J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012)
Crop Calendar Adjustment Study of Hirakud Multipurpose Reservoir for Irrigation System using Genetic Algorithm U. K. TRIPATHY1 and S. N. PRADHAN2 1
Head and Professor, Department of Mathematics, VSSUT, Burla, Sambalpur, India. 2 Department of Mathematics, Sundargarh Engg. College, Sundargarh, India. (Received on : March 6, 2012) ABSTRACT
The multiple objectives and interests of various stack holders in reservoir operation bring forward many solutions to the problem. Possibly due to this complexity in practice the operating rule to be derived not only from heuristic approaches such as rule of thumb, rule curve, operator experience and engineering judgments but also through well defined mathematical models. An attempt is made to study the possibility of changing paddy and other crops to groundnut of Hirakud multipurpose reservoir, Odisa. This reservoir is mainly constructed for flood control, irrigation and power generation. Mainly water is used for irrigation and power generation only during the lean period (Jan to June). Since the demand for power generation is more in this period, it is not possible to fulfill all the demands for irrigation. Hence in this paper we study the possibilities of changing the crop from paddy and other crops to groundnut, so as to achive maximum net benefit in less demand of water for irrigation. Genetic Algorithm has been used to find out the maximum net benefit from the Hirakud multipurpose reservoir. It has been observed that during lean period with scanty of water for irrigation, the net benefit of the farmers will be more if they change their crop from paddy to groundnut. Keywords: Genetic Algorithm, Hirakud dam, Multipurpose reservoir. Journal of Computer and Mathematical Sciences Vol. 3, Issue 2, 30 April, 2012 Pages (131-247)
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U. K. Tripathy, et al., J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012)
I. INTRODUCTION The optimal reservoir operation policy for multipurpose reservoir should specify how the total demand of water for irrigation and power generation could be meet with the available supply of water from reservoir. The operating policies are generally defined by a set of rules that specify either reservoir target storage volume or target release. Generally the construction of a reservoir is based on inflow of water, command area requirement, types of crop to be cultivated, water demand of the crop and power generation, flood control etc. In many practical situations, generally the operating policies are established at the planning stage of reservoir to meet the planned demand. However, after a few year of experience, the farmers may cultivate different crops in their own interest which can give them more profit. Again the water requirement for power generation is going on increasing as the demand becomes more and more. It is also very important for the government to release water for industry purpose to improve the economic standard of the state. For changing scenario, the farmers have to change their planning of cultivation to get maximum benefit. With the change in economic scenario, climate and attitude of the farmers, the necessity for proper management and optimum utilization of available water is gaining much importance. A large body of literature on the use of optimization and simulation models for water resources planning and management are reported by Yeh20, Wurbs19. Models like linear programming, dynamic programming and variance of them work under rigid
framework and it is very cumbersome to make the model flexible for more realistic modeling. Cancelliere et al.4 suggested a combined use of a soil water balance model, dynamic programming and neural network techniques for deriving operating rules of an irrigation supply reservoir. Teegavarapu and Simonovic16 used a stochastic search technique-simulated annealing (SA) to optimize the operation of multi-purpose reservoir. Kumar and Reddy11 used a metaheuristic technique called Ant Colony Optimization to derive operating policies for a multi-purpose reservoir system. Kumar et al.12 adopted Folded Dynamic programming for developing optimal reservoir operation policies for flood control. Heuristic models like Genetic Algorithm (GA) are highly suited to optimize the reservoir operation, as it is highly flexible. Genetic algorithm is one of the most often used optimization tool, used by many researchers for its efficiency in fast convergence to optimal solution. The study of GA based on Darwin’s principle of evolution was first proposed in 1975 by Holland9. Since then Genetic Algorithms (GAs) have been used in various fields of optimization problem. Some application of GAs to water resources problem include calibration of conceptual rainfall runoff model Wang17, reservoir system optimization Esat and Hall6, ground water management problems Cieniawski et al.5, identification of multiple reservoir operating rules Oliveira and Loucks14, reservoir system operation Wardlaw and Sharif18, waste load allocation Burn and Yulianti2. Oliveira and Loucks14 used a GA to evaluate operating rules for multi reservoir systems, demonstrating that GAs
