Optimal Operation of a Multiple Reservoir System

Author(s): Marino, Miguel A; Loaiciga, Hugo A | Abstract: This report presents a methodology to obtain optimal reservoir operation policies for a large-scale reservoir system. The model maximizes the system annual energy generation while satisfying constraints imposed on the operation of the reservoir network. The model incorporates the stochasticity of river flows and keeps future operating schedules up-to-date with the actual realization of those random variables. It yields medium-term (one-year ahead) optimal release policies that allow the planning of activities within the current water year, with the possibility of updating preplanned activities to account for uncertain events that affect the state of the system. The solution approach is a sequential dynamic decomposition algorithm that keeps computational requirements and dimensionality problems at low levels. The model is applied to a nine-reservoir portion of the California Central Valley Project and the results are compared with those from conventional operation methods currently in use, showing that the use of the model can improve the levels of energy production (about 30 percent increase) while the optimal release policies meet satisfactorily all other functions of the reservoir system. Sensitivity analysis is conducted to assess the optimality of the solutions and several alternative formulations of the model are developed and tested, the results showing the robustness of the optimal policies to the choice of model.

[1]  D. Jacobson.  Differential dynamic programming methods for solving bang-bang control problems , 1968 .

[2]  R. E. Larson,et al.  A dynamic programming successive approximations technique with convergence proofs , 1970 .

[3]  C. Revelle,et al.  The Linear Decision Rule in Reservoir Management and Design: 1, Development of the Stochastic Model , 1969 .

[4]  A. Turgeon.  Optimal operation of multireservoir power systems with stochastic inflows , 1980 .

[5]  Dan M. Fults,et al.  Optimum Operations Model for Shasta-Trinity System , 1972 .

[6]  D. M. Fults,et al.  A practical monthly optimum operations model , 1976 .

[7]  T. W. Anderson.  Repeated Measurements on Autoregressive Processes , 1978 .

[8]  M. Mariño,et al.  Reservoir management: A reliability programming approach , 1983 .

[9]  J. Mendel,et al.  Computational requirements for a discrete Kalman filter , 1971 .

[10]  Welby R. Madsen,et al.  Coordinated Operation of Central Valley and State Water Projects , 1974 .

[11]  D. G. Jamieson,et al.  River Dee Research Program: 3. A short‐term control strategy for multipurpose reservoir systems , 1972 .

[12]  U. Boscain,et al.  An Introduction to Optimal Control , .

[13]  A. Colorni,et al.  Reservoir management via reliability programing , 1976 .

[14]  R. Kalman,et al.  New results in linear prediction and filtering theory Trans. AMSE , 1961 .

[15]  Philip E. Gill,et al.  Newton-type methods for unconstrained and linearly constrained optimization , 1974, Math. Program..

[16]  Alston S. Householder,et al.  The Theory of Matrices in Numerical Analysis , 1964 .

[17]  William Anthony Thomas.  Hydrologic Engineering Methods for Water Resources Development. Volume 12. Sediment Transport. , 1977 .

[18]  Daniel Matthys Murray,et al.  DIFFERENTIAL DYNAMIC PROGRAMMING FOR THE EFFICIENT SOLUTION OF OPTIMAL CONTROL PROBLEMS , 1978 .

[19]  G. K. Young,et al.  Hydrologic estimation and economic regret , 1975 .

[20]  David J. Jaquette.  Efficient water use in California: Conjunctive management of ground and surface reservoirs , 1981 .

[21]  W. Yeh,et al.  Optimization of real time operation of a multiple-reservoir system , 1974 .

[22]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[23]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[24]  David A. Wismer,et al.  Introduction to nonlinear optimization , 1978 .

[25]  Averill M. Law,et al.  The art and theory of dynamic programming , 1977 .

[26]  Miguel A. Mariño,et al.  Reliability programing in reservoir management: 1. Single multipurpose reservoir , 1980 .

[27]  R. H. Hicks,et al.  Large Scale, Nonlinear Optimization of Energy Capability for the Pacific Northwest Hydroelectric System , 1974 .

[28]  P. Dorato,et al.  Optimal linear regulators: The discrete-time case , 1971 .

[29]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[30]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[31]  D. Joseph,et al.  On linear control theory , 1961, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[32]  L. Bodin,et al.  Multireservoir Operation Studies , 1970 .

[33]  André Turgeon.  Incremental dynamic programing may yield nonoptimal solutions , 1982 .

[34]  K. Takeuchi,et al.  Optimal control of multiunit interbasin water resource systems , 1974 .

[35]  S. Yakowitz,et al.  Constrained differential dynamic programming and its application to multireservoir control , 1979 .

[36]  Charles ReVelle,et al.  Linear Decision Rule in Reservoir Management and Design: 2. Performance Optimization , 1970 .

[37]  John Eastman,et al.  Linear decision rule in reservoir management and design: 3. Direct capacity determination and intraseasonal constraints , 1973 .

[38]  Miguel A. Mariño,et al.  Reservoir Operation: Choice of Objective Functions , 1984 .

[39]  Charles ReVelle,et al.  Linear decision rule in reservoir management and design: 4. A rule that minimizes output variance , 1975 .

[40]  W. Wonham.  Random differential equations in control theory , 1970 .