Transmission expansion planning with re-design

Expanding an electrical transmission network requires heavy investments that need to be carefully planned, often at a regional or national level. We study relevant theoretical and practical aspects of transmission expansion planning, set as a bilinear programming problem with mixed 0–1 variables. We show that the problem is NP-hard and that, unlike the so-called Network Design Problem, a transmission network may become more efficient after cutting-off some of its circuits. For this reason, we introduce a new model that, rather than just adding capacity to the existing network, also allows for the network to be re-designed when it is expanded. We then turn into different reformulations of the problem, that replace the bilinear constraints by using a “big-M” approach. We show that computing the minimal values for the “big-M” coefficients involves finding the shortest and longest paths between two buses. We assess our theoretical results by making a thorough computational study on real electrical networks. The comparison of various models and reformulations shows that our new model, allowing for re-design, can lead to sensible cost reductions.

[1]  W. W. Hardgrave,et al.  On the Relation Between the Traveling-Salesman and the Longest-Path Problems , 1962 .

[2]  L. L. Garver,et al.  Transmission Network Estimation Using Linear Programming , 1970 .

[3]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[4]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[5]  Richard T. Wong,et al.  A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..

[6]  I. Grossmann,et al.  An LP/NLP based branch and bound algorithm for convex MINLP optimization problems , 1992 .

[7]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[8]  R. Raman,et al.  Modelling and computational techniques for logic based integer programming , 1994 .

[9]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[10]  P. Carpentier,et al.  Transmission Network Planning Under Uncertainty with Benders Decomposition , 2000 .

[11]  Teodor Gabriel Crainic,et al.  Service network design in freight transportation , 2000, Eur. J. Oper. Res..

[12]  Michael J. Townsend,et al.  Thomas Piketty: Capital in the twenty-first century , 2014, Public Choice.

[13]  M. Pereira,et al.  A Mixed Integer Disjunctive Model for Transmission Network Expansion , 2001, IEEE Power Engineering Review.

[14]  S. Binato,et al.  A Greedy Randomized Adaptive Search Procedure for Transmission Expansion Planning , 2001 .

[15]  D. J. Hill,et al.  A New Strategy for Transmission Expansion in Competitive Electricity Markets , 2002, IEEE Power Engineering Review.

[16]  D. J. Hill,et al.  A New Strategy for Transmission Expansion in Competitive Electricity Markets , 2002, IEEE Power Engineering Review.

[17]  G. Latorre,et al.  Classification of publications and models on transmission expansion planning , 2003 .

[18]  Antonio J. Conejo,et al.  Transmission expansion planning: a mixed-integer LP approach , 2003 .

[19]  A. Philpott,et al.  Column-Generation for Design of Survivable Electricity Distribution Networks , 2004 .

[20]  M. Shahidehpour,et al.  Market based transmission expansion planning: fuzzy risk assessment , 2004, 2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies. Proceedings.

[21]  S. Binato,et al.  Security-constrained transmission planning : A mixed-integer disjunctive approach , 2004 .

[22]  P.M.S. Carvalho,et al.  Reinforcement scheduling convergence in power systems transmission planning , 2005, IEEE Transactions on Power Systems.

[23]  Z.Y. Dong,et al.  A Framework for Transmission Planning in a Competitive Electricity Market , 2005, 2005 IEEE/PES Transmission & Distribution Conference & Exposition: Asia and Pacific.

[24]  I. C. da Silva,et al.  Transmission system expansion planning using a sigmoid function to handle integer investment variables , 2006, IEEE Transactions on Power Systems.

[25]  Irênio De Jesus Silva Junior,et al.  Planejamento da expansão de sistemas de transmissão considerando segurança e planos de programação da geração , 2005 .

[26]  Jaeseok Choi.  A method for transmission system expansion planning considering probabilistic reliability criteria , 2005, IEEE Transactions on Power Systems.

[27]  Roy Billinton,et al.  A method for composite power system expansion planning considering probabilistic reliability criteria , 2005 .

[28]  M.J. Rider,et al.  Transmission Network Expansion Planning Considering Uncertainty in Demand , 2006, IEEE Transactions on Power Systems.

[29]  Jaeseok Choi.  A Method for Transmission System Expansion Planning Considering Probabilistic Reliability Criteria , 2006 .

[30]  M. Shahidehpour,et al.  Network planning in unbundled power systems , 2006, IEEE Transactions on Power Systems.

[31]  S. Carneiro,et al.  Transmission system expansion planning using a sigmoid function to handle integer investment variables , 2005, 2006 IEEE Power Engineering Society General Meeting.

[32]  Daniel Bienstock,et al.  Using mixed-integer programming to solve power grid blackout problems , 2007, Discret. Optim..

[33]  Ryuhei Uehara,et al.  On Computing Longest Paths in Small Graph Classes , 2007, Int. J. Found. Comput. Sci..

[34]  Jaeseok Choi,et al.  Transmission Expansion Planning Using Contingency Criteria , 2007, IEEE Transactions on Power Systems.

[35]  V. Quintana,et al.  Generation and Transmission Expansion Under Risk Using Stochastic Programming , 2007, IEEE Transactions on Power Systems.

[36]  S. Binato,et al.  Value-Based Transmission Expansion Planning of Hydrothermal Systems Under Uncertainty , 2007, IEEE Transactions on Power Systems.

[37]  Jeff T. Linderoth,et al.  FilMINT: An Outer-Approximation-Based Solver for Nonlinear Mixed Integer Programs , 2008 .

[38]  M. Shahidehpour,et al.  Congestion-driven transmission planning considering the impact of generator expansion , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[39]  J. Contreras,et al.  Transmission Expansion Planning in Electricity Markets , 2008, IEEE Transactions on Power Systems.

[40]  Zhao Yang Dong,et al.  Flexible Transmission Expansion Planning With Uncertainties in an Electricity Market , 2009, IEEE Transactions on Power Systems.

[41]  M. Shahidehpour,et al.  A Multi-Objective Framework for Transmission Expansion Planning in Deregulated Environments , 2009, IEEE Transactions on Power Systems.

[42]  John R. Birge,et al.  Introduction to Stochastic programming (2nd edition), Springer verlag, New York , 2011 .

[43]  W. Marsden.  I and J , 2012 .