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Distributed Monitoring for the Prevention of Cascading Failures In ARTICLE IN PRESS JID: IJCIP [m7; April 24, 2017;15:20 ] international journal of critical infrastructure protection 000 (2017) 1–13 Available online at www.sciencedirect.com journal homepage: www.elsevier.com/locate/IJCIP Distr ibuted monitor ing for the prevention of cascading failures in operational power grids ∗ Martijn Warnier a, , Stefan Dulman b, Yakup Koç a,c, Eric Pauwels b a Systems Engineering, Faculty of Technology, Policy and Management, Delft University of Technology, Jaffalaan 5, Delft 2628 BX, The Netherlands b Intelligent Systems Group, Centrum Wiskunde and Informatica (CWI), Science Park 123, Amsterdam 1098 XG, The Netherlands c Risk and Information Management, Stedin, Blaak 8, Rotterdam 3011 TA, The Netherlands a r t i c l e i n f o a b s t r a c t Article history: Electrical power grids are vulnerable to cascading failures that can lead to large blackouts. Received 7 April 2016 The detection and prevention of cascading failures in power grids are important problems. Revised 2 November 2016 Currently, grid operators mainly monitor the states (loading levels) of individual compo- Accepted 8 February 2017 nents in a power grid. The complex architecture of a power grid, with its many interdepen- Available online xxx dencies, makes it difficult to aggregate the data provided by local components in a mean- ingful and timely manner. Indeed, monitoring the resilience of an operational power grid to Keywords: cascading failures is a major challenge. Power Grids This paper attempts to address this challenge. It presents a robustness metric based on Cascading Failures the topology and operative state of a power grid to quantify the robustness of the grid. Also, Robustness it presents a distributed computation method with self-stabilizing properties that can be Real-Time Monitoring used for near real-time monitoring of grid robustness. The research thus provides insights Distributed Computation into the resilience of a dynamic operational power grid to cascading failures during real- time in a manner that is both scalable and robust. Computations are pushed to the power grid network, making the results available at each node and enabling automated distributed control mechanisms to be implemented. © 2017 Elsevier B.V. All rights reserved. sumers are becoming producers of electricity by installing so- 1. Introduction lar panels and wind mills [29] . Part of this produced power will be used locally, but excess power will be fed into the power Power grids are major critical infrastructure assets—all kinds grid. This contributes to grid instability [47] because it is diffi- of basic, government and private services depend on the con- cult to predict and, thus, balance electricity production when tinuous and reliable delivery of electricity. Power grid outages power is supplied by a large number of small producers spread can have significant societal impacts in terms of human safety over a large geographical region, instead of a few large produc- and economic losses. ers. The large-scale introduction of renewable energy sources Unfortunately, the current power grid architecture does not and the current (centralized) architecture of the power grid support the large-scale introduction of small producers [1] . increase the likelihood of power outages. Encouraged by gov- This significantly increases the possibility of a major power ernment subsidies and the trend to become more “green,” con- grid failure—initial local disruptions spread to the rest of a grid, evolving into a system-wide outage [10] . An initial ∗ Corresponding author . failure can be caused by an external event such as a storm E-mail address: [email protected] (M. Warnier). http://dx.doi.org/10.1016/j.ijcip.2017.03.003 1874-5482/© 2017 Elsevier B.V. All rights reserved. Please cite this article as: Martijn Warnier et al., Distributed monitoring for the prevention of cascading failures in operational power grids, International Journal of Critical Infrastructure Protection (2017), http://dx.doi.org/10.1016/j.ijcip.2017.03.003 ARTICLE IN PRESS JID: IJCIP [m7; April 24, 2017;15:20 ] 2 international journal of critical infrastructure protection 000 (2017) 1–13 and the failure effects can spread to the rest of the network in trality [15] and gap metric [14] . These metrics can be used to different ways, including voltage and frequency instabilities, determine the most critical nodes in a power grid. hidden failures of protection systems, software and operator However, in addition to its topological characteristics, a errors, and line overloads. power grid has a physical aspect. In particular, electrical cur- For example, a large-scale outage can be initiated by an rent in a power grid behaves according to Kirchhoff’s laws [5] . overloaded line that is “tripped” by a circuit breaker. At