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, Volume 13, Issue 2, pp 115–171 | Cite as

Large-scale Unit Commitment under uncertainty

  • Milad Tahanan
  • Wim van Ackooij
  • Antonio FrangioniEmail author
  • Fabrizio Lacalandra
Invited Survey

Abstract

The Unit Commitment problem in energy management aims at finding the optimal productions schedule of a set of generation units while meeting various system-wide constraints. It has always been a large-scale, non-convex difficult problem, especially in view of the fact that operational requirements imply that it has to be solved in an unreasonably small time for its size. Recently, the ever increasing capacity for renewable generation has strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex, uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focusing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, also providing entry points to the relevant literature on optimization under uncertainty.

Keywords

Unit Commitment Uncertainty Large-scale optimization Survey 

Mathematics Subject Classification

90-02 90B30 90C06 90C90 

Notes

Acknowledgments

The first author would like to thank Afsaneh Salari and Maryam Arbabzadeh for their input and their intellectual support. The second and third author gratefully acknowledge the support of the Gaspard Monge program for Optimization and Operations Research (PGMO) Project “Consistent Dual Signals and Optimal Primal Solutions”.

References

  1. Abdelaziz AY, Kamh MZ, Mekhamer SF, Badr MAL (2010) An augmented hopfield neural network for optimal thermal unit commitment. Int J Power Syst Optim 2(1):37–49Google Scholar
  2. Aganagic M, Mokhtari S (1997) Security constrained economic dispatch using nonlinear Dantzig–Wolfe decomposition. IEEE Trans Power Syst 12(1):105–112Google Scholar
  3. Aïd R, Guigues V, Ndiaye PM, Oustry F, Romanet F (2006) A value-at-risk approach for robust management of electricity power generation. Rapport de recherche, IMAG-LMC (submitted)Google Scholar
  4. Al-Kalaani Y, Villaseca FE, Renovich F Jr (1996) Storage and delivery constrained unit commitment. IEEE Trans Power Syst 11(2):1059–1066Google Scholar
  5. Amiri M, Khanmohammadi S (2013) A primary unit commitment approach with a modification process. Appl Soft Comput 13(2):1007–1015Google Scholar
  6. Anders GJ (1981) Genetration planning model with reliability constraints. IEEE Trans Power Appar Syst PAS–100(12):4901–4908Google Scholar
  7. Anderson EJ, Philpott AB (2002) Optimal offer construction in electricity markets. Math Oper Res 27(1):82–100Google Scholar
  8. Annakkage UD, Numnonda T, Pahalawaththa NC (1995) Unit commitment by parallel simulated annealing. IEE Proc Gener Transm Distrib 142(6):595–600Google Scholar
  9. Anstine LT, Burke RE, Casey JE, Holgate R, John RS, Stewart HG (1963) Application of probability methods to the determination of spinning reserve requirements for the pennsylvania-new jersey-maryland interconnection. IEEE Trans Power Appar Syst 82(68):726–735Google Scholar
  10. Anstreicher KM, Wolsey LA (2009) Two “well-known” properties of subgradient optimization. Math Program 120(1):213–220Google Scholar
  11. Aoki K, Satoh T, Itoh M, Ichimori T, Masegi K (1987) Unit commitment in a large-scale power system including fuel constrained thermal and pumped-storage hydro. IEEE Trans Power Syst 2(4):1077–1084Google Scholar
  12. Aoki K, Itoh M, Satoh T, Narah K, Kanezashi M (1989) Optimal long-term unit commitment in large scale systems including fuel constrained thermal and pumped storage hydro. IEEE Trans Power Syst 4(3):1065–1073Google Scholar
  13. Apparigliato R (2008) Règles de décision pour la gestion du risque: Application á la gestion hebdomadaire de la production électrique. Ph.D. thesis, École Polytechnique, JuinGoogle Scholar
  14. Archibald TW, Buchanan CS, McKinnon KIM, Thomas LC (1999) Nested benders decomposition and dynamic programming for reservoir optimisation. J Oper Res Soc 50(5):468–479Google Scholar
  15. Ardakani AJ, Bouffard F (2013) Identification of umbrella constraints in dc-based security-constrained optimal power flow. IEEE Trans Power Syst 28(4):3924–3934Google Scholar
  16. Arroyo JM, Conejo AJ (2000) Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst 15(3):1098–1104Google Scholar
  17. Arroyo JM, Conejo AJ (2004) Modeling of start-up and shut-down power trajectories of thermal units. IEEE Trans Power Syst 19(3):1562–1568Google Scholar
  18. Astorino A, Frangioni A, Gaudioso M, Gorgone E (2011) Piecewise quadratic approximations in convex numerical optimization. SIAM J Optim 21(4):1418–1438Google Scholar
  19. Attouch H, Bolte J, Redont P, Soubeyran A (2010) Proximal alternating minimization and projection methods for nonconvex problems. An approach based on the Kurdyka–Lojasiewicz inequality. Math Oper Res 35(2):438–457Google Scholar
  20. Babonneau F, Vial JP, Apparigliato R (2010) Robust optimization for environmental and energy planning. In: Filar JA, Haurie A (eds) Uncertainty and environmental decision making: a handbook of research and best practice, chap 3. International series in operations research & management science, vol 138. Springer, HeidelbergGoogle Scholar
  21. Bacaud L, Lemaréchal C, Renaud A, Sagastizábal C (2001) Bundle methods in stochastic optimal power management: a disaggregate approach using preconditionners. Comput Optim Appl 20(3):227–244Google Scholar
  22. Bahiense L, Maculan N, Sagastizábal C (2002) The volume algorithm revisited: relation with bundle methods. Math Program 94(1):41–69Google Scholar
  23. Baillo A, Ventosa M, Rivier M, Ramos A (2004) Optimal offering strategies for generation companies operating in electricity spot markets. IEEE Trans Power Syst 19(2):745–753Google Scholar
  24. Balas E, Ceria S, Cornuéjols G (1993) A lift-and-project cutting plane algorithm for mixed 0–1 programs. Math Program 58(1–3):295–324Google Scholar
  25. Baldick R (1995) The generalized unit commitment problem. IEEE Trans Power Syst 10(1):465–475Google Scholar
  26. Baldwin CJ, Dale KM, Dittrich RF (1959) A study of the economic shutdown of generating units in daily dispatch. Part III. Trans Am Inst Electr Eng Power Appar Syst 78(4):1272–1282Google Scholar
  27. Bandi C, Bertsimas D (2012) Tractable stochastic analysis in high dimensions via robust optimization. Math Program 134(1):23–70Google Scholar
  28. Barahona F, Anbil R (2000) The volume algorithm: producing primal solutions with a subgradient method. Math Program 87(3):385–399Google Scholar
  29. Bard JF (1988) Short-term scheduling of thermal-electric generators using Lagrangian relaxation. Oper Res 36(5):765–766Google Scholar
  30. Baringo L, Conejo AJ (2011) Offering strategy via robust optimization. IEEE Trans Power Syst 26(3):1418–1425Google Scholar
  31. Batut J, Renaud A (1992) Daily scheduling with transmission constraints: a new class of algorithms. IEEE Trans Power Syst 7(3):982–989Google Scholar
  32. Bechert TE, Kwatny HG (1972) On the optimal dynamic dispatch of real power. IEEE Trans Power Appar Syst PAS–91(1):889–898Google Scholar
  33. Bellman RE, Dreyfus SE (1962) Applied dynamic programming. Princeton University Press, New JerseyGoogle Scholar
  34. Belloni A, Diniz AL, Maceira ME, Sagastizábal C (2003) Bundle relaxation and primal recovery in unit-commitment problems. The brazilian case. Ann Oper Res 120(1–4):21–44Google Scholar
  35. Beltran C, Heredia FJ (2002) Unit commitment by augmented lagrangian relaxation: testing two decomposition approaches. J Optim Theory Appl 112(2):295–314Google Scholar
  36. Ben-Salem S (2011) Gestion Robuste de la production électrique à horizon court-terme. Ph.D. thesis, Ecole Centrale Paris, MarsGoogle Scholar
  37. Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805Google Scholar
  38. Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25(1):1–13Google Scholar
  39. Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program Ser A 88:411–424Google Scholar
  40. Ben-Tal A, Nemirovski A (2009) On safe tractable approximations of chance-constrained linear matrix inequalities. Math Oper Res 34(1):1–25Google Scholar
  41. Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2003) Adjustable robust counterpart of uncertain linear programs. Math Program Ser A 99:351–376Google Scholar
  42. Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, New JerseyGoogle Scholar
  43. Ben-Tal A, Bertsimas D, Brown D (2010) A soft robust model for optimization under ambiguity. Oper Res 58(4):1220–1234Google Scholar
  44. Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238–252Google Scholar
  45. Benth FE, Kiesel R, Nazarova A (2012) A critical empirical study of three electricity spot price models. Energy Econ 34(5):1589–1616Google Scholar
  46. Beraldi P, Conforti D, Violi A (2008) A two-stage stochastic programming model for electric energy producers. Comput Oper Res 35:3360–3370Google Scholar
  47. Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena Scientific, CambridgeGoogle Scholar
  48. Bertsekas DP (2005) Dynamic programming and optimal control, vol I, 3rd edn. Athena Scientific, CambridgeGoogle Scholar
  49. Bertsekas DP (2012) Dynamic programming and optimal control, vol II: approximate dynamic programming, 4th edn. Athena Scientific, CambridgeGoogle Scholar
  50. Bertsekas D, Lauer G, Sandell-Jr NR, Posbergh TA (1983) Optimal short-term scheduling of large-scale power systems. IEEE Trans Autom Control 28(1):1–11Google Scholar
