OPTIMAL CONTROL OF MULTIPLE RESERVOIRS SYSTEM UNDER WATER SCARCITY By Iftikhar Ahmad M.Sc (Geology) M.Phil (Hydrology) A thesis submitted in the fulfillment of requirements for the degree of Doctor of Philosophy INSTITUTE OF GEOLOGY UNIVERSITY OF THE PUNJAB, LAHORE-PAKISTAN 2009 OPTIMAL CONTROL OF MULTIPLE RESERVOIRS SYSTEM UNDER WATER SCARCITY By Iftikhar Ahmad M.Sc (Geology) M.Phil (Hydrology) Under the Supervision of Prof. Dr. Nasir Ahmad Ph.D. (U.K), M.Sc. (Pb) A thesis submitted to the Punjab University in the fulfillment of requirements for the degree of Doctor of Philosophy INSTITUTE OF GEOLOGY UNIVERSITY OF THE PUNJAB, LAHORE-PAKISTAN 2009 Dedicated to my family and brother CERTIFICATE It is hereby certified that this thesis is based on the results of modeling work carried out by Iftikhar Ahmad under our supervision. We have personally gone through all the data/results/materials reported in the manuscript and certify their correctness/ authenticity. We further certify that the materials included in this thesis have not been used in part or full in a manuscript already submitted or in the process of submission in partial/complete fulfillment for the award of any other degree from any other institution. Iftikhar Ahmad has fulfilled all conditions established by the University for the submission of this dissertation and we endorse its evaluation for the award of PhD degree through the official procedures of the University. SUPERVISOR SUPERVISOR Prof. Dr. Nasir Ahmad Prof. Dr. Zulfiqar Ahmad Director Institute of Geology Chairman Department of Earth Sciences University of the Punjab Quad-i-Azam University Lahore, Pakistan Islamabad, Pakistan i ABSTRACT The use of mathematical programming for short term (10-day) operation of Indus River System under uncertainty was investigated. A two stage mix optimization procedure was proposed for the stochastic optimization of the Indus River System. The first stage of the proposed procedure cycles through three main programs, a transition probability matrix (tmp) computation algorithm, a DDP-SDP (Deterministic-Stochastic Dynamic Programming) model and a simulation program. In DDP-SDP program, four model types and three objective types were investigated for multiresevoir system. These non-linear objectives were calibrated for the large scale complex system to minimize the irrigation shortfalls, to maximize the hydropower generation and to optimize the flood storage benefits. Simulation program was used for the validation of each policy derived through this cycle. The accumulation of these programs is called 10 day reservoir operation model of the multireservoir Indus River System. Various model types in SDP/DDP formulation may produce different results in different reservoir conditions and different hydrologic regimes. The model types are therefore system specific. For the Indus Reservoir System best fit SDP model type was identified, alternate multi objective functions were proposed and analysed. Taking one or two objectives and ignoring other or considering all the objectives to optimize, produced different results in different model types. Especially the results were significantly different in terms of storage contents of the reservoir during simulation. The proposed procedure identifies the best stochastic operational policies for the system under uncertainty. The second stage of proposed procedure uses advantages of the stochastic optimal policies derived in the first stage of the optimization with a Network Flow programming (NFP) model developed for the Indus River System for 10 day operation. The whole system was represented by a capacitated network in which nodes are reservoirs, system inflow locations or canal diversion locations. The nodes are connected with the arcs which represent rivers, canal reaches or syphons in the system. The maximum and minimum flow conditions were defined from the physical data. The NFP model was solved with the help of two main programs, the out of kilter algorithm and on line reservoir operation model with stochastic operating policies. The accumulation of these programs is called 10 day stochastic network flow programming (SNFP) model of the multireservoir Indus River System. The proposed SNFP model provides two main benefits. First, the incorporation of the stochastic operating policies at reservoir nodes controls the uncertainty and improves the system operation performance. The stochastic behaviour of the inputs and non-linear objectives in the linear programming model is incorporated in this way. Second, the complete system is under control and presents acomplete physical picture of the system. The results obtained from the above two stage procedure were verified with help of simulating the system with forecasted inflows and