Optimization Approaches to Security-Constrained Unit Commitment and Economic Dispatch with Uncertainty Analysis

  • Dzung T. PhanEmail author
  • Ali Koc
Part of the Energy Systems book series (ENERGY)


At the heart of the future smart grid lie two related challenging optimization problems: unit commitment and economic dispatch. The contemporary practices such as intermittent renewable power, distributed generation, demand response, etc., induce uncertainty into the daily operation of an electric power system, and exacerbate the ability to handle the already complicated intermingled problems. We introduce the mathematical formulations for the two problems, present the current practice, and survey solution methods for solving these problems. We also discuss a number of important avenues of research that will receive noteworthy attention in the coming decade.


Economic dispatch Power flow Uncertainty Stochastic Security-constrained Unit commitment 



The authors would like to thank Andrew Conn, Peter Feldmann, Brian Gaucher, Bhavna Agrawal, Jayant Kalagnanam, and Jinjun Xiong for their many valuable comments and suggestions during the course of this work.


  1. Acar E, Agrawal B, Conn AR, Ditlow G, Feldmann P, Finkler U, Gaucher B, Gupta A, Heng F, Kalagnanam J, Koc A, Kung D, Phan D, Singhee A, Smith B, Xiong J (2011) Framework for large-scale modeling and simulation of electricity systems for planning, monitoring, and secure operations of next generation electricity grids. In: Proceedings of Computational Needs for the Next Generation Electric Grid, pp 1–73Google Scholar
  2. Acha E, Fuerte-Esquivel CR, Ambriz-Pérez H, Angeles-Camacho C (eds) (2005) FACTS: modelling and simulation in power networks. Wiley, ChichesterGoogle Scholar
  3. Ahmed A, King A, Parija G (2003) A multistage stochastic integer programming approach for capacity expanstion under uncertainty. J Global Optim 26:3–24MathSciNetzbMATHGoogle Scholar
  4. Alguacil N, Conejo A (2000) Multiperiod optimal power flow using Benders decomposition. IEEE Trans Power Syst 15(1):196–201Google Scholar
  5. Alsac O, Bright J, Prais M, Stott B (1990) Further developments in LP-based optimal power flow. IEEE Trans Power Syst 5(3):697–711Google Scholar
  6. Alsac O, Stott B (1974) Optimal load flow with steady state security. IEEE Trans Power App Syst PAS-93(3):745–751Google Scholar
  7. Alves JMT, Borges CLT, Filho ALO (2007) Distributed security constrained optimal power flow integrated to a dsm based energy management system for real time power systems security control. In: VECPAR’06: Proceedings of the 7th international conference on high performance computing for computational science, Springer, Berlin, pp 131–144Google Scholar
  8. van Amerongen RAM (1988) Optimal power flow solved with sequential reduced quadratic programming. Electr Eng 71(3):213–219Google Scholar
  9. Aoki A, 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 2:1077–1084Google Scholar
  10. Arroyo JM, Conejo AJ (2000) Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst 15:1098–1104Google Scholar
  11. Arroyo JM, Conejo AJ (2004) Modeling of start-up and shut-down power trajectories of thermal units. IEEE Trans Power Syst 19:1562–1568Google Scholar
  12. Ayoub AK, Patton AD (1971) Optimal thermal generating unit commiment. IEEE Trans Power App Syst 90:1752–1756Google Scholar
  13. Bai X, Wei H, Fujsawa K, Wang Y (2008) Semidefinite programming for optimal power flow problems. Int J Electr Power Energy Syst 30:383–392Google Scholar
  14. Baldick R (1995) The generalized unit commitment problem. IEEE Trans Power Syst 10:465–475Google Scholar