  51. Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98(1):49–71Google Scholar
  52. Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53Google Scholar
  53. Bertsimas D, Brown D, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464–501Google Scholar
  54. Bertsimas D, Litvinov E, Sun XA, Zhao J, Zheng T (2013) Adaptive robust optimization for the security constrained unit commitment problem. IEEE Trans Power Syst 28(1):52–63Google Scholar
  55. Bienstock D (2013) Progress on solving power flow problems. Optima 93:1–8Google Scholar
  56. Bienstock D, Verma A (2011) The \(n - k\) problem in power grids: new models, formulations and numerical experiments. SIAM J Optim 20(5):2352–2380. doi: 10.1137/08073562X
  57. Billinton R, Karki R (1999) Capacity reserve assessment using system well-being analysis. IEEE Trans Power Syst 14(2):433–438Google Scholar
  58. Birge JR, Louveaux F (1988) A multicut algorithm for two-stage stochastic linear programs. Eur J Oper Res 34(3):384–392Google Scholar
  59. Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, New YorkGoogle Scholar
  60. Bompard E, Ma Y (2012) Models of strategic bidding in electricity markets under network constraints. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems, vol I. Springer, Heidelberg, pp 3–39Google Scholar
  61. Bond SD, Fox B (1986) Optimal thermal unit scheduling using improved dynamic programming algorithm. IEEE Proc C 133(1):1–5Google Scholar
  62. Bonnans JF, Gilbert JC, Lemaréchal C, Sagastizábal C (2006) Numerical optimization: theoretical and practical aspects, 2nd edn. Springer, HeidelbergGoogle Scholar
  63. Borghetti A, Frangioni A, Lacalandra F, Lodi A, Martello S, Nucci CA, Trebbi A (2001) Lagrangian relaxation and tabu search approaches for the unit commitment problem. In: IEEE Power Tech proceedings, 2001 Porto volume 3Google Scholar
  64. Borghetti A, Frangioni A, Lacalandra F, Nucci CA (2003a) Lagrangian heuristics based on disaggregated bundle methods for hydrothermal unit commitment. IEEE Trans Power Syst 18:313–323Google Scholar
  65. Borghetti A, Frangioni A, Lacalandra F, Nucci CA, Pelacchi P (2003b) Using of a cost-based unit commitment algorithm to assist bidding strategy decisions. In: Borghetti A, Nucci CA, Paolone M (eds) Proceedings IEEE 2003 Powertech, Bologna conference volume paper no. 547Google Scholar
  66. Borghetti A, D’Ambrosio C, Lodi A, Martello S (2008) A MILP approach for short-term hydro scheduling and unit commitment with head-dependent reservoir. IEEE Trans Power Syst 23(3):1115–1124Google Scholar
  67. Bouffard F, Galiana FD (2008) Stochastic security for operations planning with significant wind power generation. IEEE Trans Power Syst 23(2):306–316Google Scholar
  68. Briant O, Lemaréchal C, Meurdesoif Ph, Michel S, Perrot N, Vanderbeck F (2008) Comparison of bundle and classical column generation. Math Program 113(2):299–344Google Scholar
  69. Büsing C, D’Andreagiovanni F (2012) New results about multi-band uncertainty in robust optimization. In: Klasing R (ed) Experimental algorithms—SEA 2012 volume 7276 of LNCS, pp 63–74Google Scholar
  70. Büsing C, D’Andreagiovanni F (2013) Robust optimization under multi-band uncertainty—part i: theory. Technical report ZIB-Report 13–10, Zuse-Institut Berlin (ZIB)Google Scholar
  71. Calafiore GC, Campi MC (2005) Uncertain convex programs: randomized solutions and confidence levels. Math Program 102(1):25–46Google Scholar
  72. Carøe CC, Ruszczyński A, Schultz R (1997) Unit commitment under uncertainty via two-stage stochastic programming. In: Proceedings of NOAS 1997Google Scholar
  73. Carøe CC, Schultz R (1998) A two-stage stochastic program for unit-commitment under uncertainty in a hydro-thermal power system. Technical report, ZIBGoogle Scholar
  74. Carpentier P, Cohen G, Culioli JC, Renaud A (1996) Stochastic optimization of unit commitment: a new decomposition framework. IEEE Trans Power Syst 11(2):1067–1073Google Scholar
  75. Carrión M, Arroyo JM (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans Power Syst 21(3):1371–1378Google Scholar
  76. Catalão JPS, Mariano SJPS, Mendes VMF, Ferreira LAFM (2006) Parameterisation effect on the behavior of a head-dependent hydro chain using a nonlinear model. Electr Power Syst Res 76:404–412Google Scholar
  77. Catalão JPS, Mariano SJPS, Mendes VMF, Ferreira LAFM (2010) Nonlinear optimization method for short-term hydro scheduling considering head-dependency. Eur Trans Electr Power 20:172–183Google Scholar
  78. Cerisola S (2004) Benders decomposition for mixed integer problems: application to a medium term hydrothermal coordination problem. Ph.D. thesis, Instituto Investigación Tecnológica, MadridGoogle Scholar
  79. Cerisola S, Baíllo A, Fernández-López JM, Ramos A, Gollmer R (2009) Stochastic power generation unit commitment in electricity markets: a novel formulation and a comparison of solution methods. Oper Res 57(1):32–46Google Scholar
  80. Cerjan M, Marcic D, Delimar M (2011) Short term power system planning with water value and energy trade optimisation. In: International conference on the European energy market (EEM)Google Scholar
  81. Chandrasekaran K, Simon SP (2012a) Multi-objective scheduling problem: hybrid approach using fuzzy assisted cuckoo search algorithm. Swarm Evolut Comput 5:1–12Google Scholar
  82. Chandrasekaran K, Simon SP (2012b) Network and reliability constrained unit commitment problem using binary real coded firefly algorithm. Electr Power Energy Syst 43:921–932Google Scholar
  83. Chang GW, Aganagic M, Waight JG, Medina J, Burton T, Reeves S, Christoforidis M (2001) Experiences with mixed integer linear programming based approaches on short-term hydro scheduling. IEEE Trans Power Syst 16(4):743–749Google Scholar
  84. Chen X, Sim M, Sun P (2007) A robust optimization perspective on stochastic programming. Oper Res 55(6):1058–1071Google Scholar
  85. Chinneck JW, Ramadan K (2000) Linear programming with interval coefficients. J Oper Res Soc 51(2):209–220Google Scholar
  86. Chitra-Selvi S, Kumundi-Devi RP, Asir-Rajan CC (2009) Hybrid evolutionary programming approach to multi-area unit commitment with import and export constraints. Int J Recent Trends Eng 1(3):223–228Google Scholar
  87. Cohen G (1980) Auxiliairy problem principle and decomposition of optimization problems. J Optim Theory Appl 32(3):277–305Google Scholar
  88. Cohen AI, Yoshimura M (1983) A branch-and-bound algorithm for unit commitment. IEEE Trans Power Appar Syst 102(2):444–451Google Scholar
  89. Cohen G, Zhu DL (1984) Decomposition-coordination methods in large-scale optimization problems. The non-differentiable case and the use of augmented Lagrangians. In: Cruz JB (ed) Advances in large scale systems, vol I. JAI Press, Greenwich, Connecticut, pp 203–266Google Scholar
  90. Cohen AI, Wan SH (1987) A method for solving the fuel constrained unit commitment problem. IEEE Trans Power Syst 2(3):608–614Google Scholar
  91. Conejo AJ, Prieto FJ (2001) Mathematical programming and electricity markets. TOP 9(1):1–53Google Scholar
  92. Conejo AJ, Contreras J, Arroyo JM, de la Torre S (2002a) Optimal response of an oligopolistic generating company to a competitive pool-based electric power market. IEEE Trans Power Syst 17(2):424–430Google Scholar
  93. Conejo AJ, Nogales FJ, Arroyo JM (2002b) Price-taker bidding strategy under price uncertainty. IEEE Trans Power Syst 17(4):1081–1088Google Scholar
  94. Conejo AJ, Carrión M, Morales JM (2010) Decision making under uncertainty in electricity markets, volume 153 of international series in operations research and management science, 1st edn. Springer, HeidelbergGoogle Scholar
  95. Constantinescu EM, Zavala VM, Rocklin M, Lee S, Anitescu M (2011) A computational framework for uncertainty quantification and stochastic optimization in unit commitment with wind power generation. IEEE Trans Power Syst 26(1):431–441Google Scholar
  96. Corchero C, Mijangos E, Heredia F-J (2013) A new optimal electricity market bid model solved through perspective cuts. TOP 21(1):84–108Google Scholar
  97. Chertkov M, Bienstock D, Harnett S (2014) Chance-constrained dc-opf. Working paper (submitted)Google Scholar
  98. Cour des Comptes (2012) Les coûts de la filière électronucléaire. Technical report, Cour des ComptesGoogle Scholar
  99. d’Ambrosio C, Lodi A, Martello S (2010) Piecewise linear approxmation of functions of two variables in MILP models. Oper Res Lett 38:39–46Google Scholar
  100. d’Antonio G, Frangioni A (2009) Convergence analysis of deflected conditional approximate subgradient methods. SIAM J Optim 20(1):357–386Google Scholar
  101. Daniildis A, Lemaréchal C (2005) On a primal-proximal heuristic in discrete optimization. Math Program Ser A 104:105–128Google Scholar
  102. Dantzig GB, Wolfe P (1960) The decomposition principle for linear programs. Oper Res 8:101–111Google Scholar
  103. Dasgupta D, McGregor DR (1994) Thermal unit commitment using genetic algorithms. IEEE Proc Gener Transm Distrib 141(5):459–465Google Scholar
  104. David AK, Wen F (2001) Strategic bidding in competitive electricity markets: a literature survey. Proc IEEE PES Summer Meet 4:2168–2173Google Scholar
  105. de Farias DP, Van Roy B (2003) The linear programming approach to approximate dynamic programming. Oper Res 51(6):850–865Google Scholar
  106. de la Torre S, Arroyo JM, Conejo AJ, Contreras J (2002) Price maker self-scheduling in a pool-based electricity market: a mixed-integer LP approach. IEEE Trans Power Syst 17(4):1037–1042Google Scholar
