A Spectral Approach for the Efficient Identification of Power Transmission Network Uncontrolled Separation

Abstract Uncontrolled network separation (system island formation) is one of the most critical contingencies in power systems. The integrity of the whole power transmission network is a prerequisite for reliable system operation. Therefore, in order to safeguard the system operation and control, it is imperative to quickly identify the topological changes, especially the formation of system islands. In this paper, we developed a spectral clustering-based approach to efficiently detect the existing or the potential network islands. The core of this approach is a graph-algebraic model, which combines the real-power deliverability and topological information of a power transmission network. Based on an improved spectral clustering algorithm, the proposed approach can efficiently identify the critical situations of the network splitting under multiple line outages. This approach has been successfully tested by using the New England 39-bus and 118-bus systems under different scenarios.

[1]  Albert M. Sasson,et al.  Automatic Power System Network Topology Determination , 1973 .

[2]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[3]  G. P. Granelli,et al.  Detection of Jacobian singularity and network islanding in power flow computations , 1995 .

[4]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[5]  James S. Thorp,et al.  Expose hidden failures to prevent cascading outages [in power systems] , 1996 .

[6]  Massimo Marchiori,et al.  A topological analysis of the Italian electric power grid , 2004 .

[7]  G. Caldarelli,et al.  Detecting communities in large networks , 2004, cond-mat/0402499.

[8]  Lawrence R. Rabiner,et al.  A modified K-means clustering algorithm for use in isolated work recognition , 1985, IEEE Trans. Acoust. Speech Signal Process..

[9]  X. Wang,et al.  Modern power system planning , 1994 .

[10]  Ulrik Brandes,et al.  Engineering graph clustering: Models and experimental evaluation , 2008, JEAL.

[11]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[12]  Fang Wu,et al.  Finding communities in linear time: a physics approach , 2003, ArXiv.

[13]  Luigi Berardi,et al.  Efficient multi-objective optimal design of water distribution networks on a budget of simulations using hybrid algorithms , 2009, Environ. Model. Softw..

[14]  Y. Lai,et al.  Attacks and cascades in complex networks , 2004 .

[15]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[16]  Chao Yang,et al.  Identification of severe multiple contingencies in electric power networks , 2005, Proceedings of the 37th Annual North American Power Symposium, 2005..

[17]  Michael William Newman,et al.  The Laplacian spectrum of graphs , 2001 .

[18]  Mahdi Jalili,et al.  Social power and opinion formation in complex networks , 2013 .

[19]  M. Bertran,et al.  On the Validation and Analysis of a New Method for Power Network Connecticity Determination , 1982, IEEE Transactions on Power Apparatus and Systems.

[20]  J. S. Thorp,et al.  A reliability study of transmission system protection via a hidden failure DC load flow model , 2002 .

[21]  Marco Aiello,et al.  The Power Grid as a Complex Network: a Survey , 2011, ArXiv.

[22]  Men-Shen Tsai.  Development of islanding early warning mechanism for power systems , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).

[23]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

[25]  Honghai Li,et al.  The effect on the second smallest eigenvalue of the normalized Laplacian of a graph by grafting edges , 2008 .

[26]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[27]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[28]  F. Goderya,et al.  Fast Detection and Identification of Islands in Power Networks , 1980, IEEE Transactions on Power Apparatus and Systems.

[29]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[30]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[31]  Tomas E. Dy Liacco,et al.  Processing by Logic Programming of Circuit-Breaker and Protective-Relaying Information , 1969 .

[32]  S Arianos,et al.  Power grid vulnerability: a complex network approach. , 2008, Chaos.

[33]  Stefan Bornholdt,et al.  Detecting fuzzy community structures in complex networks with a Potts model. , 2004, Physical review letters.

[34]  M. A. Muñoz,et al.  Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Detecting network communities: a new systematic and efficient algorithm , 2004 .

[35]  W. Haemers,et al.  A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo , 2008 .

[36]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  D. Newth,et al.  Optimizing complex networks for resilience against cascading failure , 2007 .