilevel optimisation problem where the outer level problem represents a small number of transmission lines on which attack is coordinated that maximises the inner level system load shed problem. The solution of the mixed-integer problem in ref. [14] is done by relaxing the binary variables to continuous variables, while in ref. [15], a method is proposed using graph theory that identifies some transmission lines whose removal partitions the network into generation and load dominant areas that increases the load shed in the power system. ...
... The research work in ref. [14] and [15] presents vulnerability assessment in the power system which is formulated as a bilevel optimisation problem where the outer level problem represents a small number of transmission lines on which attack is coordinated that maximises the inner level system load shed problem. The solution of the mixed-integer problem in ref. [14] is done by relaxing the binary variables to continuous variables, while in ref. [15], a method is proposed using graph theory that identifies some transmission lines whose removal partitions the network into generation and load dominant areas that increases the load shed in the power system. In ref. [16], the interdiction problem is solved using Benders decomposition where line switching is used as mitigation before load shed is implemented. ...
In this paper, the problem of identification of critical k‐line contingencies that fail one after another in quick succession that render large load shed in the power system is addressed. The problem is formulated as a mixed‐integer non‐linear programming problem (MINLP) that determines total demand that cannot be satisfied under various k‐line removal scenarios. Due to the large search space of the problem, the solution through enumeration is intractable. Two algorithms are proposed using a proposed power flow sensitivity and a topological metric to identify a reduced number of k‐line contingencies that initiate cascading overload failure and islanding of power system respectively, that are used to solve the MINLP iteratively for identification of critical k‐line contingencies. The algorithms identify a reduced number of k‐line contingencies in linear time as compared to the exponential time complexity of brute‐force search for solutions of the MINLP. Case studies show that the proposed algorithms significantly reduce the search space and the computation time of the MINLP problem to find the most critical k‐line contingency in the IEEE 30 and 118 bus systems at 2≤k≤4$2 \le k \le 4$ that are also obtained in the list of k‐line contingencies identified using the proposed algorithms.
... Several indices and approaches have been introduced in the literature. References [8][9][10][11][12][13][14][15][16][17][18][19][20] propose ranking approaches based on certain performance indices, which consider information as well as active and reactive power, bus voltages of the power grid. Authors in [8] have tried to provide a deep-learning-based effective method in order to model the security-constrained optimal power flow considering the automatic primary response of generation units. ...
... Hence, references [14,15] have provided an effective model based on grid operation taking into account the different contingencies in the electrical grid. Authors in [16,17] have tried getting into a comprehensive survey of uncertainty modeling emerging from renewable sources within a smart grid. The presence of uncertain parameters in the grid causes the emergence of vulnerability challenges facing the electrical power operation, which is proven in [18][19][20]. ...
To comply with electric power grid automation strategies, new cyber-security protocols and protection are required. What we now experience is a new type of protection against new disturbances namely cyber-attacks. In the same vein, the impact of disturbances arising from faults or cyber-attacks should be surveyed by network vulnerability criteria alone. It is clear that the diagnosis of vulnerable points protects the power grid against disturbances that would inhibit outages such as blackouts. So, the first step is determining the network vulnerable points, and then proposing a support method to deal with these outages. This research proposes a comprehensive approach to deal with outages by determining network vulnerable points due to physical faults and cyber-attacks. The first point, the network vulnerable points against network faults are covered by microgrids. As the second one, a new cyber-security protocol named multi-layer security is proposed in order to prevent targeted cyber-attacks. The first layer is a cyber-security-based blockchain method that plays a general role. The second layer is a cyber-security-based reinforcement-learning method, which supports the vulnerable points by monitoring data. On the other hand, the trend of solving problems becomes routine when no ambiguity arises in different sections of the smart grid, while it is far from a big network’s realities. Hence, the impact of uncertainty parameters on the proposed framework needs to be considered. Accordingly, the unscented transform method is modeled in this research. The simulation results illustrate that applying such a comprehensive approach can greatly pull down the probability of blackouts.
... DNS). Furthermore, methods using optimization are also applied to uncover small subsets of events with high impact [26,27]. However, these methods rely primarily on detecting limit violations and load shedding actions, and they do not simulate the full propagation of disturbance events, i.e. do not perform cascading failure analyses. ...
Power systems as critical infrastructure are an integral part of human society and are therefore of paramount importance to modern life. Vulnerabilities in the system, that are revealed either by accidental or deliberate events, can cause large losses of power supply with sever social and economic consequences. A tool that identifies the vulnerabilities in a power system can provide the operators the means to support reliable power system operations. This paper presents a methodology for power system vulnerability assessment that couples an AC based cascading failure simulation model and a meta-heuristic optimization procedure. The objectives of the assessment is to (1) rank the most important branches in the transmission grid, and (2) identify sets of branches if simultaneously tripped will cause the cascade with highest intensity. The first objective is achieved by ranking the criticality of the branches using two criteria (i) the impact that each branch failure has on the DNS and (ii) the frequency of line overload. The second objective is achieved by hard linking an AC based cascading failure simulation model and a meta-heurist based optimization procedure. The methodology allows the generation and the identification of vulnerability scenarios, and therefore, provides insights that can be used by operators in developing strategies to minimize the effects of accidental and deliberate events. The algorithm developed for the purpose of this study is applied to the IEEE 118-bus test system and the Swiss power grid. The results demonstrate the capability of the proposed methodology for assessing power system vulnerability.
