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 (ISBN-13: 9780511282973)

Dynamic Programming Based Operation of Reservoirs

Cambridge University Press
9780521874083 - Dynamic Programming Based Operation of Reservoirs - Applicability and Limits - by K. D. W. Nandalal and Janos J. Bogardi

Dynamic Programming Based Operation of Reservoirs

Applicability and Limits

Dynamic programming is a method of solving multi-stage problems in which decisions at one stage become the conditions governing the succeeding stages. It can be applied to the management of water reservoirs, allowing them to be operated more efficiently.

This is one of the few books dedicated solely to dynamic programming techniques used in reservoir management. It presents the applicability of these techniques and their limits in the operational analysis of reservoir systems. In addition to providing optimal reservoir operation models that take into account water quantity, the book also examines models that consider water quality. The dynamic programming models presented in this book have been applied to reservoir systems all over the world, helping the reader to appreciate the applicability and limits of these models. The book also includes a model for the operation of a reservoir during an emergency situation. This volume will be a valuable reference to researchers in hydrology, water resources and engineering, as well as to professionals in reservoir management.

K. D. W. NANDALAL is Senior Lecturer in the Department of Civil Engineering at the University of Peradeniya, Sri Lanka. His research interests include water resources systems analysis and reservoir water quality modeling.

JANOS J. BOGARDI is Director of the United Nations University Institute for Environmental and Human Security. He was co-editor of Risk, Reliability, Uncertainty, and Robustness of Water Resource Systems (Cambridge University Press 2002).


The International Hydrological Programme (IHP) was established by the United Nations Educational, Scientific and Cultural Organization (UNESCO) in 1975 as the successor to the International Hydrological Decade. The long-term goal of the IHP is to advance our understanding of processes occurring in the water cycle and to integrate this knowledge into water resources management. The IHP is the only UN science and educational programme in the field of water resources, and one of its outputs has been a steady stream of technical and information documents aimed at water specialists and decision-makers.

The International Hydrology Series has been developed by the IHP in collaboration with Cambridge University Press as a major collection of research monographs, synthesis volumes and graduate texts on the subject of water. Authoritative and international in scope, the various books within the series all contribute to the aims of the IHP in improving scientific and technical knowledge of fresh-water processes, in providing research know-how and in stimulating the responsible management of water resources.

Secretary to the Advisory Board
Dr Michael Bonell Division of Water Science, UNESCO, I rue Miollis, Paris 75732, France

Members of the Advisory Board
Professor B. P. F. Braga Jr Centro Technológica de Hidráulica, São Paulo, Brazil
Professor G. Dagan Faculty of Engineering. Tel Aviv University, Israel
Dr. J. Khouri Water Resources Division, Arab Centre for Studies of Arid Zones and Dry Lands, Damascus, Syria
Dr G. Leavesley US Geological Survey, Water Resources Division, Denver Federal Center, Colorado, USA
Dr E. Morris Scott Polar Research Institute, Cambridge, UK
Professor L. Oyebande Department of Geography and Planning, University of Lagos, Nigeria
Professor S. Sorooshian Department of Civil and Environmental Engineering, University of California, Irvine, California, USA
Professor K. Takeuchi Department of Civil and Environmental Engineering, Yamanashi University, Japan
Professor D. E. Walling Department of Geography, University of Exeter, UK
Professor I. White Centre for Resource and Environmental Studies, Australian National University, Canberra, Australia

