246 research outputs found

    Optimizing the robustness of electrical power systems against cascading failures

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    Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a complete understanding of system robustness by i) deriving an expression for the final system size as a function of the size of initial attacks; ii) deriving the critical attack size after which system breaks down completely; iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load.Comment: 18 pages including 2 pages of supplementary file, 5 figure

    Measuring cascade effects in interdependent networks by using effective graph resistance

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    Understanding the correlation between the underlie network structure and overlay cascade effects in the interdependent networks is one of major challenges in complex network studies. There are some existing metrics that can be used to measure the cascades. However, different metrics such as average node degree interpret different characteristic of network topological structure, especially less metrics have been identified to effectively measure the cascading performance in interdependent networks. In this paper, we propose to use a combined Laplacian matrix to model the interdependent networks and their interconnectivity, and then use its effective resistance metric as an indicator to its cascading behavior. Moreover, we have conducted extensive comparative studies among different metrics such as average node degree, and the proposed effective resistance. We have found that the effective resistance metric can describe more accurate and finer characteristics on topological structure of the interdependent networks than average node degree which is widely adapted by the existing research studies for measuring the cascading performance in interdependent networks

    Competitive percolation strategies for network recovery

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    Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem of finding the optimal order of repairing elements in power grids and similar infrastructure. Most existing methods either only consider system network structure, potentially ignoring important features, or incorporate component level details leading to complex optimization problems with limited scalability. We aim to narrow the gap between the two approaches. Analyzing realistic recovery strategies, we identify over- and undersupply penalties of commodities as primary contributions to reconstruction cost, and we demonstrate traditional network science methods, which maximize the largest connected component, are cost inefficient. We propose a novel competitive percolation recovery model accounting for node demand and supply, and network structure. Our model well approximates realistic recovery strategies, suppressing growth of the largest connected component through a process analogous to explosive percolation. Using synthetic power grids, we investigate the effect of network characteristics on recovery process efficiency. We learn that high structural redundancy enables reduced total cost and faster recovery, however, requires more information at each recovery step. We also confirm that decentralized supply in networks generally benefits recovery efforts.Comment: 14 pages, 6 figure

    Resilience of power grids and other supply networks: structural stability, cascading failures and optimal topologies

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    The consequences of the climate crisis are already present and can be expected to become more severe in the future. To mitigate long-term consequences, a major part of the world's countries has committed to limit the temperature rise via the Paris Agreement in the year 2015. To achieve this goal, the energy production needs to decarbonise, which results in fundamental changes in many societal aspects. In particular, the electrical power production is shifting from fossil fuels to renewable energy sources to limit greenhouse gas emissions. The electrical power transmission grid plays a crucial role in this transformation. Notably, the storage and long-distance transport of electrical power becomes increasingly important, since variable renewable energy sources (VRES) are subjected to external factors such as weather conditions and their power production is therefore regionally and temporally diverse. As a result, the transmission grid experiences higher loadings and bottlenecks appear. In a highly-loaded grid, a single transmission line or generator outage can trigger overloads on other components via flow rerouting. These may in turn trigger additional rerouting and overloads, until, finally, parts of the grid become disconnected. Such cascading failures can result in large-scale power blackouts, which bear enormous risks, as almost all infrastructures and economic activities depend on a reliable supply of electric power. Thus, it is essential to understand how networks react to local failures, how flow is rerouted after failures and how cascades emerge and spread in different power transmission grids to ensure a stable power grid operation. In this thesis, I examine how the network topology shapes the resilience of power grids and other supply networks. First, I analyse how flow is rerouted after the failure of a single or a few links and derive mathematically rigorous results on the decay of flow changes with different network-based distance measures. Furthermore, I demonstrate that the impact of single link failures follows a universal statistics throughout different topologies and introduce a stochastic model for cascading failures that incorporates crucial aspects of flow redistribution. Based on this improved understanding of link failures, I propose network modifications that attenuate or completely suppress the impact of link failures in parts of the network and thereby significantly reduce the risk of cascading failures. In a next step, I compare the topological characteristics of different kinds of supply networks to analyse how the trade-off between efficiency and resilience determines the structure of optimal supply networks. Finally, I examine what shapes the risk of incurring large scale cascading failures in a realistic power system model to assess the effects of the energy transition in Europe

