Optimization issues for demand side management in irrigation networks

In this Thesis, we will discuss an high-level optimizer solving the problem of finding optimal solutions for scheduling issues on a gravity-fed large-scale irrigation network. Our aim will be the scheduling of the requests from the farmers fulfilling given constraints on the water-level and minimizing the delivery delays in water supply. In this regard, we will develop different optimization problems in order to achieve our objective. In particular, first of all, we will discuss a suitable model of an irrigation network's channel. Starting from the continuous-time model of a pool, we will develop a state-space discrete-time model of a string of pools in the centralized fashion. Secondly, to guarantee the water-level to fulfill given upper and lower bounds among the entire prediction horizon, we will define a generic optimization problem formulation whose dynamical constraints are included. Since our aim is to minimize the delivery delays, we will choose the initial time of the water supply as the decision variable. This will lead to a non-linear optimization problem. We will, then, turn into a $\{0,1\}$ integer linear formulation via change of variables. Afterwards, we will reformulate it by relaxing the integer constraints. We will, hence, obtain two relaxed problem formulations that do not guarantee the preservation of the original shape of the requested profile. Consequently, we will devise different possible objective functions for the problems. In particular, regarding the relaxed formulations, one linear and two quadratic solutions will be discussed and tested. Finally, we will apply two distributed algorithms on the decomposed problem. On one hand, we will implement and test the Round Robin algorithm. On the other hand, a Primal Decomposition method will be applied. In the end, we will compare the results of both the distributed solutions and we will remark the drawbacks and the advantages of both.