M. Bonnell, M. M. Hufschmidt and J. S. Gladwell Hydrology and Water Management in the Humid Tropics: Hydrological Research Issues and Strategies for Water Management
Z. W. Kundzewicz New Uncertainty Concepts in Hydrology and Water Resources
R. A. Feddes Space and Time Scale Variability and Interdependencies in Hydrological Processes
J. Gibbert, J. Mathieu and F. Fournier Groundwater/Surface Water Ecotones: Biological and Hydrological Interactions and Management Options
G. Dagan and S. Neuman Subsurface Flow and Transport: A Stochastic Approach
J. C. van Dam Impacts of Climate Change and Climate Variability on Hydrological Regimes
J. J. Bogardi and Z. W. Kundzewicz Risk, Reliability, Uncertainty, and Robustness of Water Resources Systems
G. Kaser and H. Osmaston Tropical Glaciers
I. A. Shiklomanov and J. C. Rodda World Water Resources at the Beginning of the Twenty-First Century
A. S. Issar Climate Changes during the Holocene and their Impact on Hydrological Systems
M. Bonnell and L. A. Bruijnzeel Forests, Water and People in the Humid Tropics: Past, Present and Future Hydrological Research for Integrated Land and Water Management
F. Ghassemi and I. White Inter-Basin Water Transfer: Case Studies from Australia, United States, Canada, China and India
K. D. W. Nandalal and J. J. Bogardi Dynamic Programming Based Operation of Reservoirs: Applicability and Limits

Dynamic Programming Based Operation of Reservoirs

Applicability and Limits

K. D. W. Nandalal

University of Peradeniya, Sri Lanka

Janos J. Bogardi

United Nations University, Bonn, Germany

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York
Information on this title:

© UNESCO 2007

This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2007

Printed in the United Kingdom at the University Press, Cambridge

A catalog record for this publication is available from the British Library

ISBN 978-0-521-87408-3 hardback

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites
referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.


List of figurespage vi
List of tablesviii
1Water resources management1
1.2Role of reservoirs2
1.3Optimal reservoir operation3
1.4Conventional dynamic programming4
1.5Incremental dynamic programming4
1.6Stochastic dynamic programming6
1.7Dynamic programming in reservoir operations9
1.8Developments in dynamic programming13
2Incremental dynamic programming in optimal reservoir operation16
2.1IDP in optimal reservoir operation: single reservoir16
2.2IDP in optimal reservoir operation: multiple-reservoir system23
3Stochastic dynamic programming in optimal reservoir operation31
3.1SDP in optimal reservoir operation: single reservoir31
3.2SDP in optimal reservoir operation: multiple-reservoir system32
3.3Some algorithmic aspects of stochastic dynamic programming38
4Optimal reservoir operation for water quality59
4.1IDP based models in reservoir operation for quality60
4.2The Jarreh Reservoir in Iran63
4.3Application of the models to the Jarreh Reservoir65
5Large-scale reservoir system operation73
5.1Use of dynamic programming in multiple-reservoir operation73
5.2Decomposition method78
5.3Composite reservoir model formulation94
5.4Implicit stochastic dynamic programming analysis103
5.5Disaggregation/aggregation techniques based on dynamic programming106
6Optimal reservoir operation for flood control110
6.1Feitsui Reservoir Project in Taiwan110
6.2Operational mode switch system between long-term and short-term operation112
6.3Development of SDP model for long-term operation112
6.4Operational mode switch system118
6.5Application and sensitivity analysis121
6.6Some remarks on operational mode switch system123


