Heuristic algorithm with simulation model for searching optimal reservoir rule curves

American Journal of Applied Sciences, Feb, 2009 by Anongrit Kangrang, Sudarat Compliew, Witsanukorn Chaiyapoom

INTRODUCTION

An integrated water resources management of demand and supply management is addressed in the possible practice and high efficiency. To manage the supply side, a reservoir simulation model is widely used to analyze the behavior of a system on the computer. Reservoir rule curves are fundamental guidelines for long term reservoir operation. Often, they are searched by reservoir simulation model and optimization techniques. Firstly, the rule curves are obtained from trial error of rule curves in reservoir simulation model (1). This method is straightforward and applicable for both simple and complex systems. However, the reservoir simulation method does not guarantee to yield the optimal rule curves because of the experienced person.

A Dynamic Programming (DP) is another optimization technique applied to search the non-linear problems of water resource (2-4). Unfortunately, the application of DP to multi-reservoir system is limited due to a dimension problem. To overcome this problem Chleeraktrakoon and Kangrang (5) applied the DP with a principle progressive optimality (DP-PPO) to determine the optimal rule curves. However, this technique is complicated application.

Last decade, Genetic Algorithms (GAs) has been applied to search optimal rule curves of the reservoir system (6-9). The best part of GAs is that they can handle any type of objective function. Furthermore, the proposed model can handle any condition of reservoir simulation such as initial reservoir capacity and the period of inflow record. The accepted objective functions are a shortage index, frequency of water shortage, average water shortage and magnitude of water deficit. However, the appropriate objective function for searching the curves is average water shortage. Also, a smoothing function constraint is required to include into the proposed GAs for fitting the rule curves (10). However, GAs is complex to optimization technique because this method is complicacy for creating multi-computation to analysis the optimal reservoir rule curves.

A Heuristic Algorithm (HA) is an optimization technique which belongs to the family of local search. It is a relatively simple technique to implement, making it a popular first choice. The heuristic algorithm begins with one initial solution to the problem at hand, usually chosen at random. The string is then mutated and if the mutation results in higher fitness for the new solution than for the previous one, the new solution is kept, otherwise, the current solution is retained. The algorithm is then repeated until no mutation can be found that causes an increase in the current solution's fitness and this solution is returned as the result (11-13).

This study proposes a heuristic algorithm to connect with simulation model for searching the optimal reservoir rule curves. A minimum average water shortage was used be the objective function for searching procedure. A smoothing function constraint is applied to fit the obtained rule curves. The proposed model was applied to determine the optimal rule curves of the Ubolratana reservoir (the Chi River Basin, Thailand).

MATERIALS AND METHODS

Simulation model: The developed simulation model in the previous study (10) was adopted to modify in this study. This simulation model had been constructed on the concept of HEC-3 (14) and it can be used to simulate the reservoir operation. The reservoir operating policies are based on the rule curves of individual reservoirs and the principles of water balance concept. The reservoir system operated along the standard operating policy as expressed in Eq. 1:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

which [R.sub.v,[tau]] is the release discharges form the reservoir during year v and period [tau] ([tau] = 1 to 12, representing January to December), [D.sub.[tau]] is the water requirement of month [tau], [x.sub.[tau]] is lower rule curve of month [tau], [y.sub.[tau]] is upper rule curve of month [tau], and [W.sub.v,[tau]] is the available water calculated by simple water balance as described in Eq. 2:

[W.sub.[nu],[tau] + 1] = [S.sub.[nu],[tau]] + [Q.sub.[nu],[tau]] - [R.sub.[nu],[tau]] - [E.sub.[tau]] - D (2)

where, [S sub.v,[tau]] is the stored water at the end of month [tau], [Q.sub.v,[tau]] is monthly reservoir inflow, [E.sub.[tau]] is average value of evaporation loss, and DS is the minimum reservoir storage capacity (the capacity of dead storage). In the Eq. 1, if available water is in a range of the upper and lower rule level, then demands are satisfied in full. If available water over the top of the upper rules level, then the water is spilled from the reservoir in downstream river in order to maintain water level at upper rule level. If available water is below the lower rule level, a reduction of supply is required. The policy usually reserves the available water ([W.sub.v,[tau]]) for reducing the risk of water shortage in the future, when 0[less than or equal to][W.sub.v,[tau]]<[x.sub.[tau]]-[D.sub.[tau]].

The results of reservoir simulation are the situations of water shortage and excess release water such as the number of failure year, the number of excess release water and the average annual shortage. They will be then recorded for using in developed HA.