  107. de Oliveira W, Sagastizábal C (2014) Level bundle methods for oracles with on demand accuracy. Optim Methods Softw 29(6):1180–1209. doi: 10.1080/10556788.2013.871282
  108. de Oliveira W, Sagastizábal CA, Scheimberg S (2011) Inexact bundle methods for two-stage stochastic programming. SIAM J Optim 21(2):517–544Google Scholar
  109. de Oliveira W, Sagastizábal C, Lemaréchal C (2013) Bundle methods in depth: a unified analysis for inexact oracles. http://www.optimization-online.org/DB_HTML/2013/02/3792.html
  110. Demartini G, De Simone TR, Granelli GP, Montagna M, Robo K (1998) Dual programming methods for large-scale thermal generation scheduling. IEEE Trans Power Syst 13:857–863Google Scholar
  111. Dentcheva D (2009) Optimisation models with probabilistic constraints. In: Shapiro A, Dentcheva D, Ruszczyński A (eds) Lectures on stochastic programming. Modeling and theory, chap 4. MPS-SIAM series on optimization, vol 9. SIAM and MPS, PhiladelphiaGoogle Scholar
  112. Dentcheva D, Römisch W (1998) Optimal power generation under uncertainty via stochastic programming. In: Marti K, Kall P (eds) Stochastic programming methods and technical applications, volume 458 of lecture notes in economics and mathematical systems. Springer, Heidelberg, pp 22–56Google Scholar
  113. Di Lullo M (2013) Modelli di ottimizzazione per lo unit commitment con optimal transmission switching: Analisi e implementazione. Master’s thesis, Facoltá di Ingegneria dell’Informazione, Informatica e Statistica, Universitá di Roma La Sapienza, Piazzale Aldo Moro, 5 00185, RomaGoogle Scholar
  114. Dieu VN, Ongsakul W (2008) Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network. Electr Power Syst Res 78(3):291–301Google Scholar
  115. Dillon TS, Egan GT (1976) The application of combinatorial methods to the problems of maintenance scheduling and unit commitment in large power system. In: 1st IFAC symposium on large scale systems theory and applications, Udine, ItalyGoogle Scholar
  116. Dillon TS, Edwin KW, Kochs HD, Taud RJ (1978) Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination. IEEE Trans Power Appar Syst PAS-97(6):2154–2166Google Scholar
  117. Ding X, Lee W-J, Jianxue W, Liu L (2010) Studies on stochastic unit commitment formulation with flexible generating units. Electr Power Syst Res 80:130–141Google Scholar
  118. Diongue AK (2005) Modélisation longue mémoire multivariée : applications aux problématiques du producteur d’EDF dans le cadre de la libéralisation du marché européen de l’électricité. Ph.D. thesis ENS CachanGoogle Scholar
  119. du Merle O, Goffin J-L, Vial J-P (1998) On improvements to the analytic center cutting plane method. Comput Optim Appl 11:37–52Google Scholar
  120. Dubost L, Gonzalez R, Lemaréchal C (2005) A primal–proximal heuristic applied to french unitcommitment problem. Math Program 104(1):129–151Google Scholar
  121. Duo H, Sasaki H, Nagata T, Fujita H (1999) A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming. Electr Power Syst Res 51(1):71–77Google Scholar
  122. Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming: an approach using probability metrics. Math Program 95(3):493–511Google Scholar
  123. Ea K (2012) The electricity spot markets prices modeling: proposal for a new mathematical formulation taking into account the market player strategy. In: International conference on the European energy market (EEM)Google Scholar
  124. Eichhorn A, Heitsch H, Römisch W (2010) Stochastic optimization of electricity portfolios: scenario tree modeling and risk management. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems II. Springer, Heidelberg, pp 405–432Google Scholar
  125. El Sayed MAH (2005) Solar supported steam production for power generation in Egypt. Energy Policy 33(10):1251–1259Google Scholar
  126. El Ghaoui L, Lebret H (2006) Robust solutions to least-squares problems with uncertain data. SIAM J Matrix Anal Appl 18(4):1035–1064Google Scholar
  127. El Ghaoui L, Oustry F, Lebret H (1998) Robust solutions to uncertain semidefinite programs. SIAM J Optim 9(1):33–52Google Scholar
  128. Erkmen I, Karatas B (1994) Short-term hydrothermal coordination by using multi-pass dynamic programming with successive approximation. In: 7th Mediterranean electrotechnical conference, vol 3, pp 925–928Google Scholar
  129. Fábián CI (2013) Computational aspects of risk-averse optimisation in two-stage stochastic models. Technical report, Institute of Informatics, Kecskemét College, Hungary, Optimization Online reportGoogle Scholar
  130. Fan W, Guan X, Zhai Q (2002) A new method for unit commitment with ramping constraints. Electr Power Syst Res 62(3):215–224Google Scholar
  131. Farhat IA, El-Hawary ME (2009) Optimization methods applied for solving the short-term hydrothermal coordination problem. Electr Power Syst Res 79:1308–1320Google Scholar
  132. Feltenmark S, Kiwiel KC (2000) Dual applications of proximal bundle methods, including Lagrangian relaxation of nonconvex problems. SIAM J Optim 10(3):697–721Google Scholar
  133. Ferreira LAFM (1994) On the convergence of the classic hydro-thermal coordination algorithm. IEEE Trans Power Syst 9:1002–1008Google Scholar
  134. Finardi EC, Da Silva EL (2006) Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming. IEEE Trans Power Syst 21(2):835–844Google Scholar
  135. Finardi EC, Scuzziato MR (2013) Hydro unit commitment and loading problem for day-ahead operation planning problem. Electr Power Energy Syst 44:7–16Google Scholar
  136. Finardi EC, Scuzziato MR (2014) A comparative analysis of different dual problems in the Lagrangian relaxation context for solving the hydro unit commitment problem. Electr Power Syst Res 107:221–229Google Scholar
  137. Fischetti M, Monaci M (2009) Light robustness. In: Ahuja RK, Möhring R, Zaroliagis C (eds) Robust and online large-scale optimization, volume 5868 of LNCS, pp 61–84Google Scholar
  138. Fisher ML (1973) Optimal solution of scheduling problems using Lagrange multipliers: part i. Oper Res 21(5):1114–1127Google Scholar
  139. Fisher EB, O’Neill RP, Ferris MC (2008) Optimal transmission switching. IEEE Trans Power Syst 23(3):1346–1355Google Scholar
  140. Fleten S-E, Kristoffersen TK (2008) Short-term hydropower production planning by stochastic programming. Comput Oper Res 35:2656–2671Google Scholar
  141. Fonoberova M (2010) Algorithms for finding optimal flows in dynamic networks. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems II. Springer, Heidelberg, pp 31–54Google Scholar
  142. Fotuhi-Firuzabad M, Billinton R (2000) A reliability framework for generating unit commitment. Electr Power Syst Res 56(1):81–88Google Scholar
  143. Frangioni A (2002) Generalized bundle methods. SIAM J Optim 13(1):117–156Google Scholar
  144. Frangioni A (2005) About Lagrangian methods in integer optimization. Ann Oper Res 139(1):163–193Google Scholar
  145. Frangioni A, Gentile C (2006a) Perspective cuts for a class of convex 0–1 mixed integer programs. Math Program 106(2):225–236Google Scholar
  146. Frangioni A, Gentile C (2006b) Solving non-linear single-unit commitment problems with ramping constraints. Oper Res 54(4):767–775Google Scholar
  147. Frangioni A, Gentile C, Lacalandra F (2008) Solving unit commitment problems with general ramp contraints. Int J Electr Power Energy Syst 30:316–326Google Scholar
  148. Frangioni A, Gentile C, Lacalandra F (2009) Tighter approximated MILP formulations for unit commitment problems. IEEE Trans Power Syst 24(1):105–113Google Scholar
  149. Frangioni A, Gentile C, Lacalandra F (2011) Sequential Lagrangian-MILP approaches for unit commitment problems. Int J Electr Power Energy Syst 33:585–593Google Scholar
  150. Fu Y, Shahidehpour M (2007) Fast SCUC for large-scale power systems. IEEE Trans Power Syst 22(4):2144–2151Google Scholar
  151. Fu Y, Shahidehpour M, Li Z (2005) Long-term security-constrained unit commitment: hybrid Dantzig–Wolfe decomposition and subgradient approach. IEEE Trans Power Syst 20(4):2093–2106Google Scholar
  152. Fu Y, Li Z, Wu L (2013) Modeling and solution of the large-scale security-constrained unit commitment. IEEE Trans Power Syst 28(4):3524–3533Google Scholar
  153. Gabriel SA, Conejo AJ, Fuller JD, Hobbs BF, Ruiz C (2013) Complementarity modeling in energy markets, volume 180 of international series in operations research and management science, 1st edn. Springer, HeidelbergGoogle Scholar
  154. García-González J, San Roque AM, Campos FA, Villar J (2007) Connecting the intraday energy and reserve markets by an optimal redispatch. IEEE Trans Power Syst 22(4):2220–2231Google Scholar
  155. Garver LL (1962) Power generation scheduling by integer programming-development of theory. Part III. Trans Am Inst Electr Eng Power Appar Syst 81(3):730–734Google Scholar
  156. Ge W (2010) Ramp rate constrained unit commitment by improved priority list and enhanced particle swarm optimization. In: International conference on computational intelligence and software engineering (CiSE), 2010, pp 1–8Google Scholar
  157. Georges D (1994) Optimal unit commitment in simulations of hydrothermal power systems: an augmented Lagrangian approach. Simul Pract Theory 1(4):155–172Google Scholar
  158. Gil HA, Gómez-Quiles C, Gómez-Exposito A, Santos JR (2012) Forecasting prices in electricity markets: needs, tools and limitations. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 123–150Google Scholar
