Maximal network reliability for a stochastic power transmission network

Many studies regarded a power transmission network as a binary-state network and constructed it with several arcs and vertices to evaluate network reliability. In practice, the power transmission network should be stochastic because each arc (transmission line) combined with several physical lines is multistate. Network reliability is the probability that the network can transmit d units of electric power from a power plant (source) to a high voltage substation at a specific area (sink). This study focuses on searching for the optimal transmission line assignment to the power transmission network such that network reliability is maximized. A genetic algorithm based method integrating the minimal paths and the Recursive Sum of Disjoint Products is developed to solve this assignment problem. A real power transmission network is adopted to demonstrate the computational efficiency of the proposed method while comparing with the random solution generation approach.

[1]  Enrico Zio,et al.  Randomized flow model and centrality measure for electrical power transmission network analysis , 2010, Reliab. Eng. Syst. Saf..

[2]  Enrico Zio,et al.  Optimal expansion of an existing electrical power transmission network by multi-objective genetic algorithms , 2010, Reliab. Eng. Syst. Saf..

[3]  Kailash C. Kapur,et al.  Reliability Bounds for Multistate Systems with Multistate Components , 1985, Oper. Res..

[4]  Juan Li,et al.  Reliability based assignment in stochastic-flow freight network , 2009, Appl. Math. Comput..

[5]  Christian Posse,et al.  Evaluating North American Electric Grid Reliability Using the Barabasi-Albert Network Model , 2004, nlin/0408052.

[6]  Gregory Levitin,et al.  MSS Reliability Optimization , 2003 .

[7]  Yi-Kuei Lin,et al.  Reliability of a stochastic-flow network with unreliable branches & nodes, under budget constraints , 2004, IEEE Trans. Reliab..

[8]  Sheng-Tzong Cheng.  Topological optimization of a reliable communication network , 1998 .

[9]  Gregory Levitin,et al.  Multi-State System Reliability - Assessment, Optimization and Applications , 2003, Series on Quality, Reliability and Engineering Statistics.

[10]  Yi-Kuei Lin,et al.  On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint , 2007, Eur. J. Oper. Res..

[11]  Yi-Ting Chen,et al.  Resource allocation decisions under various demands and cost requirements in an unreliable flow network , 2005, Comput. Oper. Res..

[12]  Gregory Levitin,et al.  A new approach to solving problems of multi‐state system reliability optimization , 2001 .

[13]  Chung-Chi Hsieh,et al.  Reliability-oriented multi-resource allocation in a stochastic-flow network , 2003, Reliab. Eng. Syst. Saf..

[14]  Laura Painton,et al.  Genetic algorithms in optimization of system reliability. , 1995 .

[15]  John E. Beasley,et al.  A genetic algorithm for the generalised assignment problem , 1997, Comput. Oper. Res..

[16]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[17]  Wei-Chang Yeh.  An improved algorithm for searching all minimal cuts in modified networks , 2008, Reliab. Eng. Syst. Saf..

[18]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[19]  Weng-Ming Chu,et al.  A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements , 2008 .

[20]  Ake J Holmgren,et al.  Using Graph Models to Analyze the Vulnerability of Electric Power Networks , 2006, Risk analysis : an official publication of the Society for Risk Analysis.

[21]  Yi-Kuei Lin,et al.  Optimal routing policy of a stochastic-flow network , 2009, Comput. Ind. Eng..

[22]  Ricard V. Solé,et al.  Topological Vulnerability of the European Power Grid under Errors and Attacks , 2007, Int. J. Bifurc. Chaos.

[23]  David W. Coit,et al.  Reliability optimization of series-parallel systems using a genetic algorithm , 1996, IEEE Trans. Reliab..

[24]  David W. Coit,et al.  Multi-state component criticality analysis for reliability improvement in multi-state systems , 2007, Reliab. Eng. Syst. Saf..

[25]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[26]  Qiang Liu,et al.  Genetic Algorithm-based Study on Flow Allocation in a Multicommodity Stochastic-flow Network with Unreliable Nodes , 2007, Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007).

[27]  John Yuan,et al.  Reliability evaluation of a limited-flow network in terms of minimal cutsets , 1993 .

[28]  Yi-Ting Chen,et al.  Reliable and economic resource allocation in an unreliable flow network , 2005, Comput. Oper. Res..

[29]  John M. Wilson,et al.  A genetic algorithm for the generalised assignment problem , 1997 .

[30]  Yi-Kuei Lin,et al.  Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs , 2002, Reliab. Eng. Syst. Saf..

[31]  Hong-Zhong Huang,et al.  An efficient method for reliability evaluation of multistate networks given all minimal path vectors , 2007 .

[32]  Devika Subramanian,et al.  Performance assessment of topologically diverse power systems subjected to hurricane events , 2010, Reliab. Eng. Syst. Saf..

[33]  Yi-Kuei Lin,et al.  A simple algorithm for reliability evaluation of a stochastic-flow network with node failure , 2001, Comput. Oper. Res..

[34]  S. Rahman.  Reliability Engineering and System Safety , 2011 .

[35]  Terje Aven,et al.  Reliability Evaluation of Multistate Systems with Multistate Components , 1985, IEEE Transactions on Reliability.

[36]  Wei-wei Wu,et al.  Evaluation of the reliability of transport networks based on the stochastic flow of moving objects , 2008, Reliab. Eng. Syst. Saf..

[37]  M. Fisher,et al.  A multiplier adjustment method for the generalized assignment problem , 1986 .

[38]  Yi-Kuei Lin,et al.  Reliability Evaluation for an Information Network With Node Failure Under Cost Constraint , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[39]  Ignacio J. Ramirez-Rosado,et al.  Reliability and Costs Optimization for Distribution Networks Expansion Using an Evolutionary Algorithm , 1989 .

[40]  H. Salehi Fathabadi,et al.  A note on "A simple approach to search for all d-MCs of a limited-flow network" , 2009, Reliab. Eng. Syst. Saf..

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

[42]  Anthoula Menti,et al.  Genetic algorithm-based optimal design of shunt compensators in the presence of harmonics , 2008 .

[43]  Wei-Chang Yeh.  A simple approach to search for all d-MCs of a limited-flow network , 2001, Reliab. Eng. Syst. Saf..

[44]  Gregory Levitin,et al.  Reliability evaluation for acyclic consecutively connected networks with multistate elements , 2001, Reliab. Eng. Syst. Saf..

[45]  Xue Janan,et al.  On Multistate System Analysis , 1985, IEEE Transactions on Reliability.

[46]  Chin-Chia Jane,et al.  On reliability evaluation of a capacitated-flow network in terms of minimal pathsets , 1995, Networks.