Journal of Computer and Mathematical Sciences Vol. 3, Issue 2, 30 April, 2012 Pages (131-247)
U. K. Tripathy, et al., J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012)
can be used to identify effective operating rules. Wardlaw and Sharif18 used GA to a deterministic finite horizon multi-reservoir system operation and concluded that the approach can be easily applied to non-linear and complex systems. Very recently Ahmed J.A. et al.1 compared the results of optimal reservoir policy of the multipurpose reservoir located on river Pagladia, a major tributary of the river Brahmaputra by SDP model and GA. They have shown that GA gives a better operating policy then SDP. Chang F.J. et al.3 have developed the
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reservoir operating rule curves of the ShihMen reservoir in Taiwan. They have shown that the operating rule curves obtained by GA have better performance in terms of water released for irrigation and hydro power than the current M-5 rule curves. Mathur Y.P. and Nikam S.J.13 developed a GA model for deriving optimal operating policy for a reservoir. Jyothi Prakash and et al.10 has also developed an operational policy for multipurpose reservoir system in India using genetic algorithm.
Fig.1 Hirakud Reservoir, Sambalpur, Odisha Journal of Computer and Mathematical Sciences Vol. 3, Issue 2, 30 April, 2012 Pages (131-247)
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U. K. Tripathy, et al., J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012)
II. STUDY AREA The reservoir consider in this study is the Hirakud Dam, Multi-purpose reservoir located in the river Mahanadi at latitude 210 32’ N, and longitude 830 - 52’ E. The reservoir is constructed in the year 1956. The reservoir required to meet irrigation demand, hydro power demand and flood control, which are different in different months. The reservoir is irrigating 1,55,635 hectors of kharif, 1,08,385 hectors of rabi in Sambalpur, Bargarh, Balangir and Subarnapur district of Orissa. The water released by the power plant irrigates another 4560 km2 of the CCA area in the Mahanadi delta. Again it generates 307 MW hydro electricity through two hydro electric controlling the river flow of 9500 power plant i.e. Burla and Chiplima. The dam is also km2 of the delta area in Cuttack and Puri district through the drainage system. The multipurpose Hirakud dam across the river Mahanadi was constructed for flood control, irrigation and power generation. Hirakud dam is a composite structure of earth, concrete and masonry. The main dam having an overall length of 4.8 km spans between hills Lamdunguri on left and Chandli dunguri on the right sides to close the low saddles beyond the abutment hills. It has the distinction of being one time this longest dam in the world, being 25.8 km long with dams and dykes taken together. It also has the rare distinction of forming the biggest artificial lake in Asia with reservoir spread of 743 square kilometers at full reservoir level. The reservoir has life storage of 5818 million cubic meters with gross storage of 8136 million cubic meters (mcm). Spilling can be
affected by the operation of sluice gates incorporated in the concrete dam .The crest level of the spill way is at reservoir level 185.928 meter (610ft.) Both the split way contain 64 number under sluices, out of which 40 numbers are in the left and 24 number are in the right with floor at reservoir level 154.43 meters(510 ft) Each sluice has width of 3.658m(12ft) and height of 6.08m(20.34ft) .The sluices can discharge up to 0.95 million cubic meter per second .Free board is to be controlled during the filling season by the expected input capacity of the power channel and the discharge capacity of the spilling system subject to the flood control restraint. III. MODEL DEVELOPMENT Genetic algorithm is a search and optimization technique based on the principle of natural selection and genetics. This is efficient, adaptive and robust search process, producing near optimal solution. Genetic Algorithm are heuristic technique for searching over the solution space of a given problem in an attempt to find the best solution or set of solution Forrest8. In the present study, the fitness function of the GA model is to maximize the net benefit in terms of economic profit from the paddy crop and groundnut crop in the direct command. The objective function Ramakrishnan15. Maximize Pp(1-K1)K2TaNp+ Pg(1-K1)(1-K2)TaNg
