Network-Constrained AC Unit Commitment Under Uncertainty: A Benders’ Decomposition Approach

This paper proposes an efficient solution approach based on Benders' decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders' approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach.

[1]  Ross Baldick,et al.  The generalized unit commitment problem , 1995 .

[2]  John R. Birge,et al.  A stochastic model for the unit commitment problem , 1996 .

[3]  Jose Restrepo,et al.  Security-Constrained Unit Commitment With Uncertain Wind Generation: The Loadability Set Approach , 2013, IEEE Transactions on Power Systems.

[4]  M. Anjos,et al.  Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem , 2012, IEEE Transactions on Power Systems.

[5]  A. Conejo,et al.  Market-clearing with stochastic security-part I: formulation , 2005, IEEE Transactions on Power Systems.

[6]  D. Bertsekas,et al.  Estimates of the duality gap for large-scale separable nonconvex optimization problems , 1982, 1982 21st IEEE Conference on Decision and Control.

[7]  R. W. De Doncker,et al.  Doubly fed induction generator systems for wind turbines , 2002 .

[8]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[9]  Robert J. Thomas,et al.  Secure Planning and Operations of Systems With Stochastic Sources, Energy Storage, and Active Demand , 2013, IEEE Transactions on Smart Grid.

[10]  Antonio J. Conejo,et al.  Decomposition Techniques in Mathematical Programming: Engineering and Science Applications , 2006 .

[11]  A.J. Conejo,et al.  Optimal Network Placement of SVC Devices , 2007, IEEE Transactions on Power Systems.

[12]  P. Carpentier,et al.  Stochastic optimization of unit commitment: a new decomposition framework , 1996 .

[13]  A. Conejo,et al.  Scenario Reduction for Futures Market Trading in Electricity Markets , 2009, IEEE Transactions on Power Systems.

[14]  A. Conejo,et al.  Market-clearing with stochastic security - part II: case studies , 2006, 2006 IEEE Power Engineering Society General Meeting.

[15]  B. Janani,et al.  Network-Constrained AC Unit Commitment under Uncertainty Using a Bender’s Decomposition Approach , 2016 .

[16]  Antonio J. Conejo,et al.  Short-term hydro-thermal coordination by Lagrangian relaxation: solution of the dual problem , 1999 .

[17]  A. Conejo,et al.  Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power , 2009 .

[18]  Silvano Martello,et al.  Decision Making under Uncertainty in Electricity Markets , 2015, J. Oper. Res. Soc..

[19]  Francisco D. Galiana,et al.  Towards a more rigorous and practical unit commitment by Lagrangian relaxation , 1988 .

[20]  A. L. Diniz,et al.  Feasibility and optimality cuts for the MultiStage benders decomposition approach: Application to the network constrained hydrothermal scheduling , 2009, 2009 IEEE Power & Energy Society General Meeting.

[21]  M. Shahidehpour,et al.  Security-Constrained Unit Commitment With Volatile Wind Power Generation , 2008, IEEE Transactions on Power Systems.

[22]  Ali Ahmadi-Khatir,et al.  Multi-Area Unit Scheduling and Reserve Allocation Under Wind Power Uncertainty , 2014, IEEE Transactions on Power Systems.

[23]  W.S. Sifuentes,et al.  Hydrothermal Scheduling Using Benders Decomposition: Accelerating Techniques , 2007, IEEE Transactions on Power Systems.

[24]  A. Conejo,et al.  Decision making under uncertainty in electricity markets , 2010, 2006 IEEE Power Engineering Society General Meeting.

[25]  M. O'Malley,et al.  Unit Commitment for Systems With Significant Wind Penetration , 2009, IEEE Transactions on Power Systems.

[26]  Yong Fu,et al.  Security-constrained unit commitment with AC constraints , 2005, IEEE Transactions on Power Systems.

[27]  Xu Cheng,et al.  PTDF-based power system equivalents , 2005, IEEE Transactions on Power Systems.

[28]  Mohammad Shahidehpour,et al.  The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee , 1999 .

[29]  Antonio J. Conejo,et al.  Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power , 2009, IEEE Transactions on Power Systems.

[30]  Jianhui Wang,et al.  Stochastic Optimization for Unit Commitment—A Review , 2015, IEEE Transactions on Power Systems.

[31]  Yongpei Guan,et al.  Price-Based Unit Commitment With Wind Power Utilization Constraints , 2013, IEEE Transactions on Power Systems.

[32]  Anthony Papavasiliou,et al.  Multiarea Stochastic Unit Commitment for High Wind Penetration in a Transmission Constrained Network , 2013, Oper. Res..