Optimal management of a multireservoir water supply system

Abstract

This paper presents a pilot study of a method for finding an approximation for the optimal policy of a dynamic system which depends on stochastic state variables. The systems being considered are multi‐reservoir water supply systems whose (stochastic) state variables are the quantities of water in each reservoir and some previous inflows which affect future inflows. Of special importance is the three‐reservoir system which represents the major part of Israel's water supply system: Lake Kinneret and two underground aquifers. This system can be represented by five stochastic state variables: the quantities of water in each of the three reservoirs and the inflows into the Kinneret for the two previous months. Since this system is too large to be solved by the usual dynamic programing approach, a method was devised in this study for obtaining an approximate solution which does not consume too much time or space. This method will be referred to as the parameters iteration method. It has been tested on a smaller system which contains only three stochastic state variables: the amount of water in the Kinneret and two previous monthly inflows. The results were satisfactory in the sense that the approximate solution obtained by this method was as good as the optimal solution obtained by a dynamic programing approach to this problem. Thus it can be expected that the parameter iteration method would be efficient for the three reservoir problems as well and for larger problems.

Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling

“…We point out that more complex inflow dynamics can be included without affecting the applicability of the methodologies that we are going to propose. For instance, autoregressive linear models of a given order N can be employed (see, e.g., [24][25][26]), simply leading to a higherdimensional state vector (in order to include the inflows of the past N time periods). Concerning the cost, according to [12] we suppose that one wants to keep the releases at each stage as close as possible to 1, assuming that this value is the correct regime amount needed, e.g., for power generation or irrigation.…”

Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

“…In particular, the wastewater treatment SDP model has many levels (17 in total), unlike the inventory forecasting problems of Chen et al 3 , which only have three levels. Unlike the inventory forecasting problems and water reservoir problems of Gal 11 and Johnson et al 12 , the wastewater treatment SDP model should allow different M max in each level because the decision variables are completely different. For the inventory forecasting problems, the best M max , common to all levels, was identified by solving several SDP models with varying M max , and comparing the mean absolute deviation (MAD) calculated over a test data set 6 .…”

An alternative approach to the operation of multinational reservoir systems: Application to the Amistad & Falcon system (Lower Rio Grande/Río Bravo)

“…Then, another reservoir policy would be optimized recursively until all the reservoir policies in the system do not change or the successive improvements are below a certain level. Gal (1979) and Turgeon (1980Turgeon ( , 1981 presented techniques such as parametric-SDP, aggregation-decomposition-SDP optimizing reservoirs successively, and aggregation-SDP algorithms to help derive multiple-reservoir operating policies. The lack of consideration for other reservoir states, or lack of cross-dependent operating policies between reservoirs within the same system, is a common problem for the previous techniques.…”