[1] Water resources development projects often involve multiple and conflicting objectives as well as stochastic hydrologic inputs. Multiobjective optimization techniques can be used to identify noninferior solutions and to construct a trade-off relationship between conflicting objectives. This paper presents a methodology for analyzing trade-offs and risks associated with large-scale water resource projects under hydrologic uncertainty. The proposed methodology relies on the stochastic dual dynamic programming (SDDP) model to derive monthly or weekly operating rules for multipurpose multireservoir systems taking into account the stochasticity of the inflows, irrigation water withdrawals, minimum/maximum flow requirements for navigation, fishing, and/or for ecological purposes. In SDDP, release decisions are chosen so as to minimize the operating costs of a hydrothermal electrical system. Irrigation water demands and other operating constraints are imposed on the system through the SDDP model. The proposed methodology is illustrated with the Southeastern Anatolia Development project, commonly called GAP, in Turkey. The GAP is a multidimensional development project involving primarily the production of hydroelectricity and irrigation. Simulation results using 50 hydrologic scenarios show that the complete development of the irrigation projects would reduce the total energy output by 6.5% and will increase the risk of not meeting minimum outflow at the Syrian border from 5% to 25%.Citation: Tilmant, A., and R. Kelman (2007), A stochastic approach to analyze trade-offs and risks associated with large-scale water resources systems, Water Resour. Res., 43, W06425,

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The firm energy of generation plants is a critical component in some electricity markets. It is usually calculated by the regulator and sets a cap to the amount a plant can trade in capacity markets (or auctions), in order to avoid free-riding behaviors. Firm energy is a systemic property and, in case of hydro plants, a synergy is observed whenever a cooperative operation occurs, i.e., the firm energy of a system is greater than the sum of the individual plants. This immediately raises the question of how to divide the system's firm energy among the individual hydro plants. The objective of this work is to investigate the application of different allocation methods of firm energy rights among hydro plants using a game-theoretic framework. It is shown that there is not an optimal and unique approach to make this allocation. The paper investigates the advantages and disadvantages of different methods, such as marginal allocation, average production during the critical period, incremental allocation, finally recommending the Aumann-Shapley as the allocation method. This method is tested for the Brazilian power system, which has around 100 hydro plants. The results obtained are compared with the current allocation adopted by the electricity regulatory agency of Brazil.