An overview on mathematical programming approaches for the deterministic unit commitment problem in hydro valleys

van Ackooij, W., Henrion, R., Möller, A., Zorgati, R.: Joint chance constrained programming for hydro reservoir management. Optim. Eng. 15(2), 509–531 (2014)

Ahmadi, A., Aghaei, J., Shayanfar, H.A., Rabiee, A.: Mixed integer programming of multiobjective hydro-thermal self scheduling. Appl. Soft Comput. 12(8), 2137–2146 (2012)

Allen, R., Bridgeman, S.: Dynamic programming in hydropower scheduling. J. Water Resour. Plan. Manag. 112(3), 339–353 (1986)

Álvarez López, J., Ceciliano-Meza, J.L., Guillén Moya, I., Nieva Gómez, R.: A MIQCP formulation to solve the unit commitment problem for large-scale power systems. Int. J. Electr. Power Energy Syst. 36(1), 68–75 (2012)

Anjos, M.F.: Recent progress in modeling unit commitment problems. In: Zuluaga, L.F., Terlaky, T. (eds.) Modeling and Optimization: Theory and Applications, pp. 1–29. Springer (2013)

Arce, A., Ohishi, T., Soares, S.: Optimal dispatch of generating units of the Itaipú hydroelectric plant. IEEE Trans. Power Syst. 17(1), 154–158 (2002)

Bacaud, L., Lemaréchal, C., Renaud, A., Sagastizábal, C.: Bundle methods in stochastic optimal power management: a disaggregated approach using preconditioners. Comput. Optim. Appl. 20(3), 227–244 (2001)

Belloni, A., Lima, A.D.S., Maceira, M.P., Sagastizábal, C.A.: Bundle relaxation and primal recovery in unit commitment problems. The Brazilian case. Ann. Oper. Res. 120(1–4), 21–44 (2003)

Bhardwaj, A., Tung, N.S., Kamboj, V.: Unit commitment in power system: a review. Int. J. Electr. Power Eng. 6(1), 51–57 (2012)

Borghetti, A., D’Ambrosio, C., Lodi, A., Martello, S.: An MILP approach for short-term hydro scheduling and unit commitment with head-dependent reservoir. IEEE Trans. Power Syst. 23(3), 1115–1124 (2008)

Catalão, J., Mariano, S., Mendes, V., Ferreira, L.: Nonlinear approach for short-term scheduling of a head-sensitive hydro chain. In: IEEE Power Tech, 2005 Russia, pp. 1–6 (2005)

Catalão, J., Mariano, S., Mendes, V., Ferreira, L.: Parameterisation effect on the behaviour of a head-dependent hydro chain using a nonlinear model. Electr. Power Syst. Res. 76(6), 404–412 (2006)

Catalão, J., Mariano, S., Mendes, V., Ferreira, L.: Scheduling of head-sensitive cascaded hydro systems: a nonlinear approach. IEEE Trans. Power Syst. 24(1), 337–346 (2009)

Catalão, J., Mariano, S., Mendes, V., Ferreira, L.: Nonlinear optimization method for short-term hydro scheduling considering head-dependency. Eur. Trans. Electr. Power 20(2), 172–183 (2010)

Catalão, J., Pousinho, H., Mendes, V.: Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain. Electr. Power Syst. Res. 80(8), 935–942 (2010)

Catalão, J., Pousinho, H., Mendes, V.: Scheduling of head-dependent cascaded hydro systems: mixed-integer quadratic programming approach. Energy Convers. Manag. 51(3), 524–530 (2010)

Catalão, J., Pousinho, H., Mendes, V.: Scheduling of head-dependent cascaded reservoirs considering discharge ramping constraints and start/stop of units. Int. J. Electr. Power Energy Syst. 32(8), 904–910 (2010)

Catalão, J., Pousinho, H., Mendes, V.: Hydro energy systems management in Portugal: profit-based evaluation of a mixed-integer nonlinear approach. Energy 36(1), 500–507 (2011)

Chancelier, J.P., Renaud, A.: Daily generation scheduling: decomposition methods to solve the hydraulic problems. Int. J. Electr. Power Energy Syst. 16(3), 175–181 (1994)

