Robust unit commitment problem with demand response and wind energy

Currently, both demand response (DR) strategy and renewable energy have been adopted to improve power generation efficiency and reduce greenhouse gas emission. However, the uncertainty and intermittent generation pattern in wind farms and the complexity of demand side management pose huge challenges. In this paper, we analytically investigate how to integrate DR and wind energy with fossil fuel generators to (i) minimize power generation cost; and (2) fully take advantage of the wind energy with the managed demand to reduce greenhouse emission. We first build a two-stage robust unit commitment (UC) model to obtain day-ahead generator schedules where wind uncertainty is captured by a polytopic uncertainty set. Then, we extend our model to include DR strategy such that both price levels and generator schedules will be derived for the next day. For these two challenging models, we derive their mathematical properties and develop a novel solution method. Our computational study on an IEEE 118-bus system with 36 units shows that robust UC models can fully make use of wind generation with less generation cost. Also, the developed algorithm is computationally superior to classical Benders decomposition method.

[1]  Laurent El Ghaoui,et al.  Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach , 2003, Oper. Res..

[2]  Masood Parvania,et al.  Demand Response Scheduling by Stochastic SCUC , 2010, IEEE Transactions on Smart Grid.

[3]  Samer Takriti,et al.  Incorporating Fuel Constraints and Electricity Spot Prices into the Stochastic Unit Commitment Problem , 2000, Oper. Res..

[4]  Dimitris Bertsimas,et al.  A Robust Optimization Approach to Inventory Theory , 2006, Oper. Res..

[5]  Tao Li,et al.  Cost of Reliability Analysis Based on Stochastic Unit Commitment , 2008, IEEE Transactions on Power Systems.

[6]  Arkadi Nemirovski,et al.  Robust Convex Optimization , 1998, Math. Oper. Res..

[7]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[8]  Claudio Gentile,et al.  Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints , 2006, Oper. Res..

[9]  N.P. Padhy,et al.  Unit commitment-a bibliographical survey , 2004, IEEE Transactions on Power Systems.

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

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

[12]  Jianhui Wang,et al.  Impact of Wind Power Forecasting on Unit Commitment and Dispatch , 2009 .

[13]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2004, Math. Program..

[14]  S. M. Shahidehpour,et al.  Unit commitment with transmission security and voltage constraints , 1999 .

[15]  Sangmin Lee,et al.  A Computational Framework for Uncertainty Quantification and Stochastic Optimization in Unit Commitment With Wind Power Generation , 2011, IEEE Transactions on Power Systems.

[16]  M. Shahidehpour,et al.  Security-Constrained Unit Commitment With AC/DC Transmission Systems , 2010, IEEE Transactions on Power Systems.

[17]  Georgia Perakis,et al.  Dynamic Pricing and Inventory Control: Uncertainty and Competition , 2010, Oper. Res..

[18]  James E. Falk,et al.  A linear max—min problem , 1973, Math. Program..

[19]  D. Kirschen,et al.  Quantifying the Effect of Demand Response on Electricity Markets , 2007, IEEE Transactions on Power Systems.

[20]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[21]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[22]  Shabbir Ahmed,et al.  On robust optimization of two-stage systems , 2004, Math. Program..

[23]  Ralf Gollmer,et al.  Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods , 2009, Oper. Res..

[24]  Arkadi Nemirovski,et al.  Robust optimization – methodology and applications , 2002, Math. Program..

[25]  Sanem Sergici,et al.  Household Response to Dynamic Pricing of Electricity - A Survey of the Empirical Evidence , 2010 .

[26]  Dimitris Bertsimas,et al.  A Robust Optimization Approach to Supply Chain Management , 2004, IPCO.

[27]  Alper Atamtürk,et al.  Two-Stage Robust Network Flow and Design Under Demand Uncertainty , 2007, Oper. Res..

[28]  Melvyn Sim,et al.  Robust Approximation to Multiperiod Inventory Management , 2010, Oper. Res..

[29]  Melvyn Sim,et al.  Robust discrete optimization and network flows , 2003, Math. Program..

[30]  Arkadi Nemirovski,et al.  Selected topics in robust convex optimization , 2007, Math. Program..

[31]  Arkadi Nemirovski,et al.  Robust solutions of uncertain linear programs , 1999, Oper. Res. Lett..

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

[33]  Zhaosong Lu A computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set , 2011, Math. Program..

[34]  W. Short,et al.  Evaluating the Impacts of Real-Time Pricing on the Usage of Wind Generation , 2009, IEEE Transactions on Power Systems.

[35]  R. Tütüncü,et al.  Adjustable Robust Optimization Models for a Nonlinear Two-Period System , 2008 .

[36]  Kory W Hedman,et al.  Co-Optimization of Generation Unit Commitment and Transmission Switching With N-1 Reliability , 2010, IEEE Transactions on Power Systems.