  159. Gill PE, Murray W, Wright MH (1982) Practical optimization, 1st edn. Emerald Group Publishing, LondonGoogle Scholar
  160. Gjengedal T (1996) Emission constrained unit-commitment (ECUC). IEEE Trans Energy Convers 11(1):132–138Google Scholar
  161. Gollmer R, Moller A, Nowak MP, Romisch W, Schultz R (1999) Primal and dual methods for unit commitment in a hydro-thermal power system. In: Proceedings 13th power systems computation conference, pp 724–730Google Scholar
  162. Gooi HB, Mendes DP, Bell KRW, Kirschen DS (1999) Optimal scheduling of spinning reserve. IEEE Trans Power Syst 14(4):1485–1492Google Scholar
  163. Gröwe-Kuska N, Kiwiel KC, Nowak MP, Römisch W, Wegner I (2002) Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation. In: Greengard C, Ruszczyński A (eds) Decision making under uncertainty, volume 128 of the IMA volumes in mathematics and its applications. Springer, New York, pp 39–70Google Scholar
  164. Guan Y, Wang J (2014) Uncertainty sets for robust unit commitment. IEEE Trans Power Syst 29(3):1439–1440Google Scholar
  165. Guan X, Luh PB, Houzhong Y, Amalfi JA (1991) Environmentally constrained unit commitment. In: Power industry computer application conference, Baltimore, MDGoogle Scholar
  166. Guan X, Luh PB, Yan H, Rogan P (1994) Optimization-based scheduling of hydrothermal power systems with pumped-storage units. IEEE Trans Power Syst 9:1023–1031Google Scholar
  167. Guan X, Luh PB, Zhang L (1995) Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling. IEEE Trans Power Syst 10:772–778Google Scholar
  168. Guan X, Ni E, Li R, Luh PB (1997) An optimization-based algorithm for scheduling hydrothermal power systems with cascaded reservoirs and discrete hydro constraints. IEEE Trans Power Syst 12:1775–1780Google Scholar
  169. Guignard M (2003) Lagrangean relaxation. TOP 11(2):151–228Google Scholar
  170. Guignard M, Kim S (1987) Lagrangian decomposition: a model yielding stronger Lagrangian bounds. Math Program 39:215–228Google Scholar
  171. Guigues V (2009) Robust product management. Optim Eng 10(4):505–532Google Scholar
  172. Guigues V (2013) SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning. Comput Optim Appl 10(4):505–532Google Scholar
  173. Habibollahzadeh H, Bubenko JA (1986) Application of decomposition techniques to short-term operation planning of hydrothermal power system. IEEE Trans Power Syst 1(1):41–47Google Scholar
  174. Hara K, Kimura M, Honda N (1966) A method for planning economic unit commitment and maintenance of thermal power systems. IEEE Trans Power Appar Syst PAS–85(5):427–436Google Scholar
  175. Harris C (2011) Electricity markets: pricing, structures and economics, volume 565 of the Wiley finance series. Wiley, LondonGoogle Scholar
  176. Hedman KW, O’Neill RP, Fisher EB, Oren SS (2009) Optimal transmission switching with contingency analysis. IEEE Trans Power Syst 24(3):1577–1586Google Scholar
  177. Hedman KW, Ferris MC, O’Neill RP, Fisher EB, Oren SS (2010) Co-optimization of generation unit commitment and transmission switching with \(n-1\) reliability. IEEE Trans Power Syst 25(2):1052–1063Google Scholar
  178. Hedman KW, Oren SS, O’Neill RP (2011a) Optimal transmission switching: economic efficiency and market implications. J Regul Econ 40(3):111–140Google Scholar
  179. Hedman KW, Oren SS, O’Neill RP (2011b) A review of transmission switching and network topology optimization. In: Power and energy society general meeting, 2011 IEEE. IEEE, pp 1–7Google Scholar
  180. Heitsch H, Römisch W (2003) Scenario reduction algorithms in stochastic programming. Comput Optim Appl 24(2–3):187–206Google Scholar
  181. Heitsch H, Römisch W (2009) Scenario tree reduction for multistage stochastic programs. CMS 6(2):117–133Google Scholar
  182. Heitsch H, Römisch W (2011) Scenario tree generation for multi-stage stochastic programs. In: Bertocchi M, Consigli G, Dempster MAH (eds) Stochastic optimization methods in finance and energy: new financial products and energy market strategies volume 163 of international series in operations research and management science. Springer, Heidelberg, pp 313–341Google Scholar
  183. Heredia FJ, Nabona N (1995) Optimum short-term hydrothermal scheduling with spinning reserve through network flows. IEEE Trans Power Syst 10:1642–1651Google Scholar
  184. Henrion R, Römisch W (2004) Hölder and lipschitz stability of solution sets in programs with probabilistic constraints. Math Program 100:589–611Google Scholar
  185. Henrion R, Möller A (2012) A gradient formula for linear chance constraints under Gaussian distribution. Math Oper Res 37:475–488Google Scholar
  186. Henrion R, Küchler C, Römisch W (2008) Discrepancy distances and scenario reduction in two-stage stochastic integer programming. J Ind Manag Optim 4:363–384Google Scholar
  187. Henrion R, Küchler C, Römisch W (2009) Scenario reduction in stochastic programming with respect to discrepancy distances. Comput Optim Appl 43:67–93Google Scholar
  188. Higgs H, Worthington A (2008) Stochastic price modeling of high volatility, mean-reverting, spike-prone commodities: the Australian wholesale spot electricity market. Energy Econ 30(6):3172–3185Google Scholar
  189. Hijazi HL, Coffrin C, Van Hentenryck P (2013) Convex quadratic relaxations of nonlinear programs in power systems (submitted)Google Scholar
  190. Hobbs WJ, Hermon G, Warner S, Shelbe GB (1988) An enhanced dynamic programming approach for unit commitment. IEEE Trans Power Syst 3(3):1201–1205Google Scholar
  191. Hobbs BF, Rothkopf M, O’Neill RP, Chao HP (2001) The next generation of electric power unit commitment models. Number 36 in international series in operations research and management science. Springer, HeidelbergGoogle Scholar
  192. Hsu YY, Su C-C, Lin C-J, Huang C-T (1991) Dynamic security constrained multi-area unit commitment. IEEE Trans Power Syst 6(3):1049–1055Google Scholar
  193. Huang KY, Yang HT, Huang CL (1998) A new thermal unit commitment approach using constraint logic programming. IEEE Trans Power Syst 13(3):936–945Google Scholar
  194. Jabr RA (2006) Radial distribution load flow using conic programming. IEEE Trans Power Syst 21(3):1458–1459Google Scholar
  195. Jabr RA (2008) Optimal power flow using an extended conic quadratic formulation. IEEE Trans Power Syst 23(3):1000–1008Google Scholar
  196. Jabr RA (2010) Recent developments in optimal power flow modeling. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems II. Springer, Heidelberg, pp 3–30Google Scholar
  197. Jabr RA (2012) Tight polyhedral approximation for mixed-integer linear programming unit commitment formulations. IET Gener Transm Distrib 6(11):1104–1111Google Scholar
  198. Jabr RA (2013) Adjustable robust OPF with renewable energy sources. IEEE Trans Power Syst 28(4):4741–4751Google Scholar
  199. Jia J, Guan X (2011) Milp formulation for short-term scheduling of cascaded reservoirs with head effects. In: 2011 2nd international conference on artificial intelligence, management science and electronic commerce (AIMSEC), pp 4061–4064Google Scholar
  200. Jiang R, Zhang M, Li G, Guan Yi (2010) Two-stage robust power grid optimization problem. Preprint: http://www.optimization-online.org/DB_HTML/2010/10/2769.html, pp 1–34
  201. Jiang R, Wang J, Guan Y (2012) Robust unit commitment with wind power and pumped storage hydro. IEEE Trans Power Syst 27(2):800–810Google Scholar
  202. Johnson RC, Happ HH, Wright WJ (1971) Large scale hydro-thermal unit commitment-method and results. IEEE Trans Power Appar Syst PAS–90(3):1373–1384Google Scholar
  203. Juste KA, Kita H, Tanaka E, Hasegawa J (1999) An evolutionary programming solution to the unit commitment problem. IEEE Trans Power Syst 14(4):1452–1459Google Scholar
  204. Kall P, Mayer J (2005) Stochastic linear programming: models, theory and computation. International series in operations research and management science, 1st edn. Springer, HeidelbergGoogle Scholar
  205. Kelley JE (1960) The cutting-plane method for solving convex programs. J Soc Ind Appl Math 8(4):703–712Google Scholar
  206. Kerr RH, Scheidt JL, Fontanna AJ, Wiley JK (1966) Unit commitment. IEEE Trans Power Appar Syst PAS–85(5):417–421Google Scholar
  207. Keyhani A, Marwali MN, Dai M (2010) Integration of green and renewable energy in electric power systems, 1st edn. Wiley, LondonGoogle Scholar
  208. Kiwiel KC (2012) Bundle methods for convex minimization with partially inexact oracles. Comput Opt Appl (to appear)Google Scholar
  209. Korad K, Hedman AS (2013) Robust corrective topology control for system reliability. IEEE Trans Power Syst 28(4):1346–1355Google Scholar
  210. Kort BW, Bertsekas DP (1972) A new penalty function method for constrained optimization. IEEE Conf Decis Control 1972:162–166Google Scholar
  211. Kuloor S, Hope GS, Malik OP (1992) Environmentally constrained unit commitment. IEE Proc C Gener Transm Distrib 139(2):122–128Google Scholar
  212. Kwon RH, Frances D (2012) Optimization-based bidding in day-ahead electricity auction markets: a review of models for power producers. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 41–60Google Scholar
  213. Laporte G, Louveaux FV (1993) The integer l-shaped method for stochastic integer programs with complete recourse. Oper Res Lett 13(3):133–142Google Scholar
  214. Lauer GS, Sandell NR, Bertsekas DP, Posbergh TA (1982) Solution of large-scale optimal unit commitment problems. IEEE Trans Power Appar Syst PAS–101(1):79–86Google Scholar