... For instance, [32] used graph partitioning methods to find subgraphs of the grid with large imbalances, and [33] used graph theory to consider the feasibility boundary of the power flow equations for the system. The latter work was later extended in [34], and more details on this and related work can be found in [35]. However, most work along this line of research analyse multiple contingencies without considering the sequences of events that give rise to them. ...
Major blackouts may have critical societal consequences and are very challenging to analyse and mitigate. Part of the challenge lies in the complex sequences of events that characterize such blackouts and that involve a diverse set of mechanisms propagating the events. The analysis is also challenged by the great uncertainties associated with individual mechanisms and thus with the overall likelihood of sequences of event. This article proposes a general framework which uses a graph to describe the causal relationship between consequences, system states, initiating events and barriers. A concrete implementation of the framework is presented by implementing exemplary models for three transition mechanisms, namely i) protection system failures, ii) failure of corrective actions, and iii) failure of islanding. In the implementation, a graph is automatically generated where edges are associated with these transition mechanisms. A vulnerability analysis methodology based on the modelling framework is proposed that allows for identifying how critical consequences might occur as well as estimating their likelihoods of occurring. The vulnerability analysis methodology moreover incorporates a possibilistic uncertainty analysis to explicitly capture uncertainties associated with the likelihood of events. Finally, a case study considering a small but realistic test system is used to illustrate the approach and demonstrate its main advantages: i) The vulnerability analysis can identify critical sequences of events and barriers to mitigate them, ii) the graph-based representation allows for exploring the sequences of events and understanding the vulnerabilities, iii) the modelling framework is general and can incorporate multiple transition mechanisms, and iv) the analysis accounts for the large uncertainty associated with the critical sequences of events.
... Contingency analysis is often combined with N-k interdiction modeling to identify sets of k components whose simultaneous failure leads to the worst outcome (typically outages) during a contingency analysis. While solving an interdiction problem itself is challenging, the state-of-the-art has improved considerably over the last several decades and (at least heuristic) solutions are regularly reported on problems with large N and k (see [2][3][4][5][6][7][8] and references therein). ...
Although electricity transmission systems are typically very robust, the impacts that arise when they are disrupted motivate methods for analyzing outage risk. For example, N-k interdiction models were developed to characterize disruptions by identifying the sets of k power system components whose failure results in “worst case” outages. While such models have advanced considerably, they generally neglect how failures outside the power system can cause large-scale outages. Specifically, failures in natural gas pipeline networks that provide fuel for gas-fired generators can affect the function of the power grid. In this study, we extend N-k interdiction modeling to gas pipeline networks. We use recently developed convex relaxations for natural gas flow equations to yield tractable formulations for identifying sets of k components whose failure can cause curtailment of natural gas delivery. We then present a novel cutting-plane algorithm to solve these problems. Finally, we use test instances to analyze the performance of the approach in conjunction with simulations of outage effects on electrical power grids.
... HIS work is motivated by extreme events in electric power systems that are caused by multiple contingencies. Robust operation of the power grid requires anticipation of unplanned component outages that could trigger extreme events [1].Although electric power grids are designed to be resilient against any single contingency (N-1 contingency), loss of multiple components can lead to system instability, uncontrolled separation, cascading outages, voltage collapse, etc [1].Additionally, smart grid deployment exposes the electric power grid to purposeful and malicious attacks which raises concerns about the possibility of malicious N-x scenarios. Thus, it is important to make the system secure not only for any given N-1contingency but also for selected N-x contingencies. ...
... HIS work is motivated by extreme events in electric power systems that are caused by multiple contingencies. Robust operation of the power grid requires anticipation of unplanned component outages that could trigger extreme events [1].Although electric power grids are designed to be resilient against any single contingency (N-1 contingency), loss of multiple components can lead to system instability, uncontrolled separation, cascading outages, voltage collapse, etc [1].Additionally, smart grid deployment exposes the electric power grid to purposeful and malicious attacks which raises concerns about the possibility of malicious N-x scenarios. Thus, it is important to make the system secure not only for any given N-1contingency but also for selected N-x contingencies. ...
Identifying the multiple critical components in power systems whose absence together has severe impact on system performance is a crucial problem for power systems known as (N-x) contingency analysis. However, the inherent combinatorial feature of the N-x contingency analysis problem incurs by the increase of x in the (N-x) term, making the problem intractable for even relatively small test systems. We present a new framework for identifying the N-x contingencies that captures both topology and physics of the network. Graph theory provides many ways to measure power grid graphs, i.e. buses as nodes and lines as edges, allowing researchers to characterize system structure and optimize algorithms. This paper proposes a scalable approach based on the group betweenness centrality (GBC) concept that measures the impact of multiple components in the electric power grid as well as line outage distribution factors (LODFs) that find the lines whose loss has the highest impact on the power flow in the network. The proposed approach is a quick and efficient solution for identifying the most critical lines in power networks. The proposed approach is validated using various test cases, and results show that the proposed approach is able to quickly identify multiple contingencies that result in violations.
