Abstract
This study applies implicit stochastic optimization (ISO) to develop monthly operating rules for a reservoir located in Northeast Brazil. The proposed model differs from typical ISO applications as it uses the forecast of the mean inflow for a future horizon instead of the current-month inflow. Initially, a hundred different 100-year monthly inflow scenarios are synthetically generated and employed as input to a deterministic operation optimization model in order to build a database of optimal operating data. Later, such database is used to fit monthly reservoir rule curves by means of nonlinear regression analysis. Finally, the established rule curves are validated by operating the system under 100 new inflow ensembles. The performance of the proposed technique is compared with those provided by the standard reservoir operating policy (SOP), stochastic dynamic programming (SDP) and perfect-forecast deterministic optimization (PFDO). Different forecasting horizons are tested. For all of them, the results indicate the feasibility of using ISO in view of its lower vulnerability in contrast to the SOP as well as the proximity of its operations with those by PFDO. The results also reveal that there is an optimal choice for the forecasting horizon. The comparison between ISO and SDP shows small differences between both, justifying the adoption of ISO for its simplified mathematics as opposed to SDP.
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Notes
For each variable, i.e., release and storage. Optimal reservoir spills are also determined by the optimization model but these data are not used to construct the rule curves.
Since t varies along the operating horizon of N months. The month of the year \(\tau\) corresponding to t is calculated by \(\tau ={\text {rem}}\left( \tfrac{t}{12}\right)\), which has the meaning that t is divided by 12 and the remainder is taken as the value for \(\tau\). If \(\text {rem}\left( \tfrac{t}{12}\right) =0\), then \(\tau =12\).
Because of computer limitations at the time, Celeste and Billib (2012) used only 20 scenarios of 20 years each to calibrate/validate their models in contrast to the 100 scenarios of 100-year inflows used here.
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The second author acknowledges the Brazilian National Council for Scientific and Technological Development (CNPq) for the financial support.
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de Santana Moreira, R.M., Celeste, A.B. Performance evaluation of implicit stochastic reservoir operation optimization supported by long-term mean inflow forecast. Stoch Environ Res Risk Assess 31, 2357–2364 (2017). https://doi.org/10.1007/s00477-016-1341-4
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DOI: https://doi.org/10.1007/s00477-016-1341-4