  215. Lavaei J, Low S (2012) Zero duality gap in optimal power flow problem. IEEE Trans Power Syst 27(1):92–107Google Scholar
  216. Le KD, Jackups RR, Feinstein J, Griffith JS (1990) Operational aspects of generation cycling. IEEE Trans Power Syst 5(4):1194–1203Google Scholar
  217. Lee FN (1988) Short-term thermal unit commitment—a new method. IEEE Trans Power Syst 3(2):421–428Google Scholar
  218. Lee FN (1991) The application of commitment utilization factor (CUF) to thermal unit commitment. IEEE Trans Power Syst 6(2):691–698Google Scholar
  219. Lee FN, Feng Q (1992) Multi-area unit commitment. IEEE Trans Power Syst 7(2):591–599Google Scholar
  220. Lee FN, Huang J, Adapa R (1994) Multi-area unit commitment via sequential method and a dc power flow network model. IEEE Trans Power Syst 9(1):287–297Google Scholar
  221. Lemaréchal C (1975) An extension of davidon methods to nondifferentiable problems. Math Program Study 3:95–109Google Scholar
  222. Lemaréchal C (2001) Lagrangian relaxation. In: Jünger M, Naddef D (eds) Computational combinatorial optimization: optimal or provably near-optimal solutions, chap 4. Lecture notes incomputer science. Springer, HeidelbergGoogle Scholar
  223. Lemaréchal C, Sagastizábal C (1994) An approach to variable metric bundle methods. Lect Notes Control Inf Sci 197:144–162Google Scholar
  224. Lemaréchal C, Sagastizábal C (1995) Application of bundle methods to the unit-commitment problem. Rapport Technique Nb 0184 INRIA, pp 1–19Google Scholar
  225. Lemaréchal C, Nemirovskii A, Nesterov Y (1995) New variants of bundle methods. Math Program 69(1):111–147Google Scholar
  226. Leveque F (2002) Competitive electricity markets and sustainability. Edward Elgar, CheltenhamGoogle Scholar
  227. Li Z, Shahidehpour M (2003) Generation scheduling with thermal stress constraints. IEEE Trans Power Syst 18(4):1402–1409Google Scholar
  228. Li T, Shahidehpour M (2005) Strategic bidding of transmission-constrained GENCOs with incomplete information. IEEE Trans Power Syst 20(1):437–447Google Scholar
  229. Li C, Johnson RB, Svoboda AJ (1997) A new unit commitment method. IEEE Trans Power Syst 12(1):113–119Google Scholar
  230. Li G, Lawarree J, Liu CC (2010) State-of-the-art of electricity price forecasting in a grid. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems II. Springer, Heidelberg, pp 161–188Google Scholar
  231. Liang R-H, Kang F-C (2000) Thermal generating unit commitment using an extended mean field annealing neural network. IEE Proc Gener Transm Distrib 147(3):164–170Google Scholar
  232. Lin W-M, Cheng F-S, Tsay M-T (2002) An improved tabu search for economic dispatch with multiple minima. IEEE Trans Power Syst 17(1):108–112Google Scholar
  233. Liu C, Shahidehpour M, Wu L (2010) Extended benders decomposition for two-stage SCUC. IEEE Trans Power Syst 25(2):1192–1194Google Scholar
  234. Liu C, Wang J, Ostrowski J (2012a) Heuristic prescreening switchable branches in optimal transmission switching. IEEE Trans Power Syst 27(4):2289–2290Google Scholar
  235. Liu C, Wang J, Ostrowski J (2012b) Static security in multi-period transmission switching. IEEE Trans Power Syst 27(4):1850–1858Google Scholar
  236. Løkketangen A, Woodruff DL (1996) Progressive hedging and tabu search applied to mixed integer (0, 1) multistage stochastic programming. J Heuristics 2(2):111–128Google Scholar
  237. Louveaux FV, Schultz R (2003) Stochastic integer programming. In: Ruszczyński A, Shapiro A (eds) Stochastic programming, chap 4. Handbooks in operations research and management science, vol 10. Elsevier, AmsterdamGoogle Scholar
  238. Lu B, Shahidehpour M (2005) Unit commitment with flexible generating units. IEEE Trans Power Syst 20(2):1022–1034Google Scholar
  239. Lucas J-Y, Triboulet T (2012) Hybridization of augmented lagrangian and genetic algorithm for day-to-day unit commitment problem. In: META 12: international conference on metaheuristics and nature inspired computingGoogle Scholar
  240. Luedtke J (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math Program 146:219–244Google Scholar
  241. Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J Optim 19:674–699Google Scholar
  242. Luenberger DG, Ye Y (2010) Linear and nonlinear programming, volume 116 of international series in operations research and management science, 3rd edn. Springer, HeidelbergGoogle Scholar
  243. Luh PB, Tomastik RN (1998) An algorithm for solving the dual problem of hydrothermal scheduling. IEEE Trans Power Syst 13:593–600Google Scholar
  244. Luh PB, Wang Y, Zhao X (1999) Lagrangian relaxation neural network for unit commitment. In: IEEE Power Engineering Society 1999 winter meeting, vol 1, pp 490–495Google Scholar
  245. Madrigal M, Quintana VH (2000) An interior-point/cutting-plane method to solve unit commitment problems. IEEE Trans Power Syst 15(3):1022–1027Google Scholar
  246. Makkonen S, Lahdelma R (2006) Non-convex power plant modelling in energy optimisation. Eur J Oper Res 171:1113–1126Google Scholar
  247. Mantawy AH, Abdel-Magid YL, Selim SZ (1998) A simulated annealing algorithm for unit commitment. IEEE Trans Power Syst 13(1):197–204Google Scholar
  248. Mantawy AH, Soliman SA, El-Hawary ME (2002) A new tabu search algorithm for the long-term hydro scheduling problem. In: LESCOPE 02 large engineering systems conference on power engineering, pp 29–34Google Scholar
  249. Merlin A, Sandrin P (1983) A new method for unit commitment at Electricité de France. IEEE Trans Power Appl Syst PAS–102:1218–1225Google Scholar
  250. Mezger AJ, de Almeida KC (2007) Short term hydrothermal scheduling with bilateral transactions via bundle method. Electr Power Energy Syst 29:387–396Google Scholar
  251. Minoux M (2009) Solving some multistage robust decision problems with huge implicitly defined scenario trees. Algorithm Oper Res 4(1):1–18Google Scholar
  252. Minoux M (2014) Two-stage robust optimization, state-space representable uncertainty and applications. RAIRO Oper Res 48:455–475Google Scholar
  253. Miranda J, Wanga A, Botterud R, Bessa H, Keko L, Carvalho D, Issicaba J, Sumaili V (2011) Wind power forecasting uncertainty and unit commitment. Appl Energy 88:4014–4023Google Scholar
  254. Mokhtari S, Sing J, Wollenberg B (1988) A unit commitment expert system. IEEE Trans Power Syst 3(1):272–277Google Scholar
  255. Molzahn DK, Holzer JT, Lesieutre BC, DeMarco CL (2013) Implementation of a large-scale optimal power flow solver based on semidefinite programming. IEEE Trans Power Syst 28(4):3987–3998Google Scholar
  256. Momoh JA, Adapa R, El-Hawary ME (1999a) A review of selected optimal power flow literature to 1993. i. Nonlinear and quadratic programming approaches. IEEE Trans Power Syst 14:96–104Google Scholar
  257. Momoh JA, Adapa R, El-Hawary ME (1999b) A review of selected optimal power flow literature to 1993. ii. Newton, linear programming and interior point methods. IEEE Trans Power Syst 14:105–111Google Scholar
  258. Morales-España G, Latorre JM, Ramos A (2013a) Tight and compact MILP formulation for the thermal unit commitment problem. IEEE Trans Power Syst 28(4):4897–4908Google Scholar
  259. Morales-España G, Latorre JM, Ramos A (2013b) Tight and compact MILP formulation of start-up and shut-down ramping in unit commitment. IEEE Trans Power Syst 28(2):1288–1296Google Scholar
  260. Morales-España G, Ramos A, García-González J (2014) An MIP formulation for joint market-clearing of energy and reserves including ramp scheduling. IEEE Trans Power Syst 29(1):476–488Google Scholar
  261. Mori H, Matsuzaki O (2001) Embedding the priority list into tabu search for unit commitment. In: IEEE Power Engineering Society winter meeting, vol 3, pp 1067–1072Google Scholar
  262. Muckstadt JA, Koenig SA (1977) An application of Lagrangian relaxation to scheduling in power-generation systems. Oper Res 25(3):387–403Google Scholar
  263. Moura PS, de Almeida AT (2010) Large scale integration of wind power generation. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems I. Springer, Heidelberg, pp 95–120Google Scholar
  264. Muckstadt JA, Wilson RC (1968) An application of mixed-integer programming duality to scheduling thermal generating systems. IEEE Trans Power Appar Syst PAS–87(12):1968–1978Google Scholar
  265. Muñoz A, Sánchez Úbeda EF, Cruz A, Marín J (2010) Short-term forecasting in power systems: a guided tour. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems II. Springer, Heidelberg, pp 129–160Google Scholar
  266. Murillo-Sanchez C, Thomas RJ (1998) Thermal unit commitment including optimal ac power flow constraints. In: Thirty-First Hawaii international conference on system sciences, vol 3Google Scholar
  267. Nayak R, Sharma JD (2000) A hybrid neural network and simulated annealing approach to the unit commitment problem. Comput Electr Eng 26(6):461–477Google Scholar
  268. Nemirovski A, Shapiro A (2004) Scenario approximations of chance constraints. Preprint: http://www.optimization-online.org/DB_HTML/2004/11/1000.html, pp 1–45
  269. Nemirovski A, Shapiro A (2006a) Convex approximations of chance constrained programs. SIAM J Optim 17(4):969–996Google Scholar
  270. Nemirovski A, Shapiro A (2006b) Scenario approximations of chance constraints. In: Calafiore G, Dabbene F (eds) Probabilistic and randomized methods for design under uncertainty. Springer, BerlinGoogle Scholar
  271. Nesterov Y (2009) Primal–dual subgradient methods for convex problems. Math Program 120(1):221–259Google Scholar
