Βελτιστοποίηση λειτουργίας ταμιευτήρων για αρδευτικούς σκοπούς

Abstract

The research performed in the framework of the completion of the Ph.D. dissertation, is focused on the optimal reservoir operation for irrigation purposes during the irrigation period. The time interval is the 10 days. The remainder period of year determines the reservoir storage in the beginning of the irrigation period, while so much the reservoir storage in the beginning of the irrigation period and inflow during the irrigation period are regulated and used for the irrigation. The objective function maximizes the total farm income, which is based on actual yield, area, production cost and crop prices. The constraints include the state equation of reservoir, reservoir storage, irrigation requirements of a crop and reservoir release, yield and cropped area. The decision variables are the optimal allocation of cultivation areas for any number of irrigated crops and the optimal irrigation schedule, which specifies the amount of irrigation to be applied to each crop during its growing season. The actual yield is calculated with the production function given by Jensen and the maximum evapotranspiration coincides with crop evapotranspiration, which is the product of a crop factor and the reference evapotranspiration which is computed from the FAO Penman-Monteith equation. The determination of the actual evapotranspiration is becomes with the soil water balance and soil water depletion function. The optimization of the nonlinear discrete-time dynamic model is performed in two stages. During the first stage the simulated annealing (SA) global optimization stochastic search algorithm is used and in a second stage it is refined the solution reached by the SA, using a stochastic gradient descent algorithm. SA has been proved under suitable conditions (Gauss distribution to generate test points, Boltzman distribution for acceptance of these and logarithmic reduction of temperature) to converge with probability one to the global optimal solution, in the limiting case of infinite iterations. The optimisation model is applied on historical and synthetically data from a planned reservoir on the Havrias River in Northern Greece. Synthetically data are referred to rainfall, inflow and reference evapotranspiration are calculated with frequency analysis Summary 321 in a synthetic series duration of 50 years (economic life of work), which resulted from 100 synthetic series that were produced for every of this variables. The optimization computes the optimal distribution of areas and crops, the water release to satisfy irrigation requirements and the total profit. The procedure is relatively easy to apply and can be used as a decision support tool for cropping patterns of an irrigated area and irrigation scheduling.