(1)
Where Pp = Performance Indictor for paddy crop =
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U. K. Tripathy, et al., J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012)
WP=
Water demand for paddy crop = 19.625 M AC F WPd = Water deficit for paddy crop Pg = Performance Indictor for groundnut ŕł? crop = WG = Water demand for groundnut crop WGd = Water deficit for groundnut crop Ta = Total command area under direct command area in hector = 1,08,385 hector K1 = Percentage of command area to be left uncultivated = 61.5 % K2 = Percentage of paddy cultivated area = 14.5 % Np = Net benefit of paddy crop per hector = 21,500.00 Ng = Net benefit of groundnut crop per hector = 27,500.00 (1-k1) Ta = Balance command area available for cultivation (1-k1)k2 Ta = paddy cultivated command area (1-k1)(1-k2)Ta= Groundnut cultivable command area The net benefit of Paddy and groundnut crop per hector is calculated as : Yield per hector in quintal Ă— Cost per quintal per hector – Expenses per hector (Starting from cultivation of the crop to marketing) The continuity constraints, minimum and maximum storage capacity constraints are used. Based on the principle of conservation of mass, the continuity equation for the reservoir operation is given by St+1 = St + It − (Rt + SPt) − ELt
(2)
A set of storage capacity constraints are given below. Smin ≤ St ≤ Smax
(3)
where St = current available reservoir storage at the start of the period t St+1 = reservoir storage at the end of the period t It = inflow during the period t Rt = release during the period t ELt= evaporation loss in the reservoir during the period t SPt = spill during the period t = Dead storage of the reservoir = 1814.976 mcm = Maximum capacity of the reservoir = 7190.856 mcm Total paddy irrigated area is 15765 hectors K2 = % Paddy cultivated area
* 100
= 14.5 % Others cultivated area ( groundnut ) = 26093 hectors K0 = % Others ( groundnut ) cultivated area
* 100 = 24 %
K1 = % of uncultivated area (100-(K0+K2) )= 61.5 % IV. RESULT AND CONCLUSION To apply Genetic Algorithm in the above formulated model, the data are taken from department of water resources and department of agriculture, Government of Odisha. The values of K1 , K2 for different years, obtained by Genetic Algorithm are shown in table-1 . Hence the values K0 for different years calculated by the formula 100 - ( K1 + K2 ) . The comparison between the results obtained by Genetic Algorithm and linear programming (Ph.D. Thesis, 2003)7 are shown in fig-2.
Journal of Computer and Mathematical Sciences Vol. 3, Issue 2, 30 April, 2012 Pages (131-247)
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U. K. Tripathy, et al., J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012) Table -1 Year
1998
1999
2000
2001
2002
K2
12
12.2
12.3
12.5
12
K1
58
58.5
58.6
58.3
58.4
K0
30
29.3
29.1
29.2
30.6
Increase
6%
5.7 %
5.1 %
5.2 %
6.6 %
Fig.2 Histogram between results of GAs and LPP
result obtained by linear programming problem (Ph.D thesis)7. It is observed from the table-1 that if the farmers change their crop from paddy to groundnut and other crops to also groundnut then they can
cultivate a maximum of 6.6% (in 2002) area of the total command area without changing the current curve rule for release of water for irrigation from Hirakud reservoir. The water demand for irrigation may be decreased by
Journal of Computer and Mathematical Sciences Vol. 3, Issue 2, 30 April, 2012 Pages (131-247)
U. K. Tripathy, et al., J. Comp. & Math. Sci. Vol.3 (2), 177-184 (2012)
farmers and at the same time they can achieve maximum net benefit. V. CONCLUSION Any reservoir operation policy for irrigation system should be designed to benefit the farmers. The change in farmer’s attitude needs to be taken in account while revising the current irrigation policy. The irrigation policy made by this research paper is based on the engineering judgment and experience. We have taken care of achieving maximum net benefit of the farmers without any change in the current policy of release of water for irrigation from the Hirakud reservoir. Hence during lean period the farmers may change their current cultivation policy from paddy and other crops to groundnut , so as to achieve maximum net benefit. REFERENCES 1. Ahmed J. A.,Sarma A.K., ‘Genetic Algorithm For Optimal Policy of a Multipurpose Reservoir’. Water Resource Manag. 19(2):145-161 (2005). 2. Burn, D. H. and Yulianti, J. S., ‘Wasteload allocation using genetic algorithms’, J. Water Resour. Plan. Manage. ASCE 127(2), 121–129 (2001). 3. Chang Fi-John, Chen Li, Chang LiChiu,‘Optimizing the reservoir operating rule curves by Genetic Algorithms’ (2005). 4. Cancelliere A., Giuliano G., Ancarani A., Rossi G. A neural network approach for deriving irrigation reservoir operating rules. Water Resour Manage 16:71–88 (Kluwer Academic Publishers) (2002).