  272. Nguyen-Huu A (2012) Valorisation financière sur les marchés d’électricité. Ph.D. thesis, Paris DauphineGoogle Scholar
  273. Ni E, Guan X, Li R (1999) Scheduling hydrothermal power systems with cascaded and head-dependent reservoirs. IEEE Trans Power Syst 14:1127–1132Google Scholar
  274. Ni E, Luh PB, Rourke S (2004) Optimal integrated generation bidding and scheduling with risk management under a deregulated power market. IEEE Trans Power Syst 19(1):600–609Google Scholar
  275. Nilsson O, Sjelvgren D (1996) Mixed-integer programming applied to short-term planning of a hydro-thermal system. IEEE Trans Power Syst 11(1):281–286Google Scholar
  276. Nogales FJ, Contreras J, Conejo AJ, Espínola R (2002) Forecasting next-day electricity prices by time series models. IEEE Trans Power Syst 17(2):342–348Google Scholar
  277. Nowak MP (2000) Stochastic Lagrangian relaxation in power scheduling of a hydrothermal system under uncertainty. Ph.D. thesis, Humboldt University, BerlinGoogle Scholar
  278. Nowak MP, Römisch W (2000) Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Ann Oper Res 100(1–4):251–272Google Scholar
  279. Nürnberg R, Römisch W (2003) A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty. Optim Eng 3:355–378Google Scholar
  280. Oliveira ARL, Soares S, Nepomuceno L (2005) Short term hydroelectric scheduling combining network flow and interior point approaches. Electr Power Energy Syst 27:91–99Google Scholar
  281. O’Neill RP, Hedman KW, Krall EA, Papavasiliou A, Oren SS (2010) Economic analysis of the \(n-1\) reliable unit commitment and transmission switching problem using duality concepts. Energy Syst 1(2):165–195Google Scholar
  282. Oren SS, Svoboda AJ, Johnson RB (1997) Volatility of unit commitment in competitive electricity markets. Int Conf Syst Sci 5:594–601Google Scholar
  283. Ostrowski J, Wang J (2012) Network reduction in the transmission-constrained unit commitment problem. Comput Ind Eng 63(1):702–707Google Scholar
  284. Ostrowski J, Vannelli A, Anjos MF (2010) Groupe d’études et de recherche en analyse des décisions (Montréal, Québec). Symmetry in Scheduling Problems. Groupe d’études et de recherche en analyse des décisionsGoogle Scholar
  285. Ostrowski J, Anjos MF, Vannelli A (2012) Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans Power Syst 27(1):39–46Google Scholar
  286. Ostrowski J, Wang J, Liu C (2012) Exploiting symmetry in transmission lines for transmission switching. IEEE Trans Power Syst 27(3):1708–1709Google Scholar
  287. Oudjane N, Collet J, Duwig V (2006) Some non-Gaussian models for electricity spot prices. In: 9th international conference on probabilistic methods applied to power systemsGoogle Scholar
  288. Ouyang Z, Shahidehpour M (1991) An intelligent dynamic programming for unit commitment application. IEEE Trans Power Syst 6(3):1203–1209Google Scholar
  289. Ouyang Z, Shahidehpour M (1992) A hybrid artificial neural network-dynamic programming approach to unit commitment. IEEE Trans Power Syst 7(1):236–242Google Scholar
  290. Ozturk UA, Mazumdar M, Norman BA (2004) A solution to the stochastic unit commitment problem using chance constrained programming. IEEE Trans Power Syst 19(3):1589–1598Google Scholar
  291. Padhy NP (2004) Unit commitment—a bibliographical survey. IEEE Trans Power Syst 19(2):1196–1205Google Scholar
  292. Palamarchuk SI (2012) Compromise scheduling of bilateral contracts in electricity market environment. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 241–262Google Scholar
  293. Pang CK, Chen HC (1976) Optimal short-term thermal unit commitment. IEEE Trans Power Appar Syst 95(4):1336–1346Google Scholar
  294. Pang CK, Sheble GB, Albuyeh F (1981) Evaluation of dynamic programming based methods and multiple area representation for thermal unit commitments. IEEE Trans Power Appar Syst PAS–100(3):1212–1218Google Scholar
  295. Papavasiliou A, Oren SS (2012) A stochastic unit commitment model for integrating renewable supply and demand response. In: Invited panel paper, proceeding of the IEEE PES GM, San Diego, CA, July 24–28, 2012Google Scholar
  296. Papavasiliou A, Oren SS (2013) A comparative study of stochastic unit commitment and security-constrained unit commitment using high performance computing. In: Proceeding of the European control conference ECC 2013Google Scholar
  297. Papavasiliou A, Oren SS, O’Neill R (2011) Reserve requirements for wind power integration: a scenario-based stochastic programming framework. IEEE Trans Power Syst 26(4):2197–2206Google Scholar
  298. Papavasiliou A, Oren SS, O’Neill R (2013a) Multi-area stochastic unit commitment for high wind penetration in a transmission constrained network. Oper Res 61(3):578–592Google Scholar
  299. Papavasiliou A, Oren SS, Yang Z, Balasubramanian P, Hedman KW (2013b) An application of high performance computing to transmission switching. In: IREP bulk power system dynamics and control symposium, Rethymnon, Greece, 2013Google Scholar
  300. Parrilla E, García-González J (2006) Improving the B&B search for large-scale hydrothermal weekly scheduling problems. Electr Power Energy Syst 28:339–348Google Scholar
  301. Pedregal DJ, Contreras J, Sanchez de la Nieta AA (2012) Ecotool: a general matlab forecasting toolbox with applications to electricity markets. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 151–171Google Scholar
  302. Peng T, Tomsovic K (2003) Congestion influence on bidding strategies in an electricity market. IEEE Trans Power Syst 18(3):1054–1061Google Scholar
  303. Pepper W, Ring BJ, Read EG, Starkey SR (2012) Short-term electricity market prices: a review of characteristics and forecasting methods. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems II. Springer, Heidelberg, pp 3–36Google Scholar
  304. Pereira MVF, Pinto LMVG (1983) Application of decomposition techniques to the mid- and short-term scheduling of hydrothermal systems. IEEE Trans Power Appar Syst PAS–102(11):3611–3618Google Scholar
  305. Pereira MV, Granville S, Fampa MHC, Dix R, Barroso LA (2005) Strategic bidding under uncertainty: a binary expansion approach. IEEE Trans Power Syst 11(1):180–188Google Scholar
  306. Philpott A, Schultz R (2006) Unit commitment in electricity pool markets. Math Program Ser B 108:313–337Google Scholar
  307. Piekutowki M, Litwinowcz T, Frowd R (1994) Optimal short-term scheduling for a large-scale cascaded hydro system. IEEE Trans Power Syst 9(2):805–811Google Scholar
  308. Pineau PO, Murto P (2003) An oligopolistic investment model of the finnish electricity market. Ann Oper Res 121(1–4):123–148Google Scholar
  309. Polyak BT (1977) Subgradient methods: a survey of soviet research. In: Lemaréchal C, Mifflin R (eds) Nonsmooth optimization, IIASA proceedings series. Pergamon Press, New YorkGoogle Scholar
  310. Prékopa A (1995) Stochastic programming. Kluwer, DordrechtGoogle Scholar
  311. Prékopa A (2003) Probabilistic programming. In: Ruszczyński A, Shapiro A (eds) Stochastic programming, chap 5. Handbooks in operations research and management science, vol 10. Elsevier, AmsterdamGoogle Scholar
  312. Prékopa A, Rapcsák T, Zsuffa I (1978) Serially linked reservoir system design using stochastic programming. Water Resour Res 14:672–678Google Scholar
  313. Price JE (2007) Market-based price differentials in zonal and lmp market designs. IEEE Trans Power Syst 22(4):1486–1494Google Scholar
  314. Rajan CCA, Mohan MR (2004) An evolutionary programming-based tabu search method for solving the unit commitment problem. IEEE Trans Power Syst 19(1):577–585Google Scholar
  315. Rajan CCA, Mohan MR, Manivannan K (2003) Neural-based tabu search method for solving unit commitment problem. IEEE Proc Gener Transm Distrib 150(4):469–474Google Scholar
  316. Rajan CCA, Selvi SC, Kumudini Devi RP (2012) Multi-area unit commitment with transmission losses using evolutionary iteration particle swarm optimization approach. Eur J Sci Res 76(4):672–691Google Scholar
  317. Ramos A, Cerisola S, Latorre JM, Bellido R, Perea A, Lopez E (2012) A decision support model forweekly operation of hydrothermal systems by stochastic nonlinear optimization. In: Bertocchi M, Consigli G, Dempster MAH (eds) Stochastic optimization methods in finance and energy: new financial products and energy market strategies. Springer, Heidelberg, pp 143–162Google Scholar
  318. Razaviyayn M, Hong M, Luo Z-Q (2012) A unified convergence analysis of block successive minimization methods for nonsmooth optimization. Technical report, University of Minnesota, Twin CitesGoogle Scholar
  319. Read EG (2010) Co-optimization of energy and ancillary service markets. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems I. Springer, Heidelberg, pp 307–330Google Scholar
  320. Redondo NJ, Conejo AJ (1999) Short-term hydro-thermal coordination by Lagrangian relaxation: solution of the dual problem. IEEE Trans Power Syst 14:89–95Google Scholar
  321. Rocha P, Das TK (2012) Finding joint bidding strategies for day-ahead electricity and related markets. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 61–88Google Scholar
  322. Rockafellar RT, Wets Roger J-B (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16(1):119–147Google Scholar
  323. Römisch W (2003) Stability of stochastic programming problems. In: Ruszczyński A, Shapiro A (eds) Stochastic programming, chap 8. Handbooks in operations research and management science, vol 10. Elsevier, AmsterdamGoogle Scholar
