MEAN-VARIANCE MODEL FOR RESERVOIR OPERATIONS

摘要

Traditional optimization algorithms offer several stochastic models for planning and operation of reservoir systems. These optimization models are based on deriving a release policy that optimizes a given objective. Such approaches do not account for the fact that the release, which is a function of the random inflow, thus a random variable itself, may have a distribution with different variability on the available forecasts. In this paper, it is desired to minimize the variance of the objective (expected return) to obtain a robust operating (release) policy. The paper presents a mathematically sound mean-variance formulation, implemented in real time that considers spatial and temporal correlation in streamflows. The foundation of the formulation presented is rooted in stochastic portfolio optimization scheme of Markowitz [5]. The variance-constrained problem is solved by a penalty function approach in which a series of constrained nonlinear problems are solved using penalized relaxation. A Multiplier-based penalty approach is used. To implement the mean-variance formulation, the uncertain benefit (expected value of water) at the end of the operating horizon is quantified using the Parameter Iteration Method of Gal [3]. From a multivariate regression analysis, the correlation in the parameters of the benefit function of an assumed form is obtained and introduced in the variance structure for the last period in a windowed operating horizon. The model is applied to the Salt River Project multi-reservoir system in Central Arizona with power production objective.