Detailed long-term hydro-thermal scheduling for expansion planning in the Nordic power system

Detailed long-term hydro-thermal scheduling for expansion planning in the Nordic power system

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The authors describe a method for long-term hydro-thermal scheduling allowing treatment of detailed large-scale hydro systems. Decisions for each week are determined by solving a two-stage stochastic linear programming problem considering uncertainty in weather and exogenous market prices. The overall scheduling problem is solved by embedding such two-stage problems in a rolling horizon simulator. The method is verified on data for the Nordic power system, studying the incremental changes in expected socio-economic surplus for expansions in both the transmission and generation systems. Comparisons are made with a widely used existing long-term hydro-thermal scheduling model. The results indicate that the model is well suited to valuate the flexibility of hydropower in systems with a high share of intermittent renewable generation.


    1. 1)
      • 1. Fosso, O.B., Gjelsvik, A., Haugstad, A., et al: ‘Generation scheduling in a deregulated system. The Norwegian case’, IEEE Trans. Power Syst., 1999, 14, pp. 7581.
    2. 2)
      • 2. Maceira, M.E.P., Duarte, V.S., Penna, D.D.J., et al: ‘Ten years of application of stochastic dual dynamic programming in official and agent studies in Brazil - description of the Newave program’. Proc. 16th Power System Computation Conf., Glasgow, 2008.
    3. 3)
      • 3. Valdés, J. B., Filippo, J.M., Strzepek, K.M., et al: ‘Aggregation–disaggregation approach to multireservoir operation’, J. Water Resour. Plan. Manage., 1992, 118, (4), pp. 423444.
    4. 4)
      • 4. Turgeon, A., Charbonneau, R.: ‘An aggregation-disaggregation approach to long-term reservoir management’, Water Resour. Res., 1998, 34, (12), pp. 35853594.
    5. 5)
      • 5. Wolfgang, O., Haugstad, A., Mo, B., et al: ‘Hydro reservoir handling in Norway before and after deregulation’, Energy, 2009, 34, (10), pp. 16421651.
    6. 6)
      • 6. Maceira, M.E.P., Duarte, V.S., Penna, D.D.J., et al: ‘An approach to consider hydraulic coupled systems in the construction of equivalent reservoir model in hydrothermal operation planning’. Power System Computation Conf. (PSCC), Stockholm, Sweden, 2011.
    7. 7)
      • 7. Pereira, M.V.F., Pinto, L.M.V.G.: ‘Multi-stage stochastic optimization applied to energy planning’, Math. Program., 1991, 52, pp. 359375.
    8. 8)
      • 8. Gjelsvik, A., Mo, B., Haugstad, A.: ‘Long- and medium-term operations planning and stochastic modelling in hydro-dominated power systems based on stochastic dual dynamic programming’, in Rebennack, S., Pardalos, P.M., Pereira, M.V.F., Iliadis, N.A. (Eds.): Handbook of power systems I (Springer-Verlag, Berlin and Heidelberg, 2010), pp. 3355.
    9. 9)
      • 9. Halliburton, T.S.: ‘An optimal hydrothermal planning model for the New Zealand power system’, Aust. J. Electr. Electron. Eng., 2004, 1, (3), pp. 193198.
    10. 10)
      • 10. Granville, S., Oliveira, G.C., Thomé, L.M., et al: ‘Stochastic optimization of transmission constrained and large scale hydrothermal systems in a competitive framework’. Proc. IEEE General Meeting, Toronto, Canada, 2003.
    11. 11)
      • 11. Gjerden, K.S., Helseth, A., Mo, B., et al: ‘Hydrothermal scheduling in Norway using stochastic dual dynamic programming: a large-scale case study’. Proc. of IEEE PowerTech, Eindhoven, The Netherlands, 2015.
    12. 12)
      • 12. Flach, B., Barroso, L., Pereira, M.: ‘Long-term optimal allocation of hydro generation for a price-maker company in a competitive market: latest developments and a stochastic dual dynamic programming approach’, IET. Gener. Transm. Distrib., 2010, 4, (2), pp. 299314.
    13. 13)
      • 13. Cerisola, S., Latorre, J.M., Ramos, A.: ‘Stochastic dual dynamic programming applied to nonconvex hydrothermal models’, Eur. J. Oper. Res., 2012, 218, pp. 687897.
    14. 14)
      • 14. Abgottspon, H., Njálsson, K.,, Bucher, M.A., et al: ‘Risk-averse medium-term hydro optimization considering provision of spinning reserves’. Int. Conf. on Probabilistic Methods Applied to Power Systems (PMAPS), Durham, England, 2014.
    15. 15)