  15. Baldwin CJ, Dale KM, Dittrich RF (1959) A study of the economic shutdown of generating units in daily dispatch. AIEEE Trans Power App Syst Part III 78:1272–1284Google Scholar
  16. Baptisella LFB, Geromel JC (1980) Decomposition approach to problem of unit commitment schedule for hydrothermal systems. IEEE Proc Control Theory Appl 127(6):250–258Google Scholar
  17. Baptista EC, Belati EA, da Costa GRM (2005) Logarithmic barrier-augmented Lagrangian function to the optimal power flow problem. Int J Electr Power Energy Syst 27(7):528–532Google Scholar
  18. Bard JF (1988) Short-term scheduling of thermal-electric generators using lagrangian relaxation. Oper Res 36(5):756–766MathSciNetzbMATHGoogle Scholar
  19. Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238–252MathSciNetzbMATHGoogle Scholar
  20. Bertsekas DP, Lauer GS, Sandell NR, Posbergh TA (1983) Optimal short-term scheduling of large-scale power systems. IEEE Trans Autom Control 28:1–11zbMATHGoogle Scholar
  21. 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
  22. Birge J, Takriti S (2000) Using integer programming to refine lagrangian-based unit commitment solutions. IEEE Trans Power Syst 15:151–156Google Scholar
  23. Bond SD, Fox B (1986) Optimal thermal unit scheduling using improved dynamic programming algorithm. In: IEEE Proceedings of generation, transmission and distribution, vol 133. pp 1–5Google Scholar
  24. Bouffard F, Galiana FD, Arroyo JM (2005) Umbrella contingencies in security constrained optimal power flow. In: 15th power systems computation conference (PSCC 05). Liège, BelgiumGoogle Scholar
  25. Brini S, Abdallah HH, Ouali A (2009) Economic dispatch for power system included wind and solar thermal energy. Leonardo J Sci 14:204–220Google Scholar
  26. Byrd RH, Nocedal J, Waltz RA (2006) KNITRO: An integrated package for nonlinear optimization. In: di Pillo G, Roma M (eds) Large scale nonlinear optimization. Springer, New York, pp 35–59Google Scholar
  27. Capitanescu F, Glavic M, Ernst D, Wehenkel L (2007a) Contingency filtering techniques for preventive security-constrained optimal power flow. IEEE Trans Power Syst 22(4):1690–1697Google Scholar
  28. Capitanescu F, Glavic M, Ernst D, Wehenkel L (2007b) Interior-point based algorithms for the solution of optimal power flow problems. Electr Power Syst Res 77(5–6):508–517Google Scholar
  29. Capitanescu F, Wehenkel L (2007) Improving the statement of the corrective security-constrained optimal power flow problem. IEEE Trans Power Syst 22(2):887–889Google Scholar
  30. Capitanescu F, Wehenkel L (2008) A new iterative approach to the corrective security-constrained optimal power flow problem. IEEE Trans Power Syst 23(4):1533–1541Google Scholar
  31. Carpentier J (1962) Contribution to the economic dispatch problem. Bull. Soc. Franc. Elect. 8(3):431–447Google Scholar
  32. Carpentier P, Cohen G, Culioli JC, Renaud R (1996) Stochastic optimization of unit commitment: a new decomposition framework. IEEE Trans Power Syst 11:1067–1073Google Scholar
  33. Chang G, Tsai Y, Lai C, Chung J (2004) A practical mixed integer linear programming based approach for unit commitment. In: IEEE PES general meeting, vol 1, pp 221–225Google Scholar
  34. Chen H, Wang X (2002) Cooperative coevolutionary algorithm for unit commitment. IEEE Trans Power Syst 16:128–133Google Scholar
  35. Cheung K, Wang X, Chiu BC, Xiao Y, Rios-Zalapa R (2010) Generation dispatch in a smart grid environment. In: Innovative Smart Grid Technologies (ISGT). Washington, USA, pp 1–6Google Scholar