comparing these results with actual historic data record. For this purpose, 10 day forecasting models were investigated, calibrated and verified. The results also proved the methodology effective for the test case. The reservoir operation model is characterized as generalised and flexible model, and can be used for any other reservoir. The SNFP model is system (the Indus River System) specific to and needs minor modifications to be used for other water resource systems. ii The proposed optimization procedure presents the optimum operation of reservoirs for irrigation water supplies, hydropower production and flood protection, optimal allocation of water resources in the canal network of Indus River System and identifies the resource limitations at various locations in the system. While comparing with the historic data records, the model performance was found to be better than the historic data at all locations in the system during simulation. The complete model may be used as a guiding tool for the optimum 10 day operation of the Indus River System. A two stage frame work consisting of a steady state SDP 10 day reservoir operation model followed by a Network Flow model appears to be promising for the optimization of Indus River System. The model has also been used for future planning of water resources in Pakistan. The methodology developed provides a viable way of applying stochastic optimization into deterministic optimization procedure under multireservoir, multiobjective water resource system with 10 day operation under uncertainty. iii ACKNOWLEDGEMENTS I would like to extend my sincere thanks to my research supervisors, Prof. Dr. Nasir Ahmad (Director, Institute of Geology) and Prof. Dr. Zulfiqar Ahmad (Chairman, Department of Earth Sciences, Quid-e-Azam University, Islambad) for their keen interest, proficient guidance, valuable suggestions, and encouraging attitude during the course of this research work. Special recognitions go to Dr. S. M. Saeed Shah (Head of hydrology division, Centre of Excellence in Water Resources Engineering, University of Engineering and Technology Lahore) for his insightful suggestions while writing up this thesis. I am extremely grateful to Prof. Dr. Iftikhar Hussain Baloch (Principal, College of Earth and Environmental Sciences, University of The Punjab) for his cooperation and encouragement. I wish to thank many professional colleagues, specially Dr. Ashraf Malik, ex.Chief Hydrology, NESPAK, Dr. Muhammad Younas Khan, ex General Manager, Tarbela Dam WAPDA, and Dr. Maboob Alam, Director IWASRY WAPDA for their wise comments on the script. I thank to my University fellows, Mr. Muhammad Akhtar and Mr. Khursheed Alam for their co-operation. Finally, I would like to express my heartiest gratitude to my wife and children whose cooperation, prayers and well wishes strengthened my confidence to endure hardships faced during this study. iv LIST OF TABLES Table 4.1 Details of Indus Basin Rivers 124 Table 4.2 Hydraulic characteristics of Indus River and its tributaries 126 Table 4.3 Salient features of Jhelum river and its tributaries 128 Table 4.4 Hydraulic characteristics of tributaries of Ravi joining within Pakistan 132 Table 4.5 Hydraulic characteristics of important tributaries of Sutlej 132 Table 4.6 Water and Power benefits from Tarbela dam 139 Table 4.7 Water and Power benefits from Mangla dam 145 Table 4.8 Water benefits from Chasma reservoir 148 Table 4.9 Loss of reservoir capacities in MAF 149 Table 4.10 Summary of the basic Information of the Barrages located in the Indus Basin 153 Table 4.11 Indus zone and Jhelum Chenab Zone 154 Table 4.12 Average gains and losses of the 46 years of data 156 Table 5.1 Statistics of Annual Flows (Time series Oct-Sep) 161 Data Statistics, Consistency and Outliers in 10 Daily Inflows 1922-2004 Oct- Table 5.2 169 Sep, Jhelum at Mangla Data Statistics, Consistency and Outliers in 10 Daily Inflows 1961-2004 Oct- Table 5.3 170 Sep, Indus at Tarbela Table 5.4 Serial Correlation Coefficients 173 Table 5.5 Correlation Coefficients between 10 daily flows 174 Table 5.6 Transition Probability Matrix of Period August 1, Indus at Tarbela 176 Table 5.7 Variation of Rescale Range and Hurst Exponent 177 Table 5.8 Results of Gould transitional probability matrix method 179 v Table 5.9 Summary result from Rippl mass curve analysis 182 Table 5.10 Summary results of Sequent Peak Analysis 183 Table 5.11 Selected Regression Models for 10 day forecasting in Indus Rivers 199 Summary results for calibration of stochastic network flow programming model, Table 7.1 254 simulation period 1985-95. Sample result of calibration of SNFP model 10 day time period 10 year Table 7.2 255 simulation for 1985-1995 (values in 1000 x cfs) Summary results for validation of stochastic network