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Mohite, Nitin M.

Narulkar, Sandeep

English

Hydraulic Engineering Repository

Conference Paper, Published VersionMohite, Nitin M.; Narulkar, SandeepSingle Reservoir Optimization: A Genetic AlgorithmApproachZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/109984Vorgeschlagene Zitierweise/Suggested citation:Mohite, Nitin M.; Narulkar, Sandeep (2010): Single Reservoir Optimization: A GeneticAlgorithm Approach. In: Sundar, V.; Srinivasan, K.; Murali, K.; Sudheer, K.P. (Hg.): ICHE2010. Proceedings of the 9th International Conference on Hydro-Science & Engineering,August 2-5, 2010, Chennai, India. Chennai: Indian Institute of Technology Madras.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                        SINGLE RESERVOIR OPTIMIZATION: A GENETIC ALGORITHM APPROACH  Nitin M Mohite1 and Sandeep Narulkar2  Abstract: The present study deals with the application of Genetic Algorithm (GA) model for optimization of single reservoir. The GA model was used to minimize the live storage capacity of reservoir and also the canal capacity while maximizing the irrigation and inter-basin transfer releases. Constraints include continuity equation, reservoir capacity constraints, and canal capacity constraint. MATLAB software is used to solve the problem. For fixing the GA parameters the model were run for various values of population size, number of generations, crossover and mutation probabilities etc. Result obtained by GA is compared with NWDA model. GA model is found to be an effective optimization tool for the single reservoir optimization problem.   Keywords:  Optimization of single reservoir; Genetic algorithms  INTRODUCTION  The reservoir design and operation problems are quite complex and dimensionally large since it   involves various physical components including reservoir, canals, pumping stations, hydropower plants etc. and the different demands like irrigation, municipal and industrial water supply, hydropower, etc. Traditionally, simulation and optimization techniques played an important role in providing a good insight in solving these problems. Numerous researchers have solved the problems of optimum reservoir system planning and operation during past five decades using Simulation, Linear Programming (LP), Dynamic Programming (DP), Nonlinear Programming (NLP) etc. and with their variants and combination of these techniques. An exhaustive and extremely useful state-of-the-art review of simulation  and optimization methods applied to reservoir systems planning and operation problems can be seen in the works of Yeh (1985), Simonovic (1992), Wurbs (1993), Labadie (2004) and Deepti Rani and Maria (2010) etc. In the recent times various evolutionary search algorithms i.e. the Genetic Algorithms (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) etc. have taken the fore seat.  The Genetic Algorithms (GAs) are robust search technique based on the Darwinian Survival-of-the-Fittest principle (Holland 1975). Genetic Algorithms have been applied successfully to a wide range of reservoir design and optimization problems of moderate size. Wardlaw and Sharif (1999) and Sharif and Wardlaw (2000) have provided a brief account of the GA applications to water resources problems. In their work the classic problems of multiple reservoir systems have been solved.They also have stated various other aspects of the GA applications to reservoir operation problems. Raju and Nagesh kumar (2004) applied GA model for evolving an optimum cropping pattern utilizing surface water resources in the command area of a multipurpose reservoir system. ___________________________ 1 Lecturer, Department of Civil Engineering, College of Engineering, Pune-05, India, E-mail: nitinmohite265@rediffmail.com 2 Professor Dept. of Civil & Applied Mechanics S.G.S.I.T.S, Indore, 452003, India, E-mail snaulkar@gmail.com  Proceedings of ninth Internatio a  Conf ence on Hydr -Science and Engineering (ICHE 2010), IIT Madras, Chennai, India. 