  36. Chiang HD, Wang B, Jiang QY (2009) Applications of trust-tech methodology in optimal power flow of power systems. In: Kallrath J, Pardalos PM, Rebennack S, Scheidt M (eds) Optimization in the energy industry, energy systems. Springer, Berlin, pp 297–318Google Scholar
  37. Cohen AI, Sherkat VR (1987) Optimization-based methods for operations scheduling. In: Proceedings of the IEEE 75:1574–1591Google Scholar
  38. Cohen AI, Wan AH (1987) A method for solving the fuel constrained unit commitment problem. IEEE Trans Power Syst 2:608–614Google Scholar
  39. Cohen AI, Yoshimura M (1983) A branch-and-bound algorithm for unit commitment. AIEEE Trans Power App Syst Part III 102:444–451Google Scholar
  40. Contaxis GC, Delkis C, Korres G (1986) Decoupled optimal power flow using linear or quadratic programming. IEEE Trans Power Syst PWRS-1:1–7Google Scholar
  41. Dasgupta D, McGregor DR (1994) Thermal unit commitment using genetic algorithms. In: IEE Proceedings, generation, transmission and distribution 141:459–465Google Scholar
  42. Dillon T, Edwin K, Kochs H, Taud R (1978) Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination. IEEE Trans Power App Syst 97:2154–2166Google Scholar
  43. Dragoon K, Milligan M (2003) Assessing wind integration costs with dispatch models: a case study of PacifiCorp. Windpower 2003, AustinGoogle Scholar
  44. Ernst D, Ruiz-Vega D, Pavella M, Hirsch PM, Sobajic D (2001) A unified approach to transient stability contingency filtering, ranking and assessment. IEEE Trans Power Syst 16(3):435–443Google Scholar
  45. FERC (2006) Security constrained economic dispatch: definition, practices, issues and recommendations—a report to congress regarding the recommendations of regional joint boards for the study of economic dispatch pursuant to Section 223 of the Federal Power Act as added by Section 1298 of the Energy Policy Act of 2005. Technical report, Federal Energy Regulatory Comission, 31 July 2006. See
  46. Fu W, McCalley JD (2001) Risk based optimal power flow. In: 2001 IEEE Porto Power Tech Conference, Porto, PortugalGoogle Scholar
  47. Fu Y, Shahidehpour SM, Li Z (2005) Security-constrained unit commitment with AC constraints. IEEE Trans Power Syst 20:1538–1550Google Scholar
  48. Gabay D, Mercier B (1976) A dual algorithm for the solution of nonlinear variational problems via finite-element approximations. Comput Math Appl 2:17–40zbMATHGoogle Scholar
  49. Gan D, Thomas R, Zimmerman R (2000) Stability-constrained optimal power flow. IEEE Trans Power Syst 15(2):535–540Google Scholar
  50. Garver LL (1962) Power generation scheduling by integer programming—development of theory. AIEEE Trans Power App Syst Part III 81:730–734Google Scholar
  51. Geoffrion AM (1972) Generalized Benders decomposition. J Optim Theory Appl 10(4):237–260MathSciNetzbMATHGoogle Scholar
  52. Ghosh S, Kalagnanam JR, Katz D, Squillante MS, Zhang X (2011) Integration of demand response and renewable resources for power generation management. In: Proceedings of 1st IEEE power engineering society ISGT meetingGoogle Scholar
  53. Glavitsch H, Bacher R (1991) Optimal power flow algorithms. In: Leondes CT (ed) Analysis and control system techniques for electric power systems, vol 41. Academic Press, New YorkGoogle Scholar
  54. Glover JD, Sarma MS, Overbye TJ (2008) Power systems analysis and design. Thomson Learning, TorontoGoogle Scholar
  55. Glowinski R, Marrocco A (1975) Sur l’approximation par èlèments finis d’ordre un, et la rsolution, par pnalisation-dualit, d’une classe de problèmes de Dirichlet non lineaires. RAIRO Anal Numèr 2:41–76MathSciNetGoogle Scholar
  56. Gooi H, Mendes D, Bell K, Kirschen D (1999) Optimal scheduling of spinning reserve. IEEE Trans Power Syst 14(4):1485–1492Google Scholar