    A Critical Review of Robustness in Power Grids using Complex Networks Concepts

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    Complex network theory for analyzing robustness in energy gridsThis paper reviews the most relevant works that have investigated robustness in power grids using Complex Networks (CN) concepts. In this broad field there are two different approaches. The first one is based solely on topological concepts, and uses metrics such as mean path length, clustering coefficient, efficiency and betweenness centrality, among many others. The second, hybrid approach consists of introducing (into the CN framework) some concepts from Electrical Engineering (EE) in the effort of enhancing the topological approach, and uses novel, more efficient electrical metrics such as electrical betweenness, net-ability, and others. There is however a controversy about whether these approaches are able to provide insights into all aspects of real power grids. The CN community argues that the topological approach does not aim to focus on the detailed operation, but to discover the unexpected emergence of collective behavior, while part of the EE community asserts that this leads to an excessive simplification. Beyond this open debate it seems to be no predominant structure (scale-free, small-world) in high-voltage transmission power grids, the vast majority of power grids studied so far. Most of them have in common that they are vulnerable to targeted attacks on the most connected nodes and robust to random failure. In this respect there are only a few works that propose strategies to improve robustness such as intentional islanding, restricted link addition, microgrids and smart grids, for which novel studies suggest that small-world networks seem to be the best topology.This work has been partially supported by the project TIN2014-54583-C2-2-R from the Spanish Ministerial Commission of Science and Technology (MICYT), by the project S2013/ICE-2933 from Comunidad de Madrid and by the project FUTURE GRIDS-2020 from the Basque Government

    Control methods for network dynamics and criticality phenomena

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    This dissertation studies the role of the network structure on the emergence and mitigation of critical phenomena in complex power networks. In particular, the event to consider is the emergence of cascading failures due to congestion mechanism. The main contributions of this thesis are the proposal of a vulnerability analysis framework to study network influence on critical phenomena and the design of a control framework combining Network theory with Markov Decision Processes and Stochastic Games in order to choose best strategies to reduce the impact of cascading failures. The vulnerability analysis framework includes the identification of main properties influencing cascading failures triggering and propagation, the study of the central role of cut-sets in cascading propagation and the proposal of new metrics to evaluate global and local vulnerability. The control framework includes control strategies to generate worst-case failure scenarios and optimal solutions for damage control on those scenarios employing the dynamic setting of transmission lines capacity. This dissertation is developed around these two contributions, as is described in the following. The first part of this thesis studies the influence of the network connectivity in failure triggering and propagation. Network science theory had been used to study relevant network connectivity properties. A methodology based on the connectivity properties is evaluated to measure the network robustness. A cascading failures model based on hybrid systems theory is proposed to define the congestion mechanism and describe the structure-function power network interdependence. The network Cut-sets (CS) identified as central elements for failures propagation are used to propose a critical link identification algorithm evaluated over the Quasy Stable State (QSS) approach of the proposed cascading failures model. The second part of this dissertation proposes a network-based vulnerability analysis framework and propose a control framework to integrate network properties, electric properties, eventtriggered failures, and control. Several algorithms are developed to evaluate different triggers and propagation events. The framework is developed analytically by the integration of Networks theory with Markov Decision Processes and Stochastic Games. Finally, using the previously obtained results about connectivity and vulnerability, a control strategy is designed to mitigate the damage of failures propagation by dynamically control the transmission lines capacity. An attacker-defender stochastic game framework is used to formulate the control problem. In the problem, the defender selects lines which are the best candidates to apply transmission capacity control as a response to the imminent risk of cascading failures related to the attacker actions. To solve the control problem, we propose a system of multi-population state-dependent replicator dynamics where their fitness change with the long term discounted expected reward in the game. The solution of the replicator equations converges to the Nash equilibrium of the game and coincides with the best strategy for control the cascading failures damage related to worst scenarios produced by optimal attacks.Resumen Esta disertación estudia el rol que la estructura de la red y su dinámica tiene en la ocurrencia ´ de fenómenos críticos y su posible mitigación con aplicación particular en sistemas de potencia ´ siendo estos modelados como redes complejas. En particular se considera como fenómeno crítico la propagación de fallas en cascada debidas a mecanismos de congestión. La contribuciones principales de esta tesis son la integracion del concepto de conjuntos de corte y métricas de congestión en el analisis de vulnerabilidad de redes durante eventos de falla, y la propuesta de una estrategia de ´ control para disminuir el impacto de la propagacion de fallas en red mediante el control din ´ amico ´ de la capacidad de las l´ıneas. La disertacion se desarrolla alrededor de estas dos contribuciones ´ como se describe a continuacion. ´ La primera parte de esta tesis estudia la influencia de la conectividad de la red en la generacion´ y propagacion de fallas en cascada en las redes de potencia. Teor ´ ´ıa de redes complejas es utilizada para evaluar diferente propiedades de conectividad de la red y la evaluacion de su cambio bajo la ´ influencia de escenarios de falla diseados es asimilado como medida de robustez de la estructura. Los conjuntos de corte (Cut-sets) de la red son identificados como elementos propagadores de fallas en la red y un algoritmo de identificacion de elementos cr ´ ´ıticos basado en esta teor´ıa es propuesto. Un modelo de fallas en cascado dinamico basado en teor ´ ´ıa de sistemas h´ıbridos es propuesto para describir el mecanismo de propagacion de fallas por congestion. ´ La segunda parte de esta tesis desarrolla un framework de evaluacion de vulnerabilidad de re- ´ des de potencia sujetas a fallas en cascada y propone estrategias de control para mitigar el dao causado por estos fenomenos. El modelo de fallas en cascada propuesto en la parte previa es sim- ´ plificado hasta una version de estado cuasi estable (Quasy Stable State) e integrado en algoritmos ´ de ataques de red para evaluar diferentes eventos detonantes y su propagacion. El framework se ´ desarrolla anal`ıticamente tras integrar teor´ıa de redes complejas, procesos de Markov y juegos estoca sticos. Finalmente usando informaci ´ on en cuanto a la interacci ´ on entre propiedades el ´ ectricas ´ y estructurales y la evaluacion de vulnerabilidad de la red, se propone una estrategia de mitigaci ´ on´ de impacto de la propagacion de fallas en red mediante estrategias de control din ´ amico de la ca- ´ pacidad de transmision de las l ´ ´ıneas. El framework de vulnerabilidad es integrado en un juego estocastico de atacante-defensor, ´ donde el defensor selecciona las mejores candidatas para control de capacidad de transmisión como respuesta a amenazas de disparo de efectos en cascada debidas a acciones del atacante. Para solucionar el problema de control de vulnerabilidad de la red formulado como juego estocásticoDoctorad

