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The generation of a hydroelectric plant is a nonlinear function of the turbined outflow, storage and sometimes also of the spillage. Other aspects, such as forbidden operating zones and individual turbine efficiency curves, are also important. Although for the self-scheduling of a hydro plant a precise integer modeling of the hydro power production function (HPF) is convenient, in the security constrained short-term hydrothermal dispatch problem for large-scale systems a strategy which best balances an accurate representation with an acceptable computational burden is required. In this paper, a detailed review of different approaches to model the HPF is presented, and a new four-dimensional piecewise linear model is proposed. This model takes into account the water head as a function of forebay and tailrace levels and considers spillage effects. Nonconcave regions of the HPF are approximated by using convexification and regression techniques. A major advantage of this approach is to consider the influence of storage, turbined outflow and spillage in a single function that can be used in a straightforward way, instead of deriving several curves for different heads. Numerical results show the applicability of this approach to the day-ahead network constrained short-term hydrothermal dispatch problem of the large Brazilian system. Index Terms--Hydroelectric power generation, linear programming, power generation scheduling.

Recently, there has been a growing need to consider issues related to multiple uses of water—such as navigation, fishing, or recreation—in the operation planning of electrical power systems, specially in predominantly hydro systems. In short-term models, it is of particular importance to consider maximum/minimum values and ramp limits for the stream level of a river. However, in order to properly represent such constraints, it is also necessary to model in detail the river routing, i.e., the water wave propagation along the channels that connect reservoirs in cascade. This paper proposes a linear programming model to represent river stream-level constraints and river-routing effects in the short-term hydrothermal dispatch problem. Results show the high accuracy of the proposed approach to represent maximum hourly and daily river-level variations as well as the impacts of taking into account a detailed representation of river routing in the operation of hydrothermal systems. [ABSTRACT FROM PUBLISHER]

Multistage Benders decomposition (MSBD), also known as dual dynamic programming, is a well-established technique to solve hydrothermal scheduling problems, especially for predominantly hydro systems. The MSBD methodology solves the problem by iterative forward and backward recursions, approximating the cost-to-go function for each stage by Benders cuts, as opposed to traditional dynamic programming approaches that discretize the state space at each time-step. The classical definition of the stages in the MSBD approach is to assign a stage for each time period. In this paper, we propose a new strategy to decompose the problem, where each stage comprises all variables and constraints of several time periods. Numerical results of the application of this strategy to the short- term hydrothermal scheduling problem confirm the advantages of this strategy in terms of CPU time, as compared to the classical stage definition approach. We show that there is an "optimal aggregation factor," which best balances the trade-off between solving a "larger number of shorter subproblems" and solving a "smaller number of larger subproblems." The primal and dual solutions related to different aggregation factors are also compared, and the stability of the results is confirmed. Extensions of the proposed strategy to stochastic problems are discussed. [ABSTRACT FROM AUTHOR]