2 - 5  August 2010 757Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                      They concluded that GA algorithm is an effective tool for irrigation planning and can be used for more complex system involving non-linear optimization. Ahmed and Sarma (2005) presented a GA model for deriving the optimal operating policy and compared its performance with that of stochastic dynamic programming (SDP) for a multi-purpose reservoir. Nagesh Kumar et al. (2006) applied GA model for obtaining an optimal operating policy and optimal crop water allocation from an irrigation reservoir. Momtahen and Dariane (2007) proposed direct search approach to determine optimal operation policies using Real Coded Genetic Algorithm. Jothipraksh and Ganesan shanti (2009) developed comprehensive Genetic algorithm model and applied to derive optimal operational strategies of multipurpose reservoir system in India. The results were compared with Stochastic Dynamic Programming model and found that Genetic algorithm performs well in comparison to SDP. The application of GA Models has certain limitations as pointed out by Sharif and Wardlaw (2000). As Chun et. al. (2008) state, ‘The limitations of application of GA models to real life problems are premature convergence and large amount of time and number of iterations required for searching the decision space to reach the global optimum solution’. Despite these limitations the GA has wide applications and as stated by other researchers, the technique can be applied to a reservoir planning and operation problem. The present study also demonstrates an application of the GA technique for the planning problem of a single reservoir in Central India. The details of the present study is presented in the following paragraphs.    MODEL FORMULATION   The objective of the model is to optimize the capacity of a single reservoir that serves multiple purposes such as Municipal and Industrial water supply, Irrigation and Transfer of water to other reservoir. The present objective is to minimize the capacity of a reservoir while maximizing the other objectives. The objective function is:   Minimize                                            (1)  Where   = Total no of years of planning  = Total No. of time steps used for planning in each year   =Total No. of time steps in the time horizon (= u x T)  = Relative weight indicating the unit cost of capacity of reservoir.  = Live storage capacity of the reservoir in MCM  = Relative weight indicating the unit cost of capacity of canal.  = The canal Capacity in Cumec.  = Relative weight indicating the benefit coefficient of unit volume of water supplied to irrigation in Millions/MCM = Monthly irrigation released at the reservoir in period t  in MCM  758Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                       = Relative weight indicating the benefit coefficient of unit volume of water transfer in Millions/MCM  = Monthly transfer of water from the reservoir to other reservoir in period t  in MCM  The objective function is subjected to following constraints  The Reservoir Continuity Equation  The continuity equation for reservoir storage at the end of time ,   is calculated as               (2) Where    = Reservoir storage at the beginning of time period t    = Inflow in the reservoir in time period t    = Spillage in time period t    = the fixed evaporation loss at site = ,   is the evaporation rate in period t , , = water surface area at the top of the dead storage level, , and  is the surface area per unit active storage.  The  are in units of Million cubic meter (x106 m3) and is in units of millimeters (mm). The method of computation of evaporation is as per the procedure stated in Loucks et al. (1981).  Reservoir Capacity Constraint                                                                 (3)  The storage in the reservoir under consideration in any time period t cannot exceed the live storage capacity.   Canal Capacity Constraint  The water released from reservoir for irrigation and transfer from the reservoir during t  time cannot exceed the canal capacity.           (4)  = factor of conversion of MCM to cumec (m3/s)  STUDY AREA  The model formulated above is applied to the Patanpur reservoir, which is first proposed reservoir in Parbati-Kalisindh-Chambal (P-K-C) link project of the most ambitious river interlinking project envisaged by the Government of India. The proposed reservoir is located in the Biaora tehsil of Rajgarh district in Madhya Pradesh. The latitude of the proposed site is approximately 230 42’ N and the longitude as 770 9’. The reservoir is a multipurpose reservoir having municipal and industrial water supply, irrigation and water transfers to other reservoir for the purpose of inter-basin water transfer as the objectives. The climate of the area is subtropical and semi-arid. The maximum and minimum annual rainfall in the basin varies from 356 mm to 759Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                      1270 mm.  The proposed active storage capacity of the reservoir is 110 MCM and catchment area 5312 Km2. In the present study the main objective is to optimize the live storage capacity of the reservoir and the link canal capacity maximizing the fulfillment of the objectives of the inter-basin transfer.    