Chandrasekaran, K., Simon, S.P.: Multi-objective scheduling problem: hybrid approach using fuzzy assisted cuckoo search algorithm. Swarm Evol. Comput. 5, 1–16 (2012)

Chang, C., Waight, J.: A mixed integer linear programming based hydro unit commitment. In: Power Engineering Society Summer Meeting, 1999. IEEE, vol. 2, pp. 924–928 (1999)

Chang, G.W., Aganagic, M., Waight, J.G., Medina, J., Burton, T., Reeves, S., Christoforidis, M.: Experiences with mixed integer linear programming based approaches on short-term hydro scheduling. IEEE Trans. Power Syst. 16(4), 743–749 (2001)

Chang, S.C., Chen, C.H., Fong, I.K., Luh, P.B., et al.: Hydroelectric generation scheduling with an effective differential dynamic programming algorithm. Power Syst. IEEE Trans. 5(3), 737–743 (1990)

Cheng, C.T., Liao, S.L., Tang, Z.T., Zhao, M.Y.: Comparison of particle swarm optimization and dynamic programming for large scale hydro unit load dispatch. Energy Convers. Manag. 50(12), 3007–3014 (2009)

Christoforidis, M., Awobamise, B., Tong, S., Frowd, R., Rahimi, F.: Short-term hydro generation and interchange contract scheduling for Swiss rail. In: IEEE Power Industry Computer Application Conference, 1995, pp. 143–149 (1995)

Colnago, G.R., Correia, P.B.: Multiobjective dispatch of hydrogenerating units using a two-step genetic algorithm method. In: IEEE Congress on Evolutionary Computation, 2009, pp. 2554–2560 (2009)

Conejo, A.J., Arroyo, J.M., Contreras, J., Villamor, F.A.: Self-scheduling of a hydro producer in a pool-based electricity market. IEEE Trans. Power Syst. 17(4), 1265–1272 (2002)

D’Ambrosio, C., Lodi, A., Martello, S.: Piecewise linear approximation of functions of two variables in MILP models. Oper. Res. Lett. 38(1), 39–46 (2010)

De Ladurantaye, D., Gendreau, M., Potvin, J.Y.: Optimizing profits from hydroelectricity production. Comput. Oper. Res. 36(2), 499–529 (2009)

Diaz, F., Contreras, J., Muñoz, J.I., Pozo, D.: Optimal scheduling of a price-taker cascaded reservoir system in a pool-based electricity market. IEEE Trans. Power Syst. 26(2), 604–615 (2011)

Dittmann, R., Froehlich, F., Pohl, R., Ostrowski, M.: Optimum multi-objective reservoir operation with emphasis on flood control and ecology. Nat. Hazards Earth Syst. Sci. 9(6), 1973–1980 (2009)

Dreyfus, S.E., Law, A.M.: Art and Theory of Dynamic Programming. Academic Press, Inc., Orlando, FL, USA (1977)

Dubost, L., Gonzalez, R., Lemaréchal, C.: A primal-proximal heuristic applied to the French unit-commitment problem. Math. Program. 104(1), 129–151 (2005)

Duran, R.: Hydro electricity in Brazil. The Brazil Business (2015)

EdF: Document de référence/rapport financier annuel 2012 du groupe EdF. Tech. rep., EdF (2012)

Finardi, E.C., Da Silva, E.L.: Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming. IEEE Trans. Power Syst. 21(2), 835–844 (2006)

Finardi, E.C., Da Silva, E.L., Sagastizábal, C.: Solving the unit commitment problem of hydropower plants via Lagrangian relaxation and sequential quadratic programming. Comput. Appl. Math. 24(3), 317–342 (2005)

Finardi, E.C., Scuzziato, M.R.: A model to accounting for losses in the unit commitment problem at Brazilian hydro plants. In: 17th Power System Computation Conference, Stockholm, Sweden (2011)

Finardi, E.C., Scuzziato, M.R.: Hydro unit commitment and loading problem for day-ahead operation planning problem. Int. J. Electr. Power Energy Syst. 44(1), 7–16 (2013)