    The Impact of Renewable Power Generation and Extreme Weather Events on the Stability and Resilience of AC Power Grids

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    Der erste Teil dieser Arbeit beschäftigt sich mit der Frage, welchen Einfluss kurzzeitige Schwankungen der erneuerbaren Energiequellen auf die synchrone Netzfrequenz haben. Zu diesem Zweck wird eine lineare Antworttheorie für stochastische Störungen von dynamischen Systemen auf Netzwerken hergeleitet. Anschließend wird diese Theorie verwendet, um den Einfluss von kurzfristigen Wind- und Sonnenschwankungen auf die Netzdynamik zu analysieren. Hierbei wird gezeigt, dass die Frequenzantwort des Netzes weitestgehend homogen ist, aber die Anfälligkeit für Leistungsschwankungen aufgrund von Leitungsverlusten entlang des Leistungsflusses zunimmt. Der zweite Teil der Arbeit befasst sich mit der Modellierung von netzbildenden Wechselrichterregelungen. Bislang existiert kein universelles Modell zur Beschreibung der kollektiven Dynamik solcher Systeme. Um dies zu erreichen, wird unter Ausnutzung der inhärenten Symmetrie des synchronen Betriebszustandes eine Normalform für netzbildende Akteure abgeleitet. Anschließend wird gezeigt, dass dieses Modell eine gute Annäherung an typische Wechselrichter-Dynamiken bietet, aber auch für eine datengesteuerte Modellierung gut geeignet ist. Der letzte Teil der Arbeit befasst sich mit der Analyse des Risikos von Stromausfällen, welche durch Hurrikans verursacht werden. Hohe Windgeschwindigkeiten verursachen häufig Schäden an der Übertragungsinfrastruktur, welche wiederum zu Überlastungen anderer Komponenten führen und damit eine Kaskade von Ausfällen im gesamten Netz auslösen können. Simulationen solcher Szenarien werden durch die Kombination eines meteorologischen Windmodells sowie eines Modells für kaskadierende Leitungsausfälle durchgeführt. Durch Monte-Carlo-Simulationen in einer synthetischen Nachbildung des texanischen Übertragungsnetzes können einzelne kritische Leitungen identifiziert werden, welche zu großflächigen Stromausfällen führen.The first part of this thesis addresses the question which impact short-term renewable fluctuations have on the synchronous grid frequency. For this purpose, a linear response theory for stochastic perturbations of networked dynamical systems is derived. This theory is then used to analyze the impact of short-term wind and solar fluctuations on the grid frequency. It is shown that while the network frequency response is mainly homogenous, the susceptibility to power fluctuations is increasing along the power flow due to transmission line losses. The second part of the thesis is concerned with modeling grid-forming inverter controls. So far there exists no universal model for studying the collective dynamics of such systems. By utilizing the inherent symmetry of the synchronous operating state, a normal form for grid-forming actors is derived. It is shown that this model provides a useful approximation of certain inverter control dynamics but is also well-suited for a data-driven modeling approach. The last part of the thesis deals with analyzing the risk of hurricane-induced power outages. High wind speeds often cause damage to transmission infrastructure which can lead to overloads of other components and thereby induce a cascade of failures spreading through the entire grid. Simulations of such scenarios are implemented by combining a meteorological wind field model with a model for cascading line failures. Using Monte Carlo simulations in a synthetic test case resembling the Texas transmission system, it is possible to identify critical lines that trigger large-scale power outages