1.1Basic structure of dynamic programmingpage 4
1.2Incremental dynamic programming optimization procedure5
1.3Construction of the corridor for IDP5
1.4Flow diagram for the stochastic dynamic programming model8
2.1Kariba Reservoir and Zambezi River basin17
2.2Characteristic curves of the Kariba Reservoir18
2.3Rule curve of the Kariba Reservoir18
2.4Single-reservoir configuration18
2.5Rate of convergence in IDP for initial half width of 1000 × 106 m319
2.6Optimal operations to maximize energy generation of the Kariba Reservoir by IDP19
2.7Ubol Ratana Reservoir system21
2.8Characteristic curves of the Ubol Ratana Reservoir22
2.9Rule curve of the Ubol Ratana Reservoir22
2.10Optimal operation policies to maximize energy generation of the Ubol Ratana Reservoir23
2.11Schematic diagram of the Mahaweli system24
2.12System configuration: Victoria, Randenigala, Rantembe subsystem26
2.13Corridor points for two-reservoir case27
2.14Incremental dynamic programming procedure28
2.15Effect of initial corridor width in IDP29
2.16Rate of convergence for different initial corridor widths in IDP procedure29
2.17Effect of initial trial trajectory in IDP procedure29
2.18Rate of convergence for different initial trial trajectories in IDP procedure29
3.1System configuration for SDP model: single reservoir32
3.2Graphical display of the indices used in the SDP model description32
3.3System configuration for SDP model: multiple-reservoir system32
3.4SDP Flow diagram for two-reservoir case35
3.5Number of inflow, storage, and release state space discretizations44
3.6Graphical illustration of the three-dimensional (Markov-II) transition probabilities50
3.7Graphical illustration of the two-dimensional (Markov-I) transition probabilities50
3.8Graphical illustration of the one-dimensional (independence) transition probabilities51
4.1System configuration: Optimization Model 160
4.2System configuration: Optimization Model 261
4.3The Shapur–Dalaki basin64
4.4Characteristic curves of the Jarreh Reservoir65
4.5River discharges and salinities: 1975–8967
4.6Reservoir salinity: comparison of IDP optimum operation with standard release policy68
4.7Monthly average release salinity: comparison of IDP optimum operation with standard release policy68
4.8Monthly average release salinity: effect of including quality considerations in the optimization model70
4.9Objective function value for different allowable diversion limits70
4.10Monthly average release salinity: comparison of models71
4.11Monthly average release salinity: comparison of cut-off level with Optimization Model 272
5.1Tunis water supply system79
5.2Seven-reservoir Tunis system80
5.3Sequential downstream-moving decomposition flow chart and Tunis system83
5.4Iterative downstream-moving decomposition flow chart and Tunis system85
5.5Iterative up-and-downstream-moving decomposition flow chart87
5.6Iterative up-and-downstream-moving decomposition of the Tunis system88
5.7General structure of the iterative optimization model94
5.8Composite representation of a serially linked two-reservoir system96
5.9Calibration of Caledonia + Kotmale (C + K) composite reservoir97
5.10Calibration of Victoria + Randenigala (V + R) composite reservoir98
5.11Calibration of Bowatenna + Moragahakanda (B + M) composite reservoir98
5.12Real and composite configurations of the macrosystem99
5.13Monthly diversions at Polgolla based on the three-composite-reservoir IDP model102
5.14Polgolla diversion policy prespecified for the sensitivity analysis102
5.15Schematic diagram of Victoria–Randenigala–Rantembe reservoir subsystem104
6.1The Hsintien River basin111
6.2Schematic representation of the operational mode switch system112
6.3Flow chart of the OMS model for on-line reservoir operation113
6.4Relationship between variables of SDP114
6.5Block diagram of operational mode switch118
6.6Classification of typhoons121
6.7Utility functions122
6.8Switch process during Typhoon Nelson (August 21–23, 1985)122
6.9Reservoir release during Typhoon Nelson122
6.10Variation of storage during Typhoon Nelson123
6.11Sensitivity analysis of switch with initial storage 406 × 106 m3 during Typhoon Nelson123
6.12Variation of storage with the initial storage of 406 × 106 m3 during Typhoon Nelson123


