The value of rolling-horizon policies for risk-averse hydro-thermal planning

We consider the optimal management of a hydro-thermal power system in the mid and long terms. From the optimization point of view, this amounts to a large-scale multistage stochastic linear program, often solved by combining sampling with decomposition algorithms, like stochastic dual dynamic programming. Such methodologies, however, may entail prohibitive computational time, especially when applied to a risk-averse formulation of the problem. We propose instead a risk-averse rolling-horizon policy that is nonanticipative, feasible, and time consistent. The policy is obtained by solving a sequence of risk-averse problems with deterministic constraints for the current time step and future chance and CVaR constraints.

[1]  W. Romisch,et al.  Dynamic risk management in electricity portfolio optimization via polyhedral risk functionals , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[2]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[3]  Warrren B Powell,et al.  Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse , 1999 .

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

[5]  François Oustry,et al.  Robust mid-term power generation management , 2009 .

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

[7]  Andrew B. Philpott,et al.  On the convergence of stochastic dual dynamic programming and related methods , 2008, Oper. Res. Lett..

[8]  Werner Römisch,et al.  Polyhedral risk measures in electricity portfolio optimization , 2004 .

[9]  A. Ben-Tal,et al.  Adjustable robust solutions of uncertain linear programs , 2004, Math. Program..

[10]  Alexander Shapiro,et al.  On a time consistency concept in risk averse multistage stochastic programming , 2009, Oper. Res. Lett..

[11]  Vincent Guigues,et al.  SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning , 2014, Comput. Optim. Appl..

[12]  Roger J.-B. Wets Stochastic Programming Models: Wait-and-See Versus Here-and-Now , 2002 .

[13]  S. Wallace,et al.  Stochastic Programming Models in Energy , 2003 .

[14]  Vincent Guigues,et al.  Robust production management , 2009 .

[15]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[16]  Alexander Shapiro,et al.  Analysis of stochastic dual dynamic programming method , 2011, Eur. J. Oper. Res..

[17]  M. V. F. Pereira,et al.  Multi-stage stochastic optimization applied to energy planning , 1991, Math. Program..

[18]  V. Guigues A stabilized model and an efficient solution method for the yearly optimal power management , 2011, Optim. Methods Softw..

[19]  Jean-Philippe Chancelier,et al.  Dynamic consistency for stochastic optimal control problems , 2012, Ann. Oper. Res..

[20]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[21]  Werner Römisch,et al.  Sampling-Based Decomposition Methods for Multistage Stochastic Programs Based on Extended Polyhedral Risk Measures , 2012, SIAM J. Optim..

[22]  J. Cabero,et al.  A medium-term integrated risk management model for a hydrothermal generation company , 2005, IEEE Transactions on Power Systems.

[23]  Norman C. Beaulieu,et al.  Estimating the distribution of a sum of independent lognormal random variables , 1995, IEEE Trans. Commun..

[24]  J. M. Damázio,et al.  The use of PAR(p) model in the stochastic dual dynamic programming optimization scheme used in the operation planning of the Brazilian hydropower system , 2005, 2004 International Conference on Probabilistic Methods Applied to Power Systems.

[25]  Birger Mo,et al.  Integrated risk management of hydro power scheduling and contract management , 2001 .

[26]  Claudia A. Sagastizábal,et al.  Risk-averse feasible policies for large-scale multistage stochastic linear programs , 2013, Math. Program..

[27]  Jingxian Wu,et al.  Flexible lognormal sum approximation method , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[28]  F. Nogales,et al.  Risk-constrained self-scheduling of a thermal power producer , 2004, IEEE Transactions on Power Systems.

[29]  Vitor L. de Matos,et al.  Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion , 2012, Eur. J. Oper. Res..

[30]  René Henrion,et al.  A model for dynamic chance constraints in hydro power reservoir management , 2010, Eur. J. Oper. Res..

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

[32]  S. Brignol,et al.  Risk management applied to weekly generation scheduling , 1999, IEEE Power Engineering Society. 1999 Winter Meeting (Cat. No.99CH36233).