  324. Römisch W, Schultz R (1991) Distribution sensitivity for certain classes of chance-constrained models with application to power dispatch. J Optim Theory Appl 71:569–588Google Scholar
  325. Römisch W, Schultz R (1996) Decomposition of a multi-stage stochastic program for power dispatch. In: SUPPL, vol 3, pp 29–32Google Scholar
  326. Römisch W, Vigerske S (2010) Recent progress in two-stage mixed-integer stochastic programming with applications to power production planning. In: Rebennack S, Pardalos PM, Pereira MVF, Iliadis N (eds) Handbook of power systems I. Springer, Heidelberg, pp 177–208Google Scholar
  327. Ruiz PA, Philbrick CR, Zak EJ, Cheung KW, Sauer PW (2009) Uncertainty management in the unit commitment problem. IEEE Trans Power Syst 24(2):642–651Google Scholar
  328. Ruiz PA, Rudkevich A, Caramanis MC, Goldis E, Ntakou E, Philbrick CR (2012) Reduced MIP formulation for transmission topology control. In: Allerton conference. IEEE, pp 1073–1079Google Scholar
  329. Ruszczyński A (1995) On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math Oper Res 20(3):634–656Google Scholar
  330. Ruszczyński A (2003) Decomposition methods . In: Ruszczyński A, Shapiro A (eds) Stochastic programming, chap 3. Handbooks in operations research and management science, vol 10. Elsevier, AmsterdamGoogle Scholar
  331. Ruszczyński A, Shapiro A (2009a) Multi-stage problems. In: Shapiro A, Dentcheva D, Ruszczyński A (eds) Lectures on stochastic programming. Modeling and theory, chap 3. MPS-SIAM series on optimization, vol 9. SIAM and MPS, PhiladelphiaGoogle Scholar
  332. Ruszczyński A, Shapiro A (2009b) Two stage problems. In: Shapiro A, Dentcheva D, Ruszczyński A (eds) Lectures on stochastic programming. Modeling and theory, chap 2. MPS-SIAM series on optimization, vol 9. SIAM and MPS, PhiladelphiaGoogle Scholar
  333. Ruzic S, Rajakovic R (1998) Optimal distance method for Lagrangian multipliers updating in short-term hydro-thermal coordination. IEEE Trans Power Syst 13:1439–1444Google Scholar
  334. Sagastizábal C (2012) Divide to conquer: decomposition methods for energy optimization. Math Program 134(1):187–222Google Scholar
  335. Salam MS, Hamdan AR, Nor KM (1991) Integrating an expert system into a thermal unit-commitment algorithm. IEE Proc Gener Transm Distrib 138(6):553–559Google Scholar
  336. Salam S, Nor KM, Hamdan AR (1997) Comprehensive algorithm for hydrothermal coordination. IEE Trans Gener Transm Distrib 144:482–488Google Scholar
  337. Salam S, Nor KM, Hamdan AR (1998) Hydrothermal scheduling based Lagrangian relaxation approach to hydrothermal coordination. IEEE Trans Power Syst 13:226–235Google Scholar
  338. Saravanan B, Das S, Sikri S, Kothari DP (2013) A solution to the unit commitment problem: a review. Front Energy 7(2):223–236Google Scholar
  339. Sarić AT, Stankovic AM (2007) Finitely adaptive linear programming in robust power system optimization. In: Power Tech, 2007 IEEE Lausanne, pp 1302–1307Google Scholar
  340. Sasaki H, Watanabe M, Kubokawa J, Yorino N, Yokoyama R (1992) A solution method of unit commitment by artificial neural networks. IEEE Trans Power Syst 7(3):974–981Google Scholar
  341. Sauma E, Jerardino S, Barria C, Marambio R, Brugman A, Mejia J (2012) Electric interconnections in the andes community: threats and opportunities. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 345–366Google Scholar
  342. Schultz R, Nowak M, Nürnberg R, Römisch W, Westphalen M (2003) Stochastic programming for power production and trading under uncertainty. In: Jvsger W, Krebs H-J (eds) Mathematics—key technology for the future. Springer, Heidelberg, pp 623–636Google Scholar
  343. Sendaula MH, Biswas SK, Eltom A, Parten C, Kazibwe W (1991) Application of artificial neural networks to unit commitment. Proc First Int Forum Appl Neural Netw Power Syst 1991:256–260Google Scholar
  344. Senthil-Kumar S, Palanisamy V (2007) A dynamic programming based fast computation Hopfield neural network for unit commitment and economic dispatch. Electr Power Syst Res 77(8):917–925Google Scholar
  345. Shafie-Khah M, Parsa Moghaddam M, Sheikh-El-Eslami MK (2011) Unified solution of a non-convex SCUC problem using combination of modified branch-and-bound method with quadratic programming. Energy Convers Manag 52(12):3425–3432Google Scholar
  346. Shahidehpour M, Yamin H, Li Z (2002) Market operations in electric power systems: forecasting, scheduling, and risk management. Wiley-IEEE Press, LondonGoogle Scholar
  347. Sharaf TAM, Berg GJ (1982) Voltampere reactive compensation using chance-constrained programming. IEEE Proc C Gener Transm Distrib 129(1):24–29Google Scholar
  348. Shaw JJ, Gendron RF, Bertsekas DP (1985) Optimal scheduling of large hydrothermal power systems. IEEE Power Eng Rev PER–5(2):32Google Scholar
  349. Sheble GB, Fahd GN (1994) Unit commitment literature synopsis. IEEE Trans Power Syst 9(1):128–135Google Scholar
  350. Sheble GB, Maifeld TT, Brittig K, Fahd G, Fukurozaki-Coppinger S (1996) Unit commitment by genetic algorithm with penalty methods and a comparison of Lagrangian search and genetic algorithm economic dispatch example. Int J Electr Power Energy Syst 18(6):339–346Google Scholar
  351. Sherali HD, Adams WP (1998) A reformulation–linearization technique for solving discrete and continuous nonconvex problems, nonconvex optimization and its applications. Springer, HeidelbergGoogle Scholar
  352. Sherali HD, Fraticelli BMP (2002) A modification of benders’ decomposition algorithm for discrete subproblems: an approach for stochastic programs with integer recourse. J Glob Optim 22:319–342Google Scholar
  353. Shiina T (1999) Numerical solution technique for joint chance-constrained programming problem “an application to electric power capacity expansion”. J Oper Res Soc Jpn 42(2):128–140Google Scholar
  354. Shiina T, Birge JR (2004) Stochastic unit commitment problem. Int Trans Oper Res 11(1):19–32Google Scholar
  355. Siahkali H, Vakilian M (2010) Stochastic unit commitment of wind farms integrated in power system. Electr Power Syst Res 80(9):1006–1017Google Scholar
  356. Sifuentes W, Vargas A (2007a) Hydrothermal scheduling using benders decomposition: accelerating techniques. IEEE Trans Power Syst 22:1351–1359Google Scholar
  357. Sifuentes W, Vargas A (2007b) Short-term hydrothermal coordination considering an ac network modeling. Int J Electr Power Energy Syst 29:488–496Google Scholar
  358. Simopoulos DN, Kavatza SD, Vournas CD (2006) Unit commitment by an enhanced. IEEE Trans Power Syst 21(1):68–76Google Scholar
  359. Singhal PK, Sharma RN (2011) Dynamic programming approach for large scale unit commitment problem. In: International conference on communication systems and network technologies (CSNT), pp 714–717Google Scholar
  360. Siu TK, Nash GA, Shawwash ZK (2001) A practical hydro, dynamic unit commitment and loading model. IEEE Trans Power Syst 16(2):301–306Google Scholar
  361. Snyder WL, Powell HD, Rayburn JC (1987) Dynamic programming approach to unit commitment. IEEE Trans Power Syst 2(2):339–348Google Scholar
  362. Street A, Oliveira F, Arroya JM (2011) Contingency-constrained unit commitment with \(n-k\) security criterion: a robust optimization approach. IEEE Trans Power Syst 26(3):1581–1590Google Scholar
  363. Sudhakaran M, Ajay-D-Vimal Raj P (2010) Integrating genetic algorithms and tabu search for unit commitment. Int J Eng Sci Technol 2(1):57–69Google Scholar
  364. Takigawa FYK, da Silva EL, Finardi EC, Rodrigues RN (2012) Solving the hydrothermal scheduling problem considering network constraints. Electr Power Syst Res 88:89–97Google Scholar
  365. Takigawa FYK, Finardi EC, da Silva EL (2013) A decomposition strategy to solve the short-term hydrothermal scheduling based on Lagrangian relaxation. J Algorithms Optim 1(1):13–24Google Scholar
  366. Takriti S, Birge JR (2000) Using integer programming to refine Lagrangian-based unit commitment solutions. IEEE Trans Power Syst 15(1):151–156Google Scholar
  367. Takriti S, Birge JR, Long E (1996) A stochastic model for the unit commitment problem. IEEE Trans Power Syst 11:1497–1508Google Scholar
  368. Takriti S, Krasenbrink B, Wu LSY (2000) Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem. Oper Res 48(2):268–280Google Scholar
  369. Tong SK, Shahidehpour M (1989) Combination of Lagrangian-relaxation and linear-programming approaches for fuel-constrained unit-commitment problems. IEEE Proc Gener Transm Distrib 136(3):162–174Google Scholar
  370. Triki C, Beraldi P, Gross G (2005) Optimal capacity allocation in multi-auction electricity markets under uncertainty. Comput Oper Res 32:201–217Google Scholar
  371. Triki C, Conejo AJ, Garcés LP (2011) Short-term trading for electricity producers. In: Bertocchi M, Consigli G, Dempster MAH (eds) Stochastic optimization methods in finance and energy: new financial products and energy market strategies, volume 163 of international series in operations research and management science. Springer, Heidelberg, pp 181–202Google Scholar
  372. Trukhanova S, Ntaimo L, Schaefer A (2010) Adaptive multicut aggregation for two-stage stochastic linear programs with recourse. Eur J Oper Res 206(2):395–406Google Scholar
  373. Tseng P (2001) Convergence of a block coordinate descent method for nondifferentiable minimization. J Optim Theory Appl 109(3):475–494Google Scholar
  374. Tseng CL, Li CA, Oren SS (2000) Solving the unit commitment problem by a unit decommitment method. J Optim Theory Appl 105(3):707–730Google Scholar