Finardi, E.C., Scuzziato, M.R.: A comparative analysis of different dual problems in the Lagrangian relaxation context for solving the hydro unit commitment problem. Electr. Power Syst. Res. 107, 221–229 (2014)

Fleten, S.E., Kristoffersen, T.K.: Stochastic programming for optimizing bidding strategies of a nordic hydropower producer. Eur. J. Oper. Res. 181(2), 916–928 (2007)

Fleten, S.E., Kristoffersen, T.K.: Short-term hydropower production planning by stochastic programming. Comput. Oper. Res. 35(8), 2656–2671 (2008)

Fosso, O.B., Gjelsvik, A., Haugstad, A., Mo, B., Wangensteen, I.: Generation scheduling in a deregulated system. The Norwegian case. IEEE Trans. Power Syst. 14(1), 75–81 (1999)

Frangioni, A., Gentile, C.: Perspective cuts for a class of convex 0–1 mixed integer programs. Math. Program. 106(2), 225–236 (2006)

Frangioni, A., Gentile, C.: A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes. Oper. Res. Lett. 37(3), 206–210 (2009)

Frangioni, A., Gentile, C., Lacalandra, F.: Solving unit commitment problems with general ramp constraints. Int. J. Electr. Power Energy Syst. 30(5), 316–326 (2008)

Frangioni, A., Gentile, C., Lacalandra, F.: Tighter approximated MILP formulations for unit commitment problems. IEEE Trans. Power Syst. 24(1), 105–113 (2009)

Frangioni, A., Gentile, C., Lacalandra, F.: Sequential Lagrangian-MILP approaches for unit commitment problems. Int. J. Electr. Power Energy Syst. 33(3), 585–593 (2011)

Garcia-Gonzalez, J., Castro, G.A.: Short-term hydro scheduling with cascaded and head-dependent reservoirs based on mixed-integer linear programming. In: Power Tech Proceedings, 2001 IEEE Porto, vol. 3, p. 6 (2001)

García-González, J., Parrilla, E., Barquín, J., Alonso, J., Sáiz-Chicharro, A., González, A.: Under-relaxed iterative procedure for feasible short-term scheduling of a hydro chain. In: Power Tech Conference Proceedings, 2003 IEEE Bologna, vol. 2 (2003)

García-González, J., Parrilla, E., Mateo, A.: Risk-averse profit-based optimal scheduling of a hydro-chain in the day-ahead electricity market. Eur. J. Oper. Res. 181(3), 1354–1369 (2007)

Ge, X.L., Zhang, L.Z., Shu, J., Xu, N.F.: Short-term hydropower optimal scheduling considering the optimization of water time delay. Electr. Power Syst. Res. 110, 188–197 (2014)

Gentile, C., Morales-Espana, G., Ramos, A.: A tight mip formulation of the unit commitment problem with start-up and shut-down constraints. Tech. rep., IIT-14-040A (2014)

George, A., Reddy, C., Sivaramakrishnan, A.: Multi-objective, short-term hydro thermal scheduling based on two novel search techniques. Int. J. Eng. Sci. Technol. 2(12), 7021–7034 (2010)

Günlük, O., Linderoth, J.: Perspective reformulation and applications. In: Lee, J., Leyffer, S. (eds.) Mixed Integer Nonlinear Programming, pp. 61–89. Springer (2012)

Habibollahzadeh, H., Frances, D., Sui, U.: A new generation scheduling program at Ontario hydro. IEEE Trans. Power Syst. 5(1), 65–73 (1990)

Hechme-Doukopoulos, G., Brignol-Charousset, S., Malick, J., Lemaréchal, C.: The short-term electricity production management problem at EdF. Optima Newsletter-Math. Optim. Soc. 84, 1–7 (2010)

Hongling, L., Chuanwen, J., Yan, Z.: A review on risk-constrained hydropower scheduling in deregulated power market. Renew. Sustain. Energy Rev. 12(5), 1465–1475 (2008)

Huang, S.J.: Enhancement of hydroelectric generation scheduling using ant colony system based optimization approaches. Energy Convers. IEEE Trans. 16(3), 296–301 (2001)