  57. Gröve-Kuska N, Römisch W (2005) Stochastic unit commitment in hydrothermal power production planning. In: Wallace SW, Ziemba WT (eds) Applications of Stochastic Programming, SIAM, Philadelphia, pp 633–653Google Scholar
  58. Guan X, Luh PB, Amalfi JA (1996) An optimization-based method for unit commitment. Int J Electr Power Energy Syst 14:9–17Google Scholar
  59. Habibollahzadeh H, Bukenko JA (1986) Application of decomposition techniques to short-term operation planning of hydrothermal power system. IEEE Trans Power Syst 1:41–47Google Scholar
  60. Hara K, Kimura M, Honda N (1966) A method for planning economic unit commitment and maintenance of thermal power systems. IEEE Trans Power App Syst 85:427–436Google Scholar
  61. Hatami AR, Seifi H, Sheikh-El-Eslami MK (2009) Hedging risks with interruptible load programs for a load serving entity. Decis Support Syst 48(1):150–157Google Scholar
  62. Hedman K, O’neill R, Oren S (2009) Analyzing valid inequalities of the generation unit commitment problem. In: Power systems conference and exposition, pp 1–6Google Scholar
  63. Hobbs WJ, Hermon G, Warner S, Shelbe GB (1988) An enhanced dynamic programming approach for unit commitment. IEEE Trans Power Syst 3:1201–1205Google Scholar
  64. Hu Z, Wang X, Taylor G (2010) Stochastic optimal reactive power dispatch: Formulation and solution method. Int J Electr Power Energy Syst 32(6):615–621Google Scholar
  65. Huang SJ (2001) Enhancement of hydroelectric generation scheduling using ant colony system based optimization approaches. IEEE Trans Energy Conver 16:296–301Google Scholar
  66. Jabr RA (2003) A primal-dual interior-point method to solve the optimal power flow dispatching problem. Optim Eng 4(4):309–336MathSciNetzbMATHGoogle Scholar
  67. Jabr RA (2006) Radial distribution load flow using conic programming. IEEE Trans Power Syst 21(3):1458–1459MathSciNetGoogle Scholar
  68. Jabr RA (2008) Optimal power flow using an extended conic quadratic formulation. IEEE Trans Power Syst 23(3):1000–1008Google Scholar
  69. Jiang Q, Geng G (2010) A reduced-space interior point method for transient stability constrained optimal power flow. IEEE Trans Power Syst 25(3):1232–1240Google Scholar
  70. Jiang Q, Geng G, Guo C, Cao Y (2010) An efficient implementation of automatic differentiation in interior point optimal power flow. IEEE Trans Power Syst 25(1):147–155Google Scholar
  71. Jiang R, Zhang M, Li G, Guan Y (2011) Benders decomposition for the two-stage security constrained robust unit commitment problem. Optimization.
  72. Juste KA, Kita H, Tanaka E, Hasegawa J (1999) An evolutionary programming solution to the unit commitment prolem. IEEE Trans Power Syst 14:1452–1459Google Scholar
  73. Kazarlis SA, Bakirtzis AG, Petridis V (1996) A genetic algorithm solution to the unit commitment problem. IEEE Trans Power Syst 11:83–92Google Scholar
  74. Kerr R, Scheidt J, Jr AF, Wiley J (1966) Unit commitment. IEEE Trans Power App Syst 85:471–421Google Scholar
  75. Kim BH, Baldick R (1997) Coarse-grained distributed optimal power flow. IEEE Trans Power Syst 12(2):932–939Google Scholar
  76. Kim BH, Baldick R (2000) A comparison of distributed optimal power flow algorithms. IEEE Trans Power Syst 15(2):599–604Google Scholar
  77. Koc A, Ghosh S (2012) Optimal scenario tree reduction for the stochastic unit commitment problem. In: Winter simulation conference, pp 1–12Google Scholar
  78. Koc A, Kalagnanam J (2012) Parallel branch-cut-price for solving stochastic unit commitment problems for the smart grid (submitted)Google Scholar