this Therefore, a metric that is used to quantify the robustness of point, electricity can no longer flow through the line and the an operational power grid to cascading failures should con- power flows to other lines. This can overload some of the lines, sider its topological and physical characteristics. causing them to be tripped as well. As this process repeats The metric for robustness to cascading failures RCF over and over again, more and more lines are shut down, lead- [24,25] does exactly this. It is, therefore, the starting point for ing to a cascading failure of the power grid [13,39] . This paper the distributed power grid monitoring algorithm proposed in focuses on cascading effects created by line overloads and on this paper. The robustness metric RCF assesses the robustness preventing cascading failures. of a power grid to cascading failures caused by line overloads. In order to detect (and ultimately prevent) cascading fail- The metric relies on two main concepts: (i) electrical node ro- ures, it is necessary to monitor and alter the current state bustness; and (ii) electrical node significance. Higher values of (power load distribution) of a power grid. The emerging smart the RCF metric indicate greater robustness, i.e., a power grid grid is designed to do exactly this—it leverages a communi- that is able to resist cascading failures to a larger extent. The cations overlay that connects sensors and actuators. In effect, remainder of this section summarizes previous work on ro- a smart grid is a large-scale distributed system that monitors bustness metrics. Interested readers are referred to [24,25] for line loads and accordingly changing the network state by trip- additional details about robustness metrics. ping and untripping lines. This paper deals with a smart grid environment. It focuses 2.1. Electrical node robustness on two principal research questions. The first question is: What should be monitored? In other words, is there a met- The electrical node robustness quantifies the ability of a bus ric that can predict cascading failures? The second question (i.e., a node in a graph representation of a power grid) to resist is: How should the grid be monitored? In other words, how cascading line overload failures by incorporating flow dynam- should aggregation be performed and what is the appropri- ics and network topology. Three key factors are used to calcu- ate temporal resolution for the monitoring? The extension of late this robustness value for a node: (i) homogeneity of the the resulting passive monitoring scheme to an active scheme load distribution on out-going branches (i.e., links in a graph that automatically alters the state of a power grid to prevent representation of a power grid); (ii) loading level of the out- cascading failures is a topic for future research. going links; and (iii) out-degree of the node. The main contribution of the paper is a new distributed Entropy is used to capture the first and third factors de- monitoring approach that can be used to monitor the robust- scribed above. The entropy of a load distribution at a node ness of a power grid to cascading failures. The monitoring ap- increases as flows over lines are distributed more homoge- proach is based on the distributed computation of the robust- neously and the node out-degree increases. The entropy of a ness metric introduced in [24,25] . The contributions also in- given load distribution at a node i is computed as: clude an extension of distributed gossip algorithms [9] with a self-stabilization mechanism to account for network dynam- d = − ics. The resulting framework enables distributed aggregates to Hi pij log pij (1) be computed in a rapid and reliable manner; this is at the heart j=1 of the proposed power grid monitoring approach. The principal technical result is that it is possible to com- where d is the out-degree of the corresponding node and pij is pute a complex robustness metric using simple, albeit robust, the normalized flow value on the out-going link lij . The nor- distributed primitives in a manner that makes the results malized flow value pij is computed as: readily available to every node in a power grid. The result is im- fij portant because it enables the measurement infrastructure to = pij (2) d be used in real-time to implement distributed control mecha- j=1 fij nisms for a power grid. The convergence time scales very well (logarithmic order) with respect to network size. The precision where fij is the flow value in line lij . of the computations can be set by adjusting the message sizes The effect of the loading level of the power grid is expressed and is independent of network parameters such as the num- using the tolerance parameter α (see [34] ). The tolerance level α ber of nodes and network diameter. ij of line lij is the ratio of the rated limit to the load of line α lij .
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