  375. Tuohy A, Meibom P, Denny E, O’Malley MJ (2009) Unit commitment for systems with significant wind penetration. IEEE Trans Power Syst 24(2):592–601Google Scholar
  376. Turgeon A (1978) Optimal scheduling of thermal generating units. IEEE Trans Autom Control 23(6):1000–1005Google Scholar
  377. Valenzuela J, Smith AE (2002) A seeded memetic algorithm for large unit commitment problems. J Heuristics 8(2):173–195Google Scholar
  378. Valenzuela J, Mazumdar M (2003) Commitment of electric power generators under stochastic market prices. Oper Res 51(6):880–893Google Scholar
  379. van Ackooij W (2014) Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment. Math Methods Oper Res 80(3):227–253. doi: 10.1007/s00186-014-0478-5
  380. van Ackooij W, Wirth J (2007) Un jeu d’acteurs n-zones pour SSPS. synthèse et propositions. Technical report H-R33-2006-03913-FR, EDF R&DGoogle Scholar
  381. van Ackooij W, Malick J (2014) Decomposition algorithm for large-scale two-stage unit-commitment, pp 1–26 (draft submitted)Google Scholar
  382. van Ackooij W, Henrion R, Möller A, Zorgati R (2010) On probabilistic constraints induced by rectangular sets and multivariate normal distributions. Math Methods Oper Res 71(3):535–549Google Scholar
  383. van Ackooij W, Henrion R, Möller A, Zorgati R (2011) Chance constrained programming and its applications to energy management. In: [?] (Chapter 13). INTECHGoogle Scholar
  384. van Ackooij W, Henrion R, Möller A, Zorgati R (2014) Joint chance constrained programming for hydro reservoir management. Optim Eng 15:509–531Google Scholar
  385. van Slyke RM, Wets RJ-B (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17:638–663Google Scholar
  386. Ventosa M, Baíllo A, Ramos A, Rivier M (2005) Electricity market modeling trends. Energy Policy 33(7):897–913Google Scholar
  387. Victoire TAA, Jeyakumar AE (2005) Unit commitment by a tabu-search-based hybrid-optimisation technique. IEE Proc Gener Transm Distrib 152(4):563–574Google Scholar
  388. Villumsen JC, Philpott AB (2011) Column generation for transmission switching of electricity networks with unit commitment. In: Proceedings of the international multiconference of engineers and computer scientists, vol 2Google Scholar
  389. Vucetic S, Tomsovic K, Obradovic Z (2001) Discovering price–load relationships in California’s electricity market. IEEE Trans Power Syst 16(2):280–286Google Scholar
  390. Wallace SW, Fleten S-E (2003) Stochastic programming models in energy. In: Ruszczyński A, Shapiro A (eds) Stochastic programming, chap10. Handbooks in operations research and management science, vol 10. Elsevier, Amsterdam, pp 637–677Google Scholar
  391. Walsh MP, O’Malley MJ (1997) Augmented hopfield network for unit commitment and economic dispatch. IEEE Trans Power Syst 12(4):1765–1774Google Scholar
  392. Wang C, Shahidehpour M (1993) Effects of ramp-rate limits on unit commitment and economic dispatch. IEEE Trans Power Syst 8(3):1341–1350Google Scholar
  393. Wang SJ, Shahidehpour M, Kirschen DS, Mokhtari S, Irisarri GD (1995) Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation. IEEE Trans Power Syst 10(3):1294–1301Google Scholar
  394. Wang J, Wang X, Wu Y (2005) Operating reserve model in the power market. IEEE Trans Power Syst 20(1):223–229Google Scholar
  395. Wang L, Mazumdar M, Bailey MD, Valenzuela J (2007) Oligopoly models for market price of electricity under demand uncertainty and unit reliability. Eur J Oper Res 181(3):1309–1321Google Scholar
  396. Wang J, Shahidehpour M, Li Z (2008) Security-constrained unit commitment with volatile wind power generation. IEEE Trans Power Syst 23(3):1319–1327Google Scholar
  397. Wang Y, Xia Q, Kang C (2011) Unit commitment with volatile node injections by using interval optimization. IEEE Trans Power Syst 26(3):1705–1713Google Scholar
  398. Wang Q, Guan Y, Wang J (2012) A chance-constrained two-stage stochastic program for unit commitment with uncertain wind power output. IEEE Trans Power Syst 27(1):206–215Google Scholar
  399. Wang J, Wang J, Liu C, Ruiz JP (2013a) Stochastic unit commitment with sub-hourly dispatch constraints. Appl Energy 105:418–422Google Scholar
  400. Wang Q, Watson J-P, Guan Y (2013b) Two-stage robust optimization for \(n-k\) contingency-constrained unit commitment. IEEE Trans Power Syst 28(3):2366–2375Google Scholar
  401. Wen F, David AK (2001) Optimal bidding strategies and modeling of imperfect information among competitive generators. IEEE Trans Power Syst 16(1):15–21Google Scholar
  402. Wolfe P (1975) A method of conjugate subgradients for minimizing nondifferentiable functions. Math Program Study 3:143–173Google Scholar
  403. Wong KP, Wong YW (1994) Genetic and genetic/simulated-annealing approaches to economic dispatch. IEEE Proc Gener Transm Distrib 141(5):507–513Google Scholar
  404. Wong KP, Wong YW (1996) Combined genetic algorithm/simulated annealing/fuzzy set approach to short-term generation scheduling with take-or-pay fuel contract. IEEE Trans Power Syst 11(1):128–136Google Scholar
  405. Wong S, Fuller JD (2007) Pricing energy and reserves using stochastic optimization in an alternative electricity market. IEEE Trans Power Syst 22(2):631–638Google Scholar
  406. Wood AJ, Wollemberg BF (1996) Power generation operation and control. Wiley, LondonGoogle Scholar
  407. Wu L (2011) A tighter piecewise linear approximation of quadratic cost curves for unit commitment problems. IEEE Trans Power Syst 26(4):2581–2583Google Scholar
  408. Wu L (2013) An improved decomposition framework for accelerating LSF and BD based methods for network-constrained UC problems. IEEE Trans Power Syst 28(4):3977–3986Google Scholar
  409. Wu L, Shahidehpour M, Li T (2007) Stochastic security-constrained unit commitment. IEEE Trans Power Syst 22(2):800–811Google Scholar
  410. Wu L, Shahidehpour M, Li Z (2012) Comparison of scenario-based and interval optimization approaches to stochastic SCUC. IEEE Trans Power Syst 27(2):913–921Google Scholar
  411. Xiong P, Jirutitijaroen P (2011) Stochastic unit commitment using multi-cut decomposition algorithm with partial aggregation. In: IEEE power and energy society general meetingGoogle Scholar
  412. Yan H, Luh PB, Guan X, Rogan PM (1993) Scheduling of hydro-thermal power systems. IEEE Trans Power Syst 8(3):1358–1365Google Scholar
  413. Yan H, Luh PB, Zhang L (1994) Scheduling of hydrothermal power systems using the augmented Lagrangian decomposition and coordination technique. In: American control conference, vol 2, pp 1558–1562Google Scholar
  414. Yang J-S, Chen N (1989) Short term hydrothermal coordination using multi-pass dynamic programming. IEEE Trans Power Syst 4(3):1050–1056Google Scholar
  415. Yang HT, Yang PC, Huang CL (1996) Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions. IEEE Trans Power Syst 11(1):112–118Google Scholar
  416. Yu Z, Sparrow FT, Bowen B, Smardo FJ (2000) On convexity issues of short-term hydrothermal scheduling. Electr Power Energy Syst 20:451–457Google Scholar
  417. Zaourar S, Malick J (2013) Prices stabilization for inexact unit-commitment problems. Math Methods Oper Res 78(3):341–359. doi: 10.1007/s00186-013-0447-4
  418. Zareipour H (2012) Short-term electricity market prices: a review of characteristics and forecasting methods. In: Sorokin A, Rebennack S, Pardalos PM, Iliadis NA, Pereira MVF (eds) Handbook of networks in power systems I. Springer, Heidelberg, pp 89–121Google Scholar
  419. Zhang C, Wang J (2014) Optimal transmission switching considering probabilistic reliability. IEEE Trans Power Syst 29(2):974–975Google Scholar
  420. Zhang D, Luh PB, Zhang Y (1999) A bundle method for hydrothermal scheduling. IEEE Trans Power Syst 14:1355–1361Google Scholar
  421. Zhao L, Zeng B (2012) Robust unit commitment problem with demand response and wind energy. In: Proceedings of IEEE power and energy society general meetingGoogle Scholar
  422. Zhao C, Guan Y (2013) Unified stochastic and robust unit commitment. IEEE Trans Power Syst 28(3):3353–3361Google Scholar
  423. Zhao C, Wang J, Watson J-P, Guan Y (2013) Multi-stage robust unit commitment considering wind and demand response uncertainties. IEEE Trans Power Syst 28(3):2708–2717Google Scholar
  424. Zheng Q, Wang J, Pardalos P, Guan Y (2013) A decomposition approach to the two-stage stochastic unit commitment problem. Ann Oper Res 210(1):387–410Google Scholar
  425. Zhu J (2009) Optimization of power system operation. IEEE Press series on power engineering. Wiley-IEEE Press, LondonGoogle Scholar
  426. Zhuang F, Galiana FD (1988) Towards a more rigorous and practical unit commitment by Lagrangian relaxation. IEEE Trans Power Syst 3(2):763–773Google Scholar
  427. Zhuang F, Galiana FD (1990) Unit commitment by simulated annealing. IEEE Trans Power Syst 5(1):311–318Google Scholar
  428. Zorgati R, van Ackooij W (2011) Optimizing financial and physical assets with chance-constrained programming in the electrical industry. Optim Eng 12(1):237–255Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Milad Tahanan
    • 1
  • Wim van Ackooij
    • 2
  • Antonio Frangioni
    • 3
    Email author
  • Fabrizio Lacalandra
    • 4
  1. 1.Ecole Centrale ParisChatenay-MalabryFrance
  2. 2.OSIRISEDF R&DClamart CedexFrance
  3. 3.Dipartimento di InformaticaUniversità di PisaPisaItaly
  4. 4.QuanTek S.r.L.BolognaItaly

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