  79. Lai SY, Baldick R (1999) Unit commitment with ramp multipliers. IEEE Trans Power Syst 14:58–64Google Scholar
  80. Lam A, Zhang B, Tse D (2011) Distributed algorithms for optimal power flow problem.
  81. Lauer GS, Sandell NR, Bertsekas DP, Posbergh TA (1982) Solution of large-scale optimal unit commitment problems. IEEE Trans Power App Syst 101:79–86Google Scholar
  82. Lavaei J (2011) Zero duality gap for classical OPF problem convexifies fundamental nonlinear power problems. In: American control conference, pp 4566–4573Google Scholar
  83. Lavaei J, Low S (2012) Zero duality gap in optimal power flow problem. IEEE Trans Power Syst 27(1):92–107Google Scholar
  84. Lee FN (1991) The application of commitment utilization factor to the thermal unit commitment. IEEE Trans Power Syst 6:691–698Google Scholar
  85. Lee J, Leung J, Margot F (2004) Min-up/min-down polytopes. Discrete Optim 1:77–85MathSciNetzbMATHGoogle Scholar
  86. Li C, Johnson RB, Svoboda AJ (1997) A new unit commitment method. IEEE Trans Power Syst 12:113–119Google Scholar
  87. Li H, Li Y, Li Z (2007) A multiperiod energy acquisition model for a distribution company with distributed generation and interruptible load. IEEE Trans Power Syst 22(2):588–596Google Scholar
  88. Li S, Sahidehpour SM, Wang C (1993) Promoting the application of expert system in short-term unit commitment. IEEE Trans Power Syst 3:286–292Google Scholar
  89. Li T, Shahidehpour SM (2005) Price-based unit commitment: a case of Lagrangian relaxation versus mixed integer programming. IEEE Trans Power Syst 20:2015–2025Google Scholar
  90. Li Y (2008) Decision making under uncertainty in power system using benders decomposition. PhD thesis, Iowa State University, Ames, IowaGoogle Scholar
  91. Li Y, McCalley JD (2009) Decomposed SCOPF for improving effciency. IEEE Trans Power Syst 24(1):494–495Google Scholar
  92. Liang RH, Kang FC (2000) Thermal generating unit commitment using an extended mean field annealing neural network. In: IEE Proceedings generation, transmission and distribution 147:164–170Google Scholar
  93. Lin WM, Cheng FS, Tsay MT (2002) An improved tabu search for economic dispatch with multiple minima. IEEE Trans Power Syst 17:108–112Google Scholar
  94. Liu C, Shahidehpour SM, Wu L (2010) Extended benders decomposition for two-stage SCUC. IEEE Trans Power Syst 25:1192–1194Google Scholar
  95. Lowery PG (1966) Generating unit commitment by dynamic programming. IEEE Trans Power App Syst 85:422–426Google Scholar
  96. Lulli G, Sen S (2004) A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems. Manage Sci 50:786–796zbMATHGoogle Scholar
  97. Ma H, Shahidehpour SM (1998) Transmission-constraint unit commitment based on benders decomposition. Int J Electr Power Energy Syst 20:287–294Google Scholar
  98. Maifeld TT, Sheble GB (1996) Genetic-based unit commitment algorithm. IEEE Trans Power Syst 11:1359–1370Google Scholar
  99. Mantawy A, Abdel-Magid Y, Selim S (1998) Unit commitment by tabu search. In: IEE Proceedings, generation, transmission and distribution 145:56–64Google Scholar
  100. Mantawy A, Abdel-Magid Y, Selim S (1999) Integrating genetic algorithms, tabu search and simulated annealing for the unit commitment problem. IEEE Trans Power Syst 14:829–836Google Scholar
  101. Mantawy AH, Soliman SA, El-Hawary ME (2002) A new tabu search algorithm for the long-term hydro scheduling problem. In: Proceedings of large engineering systems conference, power engineering, pp 29–34Google Scholar
