OPTIMIZATION OF UKAI RESERVOIR BY GENETIC ALGORITHMS
ENVE 6026 –
In reservoir operation, appropriate methodology for deriving reservoir operating rules should be selected and operating rules should then be formulated. In the present study, Genetic Algorithm (GA) has been used to optimize the operation of existing multipurpose reservoir in India, and to derive reservoir operating rules for optimal reservoir operations. The fitness function used is minimization of irrigation deficit that is minimize sum of squared deviation of releases from demands of irrigation. The decision variables are monthly releases from the reservoir for irrigation and initial storages in reservoir at beginning of the month. The constraints considered for this optimization are reservoir capacity and bounds for decision variables. Results show that, even during the low flow condition, the present GA model if applied to the Ukai reservoir in Gujarat State, India, can satisfy downstream irrigation demand. Hence based on the present case study it can be concluded that GA model has the capability to perform efficiently, if applied in real world operation of the reservoir.
In reservoir operation problems, to achieve the best possible performance of the system, decisions need to be taken on releases and storages over a period of time considering the variations in inflows and demands. In the past, various researchers applied different kinds of mathematical programming techniques like linear programming, dynamic programming, nonlinear programming (NLP), etc. to solve such reservoir operation problems. But as far as reservoir operation is concerned, no standard algorithm is available, as each problem has its own individual physical and operational characteristics. In case of multipurpose reservoir operation, the goals are more complex than for single purpose reservoir operation and often involve various problems such as insufficient inflows and larger demands.
Genetic Algorithms (GAs) (Goldberg 1989) and Particle Swarm Optimization (PSO) (Eberhart and Kennedy 1995) are some of the techniques in this category. These evolutionary algorithms search from a population of points, so there is a greater possibility to cover the whole search space and reaching the global optimum. GA is one of the population-based search techniques, which works on the concept of “survival of the fittest” (Goldberg 1989). In the field of water resources, in earlier studies, few applications of the GA technique to derive reservoir operating policies have been reported (Oliveira and Loucks 1997; Wardlaw and Sharif 1999) and they illustrated the utility of evolutionary techniques for reservoir operation problems. Use of Genetic Algorithm (GA) in determining the optimal reservoir operation policies, is receiving significant attention from water resources engineers.
Many traditional numerical methods are available to facilitate the formation of reservoir operating policies. Yeh (1985) in state of art review on reservoir management and operation models discussed in detail the usefulness of various models for reservoir operations. In spite of extensive research in reservoir optimization, researchers are still in search of new optimizing techniques, which can derive more efficient reservoir operating policy for reservoir operation. GA is one such optimizing technique which it is robust and is considered in this study for deriving multipurpose reservoir operating policies. One of the advantages of GA is that it identifies alternative near optimal solutions. Oliveira and Loucks (1997) reported that GA can be used to identify effective operation policies.
STATEMENT OF PROBLEM
The reservoir chosen for the application of the GA model is the Ukai reservoir in Tapi river basin. Gujarat has around 21 large dams, among 541 Indian Dams. Ukai Dam near Surat is one of the major projects including Sardar Sarovar Dam. Ukai reservoir is the multipurpose reservoir situated in the Ukai village of Surat district on Tapti River, is the largest reservoir in Gujarat. It is also known as Vallabh Sagar. It is located between longitudes 73°32’25”-78°36’30″E and latitudes 20°5’0″-22°52’30″N. Ukai dam was constructed in 1971, the dam is meant for irrigation, power generation and flood control. The site is located 94 km from Surat.
The fitness function of the GA model is minimization of irrigation deficit that is to minimize sum of squared deviation of releases from demands of irrigation.
Minimize = SQDV ? ( Dl,t – Rl,t )2 + ? ( Dr,t – Rr,t )2 t is from 1 to 12 .
Where, SQDV is the sum of squared deviations of irrigation releases from demands, Dl,t and Dr,t are the irrigation demands for the left bank and right bank canal command areas respectively in period t in Mm3 ; Rl,t and Rr,t are the releases in to the left and right bank canals respectively in period t in Mm3 .
This model is subjected to following constraints.
1) STORAGE CONTINUITY
St+1 = St + It – ( R + Et + It + Ot )
Where St = active reservoir storage at the beginning of period t in Mm3
It = inflow to the reservoir during period t in Mm3
Et = the evaporation losses during period t in Mm3 ( a non-linear function of initial and final storages of period t)
Ot = Overflow from reservoir.
2) Storage limits
Smin < Sf < Smax for all t is 1 to 12
Where Smin and Smax are the minimum and maximum active storages of the reservoir.
3) Canal Capacity limits
Rl,t < Cl,max and Rr,t < Cr,max for all t is 1 to 12
Where C1,max is the maximum canal carrying capacity of the Ukai left bank canal.
4) Irrigation demands
Dlmin,t < Rl,t < Dlmax,tDrmin,t < Rr,t < Drmax,t for all t is 1 to 12
Where Dlmin,t and Dlmax,t are minimum and maximum irrigation demands for left canal respectively, Drmin,t and Drmax,t are minimum and maximum irrigation demands for right canal and left bank canal respectively in time t.
5) Overflow constraint
Ot = St+1 -7414.29.
Where St+1 = storage at the end of the month Mm3 . 7414.29 is gross storage of reservoir.
6) STEADY STATE RESERVOIR
Steady state storage constraint S13 = S1
This constraint is required to bring the steady state condition for the reservoir storage, i.e., storage at the end of a year is equal to the initial storage at the beginning of that year
MODEL APPLICATION AND DISCUSSION
For the selection of the optimal size of the different parameters such as size population, optimal probabilities of crossover, a thorough sensitivity analysis is carried out. In GA one of the important parameter is population size, obtaining optimum population is very important. In water resources applications, its values range from 64 to 300 and even up to 1000. A larger population helps to maintain greater diversity but, it involves considerable computational cost when the full model is being used to generate performance predictions. To find optimum population size in present study different population size has been considered. Population size is increased up to certain population size. Second important parameter affecting GA performance is the probability of cross over. Its effect on the system performance is studied by varying the probability of crossover from 0.6 to 0.9 with an increment of 0.01 and adopting the obtained optimal population of 100.
A comparative plot of actual demand and GA model release for an average inflow shown shows that the demand is almost satisfied with the releases obtained through GA model for Ukai left bank canal and Ukai downstream. The parameters used in applying GA to reservoir operation model were those selected after a thorough sensitivity analysis by varying each of the parameters. A population size of 100 and crossover probability of 0.8 are chosen to run the model.