Network reduction in the Transmission-Constrained Unit Commitment problem

This paper examines a preprocessing technique for a Mixed Integer Linear Programming (MILP) formulation of the Transmission-Constrained Unit Commitment problem (TC-UC). Incorporating transmission constraints into the Unit Commitment problem can significantly increase the size and difficulty of the problem. By examining the structure of the transmission network, variables that have no impact on the quality of the overall solution can be identified and removed. This preprocessing can reduce the time needed to solve the linear programming relaxation of the MILP, and as a result, the MILP itself. Illinois's transmission network was used to test the benefit of the proposed technique. Preprocessing was able to remove 30% of the buses in the transmission network. This reduction led to a significant decrease in the time needed to solve a 24h TC-UC problem. An added benefit of the preprocessing is that symmetry can be introduced into the problem. Identifying this symmetry and exploiting it can improve overall solution times even further.

[1]  Zuyi Li,et al.  Network Reduction With Unknown Transmission Line Status , 2007, 2007 39th North American Power Symposium.

[2]  Miguel F. Anjos,et al.  Symmetry in Scheduling Problems , 2010 .

[3]  Xiaohong Guan,et al.  Fast Identification of Inactive Security Constraints in SCUC Problems , 2010, IEEE Transactions on Power Systems.

[4]  S. M. Shahidehpour,et al.  Transmission constrained unit commitment based on Benders decomposition , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Shmuel S. Oren,et al.  A transmission-constrained unit commitment method in power system scheduling , 1999, Decis. Support Syst..

[6]  M. Shahidehpour,et al.  Accelerating the Benders decomposition for network-constrained unit commitment problems , 2010 .

[7]  S. M. Shahidehpour,et al.  Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation , 1995 .

[8]  Claudio Gentile,et al.  Perspective cuts for a class of convex 0–1 mixed integer programs , 2006, Math. Program..

[9]  C. Gentile,et al.  Tighter Approximated MILP Formulations for Unit Commitment Problems , 2009, IEEE Transactions on Power Systems.

[10]  A. Conejo,et al.  Optimal response of a thermal unit to an electricity spot market , 2000 .

[11]  J. J. Quada,et al.  Sparsity-enhanced network reduction for fault studies , 1991 .

[12]  J. B. Ward.  Equivalent Circuits for Power-Flow Studies , 1949, Transactions of the American Institute of Electrical Engineers.

[13]  Christian Waibel.  Pruning by Isomorphism in Branch-and-Cut , 2008 .

[14]  S. C. Srivastava,et al.  A sensitivity based network reduction technique for power transfer assessment in deregulated electricity environment , 2002, IEEE/PES Transmission and Distribution Conference and Exhibition.

[15]  Samer Takriti,et al.  The Unit Commitment Problem , 1999 .

[16]  A. Renaud,et al.  Daily generation scheduling optimization with transmission constraints: a new class of algorithms , 1992 .

[17]  Jeff T. Linderoth,et al.  Orbital Branching , 2007, IPCO.

[18]  Deepak Rajan,et al.  IBM Research Report Minimum Up/Down Polytopes of the Unit Commitment Problem with Start-Up Costs , 2005 .

[19]  Antonio J. Conejo,et al.  Multiperiod optimal power flow using Benders decomposition , 2000 .