  102. Merlin A, Sandrin P (1983) A new method for unit commitment at electricite de france. IEEE Trans Power App Syst 102:1218–1225Google Scholar
  103. Min W, Shengsong L (2005) A trust region interior point algorithm for optimal power flow problems. Int J Electr Power Energy Syst 27(4):293–300Google Scholar
  104. Mokhtari S, Singh J, Wollenberg B (1987) A unit commitment expert system. In: Proceedings of the PICA, pp 400–405Google Scholar
  105. Monticelli A, Pereira MVF, Granville S (1987) Security-constrained optimal power flow with post-contingency corrective rescheduling. IEEE Trans Power Syst 2(1):175–180Google Scholar
  106. Mori H, Matsuzaki O (2001) Embdedding the priority list into tabu search for unit commitment. In: Proceedings of Power Engineering Society Winter Meeting, pp 1067–1072Google Scholar
  107. Muckstadt A, Koenig SA (1977) An application of Lagrangian relaxation to schediling on power generation systems. Oper Res 25(3):387–403zbMATHGoogle Scholar
  108. Muckstadt JA, Wilson RC (1968) An application of mixed integer programming duality to scheduling thermal generating systems. IEEE Trans Power Syst 87:1968–1977Google Scholar
  109. Mukerji R (2010) NYISO day-ahead unit commitment design. In: Technical conference on unit commitment software. Federal Energy Regulatory Commission, Washington DCGoogle Scholar
  110. Nowak MP, Romisch W (2000) Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Ann Oper Res 100:251–272MathSciNetzbMATHGoogle Scholar
  111. Ott A (2010) Unit commitment in PJM. In: Technical conference on unit commitment software. Federal Energy Regulatory Commission, Washington DCGoogle Scholar
  112. Padhy N (2004) Unit commitment—a bibliographical survey. IEEE Trans Power Syst 19:1196–2005Google Scholar
  113. Padhy NP (2001) Unit commitment using hybrid models: a comparative study for dynamic programming, expert system, fuzzy system, and genetic algorithms. Int J Electr Power Energy Syst 23:827–836Google Scholar
  114. Pang CK, Chen HC (1976) Optimal short-term thermal unit commitment. IEEE Trans Power App Syst 95:1336–1346Google Scholar
  115. Pang CK, Sheble GB, Albuyeh F (1981) Evaluation of dynamic programming based methods and multiple area representation for thermal unit commitments. IEEE Trans Power App Syst 100:1212–1218Google Scholar
  116. Phan DT (2012) Lagrangian duality and branch-and-bound algorithms for optimal power flow. Oper Res 60(2):275–285MathSciNetzbMATHGoogle Scholar
  117. Phan DT, Ghosh S (2011) A two-stage non-linear program for optimal electrical grid power balance under uncertainty. In: Proceedings of the 2011 winter simulation conference, pp 4222–4233Google Scholar
  118. Phan DT, Kalagnanam J (2012) Distributed methods for solving the security-constrained optimal power flow problem. In: Proceedings of the 2012 IEEE PES Innovative Smart Grid Technologies (ISGT), pp 1–7Google Scholar
  119. Qiu W, Flueck AJ, Tu F (2005) A new parallel algorithm for security constrained optimal power flow with a nonlinear interior point method. In: IEEE Power Engineering Society General Meeting, pp 2422–2428Google Scholar
  120. Quyang Z, Shahidehpour S (1990) Short-term unit commitment expert system. Electr Power Syst Res 20:1–13Google Scholar
  121. Quyang Z, Shahidehpour SM (1992) An itelligent dynamic programming for unit commitment application. IEEE Trans Power Syst 6:1203–1209Google Scholar
  122. Rajan D, Takriti S (2005) Minimum up/down polytopes of the unit commitment problem with start-up costs. Technical report, IBM ResearchGoogle Scholar