Fig. 1 The Chambal Basin and the Parbati-Kalisindh- Chambal Link  MODEL APPLICATION   The model formulated above was applied to the Patanpur reservoir which is one of the reservoirs of Parbati-Kalisindh-Chambal (P-K-C) link project. In the following lines the solution process has been explained. The present values of cost parameter of dams and canals and annual benefit of irrigation and transfer of water have been computed form the available data (Pre-Feasibility Report, 2004). The unit cost of structure was calculated by dividing its design project cost by the design capacity as per NWDA.  The rate of annual interest was taken as 5% of the respective capital cost. The annual operation and maintenance cost is assumed to be 10% of the total cost of project. The cost parameter (including all costs i.e. Construction cost + Operation and Maintenance cost) of the reservoir, canal and the benefit parameters of irrigation and transfers are shown in Table 1. The water demands in various reservoirs and transfer targets are shown in Table 2 and 3 respectively. The target irrigation yield is set at 124 million cubic meters (MCM) and municipal requirement 3 MCM. An inflow record of 20 years was used to demonstrate the application. As per the priorities for water demand satisfaction set by the NWDA the highest priority demand that is municipal and industrial demand was fulfilled in all the seasons by subtracting it from the natural inflows. For model computations, the MATLAB software was 760Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                      used since it is easy to use and can accommodate large scale optimization problems.   Table 1 Cost and benefit Parameter values of Patanpur reservoir  Parameters Patanpur Cost of Dam   7.594 Cost of canal  27.4 Benefits from Irrigation 5.06 Benefits from Transfer 1.478  The cost and benefits of all the variables are in Million Rs. / MCM. MCM indicates Million Cubic Meters and Rs. Specify the Indian Rupee. The cost of canal is in Million Rs. / cumec. Cumec indicates Cubic Meter per Second.   Table 2 Water demands and transfer targets for Patanpur reservoirs (MCM) Month Water Supply Irrigation June 0.25 8.68 July 0.25 19.84 August 0.25 13.64 September 0.25 8.68 October 0.25 6.2 November 0.25 8.68 December 0.25 13.64 January 0.25 18.6 February 0.25 17.36 March 0.25 3.72 April 0.25 2.48 May 0.25 2.48 Annual 3 124 Table 3 Transfer targets for Patanpur reservoirs (MCM)  Month NWDA D1 D2 D3 June 6 6 6 6 July 67 80 100 100 August 131 400 450 475 September 24 250 230 205 October 57 5 5 5 November 4 5 5 5 December 4 5 5 5 January 4 1 1 1 February 4 1 1 1 March 4 1 1 1 April 4 1 1 1 May  4 1 1 1 Total 313 756 806 806  Initially model runs were taken without any upper bound on the capacity of the reservoir. It was 761Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                      observed that the capacity of the Patanpur Reservoir was very high. Subsequently an upper bound for the capacity was set at the NWDA specified value of 110 MCM. Further the upper bound was reduced for various model runs until the monthly irrigation targets imposed on the reservoir met satisfactorily. Four sets of monthly target transfer values were tried to maximize the inter-basin transfer to the other system. The target transfer values are indicated in Table 3.  The model was applied to the reservoir design problem for the Patanpur Reservoir with the above mentioned data. The GA component of the model had many options due to a combination of GA Parameters viz. the population size, number of generations, the crossover and mutation probabilities etc. In general a population size of 500 and a generation number of about 100000, the crossover probabilities were taken in the range of 0.7 to 1 and the mutation probabilities are taken in a range .001 to 0.3. Better results are obtained at a crossover probability at 0.65 and the mutation probability at 0.006.  RESULTS AND DISCUSSION   The results for various cases viz NWDA, D1, D2 and D3 are summarized in Table 4. The overall results indicated that the application of changed operating policies gives better result in comparison to NWDA. It is observed that in all the 20 years the M & I demands along with the irrigation demands are fulfilled. The NWDA fixed the capacity based on simulation results for a given set of hydrologic record. The case D2 gives maximum net benefit is 25078.9Millions Rs where as the maximum transfer reliability is achieved in case of NWDA policy is 80.39. The present optimization model generated better values for the capacities of the reservoir for various target transfer values. The 10.9 % reduction of reservoir capacity is achieved in case of D2 and D3.  