Ilak, P., Krajcar, S., Rajsi, I., Delimar, M.: Profit maximization of a hydro producer in a day-ahead energy market and ancillary service markets. In: EUROCON, 2013 IEEE, pp. 744–749 (2013)

Jabr, R.: Tight polyhedral approximation for mixed-integer linear programming unit commitment formulations. IET Gen. Transm. Distrib. 6(11), 1104–1111 (2012)

Jia, J., Guan, X.: 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. 4061–4064 (2011)

Johannesen, A., Flatabø, N.: Scheduling methods in operation planning of a hydro-dominated power production system. Int. J. Electr. Power Energy Syst. 11(3), 189–199 (1989)

Kadowaki, M., Ohishi, T., Martins, L., Soares, S.: Short-term hydropower scheduling via an optimization-simulation decomposition approach. In: IEEE PowerTech, 2009 Bucharest, pp. 1–7 (2009)

Kanzow, C.: Some noninterior continuation methods for linear complementarity problems. SIAM J. Matrix Anal. Appl. 17(4), 851–868 (1996)

Labadie, J.W.: Optimal operation of multireservoir systems: state-of-the-art review. J. Water Resour. Plan. Manag. 130(2), 93–111 (2004)

Lee, J., Leung, J., Margot, F.: Min-up/min-down polytopes. Discrete Optim. 1(1), 77–85 (2004)

Li, T., Shahidehpour, M.: Price-based unit commitment: a case of Lagrangian relaxation versus mixed integer programming. IEEE Trans. Power Syst. 20(4), 2015–2025 (2005)

Li, X., Li, T., Wei, J., Wang, G., Yeh, W.G.: Hydro unit commitment via mixed integer linear programming: a case study of the Three Gorges project, China (2013)

Lu, P., Zhou, J., Wang, C., Qiao, Q., Mo, L.: Short-term hydro generation scheduling of Xiluodu and Xiangjiaba cascade hydropower stations using improved binary-real coded bee colony optimization algorithm. Energy Convers. Manag. 91, 19–31 (2015)

Ma, C.: Short term hydropower dispatching optimization of cascaded hydropower stations based on two-stage optimization. In: 2010 2nd International Conference on Industrial and Information Systems (IIS), vol. 1, pp. 230–233. IEEE (2010)

Maestre, J., Doan, M., De La Peña, D.M., Van Overloop, P., Keviczky, T., Ridao, M., De Schutter, B.: Benchmarking the operation of a hydro power network through the application of agent-based model predictive controllers. In: Proceedings of the 10th International Conference on Hydroinformatics (2012)

Mahor, A., Rangnekar, S.: Short term generation scheduling of cascaded hydro electric system using novel self adaptive inertia weight PSO. Int. J. Electr. Power Energy Syst. 34(1), 1–9 (2012)

Mariano, S., Catalao, J., Mendes, V., Ferreira, L.: Profit-based short-term hydro scheduling considering head-dependent power generation. IEEE Lausanne Power Tech 2007, 1362–1367 (2007)

Mariano, S., Catalão, J., Mendes, V., Ferreira, L.: Optimising power generation efficiency for head-sensitive cascaded reservoirs in a competitive electricity market. Int. J. Electr. Power Energy Syst. 30(2), 125–133 (2008)

Mhanna, S., Jabr, R.: Application of semidefinite programming relaxation and selective pruning to the unit commitment problem. Electr. Power Syst. Res. 90, 85–92 (2012)

Mo, L., Lu, P., Wang, C., Zhou, J.: Short-term hydro generation scheduling of Three Gorges–Gezhouba cascaded hydropower plants using hybrid MACS-ADE approach. Energy Convers. Manag. 76, 260–273 (2013)

Morales-España, G., Gentile, C., Ramos, A.: Tight MIP formulations of the power-based unit commitment problem. OR Spectrum, pp. 1–22 (2015)

Morales-España, G., Latorre, J.M., Ramos, A.: Tight and compact MILP formulation of start-up and shut-down ramping in unit commitment. IEEE Trans. Power Syst. 28(2), 1288–1296 (2013)