      • 15. Steeger, G., Rebennack, S.: ‘Dynamic convexification within nested benders decomposition using Lagrangian relaxation: an application to the strategic bidding problem’, Eur. J. Oper. Res., 2017, 257, (2), pp. 669686.
    16. 16)
      • 16. Penna, D.D.J., Dámazio, M.E.P.M.J.M.: ‘Selective sampling applied to long-term hydrothermal generation planning’. Power System Computation Conf. (PSCC), Stockholm, Sweden, 2011.
    17. 17)
      • 17. Poorsepahy-Samian, H., Espanmanesh, V., Zahraie, B.: ‘Improved inflow modeling in stochastic dual dynamic programming’, J. Water Resour. Plan. Manage., 2016, 142, (12).
    18. 18)
      • 18. Philpott, A., de Matos, V.: ‘Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion’, Eur. J. Oper. Res., 2012, 218, (2), pp. 470483.
    19. 19)
      • 19. Helseth, A., Gjelsvik, A., Mo, B., et al: ‘A model for optimal scheduling of hydro thermal systems including pumped-storage and wind power’, IET. Gener. Transm. Distrib., 2013, 7, (12), pp. 14261434.
    20. 20)
      • 20. Rebennack, S.: ‘Combining sampling-based and scenario-based nested benders decomposition methods: application to stochastic dual dynamic programming’, Math. Program., 2016, 156, (1), pp. 343389.
    21. 21)
      • 21. Kelman, J., Stedinger, J.R., Cooper, L.A., et al: ‘Sampling stochastic dynamic programming applied to reservoir operation’, Water Resour. Res., 1990, 26, (3), pp. 447454.
    22. 22)
      • 22. Scharff, R., Egerer, J., Söder, L.: ‘A description of the operative decision-making process of a power generating company on the Nordic electricity market’, Energy Syst., 2014, 5, pp. 349369.
    23. 23)
      • 23. Aasgård, E.K., Andersen, G.S., Fleten, S.E., et al: ‘Evaluating a stochastic-programming-based bidding model for a multireservoir system’, IEEE Trans. Power Syst., 2014, 29, (4), pp. 17481757.
    24. 24)
      • 24. Séguin, S., Fleten, S.E., Côté, P., et al: ‘Stochastic short-term hydropower planning with inflow scenario trees’, Eur. J. Oper. Res., 2016, 259, pp. 11561168.
    25. 25)
      • 25. Martinez, L., Soares, S.: ‘Comparison between closed-loop and partial open-loop feedback control policies in long term hydrothermal scheduling’, IEEE Trans. Power Syst., 2002, 17, pp. 330336.
    26. 26)
      • 26. Zambelli, M.S., Soares, S.: ‘A predictive control approach for long term hydrothermal scheduling’. IEEE/PES Power Systems Conf. and Exposition, 2009.
    27. 27)
      • 27. Nolde, K., Uhr, M., Morari, M.: ‘Medium term scheduling of a hydro-thermal system using stochastic model predictive control’, Automatica, 2008, 44, pp. 15851594.
    28. 28)
      • 28. Powell, W.B., George, A., Simão, H., et al: ‘SMART: a stochastic multiscale model for the analysis of energy resources, technology, and policy’, INFORMS J. Comput., 2011, 24, (4), pp. 665682.
    29. 29)
      • 29. Helseth, A., Mo, B., Warland, G.: ‘Long-term scheduling of hydro-thermal power systems using scenario fans’, Energy Syst., 2010, 1, (4), pp. 377391.
    30. 30)
      • 30. Warland, G., Mo, B.: ‘Stochastic optimization model for detailed long-term hydro thermal scheduling using scenario-tree simulation’, Energy Procedia, 2016, 87, pp. 165172.
    31. 31)
      • 31. Gröwe-Kuska, N., Heitsch, H., Römisch, W.: ‘Scenario reduction and scenario tree construction for power management problems’. IEEE PowerTech Conf., Bologna, Italy, 2003.
    32. 32)
      • 32. Van Slyke, R.M., Wets, R.: ‘L-shaped linear programs with applications to optimal control and stochastic programming’, SIAM J. Appl. Math., 1969, 17, (4), pp. 638663.
    33. 33)
      • 33. Diniz, A., Maceira, M.E.P.: ‘A four-dimensional model of hydro generation for the short-term hydrothermal dispatch problem considering head and spillage effects’, IEEE Trans. Power Syst., 2008, 23, (3), pp. 12981308.
    34. 34)
      • 34. Warland, G., Haugstad, A., Huse, E.S.: ‘Including thermal unit start-up costs in a long-term hydro-thermal scheduling model’. Proc. 16th Power System Computation Conf., Glasgow, Scotland, 2008.
    35. 35)
      • 35. Helseth, A., Warland, G., Mo, B.: ‘A hydrothermal market model for simulation of area prices including detailed network analyses’, Int. Trans. Electr. Energy Syst., 2013, 23, (8), pp. 13961408.
    36. 36)
      • 36. ‘IBM ILOG CPLEX optimizer’,

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