Title of Thesis

Optimal Control Of Multiple Reservoirs System Under Water Scarcity

Author(s)

 Iftikhar Ahmad

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.
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.

1

1.1 Background

1.2 Objectives of the Study
1.3 Research and Developments
1.4 Thesis Layout

2.1 Network Flow Programming

2.2 Deterministic Dynamic Programming
2.3 Stochastic Dynamic Programming
2.4 Linear Programming
2.5 Multiobjective Optimization
2.6 Other Techniques
2.7 River Basin System Optimization
2.8 River Water Disputes
2.9 Comparison of Methods
2.10 Previous Studies on the Indus Basin

3.1 Proposed Procedure

3.2 Formulating a Mathematical Model
3.3 Dynamic Programming
3.4 Deterministic Dynamic Programming (DDP)
3.5 Stochastic Dynamic Programming (SDP)
3.6 Stochastic Dynamic Programming (Formulation of the Model)
3.7 Recent Research Trend in Stochastic Optimization
3.8 Mathematical Statement of SDP / DDP Models
3.9 System Network Optimization
3.10 The Out-of-Kilter Algorithm
3.11 Introducing Uncertainty Analysis in Network Flow Optimization
3.12 Complete River Systems Operation Optimization Model
3.13 Contribution to the Research

4.1 Rivers in the System

4.2 Reservoirs/Dams of the Indus River
4.3 Hydrological and Other Data
4.4 Barrages in the System
4.6 Canals in the System
4.7 River Gains and Losses
4.8 Complete river basin multi reservoir system

5.1 General

5.2 Hydrological Data
5.3 Statistical Analysis of Annual Flows
5.4 Water Scarcity and Identification of Drought Periods
5.5 Statistical Analysis of 10 day Flows
5.6 Unconditional Probabilities
5.7 Serial Correlation Coefficients
5.8 Transition Probabilities
5.9 Hurst Phenomenon
5.10 Gould Transition Probability Matrix Method
5.11 Rippl Mass Curve Analysis
5.12 Sequent Peak Analysis
5.13 Evaporation Losses and Rainfall Accretion to Reservoirs
5.14 Characteristics of Hydro Electric Plants
5.15 Historic Operation of Reservoirs
5.16 Release Requirements and Operation Objective
5.17 Irrigation Demands
5.18 Power Demand
5.19 Stochastic Control of Reservoir Inflows

6.1 Background

6.2 Problem Formulation for Reservoir Operation Optimization
6.3 Problem Formulation for Multiple Objective Reservoirs

6.4 Model Calibration of Reservoir Operation Optimization

6.5 Model Verification of Reservoir Operation Optimization

6.6 Improved Strategies

7.1 Background

7.2 Suggested Approach
7.3 Problem Formulation for System Network Operation

7.4 Application of the Methodology to Indus River System

7.5 Improved Strategy

7.6 Comments

8.1 Background

8.2 Indus multi-reservoir system for conjunctive operation study
8.3 Model Calibration for Conjunctive Operation of Multi Reservoirs
8.4 Model Validation for Conjunctive Operation of Multi Reservoirs
8.5 Model Prediction for Conjunctive Operation of Multi-reservoir Simulation with Future Reservoirs

9.1 General

9.2 Reservoir Operation Model
9.3 Network Flow Model

9.4 Conjunctive Operation of Mutilple Reservoirs for future Scenarios

10.1 Conclusions

10.2. Recommendations

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