The NWDA chosen canal capacity value is quite high in comparison to the maximum transfer. With an increase in the target transfer values, the canal capacities are increased in proportion to the highest volume of transfer chosen in a specific month.  The reliability of the transfer target met is around 78% for all the cases. Also there is an increase in the net benefits from the proposed system. Table 4 Summary of results of optimization for Patanpur reservoir  Reservoir Storage Capacity  (MCM) Patanpur % Reduction Adopted in planning  110  NWDA Policy 110 0 D1 103 6.3 D2 98 10.90 D3 98 10.90 Canal capacity (cumec)  Adopted in planning 199.32 % Reduction NWDA Policy 59.5475 70.12467 D1 171.9895 13.71187 D2 192.8895 3.226219 D3 203.3395 -2.01661 Total Transfer From Patanpur for 20 Years (MCM)  Maximum Value Actual Reliability of 762Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                      Transfers Target Met NWDA Policy 6260 5253.951 83.9 D1 15120 1233.39 79.58 D2 16120 12632.95 78.36 D3 16120 12682.42 78.67 Net Benefit from Proposed System (Mill. Rs.) NWDA Policy 17748.35 % Increase D1 24747.09 39.43 D2 25078.9 41.30 D3 24865.35 40.09  CONCLUSIONS  The present study demonstrates the successful application of Genetic algorithm to Patanpur reservoir located in Chambal basin in Madhya Pradesh, India. The objective of GA model is to minimize the live storage capacity of reservoir and canal while maximize the irrigation and inter-basin transfer releases. The results were compared with NWDA model; it was found that the GA performs well than the NWDA model. GA techniques most suitable for complex problems, its applicability to large scale problems has certain limitations. The performance of GA depends on probability of mutation.  It is also observed that GA suffers from the slow finishing problem. Premature convergence is another disadvantage of GA.   REFERENCES  Ahamed, J.A., and Sarma, 2005. Genetic algorithms for optimal operating policy of a multi-purpose reservoir. J. Water Resor. Manage., 19(2), 145-161. Chun, T. C., Wen, C. W., Dong, M. X., and Chau, K. W. 2008. Optimizing hydropower reservoir operation using hybrid genetic algorithm and chaos. J. Water Resources Manage, 22 (7),895-909. Deepti, Rani and Maria, M., M. 2010. Simulation-optimization modeling: a survey and potential application in reservoir system operation. J. Water Resources Manage. 24 (6), 1107-1138. Holland, J.H. 1975. Adaptation in natural and artificial systems. MIT Press, Cambridge, Mass. Jothipraksah and Ganesh Shanti 2009. Comparison of policies derived from stochastic dynamic programming and genetic algorithm models. J. Water Resources Manage. 23 (8), 1563-1580. Labadie, J. W., 2004. Optimal operation of multireservoir systems: state-of –the-art- Review. J.  Water Resour. Plan. Manage. ASCE 130(2), 93-111. Loucks, D. P., Stedinger, J. R. and Haith, D. A. 1981, Water Resources Systems Planning and Analysis. Prentice-Hall, Englewood Cliffs, New Jersey. Momtahen, Sh. And Dariane. 2007. Direct search approach using genetic algorithms for optimization of water reservoir operating policies. J. Water Resour. Plan. Manage, 133(3),202-209. Nagesh Kumar, D., K. Srinivasa Raju, and Ashok, B. 2006. Optimal reservoir operation for irrigation of multiple crop using genetic algorithms.  J. Water. Resour. Plan. Manage. ASCE 132 (2), 123-129. Preliminary study of Parbati-Kalisindh Link 2004. National Water Development Agency, New 763Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 Single Reservoir Optimization: A Genetic Algorithm Approach                      Delhi, F.R. P/9/04 vol., I & II.  Raju and Nageshkumar D. 2004. Irrigation planning using genetic algorithms. J. Water Resources Manage. 18 (2), 163-176. Simonovic, S. P. 1992. Reservoir system analysis: Closing gap between theory and practice. J. Water. Resour. Plan. Manage. ASCE 118(3), 262-280. Wardlaw, R., and Sharif, M. 1999. Multireservoir system optimization using genetic algorithm: case study. ASCE J. Water Resour. Plan.Manage., 14(4), 255-263. Sharif, M., and Wardlaw, R. 2000. Evaluation of genetic algorithms for optimal reservoir system operation. J. Water Resour. Plan.Manage. ASCE 15(2), 25-33. Wurbs, R. A. 1993. Reservoir-system simulation and optimization models. J. Water Resour. Plan. Manage. ASCE 119(4), 455-472. Yeh, W. W.G. 1985. Reservoir management and operation models: A state-of-the-art   review. Water Resour. Res., 21(12), 1797-1818.  764

Single Reservoir Optimization: A Genetic Algorithm Approach

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Single Reservoir Optimization: A Genetic Algorithm Approach

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