Stochastic Model for Power Grid Dynamics

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy...Comment: framework for a system-level analysis of the power grid from the viewpoint of complex network

Reliability of Critical Infrastructure Networks: Challenges

Critical infrastructures form a technological skeleton of our world by providing us with water, food, electricity, gas, transportation, communication, banking, and finance. Moreover, as urban population increases, the role of infrastructures become more vital. In this paper, we adopt a network perspective and discuss the ever growing need for fundamental interdisciplinary study of critical infrastructure networks, efficient methods for estimating their reliability, and cost-effective strategies for enhancing their resiliency. We also highlight some of the main challenges arising on this way, including cascading failures, feedback loops, and cross-sector interdependencies.Comment: 12 pages, 3 figures, submitted for publication in the ASCE (American Society of Civil Engineers) technical repor

Quantifizierung der Zuverlässigkeit und Komponentenbedeutung von Infrastrukturen unter Berücksichtigung von Naturkatastropheneinwirkung

The central topic is the quantification of the reliability of infrastructure networks subject to extreme wind loads. Random fields describe the wind distributions and calibrated fragility curves yield the failure probabilities of the components as a function of the wind speed. The network damage is simulated taking into account possible cascading component failures. Defined "Importance Measures" prioritize the components based on their impact on system reliability - the basis for system reliability improvement measures.Zentrales Thema ist die Quantifizierung der Zuverlässigkeit von Infrastrukturnetzen unter Einwirkung extremer Windlasten. Raumzeitliche Zufallsfelder beschreiben die Windverteilungen und spezifisch kalibrierte Fragilitätskurven ergeben die Versagenswahrscheinlichkeiten der Komponenten. Der Netzwerkschaden wird unter Berücksichtigung von kaskadierenden Komponentenausfällen simuliert. Eigens definierte „Importance Measures“ priorisieren die Komponenten nach der Stärke ihres Einflusses auf die Systemzuverlässigkeit - die Basis für Verbesserungen der Systemzuverlässigkeit

A Markovian influence graph formed from utility line outage data to mitigate large cascades

We use observed transmission line outage data to make a Markovian influence graph that describes the probabilities of transitions between generations of cascading line outages. Each generation of a cascade consists of a single line outage or multiple line outages. The new influence graph defines a Markov chain and generalizes previous influence graphs by including multiple line outages as Markov chain states. The generalized influence graph can reproduce the distribution of cascade size in the utility data. In particular, it can estimate the probabilities of small, medium and large cascades. The influence graph has the key advantage of allowing the effect of mitigations to be analyzed and readily tested, which is not available from the observed data. We exploit the asymptotic properties of the Markov chain to find the lines most involved in large cascades and show how upgrades to these critical lines can reduce the probability of large cascades

The probability, identification, and prevention of rare events in power systems

This dissertation addresses power system rare events (or major power system blackouts) comprehensively. It first proposes the use of cluster probability model to predict the long term tendency of cascading in power system. The proposed model successfully explains the distribution of existing observed statistics and gives a very well fit. The dissertation also proposes the use of the affinity index to evaluate the likelihood of power system multiple contingencies. In order to identify higher order contingencies, a systematic way is proposed to identify power system initiating contingencies (including higher-order). We use B-matrix to represent the connective of functional groups (also called protection control groups). It is the first to give the formula in matrix form to evaluate the probabilities of fault plus stuck breaker contingencies. The work extends the conventional contingency list by including a subset of high-order contingencies, which is identified through topology processing. The last part of this work also proposes the use of DET (dynamic event tree) as an operational defense tool to cascading events in power system. We tested our DET concept on a small system, which proved the effectiveness of DET as a decision support tool for control-room operator

Systemic Risk in a Unifying Framework for Cascading Processes on Networks

We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure

Identification of Cascading Failure Propagation Under Extreme Weather Conditions

As a fundamental infrastructure, power systems play a vital role in modern society, but it can be damaged by different adverse events e.g. natural, accidental, and malicious, of which the adverse natural events, especially extreme weathers, with huge destructive force can bring tremendous damages and economic losses. The high exposure and comprehensive geographical coverage of the power system make it highly vulnerable to extreme weathers, resulting in equipment damage which leads to cascading failures and blackouts. Traditional methods only focus on modeling and analysing the reliability of the power system under extreme weathers, without focusing on the propagation of the cascades. In this thesis, innovative methods of studying the cascading failure were proposed, and further extend to collectively consider the impact of extreme weathers on the transmission networks. The proposed models were further validated by applying them to a study system (IEEE-30 bus system) and a real system (Italian transmission network). A so called normal failure model based on probabilistic graphs was proposed to describe how a cascading failure propagates under a contingency analysis. This model employed Monte Carlo simulation to consider most of the possible operating conditions to establish directed probabilistic graphs to identify the cascading propa-gation by tripping all branches one by one under each operating condition. Obviously, the results of the model can clearly and legibly show the main cascading path of a given network without considering the initial operating condition and the triggering contingency. Further, an index based on branch vulnerability was designed to select the triggering event to increase the effectiveness of the failure in the simulation. Furthermore, by integrating a probabilistic model of extreme weather impact into the normal failure model, the extreme weather model was proposed based on failure networks, which maps a physical electricity network into a graph in the cascading propagation dimensions. Based on the generated failure networks, a new method based on clustering techniques was proposed to fast track the cascading failure path from any initial contingencies without recalculating the cascading failure in the physical network. The high similarity of the simulation results on the IEEE 30 bus system from the two proposed models indicates the validity of the models. Further, to demonstrate the extreme weather model, we selected a winter storm, which could happen in Northwest of Italy as an example. The data of snowfall on the Alps was collected and modeled by probability density function and probability mass function. By applying the proposed extreme weather model, the propagation paths can be predicted. The values of the study provide two powerful tools which can 1) clearly present the inherent characteristic of any one given network, i.e. main propagation paths exist regardless of the initial network and failure condition; 2) fast and reasonably predict the cascading paths in a network under extreme weather conditions