Naresh, R., Sharma, J.: Hydro system scheduling using ann approach. IEEE Trans. Power Syst. 15(1), 388–395 (2000)

Naresh, R., Sharma, J.: Short term hydro scheduling using two-phase neural network. Int. J. Electr. Power Energy Syst. 24(7), 583–590 (2002)

Nilsson, O., Sjelvgren, D.: Hydro unit start-up costs and their impact on the short term scheduling strategies of Swedish power producers. IEEE Trans. Power Syst. 12(1), 38–44 (1997)

Nilsson, O., Sjelvgren, D.: Variable splitting applied to modelling of start-up costs in short term hydro generation scheduling. IEEE Trans. Power Syst. 12(2), 770–775 (1997)

Nuñez, A., Ocampo Martínez, C.A., De Schutter, B., Valencia, F., López, J.D., Espinosa, J.: A multiobjective-based switching topology for hierarchical model predictive control applied to a hydro-power valley. In: IFAC International Conference on Intelligent Control and Automation Science, pp. 529–534 (2013)

Observ’ER EdF: Fondation Énergies pour le monde: La production d’électricité d’origine renouvelable dans le monde. Quinzième inventaire (2013)

Ohishi, T., Santos, E., Arce, A., Kadowaki, M., Cicogna, M., Soares, S.: Comparison of two heuristic approaches to hydro unit commitment. In: Power Tech, 2005 IEEE Russia, pp. 1–7 (2005)

Osorio, G., Matias, J., Catalao, J.: A review of short-term hydro scheduling tools. In: 48th International Universities’ Power Engineering Conference (UPEC), 2013, pp. 1–6 (2013)

Ostrowski, J., Anjos, M.F., Vannelli, A.: Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans. Power Syst. 27(1), 39 (2012)

Padhy, N.P.: Unit commitment—a bibliographical survey. IEEE Trans. Power Syst. 19(2), 1196–1205 (2004)

Pérez, J.I., Wilhelmi, J.R.: Nonlinear self-scheduling of a single unit small hydro plant in the day-ahead electricity market. In: Proceedings of ICREPQ ’07 (2007)

Pérez, J.I., Wilhelmi, J.R.: Assessment of the economic impact of environmental constraints on short-term hydropower plant operation. Energy Policy 38(12), 7960–7970 (2010)

Pérez-Díaz, J.I., Wilhelmi, J.R., Arévalo, L.A.: Optimal short-term operation schedule of a hydropower plant in a competitive electricity market. Energy Convers. Manag. 51(12), 2955–2966 (2010)

Pérez-Díaz, J.I., Wilhelmi, J.R., Sánchez-Fernández, J.Á.: Short-term operation scheduling of a hydropower plant in the day-ahead electricity market. Electr. Power Syst. Res. 80(12), 1535–1542 (2010)

Philpott, A.B., Craddock, M., Waterer, H.: Hydro-electric unit commitment subject to uncertain demand. Eur. J. Oper. Res. 125(2), 410–424 (2000)

Philpott, A.B., Dallagi, A., Gallet, E.: On cutting plane algorithms and dynamic programming for hydroelectricity generation. In: Kovacevic, R.M., Pflug, G.C., Vespucci, M.T. (eds.) Handbook of Risk Management in Energy Production and Trading, pp. 105–127. Springer (2013)

Piekutowski, M., Litwinowicz, T., Frowd, R.: Optimal short-term scheduling for a large-scale cascaded hydro system. In: Power Industry Computer Application Conference, 1993. Conference Proceedings, pp. 292–298. IEEE (1993)

Pousinho, H., Contreras, J., Catalao, J.: Operations planning of a hydro producer acting as a price-maker in an electricity market. In: IEEE Power and Energy Society General Meeting, 2012, pp. 1–7 (2012)

Quan, R., Jian, J.B., Mu, Y.D.: Tighter relaxation method for unit commitment based on second-order cone programming and valid inequalities. Int. J. Electr. Power Energy Syst. 55, 82–90 (2014)

Raglend, I.J., Padhy, N.P.: Solutions to practical unit commitment problems with operational, power flow and environmental constraints. In: IEEE Power Engineering Society General Meeting, 2006, pp. 1–8 (2006)