2.1Salient features of the Kariba dam, reservoir, and power housepage 17
2.2Effect of initial corridor width: Kariba Reservoir19
2.3Maximum energy generation: Kariba Reservoir19
2.4Salient features of the Ubol Ratana dam, reservoir, and power house20
2.5Effect of initial corridor width: Ubol Ratana Reservoir22
2.6Maximum energy generation: Ubol Ratana Reservoir23
2.7Principal features of the existing and proposed reservoirs/power plants25
2.8Effect of initial corridor width in IDP27
2.9Effect of initial trial trajectory in IDP29
3.1Operational performance of the Kariba Reservoir32
3.2SDP based operation policy for the Victoria and Randenigala Reservoirs for the month of October36
3.3Inflow class discretization of the operation policy of Table 3.237
3.4Storage classes of the operation policy of Table 3.237
3.5Simulation results of the Victoria–Randenigala–Rantembe reservoir subsystem according to SDP based policies38
3.6SDP model setups for the Mahaweli and Kariba reservoir systems40
3.7Example of modifications of the Markov inflow transition probabilities of the Kariba Reservoir40
3.8Operational performance of the Kariba Reservoir41
3.9Operational performance of the Mahaweli system42
3.10Example of the smoothing method43
3.11Simulated performance after smoothing43
3.12Multiple regression analysis of the Kariba Reservoir inflow (Budhakooncharoen, 1986)45
3.13Summary of the three computer experiments45
3.14Derived SDP based policy tables for the Kariba Reservoir (May)47
3.15Simulated average annual performance (Experiment 1)48
3.16Simulated average annual performance (Experiment 2)48
3.17Simulated average annual performance (Experiment 3)48
3.18Serial correlation coefficients of the three case study systems52
3.19Key points of the design of experiments53
3.20Simulated average annual performance (Experiment A)53
3.21Simulated average annual performance (Experiment B)54
3.22Simulated average annual performance (Experiment C)56
3.23Simulated average annual performance (Experiment D)57
3.24Simulated performance (Experiment E)58
4.1Monthly irrigation demands (for 13 000 ha)65
4.2Salient features of the Jarreh dam and reservoir66
4.3Comparison of different objective functions67
4.4Comparison of IDP optimum operation with simulation68
4.5Releases of IDP optimization69
4.6Comparison of two optimizations: effect of inclusion of quality70
4.7Effect of allowable maximum diversion70
4.8Comparison of optimum diversions with cut-off level diversions71
5.1Reservoir capacities and the associated demand targets78
5.2Reservoir mean monthly incremental inflows (period 1946–89) (106 m3/month)79
5.3Basic statistics of the annual inflows for the seven reservoirs (period 1946–89)80
5.4Estimated mean monthly elevation losses due to evaporation (mm/month)81
5.5Monthly water demands for the 18 demand centers in northern Tunisia (106 m3/month)81
5.6Capacities of the existing water conveyance structures82
5.7Discrete storage representation for individual reservoirs (106 m3)88
5.8An example of a typical SDP based operation policy table89
5.9Comparison of the three decomposition alternatives89
5.10Expected annual deficits of individual demand centers for SDD, IDD, and UDD models (106 m3/year)89
5.11SDD, IDD, and UDD models: relative number of different decisions in monthly policy tables (%)90
5.12Results of the sequential optimization model (objective function: maximize energy generation)92
5.13Results of the sequential optimization model (objective function: minimize squared deviation of water supply from the demand)93
5.14Results of the iterative optimization model95
5.15Results of the compromise programming analysis performed on the results of iterative and sequential optimization approaches95
5.16Results of the three-composite-reservoir IDP model101
5.17Sensitivity analysis results of the three-composite-reservoir IDP model103
5.18Combinations of independent variables selected for regression analysis of the implicit stochastic approach105
5.19Summary comparison of performance of implicit SDP based operation with that of explicit SDP based operation, deterministic optimum, and historical operation106
5.20Comparison of the simulated performance of Victoria + Randenigala (V + R) composite reservoir with that of the real Victoria and Randenigala (V&R) two-reservoir system107
5.21Comparison of the results of the composite-policy-disaggregation approach108
6.1Average monthly evaporation from the Feitsui Reservoir115
6.2Maximum and minimum storages of the Feitsui Reservoir115
6.3Firm power generation requirement at the Feitsui Reservoir116
6.4Decision making under uncertainty119
6.5Summary of information for evaluating multiattribute utility function121
6.6Sensitivity analysis, the impact of initial storage (Typhoon Nelson, August 21–23, 1985)123

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