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A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning

  • S.I. : Stochastic Optimization:Theory&Applications in Memory of M.Bertocchi
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Abstract

Power generation planning in hydrothermal systems is a complex optimization task, specially due to the high uncertainty in the inflows to hydro plants. Since it is impossible to traverse the huge scenario tree of the multistage problem, stochastic dual dynamic programming (SDDP) is the leading technique to solve it, originally from an expected-cost minimization perspective. However, there is a growing need to apply risk-averse/robust formulations to protect the system from critical hydrological scenarios. This is particularly important for predominantly hydro systems, because environmental issues prevent the construction of large reservoirs, thus reducing their water regulating capability. This paper proposes a two-level SDDP/Benders decomposition approach to include a new risk averse surface (RAS) concept for reservoir operation in power generation planning. The upper level problem is a SDDP solving strategy with expected-cost minimization criterion, where recourse functions for each time step are built through forward/backward passes. The second level consists in multi-period deterministic optimization subproblems for each node of the scenario tree, which are solved to ensure a desired level of protection from a set of given critical scenario several months ahead. An inner iterative procedure for each SDDP stage/scenario is applied, where feasibility cuts are included in the upper level subproblems to derive the RAS surface, which are multidimensional rule curves for reservoir operation. Such curves ensure that the policy provided by the SDDP algorithm yields storage levels in the reservoirs that are high enough to protect the system against such critical scenarios. A “max-type” time-linking penalization scheme for violation of RAS constraints is also proposed, which avoids the multiple application of the penalty value for the same violation in consecutive time steps, which may result in large marginal costs. Results are presented for the large-scale Brazilian system.

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Notes

  1. the complete recourse property in stochastic programming states that the subproblem related to stage t of a decomposed problem remains feasible, regardless of the values of the decision variables \({x_\tau }\) in previous stages \(\tau \le t\).

  2. We took the average elapsed time among the runs for each year.

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Acknowledgements

The authors would like to thank the CPAMP’s Validation Task Force, composed by over 60 people from the Electrical Energy Research Center (CEPEL), the Ministry of Mines and Energy (MME), the Brazilian ISO (ONS), the Energy Research Office (EPE) and the Chamber for Commercialization of Electrical Energy (CCEE) who carried out an invaluable and comprehensive analysis of the RAS methodology in the NEWAVE model. Special thanks go to A.S.Kligerman, M.P.Soares, V.S.Duarte (ONS), P.A.David, T.C.César, S.Q.Brandão (EPE), G.Arfux, C.Giglio, M.Sierra (CCEE), V.M.Ferreira, A.J.Silva (MME), L.G.B. Marzano, T. C. Justino, R.J.Pinto and P.E.R.Sangy. The authors would also like to thank L.C. Brandao for the careful review of the mathematical contents of the paper.

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  1. CEPEL, Brazilian Electric Energy Research Center, Rio de Janeiro, Brazil

    Andre Luiz Diniz, Maria Elvira P. Maceira, Cesar Luis V. Vasconcellos & Debora Dias J. Penna

  2. UERJ - State University of Rio de Janeiro, Rio de Janeiro, Brazil

    Andre Luiz Diniz & Maria Elvira P. Maceira

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  1. Andre Luiz Diniz
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Diniz, A.L., Maceira, M.E.P., Vasconcellos, C.L.V. et al. A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning. Ann Oper Res 292, 649–681 (2020). https://doi.org/10.1007/s10479-019-03419-4

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