    The effect of renewable energy incorporation on power grid stability and resilience

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    Contemporary proliferation of renewable power generation is causing an overhaul in the topology, composition, and dynamics of electrical grids. These low-output, intermittent generators are widely distributed throughout the grid, including at the household level. It is critical for the function of modern power infrastructure to understand how this increasingly distributed layout affects network stability and resilience. This paper uses dynamical models, household power consumption, and photovoltaic generation data to show how these characteristics vary with the level of distribution. It is shown that resilience exhibits daily oscillations as the grid’s effective structure and the power demand fluctuate. This can lead to a substantial decrease in grid resilience, explained by periods of highly clustered generator output. Moreover, the addition of batteries, while enabling consumer self-sufficiency, fails to ameliorate these problems. The methodology identifies a grid’s susceptibility to disruption resulting from its network structure and modes of operation

    Real-time Prediction of Cascading Failures in Power Systems

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    Blackouts in power systems cause major financial and societal losses, which necessitate devising better prediction techniques that are specifically tailored to detecting and preventing them. Since blackouts begin as a cascading failure (CF), an early detection of these CFs gives the operators ample time to stop the cascade from propagating into a large-scale blackout. In this thesis, a real-time load-based prediction model for CFs using phasor measurement units (PMUs) is proposed. The proposed model provides load-based predictions; therefore, it has the advantages of being applicable as a controller input and providing the operators with better information about the affected regions. In addition, it can aid in visualizing the effects of the CF on the grid. To extend the functionality and robustness of the proposed model, prediction intervals are incorporated based on the convergence width criterion (CWC) to allow the model to account for the uncertainties of the network, which was not available in previous works. Although this model addresses many issues in previous works, it has limitations in both scalability and capturing of transient behaviours. Hence, a second model based on recurrent neural network (RNN) long short-term memory (LSTM) ensemble is proposed. The RNN-LSTM is added to better capture the dynamics of the power system while also giving faster responses. To accommodate for the scalability of the model, a novel selection criterion for inputs is introduced to minimize the inputs while maintaining a high information entropy. The criteria include distance between buses as per graph theory, centrality of the buses with respect to fault location, and the information entropy of the bus. These criteria are merged using higher statistical moments to reflect the importance of each bus and generate indices that describe the grid with a smaller set of inputs. The results indicate that this model has the potential to provide more meaningful and accurate results than what is available in the previous literature and can be used as part of the integrated remedial action scheme (RAS) system either as a warning tool or a controller input as the accuracy of detecting affected regions reached 99.9% with a maximum delay of 400 ms. Finally, a validation loop extension is introduced to allow the model to self-update in real-time using importance sampling and case-based reasoning to extend the practicality of the model by allowing it to learn from historical data as time progresses
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