  123. Rodrigues M, Saavedra OR, Monticelli A (1994) Asynchronous programming model for the concurrent solution of the security constrained optimal power flow problem. IEEE Trans Power Syst 9(4):2021–2027Google Scholar
  124. Rothleder M (2010) Unit commitment in the CAISO market. In: Technical conference on unit commitment software. Federal Energy Regulatory Commission, Washington DCGoogle Scholar
  125. Ruzic S, Rajakovic N (1991) A new approach for solving extended unit commitment problem. IEEE Trans Power Syst 6:269–275Google Scholar
  126. Salam S (2007) Unit commitment solution methods. World Acad Sci Eng Technol 35:320–325Google Scholar
  127. Santos AJ, da Costa GRM (1995) Optimal power flow solution by Newton’s method applied to an augmented Lagrangian function. In: IEE proceedings, generation, transmission and distribution 142(1):33–36Google Scholar
  128. Sasaki H, Watanabe M, Yokoyama R (1992) A solution method of unit commitment by artificial neural networks. IEEE Trans Power Syst 7:974–981Google Scholar
  129. Schellenberg A, Rosehart W, Aguado J (2006) Cumulant-based stochastic nonlinear programming for variance constrained voltage stability analysis of power systems. IEEE Trans Power Syst 21(2):579–585Google Scholar
  130. Sheble G, Fahd G (1994) Unit commitment—literature synopsis. IEEE Trans Power Syst 9:128–135Google Scholar
  131. Singh KJ, Philpott AB, Wood RK (2009) Dantzig-wolfe decomposition for solving multistage stochastic capacity-planning problems. Oper Res 57(5):1271–1286MathSciNetzbMATHGoogle Scholar
  132. Sisworahardjo NS, El-Kaib AA (2002) Unit commitment using ant colony search algorithms. In: Proceedings of large engineering systems conference, power engineering pp 2–6Google Scholar
  133. Siu TK, Nash GA, Shawwash ZK (2001) A practical hydro, dynamic unit commitment and loading model. IEEE Trans Power Syst 16:301–306Google Scholar
  134. Snyder WL Jr, Powell HD Jr, Rayburn JC (1987) Dynamic programming approach to unit commitment. IEEE Trans Power Syst 2:339–347Google Scholar
  135. Sojoudi S, Lavaei J (2012) Network topologies guaranteeing zero duality gap for optimal power flow problem. In: Proceedings of IEEE Power and Energy Society General Meeting, pp 1–7Google Scholar
  136. Sousa A, Torres G (2007) Globally convergent optimal power flow by trust-region interior-point methods. In: Power Tech, 2007 IEEE Lausanne, pp 1386–1391Google Scholar
  137. Sousa AA, Torres GL (2011) Robust optimal power flow solution using trust region and interior-point methods. IEEE Trans Power Syst 26(2):487–499Google Scholar
  138. Street A, Oliveira F, Arroyo JM (2011) Contingency constrained unit commitment with n-k security criterion: a robust optimization approach. IEEE Trans Power Syst 26(3):1581–1590Google Scholar
  139. Sun D, Ashley B, Brewer B, Hughes A, Tinney W (1984) Optimal power flow by newton approach. IEEE Trans Power App Syst PAS-103(10):2864–2880Google Scholar
  140. Swarup KS, Yamashiro S (2002) Unit commitment solution methodology using genetic algorithm. IEEE Trans Power Syst 17:87–91Google Scholar
  141. Takriti S, Birge J, Long E (1996) A stochastic model for the unit commitment problem. IEEE Trans Power Syst 11(3):1497–1508Google Scholar
  142. Takriti S, Birge JR (1996) A stochastic model for the unit commitment problem. IEEE Trans Power Syst 11:1497–1508Google Scholar
  143. 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
  144. Tong SK, Sahidehpour SM, Quyang Z (1991) A heuristic short-term unit commitment. IEEE Trans Power Syst 6:1210–1216Google Scholar
