Hydroelectric power optimization using a decomposition procedure for the indefinite quadratic form

Abstract

The optimization of hydroelectric power is one area of water resources management where the implementation of supply management techniques could yield enormous social welfare benefits. A broad spectrum of computer modeling and analysis techniques have been applied to the hydroelectric power production model in an attempt to improve the real-time operation of reservoir systems. The nonconvex, nonseparable hydropower objective function poses a formidable task in devising a global optimization scheme. A decomposition procedure for the indefinite quadratic form is used to develop an algorithm that will find a near global optimum of a nonlinear hydroelectric power optimization model. The decomposition scheme, due to Pardalos et aI., splits the indefinite quadratic form into separable concave and convex parts. A Taylor series approximation is applied to the concave part, which, along with the separated convex part, is a convex underestimating problem (minimization) that can be solved efficiently. The decomposition technique is applied to two models of reservoir systems within the Upper Green River Basin and the models are solved using the GAMS/MINOS computer code. A comparison of the results obtained from successive linear programming, a fixed head linearization strategy, and direct nonlinear optimization of the nonconvex objective, with the results of the decomposition procedure, indicates the new algorithm has advantages over these techniques.