Assessing hydropower operational profitability considering energy and reserve markets

Assessing hydropower operational profitability considering energy and reserve markets

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The authors analyse the operational profitability of a hydropower system selling both energy and reserve capacity in a competitive market setting. A mathematical model based on stochastic dynamic programming is used to compute the water values for the system considering different power plant configurations. The uncertainties in inflow and both energy and reserve capacity prices are considered through a discrete Markov chain. Subsequently, the system operation is simulated based on the obtained water values to assess system performance and expected revenues from the two markets. The model is applied in a case study for a Norwegian hydropower producer, showing how the power plant operation changes and profitability increases when considering sale of reserve capacity. The authors emphasise on how the water values are influenced by the opportunity to sell reserve capacity, and assess how the representation of non-convex relationships in the water value computations as well as simulation influence the profitability.


    1. 1)
      • 1. Little, J.D.C.: ‘The use of storage water in a hydroelectric system’, J. Oper. Res. Soc. Am., 1955, 3, (2), pp. 187197.
    2. 2)
      • 2. Lindqvist, J.: ‘Operation of a hydrothermal electric system: a multistage decision process’, AIEE Trans.– pt. III (Power Apparatus and Systems), 1962, 81, (3), pp. 17.
    3. 3)
      • 3. Stage, S., Larsson, Y.: ‘Incremental cost of water power’, Trans. Am. Inst. Electr. Eng., 1961, 80, (3), pp. 361364.
    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. Neto, T.A.A., Pereira, M.V.F., Kelman, J.: ‘A risk-constrained stochastic dynamic programming approach to the operation planning of hydrothermal systems’, IEEE Trans. Power Apar. Syst., 1985, PAS-104, (2), pp. 273279.
    7. 7)
      • 7. Labadie, J.W.: ‘Optimal operation of multireservoir systems: state-of-the-art review’, J. Water Resour. Plan. Manage., 2004, 130, (2), pp. 93111.
    8. 8)
      • 8. Steeger, G., Barosso, L.A., Rebennack, S.: ‘Optimal bidding strategies for hydro-electric producers: a literature survey’, IEEE Trans. Power Syst., 2014, 29, (4), pp. 17581766.
    9. 9)
      • 9. Pereira, M.V.F., Pinto, L.M.V.G.: ‘Multi-stage stochastic optimization applied to energy planning’, Math. Program., 1991, 52, pp. 359375.
    10. 10)
      • 10. 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.
    11. 11)
      • 11. Goor, Q., Kelman, R., Tilmant, A.: ‘Optimal multipurpose-multireservoir operation model with variable productivity of hydropower plants’, J. Water Resour. Plan. Manage., 2011, 137, (3), pp. 258267.
    12. 12)
      • 12. Cerisola, S., Latorre, J.M., Ramos, A.: ‘Stochastic dual dynamic programming applied to nonconvex hydrothermal models’, Eur. J. Oper. Res., 2012, 218, pp. 687897.
    13. 13)
      • 13. 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.
    14. 14)
      • 14. 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.
    15. 15)
      • 15. Löhndorf, N., Wozabal, D., Minner, S.: ‘Optimizing trading decisions for hydro storage systems using approximate dual dynamic programming’, Oper. Res., 2013, 61, (4), pp. 810823.
    16. 16)
      • 16. Abgottspon, H., Andersson, G.: ‘Medium-term optimization of pumped hydro storage with stochastic intrastage subproblems’. Proc. 18th Power System Computation Conf., Wroclaw, Poland, 2014.
    17. 17)
      • 17. Helseth, A., Fodstad, M., Mo, B.: ‘Optimal medium-term hydropower scheduling considering energy and reserve capacity markets’, IEEE Trans. Sustain. Energy, 2016, 7, (3), pp. 934942.
    18. 18)
      • 18. Gjelsvik, A., Belsnes, M.M., Haugstad, A.: ‘An algorithm for stochastic medium-term hydrothermal scheduling under spot price uncertainty’. Proc. 13th Power System Computation Conf., Trondheim, Norway, 1999.
    19. 19)
      • 19. 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 Pardalos, P., Rebennack, S., Pereira, M., et al(Eds): ‘Handbook of power systems I’ (Springer, 2010), pp. 3355.
    20. 20)
      • 20. Hjelmeland, M.N., Helseth, A., Korpås, M.: ‘A case study on medium-term hydropower scheduling with sales of capacity’, Energy Proc., 2016, 87, pp. 124131.
    21. 21)
      • 21. 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.
    22. 22)
      • 22. Nandalal, K.D.W., Bogardi, J.J.: ‘Dynamic programming based operation of reservoirs, applicability and limits’ (Cambridge University Press, Cambridge, 2007).
    23. 23)
      • 23. Rajaraman, R., Kirsch, L., Alvarado, F.L., et al: ‘The next generation of electric power unit commitment models’, vol. 36, ch. 6 (Kluwer Academic Publishers, Boston, 2001).
    24. 24)
      • 24. Guisandez, I., Perez-Diaz, J.I., Wilhelmi, J.R.: ‘The influence of environmental constraints on the water value’, Energies, 2016, 9, (6), pp. 121.
    25. 25)
      • 25. Tejada-Guibert, J.A., Johnson, S., Stedinger, J.R.: ‘Comparison of two approaches for implementing multireservoir operating policies derived using stochastic dynamic programming’, Water Resour. Res., 1993, 29, (12), pp. 3693980.
    26. 26)
      • 26. Chazarra, M., Garciá-González, J., Pérez-Díaz, J.I., et al: ‘Stochastic optimization model for the weekly scheduling of a hydropower system in day-ahead and secondary regulation reserve markets’, Electr. Power Syst. Res., 2016, 130, pp. 6777.
    27. 27)
      • 27. 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., 1997, 12, (1), pp. 3844.
    28. 28)
      • 28. Martino, S., Haff, I.H., Løland, A., et al: ‘Statistical properties of historical inflow series for long-term models’. Tech. Rep. SAMBA/50/13, Norwegian Computing Center, 2014.
    29. 29)
      • 29. Fourer, R., Gay, D. M., Kerninghan, B. W.: ‘AMPL: a modeling language for mathematical programming’ (Duxburry, 2003, 2nd edn.).
    30. 30)
      • 30. ‘IBM ILOG CPLEX optimizer’. Available at
    31. 31)
      • 31. Padberg, M.: ‘Approximating separable nonlinear functions via mixed zero-one programs’, Oper. Res. Lett., 2000, 27, (1), pp. 15.
    32. 32)
      • 32. Rebennack, S.: ‘Computing tight bounds via piecewise linear functions through the example of circle cutting problems’, Math. Methods Oper. Res., 2016, 84, (1), pp. 357.

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