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5. Cieniawski, S. E., Eheart, J. W., and Ranjithan, S., ‘Using genetic algorithms to solve a multiobjective groundwater monitoring problem’, Water Resour. Res. 31(2), 399–409 (1995). 6. Esat, V. and Hall, M. J., ‘Water resources system optimization using genetic algorithms’, Hydroinformatics ’94, Proceedings of the First International Conference on Hydroinformatics, Balkema, Rotterdam, The Netherlands, pp. 225–231 (1994). 7. Garatia R., Ph.D Thesis,” Optimal reservoir operation policy of Hirakud reservoir” Sambalpur university, p-86 (2003). 8. Forrest, S., ‘Genetic algorithms: Principles of natural selection applied to computation’, Science (1993). 9. Holland, J. H., Adaption in Natural and Artificial Systems, 2nd edn., Massachusetts Institute of Technology, Cambridge (1992). 10. Jyothi Prakash. V, Shanthi. G., Development of operational Policy for a Multi-reservoir system in India using genetic algorithm, Water Resource manage (2011). 11. Kumar N. D., Reddy J. M., Ant colony optimization for multi-purpose reservoir operation. Water Resour Manage 20:879–898 (2006). 12. Kumar N.D., Singh F.B, Raju K.S. Optimal reservoir operation for flood control using folded dynamic programming.Water Resour Manage (2009). 13. Labadie J.W. Optimal operation of multi reservoir systems: state of art review. J. Water Resour Plan Manage 130(2):93– 111 (2004).
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14. Mathur Y.P. and Nikam S. J., ‘Optimal reservoir operation policies using genetic algorithm (2009). 15. Oliveira, R. and Loucks, D. P., ‘Operating rules for multireservoir systems’, Water Resour. Res. 33(4), 839–852 (1997). 16. Ramakrishnan, Suribabu C. R.,’Crop calendar Adjustment Study for Sathanur irrigation system in India Using Genetic Algorithm’, Water Resorce Manage. (2010). 17. Teegavarapu RSV, Simonovic SP. Optimal operation of a reservoir system using simulated annealing. Water Resour Manage 16:401–428 (Kluwer
Academic Publishers (2002). 18. Wang, Q. J., ‘The genetic algorithm and its application to calibrating conceptual rainfall-runoff models’, Water Resour. Res. 27(9), 2467–2471 (1991). 19. Wardlaw, R. and Sharif, M., ‘Evaluation of genetic algorithms for optimal reservoir system operation’, J. Water Resour. Plann. Manage. ASCE 125(1), 25–33 (1999). 20. Wurbs R. A. Reservoir-system simulation and optimization models. J. Water Resour Plan Manage 119(4):455– 472 (1993). 21. Yeh, W.G.W., ‘Reservoir management and operation models (1985).
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