Rajan, D., Takriti, S.: Minimum up/down polytopes of the unit commitment problem with start-up costs. IBM Research Report (2005)

Rovatti, R., D’Ambrosio, C., Lodi, A., Martello, S.: Optimistic MILP modeling of non-linear optimization problems. Eur. J. Oper. Res. 239, 32–45 (2014)

Salani, M., Giusti, A., Di Caro, G., Rizzoli, A.E., Gambardella, L.M.: Lexicographic multi-objective optimization for the unit commitment problem and economic dispatch in a microgrid. In: 2nd IEEE PES International Conference and Exhibition on Innovative Smart Grid Technologies (ISGT Europe), 2011, pp. 1–8 (2011)

Santos, T., Diniz, A.: A comparison of static and dynamic models for hydro production in generation scheduling problems. In: IEEE Power and Energy Society General Meeting, 2010, pp. 1–5 (2010)

Seguin, S., Cote, P., Audet, C.: Self-scheduling short-term unit commitment and loading problem. To appear in IEEE TRANSACTIONS ON POWER SYSTEMS

Shawwash, Z.K., Siu, T.K., Russell, S.D.: The bc hydro short term hydro scheduling optimization model. IEEE Trans. Power Syst. 15(3), 1125–1131 (2000)

Shawwash, Z.K.E.: A decision support system for real-time hydropower scheduling in a competitive power market environment (2000)

Sheble, G.B., Fahd, G.N.: Unit commitment literature synopsis. IEEE Trans. Power Syst. 9(1), 128–135 (1994)

Shu, J., Hang, B., Li, C., Zhang, L.: Self-scheduling of cascaded hydropower stations based on nonlinear complementarity approach. In: International Conference on Power System Technology (POWERCON), 2010, pp. 1–5 (2010)

Sifuentes, W.S., Vargas, A.: Hydrothermal scheduling using benders decomposition: accelerating techniques. IEEE Trans. Power Syst. 22(3), 1351–1359 (2007)

Soares, S., Ohishi, T., Cicogna, M., Arce, A.: Dynamic dispatch of hydro generating units. In: IEEE Power Tech Conference Proceedings, 2003 Bologna, vol. 2, p. 6 (2003)

Souza, T., Diniz, A.: An accurate representation of water delay times for cascaded reservoirs in hydro scheduling problems. In: IEEE Power and Energy Society General Meeting, 2012, pp. 1–7 (2012)

Tahanan, M., van Ackooij, W., Frangioni, A., Lacalandra, F.: Large-scale unit commitment under uncertainty. 4OR 13(2), 115–171 (2015)

Tong, B., Zhai, Q., Guan, X.: An MILP based formulation for short-term hydro generation scheduling with analysis of the linearization effects on solution feasibility IEEE Trans. Power Syst. 28(4), 3588–3599 (2013)

Yamin, H.: Review on methods of generation scheduling in electric power systems. Electr. Power Syst. Res. 69(2), 227–248 (2004)

Yi, J., Labadie, J.W., Stitt, S.: Dynamic optimal unit commitment and loading in hydropower systems. J. Water Resour. Plan. Manag. 129(5), 388–398 (2003)

Yuan, X., Zhang, Y., Wang, L., Yuan, Y.: An enhanced differential evolution algorithm for daily optimal hydro generation scheduling. Comput. Math. Appl. 55(11), 2458–2468 (2008)

Zárate Flórez, J., Martinez, J., Besançon, G., Faille, D.: Decentralized-coordinated model predictive control for a hydro-power valley. Math. Comput. Simul. 91, 108–118 (2013)

Zarate Florez, J., Martinez, J.J., Besançon, G., Faille, D.: Explicit coordination for MPC-based distributed control with application to hydro-power valleys. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011, pp. 830–835 (2011)

Zhai, Q., Guan, X., Gao, F.: A necessary and sufficient condition for obtaining feasible solution to hydro power scheduling with multiple operating zones. In: IEEE Power Engineering Society General Meeting, 2007, pp. 1–7 (2007)