  145. Tong SK, Shahidehpour SM (1990) An innovative approach to generation scheduling in large-scale hydro-thermal power systems with fuel constrained units. IEEE Trans Power Syst 5:665–673Google Scholar
  146. Torres G, Quintana V (1998) An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Trans Power Syst 13(4):1211–1218Google Scholar
  147. Turgeon A (1978) Optimal scheduling of thermal generating units. IEEE Trans Autom Control 23:1000–1005zbMATHGoogle Scholar
  148. Viana AMMMG (2003) Metaheuristics for the unit commitment problem: the constraint oriented neighbourhoods search strategy. PhD thesis, Universidade do PortoGoogle Scholar
  149. Virmani S, Imhof K, Mukhenjee S (1989) Implementation of a Lagrangian relaxation based unit commitment problem. IEEE Trans Power Syst 4:1065–1073Google Scholar
  150. Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57MathSciNetzbMATHGoogle Scholar
  151. Wang C, Shahidehpour SM (1993) Effects of ramp-rate limits on unit commitment and economic dispatch. IEEE Trans Power Syst 8:1341–1350Google Scholar
  152. Wang H, Murillo-Sanchez C, Zimmerman R, Thomas R (2007) On computational issues of market-based optimal power flow. IEEE Trans Power Syst 22(3):1185–1193Google Scholar
  153. Wang L, Singh C (2006) Multi-objective stochastic power dispatch through a modified particle swarm optimization algorithm. In: Proceedings of IEEE swarm intelligence symposium, pp 128–135Google Scholar
  154. Wells DW (1968) Method for economic secure loading of a power systems. In: Proceedings of IEEE vol 115, pp 606–614Google Scholar
  155. Wolkowicz H, Saigal R, Vandenberghe L (eds) (2000) Handbook of semidefinite programming: theory, algorithms, and applications. Kluwer Academic Publishers, BostonGoogle Scholar
  156. Wood AJ, Wollenberg BF (1996) Power Generation Operation and Control. Wiley, New YorkGoogle Scholar
  157. Wu L, Shahidehpour SM (2010) Accelerating the Benders decomposition for network-constrained unit commitment problems. Energy Syst 1:339–376Google Scholar
  158. Wu L, Shahidehpour SM, Li T (2007) Stochastic security-consrtained unit commitment. IEEE Trans Power Syst 22:800–811Google Scholar
  159. Xiong P, Jirutitijaroen P (2011) Stochastic unit commitment using multi-cut decomposition algorithm with partial aggregation. In: IEEE PES general meeting, pp 1–8Google Scholar
  160. Xue Y, Chang L, Meng J (2007) Dispatchable distributed generation network—a new concept to advance dg technologies. In: Power Engineering Society general meeting, 2007, IEEE, pp 1–5Google Scholar
  161. Yang H, Yang P, Huang C (1997) A parallel genetic algorithm approach to solving the unit commitment problem: implementation on the transputer networks. IEEE Trans Power Syst 12:661–668Google Scholar
  162. Yong T, Entriken R, Zhang P (2009) Reserve determination for systems with large wind generation. In: IEEE PES general meeting, pp 1–7Google Scholar
  163. Zhang J, Fuller JD, Elhedhli S (2010) A stochastic programming model for a day-ahead electricity market with real-time resrve shorage pricing. IEEE Trans Power Syst 25:703–713Google Scholar
  164. Zhang M, Guan Y (2009) Two-stage robust unit commitment problem.!
  165. Zhuang F, Galiana FD (1988) Toward a more rigorous and practical unit commitment by lagrangian relaxation. IEEE Trans Power Syst 3:763–773Google Scholar
  166. Zhuang F, Galiana FD (1990) Unit commitment by simulated annealing. IEEE Trans Power Syst 5:311–318Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Business Analytics and Mathematical Sciences DepartmentIBM T. J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations