Ministry of Higher Education and Scientific Research University of Sulaimani College of Engineering Irrigation Engineering Department

SIMULATION - OPTIMIZATION MODEL FOR DOKAN RESERVOIR SYSTEM OPERATION

A Thesis Submitted to the College of Engineering of the University of Sulaimani in Partial Fulfilment of the Requirements for the Degree of Master in Science of Water Resources Engineering

By Luqman Sabir Othman BSc. Irrigation Engineering - 2012

April 2017 AD

Nawroz 2717 KR

Rajab 1438 AH

Ministry of Higher Education and Scientific Research University of Sulaimani College of Engineering Irrigation Engineering Department

SIMULATION - OPTIMIZATION MODEL FOR DOKAN RESERVOIR SYSTEM OPERATION A Thesis Submitted to the College of Engineering of the University of Sulaimani in Partial Fulfilment of the Requirements for the Degree of Master in Science of Water Resources Engineering By Luqman Sabir Othman BSc. Irrigation Engineering - 2012

Supervised By Dr. Hekmat M. Ibrahim

April 2017 AD

Nawroz 2717 KR

Rajab 1438 AH

Linguistic Certification This is to certify that Mr. Luqman Sabir Othman’s thesis entitled “Simulation-Optimization Model for Dokan Reservoir System Operation” has been proofread and the researcher has taken the proofreader’s comments and suggestions concerning grammatical errors to this final edition.

Signature: Proofreader: Shaho Burhan Abdalla Translation Department, School of Language, University of Sulaimani Date:

.12. 2016

Supervisor Certification I certify that the preparation of this thesis entitled “SimulationOptimization Model for Dokan Reservoir System Operation” was presented by (Luqman Sabir Othman) under my supervision at the Irrigation Engineering Department of the College of Engineering in the University of Sulaimani, as partial fulfilment of the requirements for the degree of Master in Science of Water Resources Engineering.

Signature: Supervisor: Dr. Hekmat M. Ibrahim Date:

/ 11 / 2017

In view of the available recommendation, I forward this thesis for debate by the Examining Committee.

Signature: Name: Asst. Prof. Dr. Amjad M. Ali Head of Postgraduate Studies Committee Date:

/ 11 / 2017

Examining Committee Certification We, as the Examining Committee, certify that we have read this thesis entitled “Simulation-Optimization Model for Dokan Reservoir System Operation” and examined the student (Luqman Sabir Othman) in its content and in what is connected with it and that in our opinion; it meets the standard of a thesis for the degree of Master in Science of Water Resources Engineering.

Signature:

Signature:

Name: Lecturer Dr. Hekmat M. Ibrahim

Name: Lecturer Dr. Haveen M. Rashid

Date:

Date:

/

/ 2017

/

Supervisor

/ 2017 Member

Signature:

Signature:

Name: Asst. Prof. Dr. Hussein D.

Name: Prof. Dr. Bashir T. Muhammed

Mohammed

Date:

Date:

/

/ 2017

/

/ 2017 Chairman

Member

Approved by the dean of the College of Engineering of the University of Sulaimani. Signature: Name: Asst. Prof. Dr. Asso Raouf Majeed Dean of College of Engineering Date:

/

/ 2017

‫ِب ْس ِم ل ّ‬ ‫الر ِح ِيم‬ ‫الر ْح لم ِن َّ‬ ‫َلاِ َّ‬

‫ْ‬ ‫ْ‬ ‫ُ‬ ‫َّ‬ ‫ي﴾‬ ‫ح‬ ‫ء‬ ‫ي‬ ‫ش‬ ‫ل‬ ‫ك‬ ‫اء‬ ‫م‬ ‫ال‬ ‫ن‬ ‫م‬ ‫لا‬ ‫ن‬ ‫ل‬ ‫ل‬ ‫ل‬ ‫ِ‬ ‫ِ‬ ‫ل‬ ‫﴿و لجعل‬ ‫ل‬ ‫ْ‬ ‫ّ‬ ‫ل‬ ‫)األنبياء‪(٣٠‬‬

Dedication

To my lovely parents, who provided me with encouragement and moral support throughout my study life. To my brother and sisters who supported me all the way through my pursuit of higher education. To all my friends who cared for me.

Luqman Sabir Othman, 2017

Acknowledgements

Acknowledgements First of all, I thank God for giving me this great opportunity and strength with guidance that aided in concluding this study, although it often seemed hard. Then, I would like to express my deepest gratitude and grateful acknowledgement to my supervisor, Dr. Hekmat M. Ibrahim for his continuous encouragement, advice, support, valuable guidance and help through writing this study. I would like to express my sincere gratitude to Dr. Kawa Zeidan and Dr. Nawbahar Mustafa the lecturers at the faculty of engineering in the university of Sulaimani that helped me by providing useful information and guidance during the writing of this thesis. Many thanks are also extended to Mr. Rizgar Karim and Mr. Karwan Ali the lecturers at Faculty of engineering in University of Sulaimani, who helped me a lot. I would like to acknowledge the staff members of all the Dokan dam, Koya irrigation and Kirkuk water resources directorates, for their appreciable support in providing me with hydrological data, all relevant data and information required. Thanks for all those who helped me in completing this research and staff of Irrigation Engineering Department in Faculty of Engineering / University of Sulaimani for their service. Finally, grateful acknowledgements are extended to my family, my parents and siblings for supporting me spiritually throughout my life.

[I]

Abstract

Abstract Reservoir operation system is the essential part of water resources management and each reservoir has a special policy for operation. Hence, it is necessary to employ a suitable plan for operating the reservoir. Simulation and optimization are two different techniques in the operating process of any reservoir. Therefore, this study aims to develop a combined simulationoptimization (S-O) model as a new technique in recent years to minimize the deficit in hydropower generation and irrigation demand for Dokan reservoir system in Kurdistan Region, Iraq. The model has been developed by combining Simulink and genetic algorithm (GA) as techniques for simulation and optimization respectively. For the purpose of comparison, by considering the operation constraints, three additional different models were developed. These models included traditional simulation model (Model-I) based on the standard operating policy (SOP) by using Simulink toolbox in MATLAB software and two different types of optimization models (Model-II-a and Model-II-b) by using nonlinear programming (NLP) and discrete differential dynamic programming (DDDP) optimization methods respectively. In the present study, three performance evaluation criteria; reliability, resiliency and vulnerability had been used for comparing and evaluating the performance of the developed models. The proposed models were run for a period of 54 years using monthly time step interval, i.e. 648 months starting from January 1958 to December 2011. The results reveal that the SOP model (Model-I) has dangerous deficit events in minimum downstream demands, although, it has a higher reliability in the irrigation demand (0.94). In addition, the other models; NLP (Model-II-a), DDDP (Model-II-b) and S-O (Model-III) by considering weight factors (𝑤1 = 0.2) and (𝑤2 = 0.8) almost have the same reliability, 0.90, 0.90 and 0.91 respectively. Furthermore, the results show a low resilience for NLP model (Model-II-a) and a high vulnerability for S-O model (Model-III) which causes higher severity of [ II ]

Abstract

failure events. Moreover, for the operation period from 1995 to 2011, the annual productions of hydropower by considering 𝑤1 = 0.8 and 𝑤2 = 0.2 are 1280 MW, 1339 MW, 1344 MW and 1296 MW by increasing of 24.9 %, 30.64 %, 31.16 % and 26.46 % more than the actual hydropower production (1025 MW) for SOP (Model-I), NLP (Model-II-a), DDDP (Model-II-b) and S-O (Model-III) models respectively. Finally, the conclusions present that the DDDP optimization model (ModelII-b) provides high reliability as well as more power generation. Also, the model can be more easily applied to solve the nonlinear and multi objective problems with less computational time.

[ III ]

List of Contents

List of Contents Title

Page

Acknowledgements ...............................................................................................I Abstract ............................................................................................................... II List of Contents.................................................................................................. IV List of Figures .................................................................................................. VII List of Tables....................................................................................................... X List of Abbreviations....................................................................................... XII List of Notations .............................................................................................XIII Chapter One......................................................................................................... 1 Introduction ..................................................................................................... 1 1.1 General ........................................................................................................ 1 1.2 Problem Definition ...................................................................................... 3 1.3 Study Objectives ......................................................................................... 4 1.4 Methodology ............................................................................................... 4 1.5 Thesis Structure ........................................................................................... 5 Chapter Two ........................................................................................................ 7 Literature Review ............................................................................................ 7 2.1 Introduction ................................................................................................. 7 2.2 Previous Operating Reservoir Systems Studies .......................................... 8 2.3 Previous Operating Dokan Reservoir System Studies .............................. 17 2.4 Summary ................................................................................................... 18 Chapter Three ................................................................................................... 20 Theoretical Background ............................................................................... 20 3.1 Introduction ............................................................................................... 20 3.2 Reservoir Operation .................................................................................. 20 3.2.1 Reservoir Operation Policy ................................................................ 21 3.2.2 Reservoir Storage Zones .................................................................... 21 3.2.3 Hydropower Rules ............................................................................. 22 3.3 Reservoir Simulation ................................................................................. 23 [ IV ]

List of Contents

3.3.1 Reservoir Simulation Model Components ......................................... 23 3.3.2 Simulink Toolbox of MATLAB Software ......................................... 23 3.3.3 Reservoir Simulation with Standard Operating Policy (SOP) ........... 24 3.4 Nonlinear Optimization Technique ........................................................... 26 3.4.1 Multi-Objective Optimization ............................................................ 26 3.4.2 Optimization Constraints ................................................................... 27 3.4.3 Optimization Toolbox of MATLAB Software .................................. 29 3.5 Dynamic Optimization Technique ............................................................ 29 3.5.1 Formulation of DP Model for a Single Reservoir .............................. 30 3.5.2 Discrete Differential Dynamic Programming (DDDP) ..................... 32 3.6 Combined Simulation-Optimization Approach ........................................ 35 3.6.1 General Steps of Simulation-Optimization ........................................ 38 3.6.2 Genetic Algorithm (GA) .................................................................... 38 3.7 Reservoir Operation Policy Performance Criteria .................................... 40 3.7.1 Reliability ........................................................................................... 41 3.7.2 Resilience ........................................................................................... 41 3.7.3 Vulnerability....................................................................................... 41 Chapter Four ..................................................................................................... 42 Methodology and Models Building .............................................................. 42 4.1 Introduction ............................................................................................... 42 4.2 Study Area Description ............................................................................. 43 4.3 Collection and Processing ......................................................................... 47 4.3.1 Inflow Time Series of Dokan Reservoir ............................................ 47 4.3.2 Testing for Outlier Data ..................................................................... 49 4.3.3 Downstream Water Demands ............................................................ 50 4.3.3.1 Water Supply ............................................................................... 50 4.3.3.2 Irrigation Water Demand ............................................................ 51 4.3.3.3 Environmental Flow Calculation for Reservoir Downstream .... 52 4.3.4 Storage-Elevation Relationships ........................................................ 54 4.3.5 Flood Control Operation Rule............................................................ 55 [V]

List of Contents

4.4 Hydropower Generation ............................................................................ 56 4.5 Reservoir Operation Constraints ............................................................... 57 4.6 Building the Models .................................................................................. 58 4.6.1 Model-I: Simulation Model................................................................ 58 4.6.2 Model–II: Optimization Models ........................................................ 63 4.6.2.1 Model–II-a: Nonlinear Programming Optimization Model........ 63 4.6.2.2 Model-II-b: Dynamic Programming Optimization Model ......... 66 4.6.3 Model-III: Combined Simulation-Optimization Model..................... 68 Chapter Five ...................................................................................................... 73 Results and Discussions ................................................................................ 73 5.1 Introduction ............................................................................................... 73 5.2 Developed Models..................................................................................... 73 5.3 Discharge Release for Downstream Demands .......................................... 75 5.3.1 Deficit in Downstream Demands ....................................................... 78 5.3.2 Performance Criteria of Reservoir System ........................................ 81 5.4 Hydropower Generation ............................................................................ 83 5.5 Reservoir Storage ...................................................................................... 90 5.6 Spillway Discharge ................................................................................... 92 5.7 Elevation of Reservoir Water .................................................................... 94 5.8 Sensitivity Analysis of Models ................................................................. 97 5.9 Selection of Best Model .......................................................................... 101 Chapter Six ...................................................................................................... 103 Conclusions and Recommendations .......................................................... 103 6.1 Introduction ............................................................................................. 103 6.2 Conclusions ............................................................................................. 103 6.3 Recommendations ................................................................................... 104 References ........................................................................................................ 106

[ VI ]

List of Figures

List of Figures Figure

Title

Page

Fig. (3-1): Schematic description of reservoir simulation with standard operating policy (Mujumdar & Vedula. , 2005) as cited in (Sharma, et al., 2014). ..................................................................... 25 Fig. (3-2): Schematic progress of DP computations in a forward algorithm (Fayaed, et al., 2013). ..................................................... 30 Fig. (3-3): Concepts description of corridor, corridor width, trial and optimal trajectory in DDDP (Heidari, et al., 1971). ....................... 33 Fig. (3-4): Sub-domain of discrete differential dynamic programming (DDDP) computations (Heidari, et al., 1971). ................................ 34 Fig. (3-5): Important methods of simulation optimization (S-O) (Carson & Maria, 1997)................................................................................ 36 Fig. (3-6): General framework of simulation-optimization modelling approach for reservoir operation (Fayaed, et al., 2013) ................. 37 Fig. (4-1): Location of the Dokan dam and reservoir on Lesser Zab river in Iraq (Google Earth, 2016). .......................................................... 44 Fig. (4-2): Monthly inflow discharges into Dokan reservoir for the period October, 1958 to September, 2011. ................................................ 48 Fig. (4-3): Flowchart of simulation with standard operating policy (SOP)............................................................................................... 60 Fig. (4-4): Simulink model layout based on the standard operation policy (SOP) for Dokan reservoir system. ................................................. 62 Fig. (4-5): Simulink model layout based on the optimized results of NLP optimization model for Dokan reservoir system. ........................... 65 Fig. (4-6): Simulink model layout based on the optimized results of DDDP optimization model for Dokan reservoir system. ............... 67 Fig. (4-7): Fitness values versus population size of GA for Dokan reservoir. ......................................................................................... 69

[ VII ]

List of Figures

Fig. (4-8): Fitness values versus number of generation of GA for Dokan reservoir. ......................................................................................... 69 Fig. (4-9): Fitness value for various crossover probability of GA for Dokan reservoir. .............................................................................. 70 Fig. (4-10): Flow chart of S-O model based on the genetic algorithm (GA). ............................................................................................... 71 Fig. (4-11): Simulink model layout based on combined simulationoptimization (S-O) model for Dokan reservoir system. ................. 72 Fig. (5-1): Convergence initial trial trajectory to optimal trajectory through optimization iterations of DDDP method. ........................ 74 Fig. (5-2): Models outputs of discharge release for Dokan reservoir during the period (1958-2011). ....................................................... 75 Fig. (5-3): Models outputs of discharge release for Dokan reservoir during the first year of operation (1958)......................................... 76 Fig. (5-4): Actual and models outputs of average monthly discharge release for Dokan reservoir. ............................................................ 77 Fig. (5-5): Monthly deficit in downstream demands of proposed models and actual operation for Dokan reservoir. ...................................... 79 Fig. (5-6): Monthly generated power of the proposed models for Dokan reservoir system during the period (1958-2011). ........................... 85 Fig. (5-7): Monthly generated power of the proposed models for Dokan reservoir system during the first year of operation (1958). ............ 85 Fig. (5-8): Average monthly power generation of the proposed models for Dokan reservoir system. ............................................................ 86 Fig. (5-9): Average monthly discharge releases through turbines of the proposed models for Dokan reservoir system. ............................... 89 Fig. (5-10): Monthly reservoir storages of the proposed models for Dokan reservoir system during the period (1958-2011)................. 92

[ VIII ]

List of Figures

Fig. (5-11): Monthly reservoir storages of the proposed models for Dokan reservoir system during the first year of operation (1958). ............................................................................................. 92 Fig. (5-12): Discharge releases through spillway of the proposed models for Dokan reservoir during the period (1958-2011). ...................... 93 Fig. (5-13): Monthly water surface elevation of the proposed models for Dokan reservoir system during the period (1958-2011)................. 95 Fig. (5-14): Average monthly water surface elevation of the proposed models for Dokan reservoir. ........................................................... 97 Fig. (5-15): Discharge releases of DDDP optimization model (Model-IIb) for Dokan reservoir system during the period (19582011). .............................................................................................. 99 Fig. (5-16): Discharge releases of simulation-optimization (S-O) model (Model-III) for Dokan reservoir system during the period (1958-2011)..................................................................................... 99 Fig. (5-17): Power generation of DDDP optimization model (Model-II-b) for Dokan reservoir system during the period (1958-2011). ........ 100 Fig. (5-18): Power generation of simulation-optimization (S-O) model (Model-III) for Dokan reservoir system during the period (1958-2011)................................................................................... 101

[ IX ]

List of Tables

List of Tables Table

Title

Page

Table (4-1): Characteristics of Dokan dam and reservoir (Dokan Dam Directorate, 2015). .......................................................................... 46 Table ( 4-2): Statistical parameters to determine high and low outlier data. ................................................................................................. 50 Table (4-3): Downstream water demands for different uses of Dokan reservoir. ......................................................................................... 53 Table (4-4): Storage-elevation relationship of Dokan reservoir. ........................ 54 Table (4-5): Flood control operation rule of Dokan reservoir. ........................... 55 Table (4-6): Descriptions of the Simulink blocks that used in the SOP Model building (Simulink Library Browser 2013)......................... 61 Table (5-1): characteristics of discharge releases for downstream demands in the proposed models. ................................................... 77 Table (5-2): Characteristics of deficit months in Dokan reservoir operation based on the proposed models and actual operation. ........................................................................................ 80 Table (5-3): Performance criteria of proposed models for downstream discharge release. ............................................................................ 82 Table (5-4): Characteristics of hydropower generation of the proposed models. ............................................................................................ 83 Table (5-5): Characteristics of monthly energy production of the proposed models. ............................................................................ 84 Table (5-6): Average monthly discharge releases through turbines of the proposed models for Dokan reservoir system. ............................... 87 Table (5-7): Characteristics of reservoir storage of the proposed models for Dokan reservoir. ........................................................................ 91 Table (5-8): Characteristics of uncontrolled releases through spillway of the proposed models. ...................................................................... 94

[X]

List of Tables

Table (5-9): Average monthly water surface elevation of the proposed models for Dokan reservoir. ........................................................... 96 Table (5-10): Characteristics and performance criteria of discharge releases based on variable and constant demand states. ................. 98 Table (5-11): Characteristics of power generation for variable and constant demand states.................................................................. 100

[ XI ]

List of Abbreviations

List of Abbreviations Abbreviation GA DP LP NLP SDP S-O SOP DDDP SLP IDP ARIMA DPFRB FRB MOEA SCE ANN IOSGA CE SE BSDP ARSP IPSO SLOP MOPSO MSI TF-log TTM MTTM MFM GUI LR USDA NRCS

Description Genetic Algorithm. Dynamic Programming. Linear Programming. Nonlinear Programming. Stochastic Dynamic Programming. Simulation-Optimization. Standard Operating Policy. Discrete Differential Dynamic Programming. Successive Linear Programming. Incremental Dynamic Programming. Auto Regressive Integrated Moving Average. Dynamic Programming Fuzzy Rule-Based. Fuzzy Rule-Based. Multi Objective Evolutionary Algorithm. Shuffled Complex Evolution. Artificial Neural Network. Integrated Optimization Simulation Genetic Algorithm. Coefficient of Efficiency. Standard Error. Bayesian Stochastic Dynamic Programming. Acres Reservoir Simulation Program. Improved Particle Swarm Optimization. Standard Linear Operating Policy. Multi-Objective Particle Swarm Optimization. Modified Shortage Index. Thomas-Fiering model with log transformation. Two-Tier Model. Modified Two-Tier Model. Modified Fragment Model. Graphical User Interface. Loss function of the Release. United States Department of Agriculture. Natural Resources Conservation Service. [ XII ]

List of Notations

List of Notations Notation

Description

𝑅(𝑡)

Release (Mm3/month) during the time 𝑡.

𝑂(𝑡)

Overflow discharge (Mm3/month) during the time 𝑡.

𝐷(𝑡)

Water demand (Mm3/month) during the time 𝑡.

𝑄(𝑡)

Inflow discharge (Mm3/month) during the time 𝑡.

𝑆(𝑡)

Storage (Mm3) at the beginning of time 𝑡.

𝑆(𝑡 + 1)

Storage (Mm3) at the end of time 𝑡.

𝑆𝑚𝑎𝑥(𝑡)

Maximum storage (Mm3) at time 𝑡.

𝐻𝑃(𝑡)

Hydropower generation (MW) at time 𝑡.

𝑃𝐶

Maximum power capacity of turbines (MW).

𝑆𝑚𝑖𝑛

Weight factors of objective functions and their values depend on the consideration of the decision maker. The maximum capacity of outlet turbines or maximum demand which is grater (Mm3/month). Minimum discharge release (Mm3/month) required for downstream demands. Minimum storage (Mm3) of reservoir.

𝐻𝑚𝑎𝑥

Maximum net head (m) of water above turbines.

𝐻𝑚𝑖𝑛

Minimum net head (m) of water above turbines.

𝐶𝑗

Corridor.

𝑆𝑖

State variables (Mm3).

𝐷𝑖

Control or decision variables (Mm3/month).

𝑟𝑖

Return variables.

𝐹𝑖 (𝑆𝑖 )

Optimal return at stage (𝑖).

𝐹𝑖−1 (𝑆𝑖−1 )

Optimal return from the previous stage (𝑖).

𝑆𝑖̅

Storage (Mm3) at the beginning of 𝑖 𝑡ℎ period.

𝑞𝑖

Inflow (Mm3/month) to the reservoir during the period 𝑖. Maximum deviation allowed from the initial trial trajectory or optimal trajectory of the last iteration.

𝑤1 , 𝑤2 𝑅𝑚𝑎𝑥 𝑅𝑚𝑖𝑛

∆s

[ XIII ]

List of Notations

𝑆𝑆𝑖

A set of admissible states of stage 𝑖.

𝐷𝐷𝑖

A set of admissible decisions at stage 𝑖.

𝐹𝑖∗

Optimal total of the return

𝛾, 𝜆

Convergence parameters

𝑅𝑒𝑙

Reliability index.

𝑅𝑒𝑠

Resilience.

𝑉𝑢𝑙

Vulnerability (Mm3).

𝑑(𝑗)

Duration of the 𝑗𝑡ℎ failure event (Month).

𝑀

Total number of failure events (Month).

𝑣(𝑗)

Deficit volume (Mm3) of the failure event.

𝐻𝑖

Average net head (m) above turbines at time 𝑖.

𝑅𝑖

Discharge release (Mm3/month) through turbines at time 𝑖.

𝐻𝑃𝑖

Hydropower generation (MW) at time 𝑖.

𝐾

Constant of hydropower equation.

γ

Specific weight of water (9810 N/m3).

𝑒

Overall efficiency.

𝑙𝑏

Bed level (m) of turbines.

𝑅𝑒

𝑦𝐻

Environmental flow (Mm3/month) requirement. Water supply (Mm3/month) requirement for domestic and industrial uses. High outlier threshold in log unit.

𝑦̅

Logarithmic mean of the series data.

𝑘0

Frequency factor for outlier detection.

𝑆𝑦

Logarithmic standard deviation.

𝑦𝐿

Low outlier threshold in log unit.

pm

Mutation probability.

𝑝𝑐

Crossover probability.

𝑅𝑤

[ XIV ]

CHAPTER ONE INTRODUCTION

Chapter One

Introduction

Chapter One Introduction 1.1 General The available fresh water resources around the world are becoming gradually scarce caused by increase of demands by municipal, industrial, recreational, and agricultural sectors. Most of these factors are made due to increase of population and higher standards of living in different areas, but also in part due to changes in land use and global climate change as a result of rapid development. Operative management of natural and water resources is becoming one of the most essential challenges of world time to resolve, for continuing and / or improving the living standards in the developed and developing countries. In addition, the relations between energy, water, food, and environmental subjects must be considered carefully in the growth of water management plans. Actually, the relationship between water and energy consumption appears to be a real issue that requires the attention of decision makers at all levels of governments and universal organizations. The water energy connection and associated stresses do not contribute to jurisdictional and political boundaries recognized nationally or globally, and hence requires multi-organizational / stakeholders’ solutions (Goodarzi, et al., 2014). One of the most important purposes of water resources development is produced of energy in many river–reservoir systems. Usually generated hydroelectric energy in water resource systems is done by changing the mechanical energy of falling water into electrical energy by a turbine and generator without actually consuming water (Karamouz, et al., 2003). This mechanism of energy production is a renewable and a clean power source which does not create any air or water pollution, which becomes hazards on environment and is one of the most efficient ways to produce electricity. Another advantage of hydropower over other forms of electricity generation is that reservoirs can store

[1]

Chapter One

Introduction

water during times of low demand and can quickly start generating during the peak hours of electricity use (Jain & Singh, 2003). From the aforementioned it is appeared that the reservoir operation system is the essential part of water resources management. Operation system of the reservoir includes allocating the available water for different sectors, whereas also reducing the risks of water deficiencies or flooding damage. It is usually accepted in a reservoir system that involves multiple purposes include water supply for irrigation, domestic use, industrial, hydropower generation, flood control, etc. Hence, the difficulties of a multipurpose reservoir system typically require decisions on water releases and generally to be specified by an optimization or simulation model. This provides operation strategies for reservoir releases according to the current reservoir level, water demands, hydrological conditions, and the time during the year. Most of the engineering problems have a number of possible solutions. Hence, it is necessary to estimate each alternative solution and then selected the best option from the point of view of interest, known as economic or suitability. Optimization is the science of choosing the best among a number of possible alternatives. Optimize of reservoir operation system by means of optimization techniques is not a new idea. Different methods have been implemented in an attempt to increase the efficiency of reservoir operation (Ngo, 2006). Some of these techniques utilize for optimization like Genetic Algorithms (GA); Dynamic Programming (DP); Linear Programming (LP); Nonlinear Programming (NLP); Stochastic Dynamic Programming (SDP); and Experimental Programming such as Fuzzy Logic, Neural Networks, etc. Despite, the development and increasing use of optimization methods, simulation models stay in practice as a prominent approach for reservoir operation planning and management studies (Rani & Moreira, 2010). Reservoir simulation models are generally based on continuity equation and demonstrate the hydrological behaviour of reservoir systems to know how the system will reply to conditions that may be performance on it or that may happen in the future, with [2]

Chapter One

Introduction

using inflow series, initial storage, downstream demands and other operating conditions as input data in simulation model. Simulation works is proper when there are only a relatively few numbers of good alternatives to be estimated. Trial and error process of simulation for a large number of possible alternatives expended more time (Loucks, et al., 2005). Optimization techniques can be used in order to decrease the number of alternatives in simulation. In this study, a Simulation-Optimization (S-O) model has been developed for minimizing the deficiency in production of hydropower and irrigation and other water demands within the operation system of Dokan reservoir. To achieve the goal of the study, the Standard Operation Policy (SOP) was used to build the simulation model and two different optimization methods, DDDP and NLP, were applied to develop the optimization models. Also, GA technique was utilized to construct the combined simulation-optimization model for operation of Dokan reservoir. 1.2 Problem Definition Storing of water in lakes and reservoirs by construction a dam across the river is developed with evolving of countries in order to utilize the storage water for the different purpose such as agriculture, industrial, domestic uses, etc. and decreasing the disaster of flooding. Besides, production of hydroelectric power is an important role of many reservoirs without actually consuming water. Dokan reservoir is one of the large dams created on the little Zab river in Iraq. Furthermore, it is one of the sources to generate electrical power to the provinces of Kurdistan Region / Iraq and particularly to the province of Sulaimani. Current operation of this reservoir is not based on appropriate plan and it is sometimes causes deficit in downstream demands and decreases the production of hydropower. Therefore, it is necessary to employ a suitable plan for the system of reservoir operation, to give the optimum results that satisfy the downstream demand constraints of the reservoir and at the same time feeding maximum electrical power. For this purpose, the present study proposes the appropriate [3]

Chapter One

Introduction

simulation and optimization model for the operating system of Dokan reservoir that increase the production of electrical power and decrease the deficit of water required for irrigation and other uses in the downstream of the reservoir. 1.3 Study Objectives Dokan reservoir is the primary source of water for irrigation, drinking water and power generation for a number of towns and cities in Iraq, particularly in Sulaimani and Kirkuk provinces. Therefore, this study aims to develop several simulation, optimization and simulation-optimization models for operating Dokan reservoir in an optimal form. The study objectives can be summarized as follows: 1. To derive an optimal operation policy for distributing the amount of allocated water to all downstream demands (agricultural, domestic, industrial, and environmental) with regard to minimizing water deficit. 2. To increase the hydropower generation of Dokan reservoir more than the actual production. 3. Filling the main gap in the application of combined simulation-optimization for reservoir operation optimizing in Iraq, especially for Dokan reservoir. 4. Comparing the results of the applied models and determining the powerful technique to optimize and simulate reservoir operation. 1.4 Methodology The present study is an attempt towards the development of a mechanism for dealing with the operation problems in the Dokan reservoir system. Generally, the methodology of carrying out this study can be summarized as follows: 1. Data collection which includes gathering all the data and information that required for building the models such as inflow discharge time series, water requirements for downstream demands (water supply, irrigation, power generation and environmental flow) characteristics of Dokan reservoir and power station …etc. Most of these data are obtained from the directorate of Dokan dam and the directorate of irrigation in Kirkuk and Koya cities.

[4]

Chapter One

Introduction

2. Developing traditional simulation model for operation of Dokan reservoir depending on the available data and proposing a suitable mechanism for managing and operating the reservoir system to minimize the deficit in hydropower generation of the reservoir. 3. Developing traditional optimization models for optimal operation of Dokan reservoir depending on the available data. Two models have been developed based on the non-linear and dynamic optimization techniques. 4. Developing simulation-optimization model based on the genetic algorithm technique for operation of Dokan reservoir and proposing a suitable mechanism for managing and operating the reservoir system. 1.5 Thesis Structure The present thesis is organized into six chapters. In chapter two, some important of the previous works that have been done in the simulation and optimization field of reservoir operation are reviewed. The works include the application of standard operation policy, discrete differential dynamic programming, nonlinear programming and genetic algorithm for setting up the optimization and combined simulation-optimization models for reservoir operating policy. Moreover, the conclusions drawn from the literature review are presented at the end of this chapter. Theoretical background and methodology of simulation and optimization models building are accessible in chapter three. Procedures of optimization methods by DDDP, NLP and GA are presented with determination of the constraints of the optimization problem. Also, simulation processes by SOP and general descriptions of MATLAB software toolboxes (Simulink, Optimization) are provided in this chapter. Subsequently, the main works are presented in chapter four. Descriptions of the study area, characteristics of Dokan dam with reservoir and application of the developed models using the available data for reservoir operation are presented in this chapter. Four models have been developed in this chapter and these models [5]

Chapter One

Introduction

are: one traditional simulation model (SOP), two optimization models (DDDP, NLP) and one combined simulation-optimization model (S-O). In chapter five, discussion of the results obtained from the application of proposed models and comparison between the results of applied models with selection of the best model for reservoir operation are included. Finally, conclusions of all results that obtained in this study and recommendations for future works are demonstrated in chapter six.

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CHAPTER TWO LITERATURE REVIEW

Chapter Two

Literature Review

Chapter Two Literature Review 2.1 Introduction Increasing water demands, higher standards of living, growing population, climate variability, and water resource limitations have caused conflicting issues among water consumers and put stress on existing water resources across the world. Therefore, proper management of water resources and providing comprehensive programs to optimize available water supplies play an important role in satisfying existing demands. A reservoir is a natural or artificial lake to storage water; it keeps the water level at a controlled level, and releases it regularly to supply downstream requirements. Constructing dams to create reservoir and storing water allows distribution at the right time in downstream districts. The most important applications of reservoirs are: flood control, agricultural and environmental water supply, domestic and industrial water supply, hydroelectric power generation, and recreational activities. Reservoirs have significant roles in water resource engineering in which their proper design, construction and maintenance contribute considerably toward fulfilling water supply requirements and minimizing the risk of water shortages (Goodarzi, et al., 2014). There are large amounts of published material dealing with optimization and simulation of reservoirs, all of which cannot be reviewed here. However, this chapter reviews some of the previous works, which are done for simulation, optimization and combined simulation–optimization modeling for reservoir system operation. Moreover, it displays the ability of techniques were applied in these studies, to take the perspective for the future researchers about these techniques to choose the appropriate approach. To facilitate the object of optimization and simulation of reservoir operation, this review is organized in a convenient manner such that the reader can easily follow what kinds of works

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Chapter Two

Literature Review

concerning reservoir operation are being done and what sort of gaps still exist in the application for Dokan reservoir such that one could contribute to this important topic. Accordingly, in the next section, some most important contributions of historical interest will be cited. 2.2 Previous Operating Reservoir Systems Studies System analysis models that were used to optimize reservoir operation may be categorized as: simulation models; optimization models; and combination of simulation and optimization models. Simulation models are effective tools for studying the operation of complex physical and hydrological characteristics of a reservoir system including the experience and judgment of operators. However, since they are limited to predicting the performance of a reservoir for a given operation policy, optimization models have an advantage in being able to search for the optimum policy from an infinite number of feasible operation policies that are defined through decision variables (Ngo, 2006). Simulation should be the starting point in the planning of large scale systems but in view of the very large number of options of configuration, capacity and operating policy, simulation without preliminary screening through optimization would be very time consuming (Rani & Moreira, 2010). Here are several main previous studies, which have considered the issue of this study earlier by using the simulation, optimization and simulationoptimization techniques for operating of reservoirs over 30 years. (Karamouz & Houck, 1982) proposed deterministic dynamic programming to generate reservoir system operating rules and tested in 48 cases. Annual and monthly operating rules are developed for 12 and 36 cases respectively. The results of using the algorithm for the 48 cases show the ability of the algorithm in selecting reservoir operating rules. (Datta & Houck, 1984) generated a model for use a real-time daily operation based on a chance constraint formulation and assumes a particular form of the linear decision rule. It uses the conditional distribution function (CDF) of actual stream flows conditioned on the forecasted values. The objective of the operation [8]

Chapter Two

Literature Review

is to minimize the sum of penalties associated with deviation from target or ideal condition for operation over a time horizon of several days to a month. The model was shown to be extendable to a system of reservoirs and the restrictions generally associated with the linear decision rules were shown to be invalid for this model. (Grygier & Stedinger, 1985) employed a model to optimize the operation of multi-reservoir hydro-systems by using successive linear programming (SLP), optimal control algorithm and combination of linear programming with dynamic programming (LP-DP). The algorithm maximizes the value of energy generated at on-peak and off-peak rates, plus the evaluated value of water remaining in storage at the end of 12-month planning period. The results presented that the LPDP algorithm takes longer to find a solution and yields significantly less hydro power than other procedures. Moreover, successive linear programming easily finds the global maximum and the optimal control algorithm for simple systems gets the optimal solution faster than SLP, but is harder to implement. (Bayazit & Duranyildiz, 1987) used dynamic programming (DP) for optimizing the long-term operation of real-world reservoir systems. The results showed that the operation system for a large number of reservoirs cannot be optimized by classical DP due to excessive time consuming. To solve the problem, they suggested incremental dynamic programming (IDP) which is especially convenient for systems of complex configuration that cannot be optimized with other iterative methods due to very slow convergence. (Vedula & Mohan, 1990) presented a real-time operational policy for multi objective reservoir operation for irrigation and hydropower generation with application to the Bhadra reservoir system in the state of Karnataka, India. The system involves three stages of computer modeling. In the first stage, the optimal release for a given initial storage and inflow is obtained by using a stochastic dynamic programming (SDP) model. Stream flow forecasting using an adaptive auto regressive integrated moving average (ARIMA) model constitutes the second stage. Finally, in the third stage, a real-time simulation model is developed based on the forecast inflows of stage two and the operating policy of stage one. In the [9]

Chapter Two

Literature Review

results of their study, two potential reservoir operating policies were recognized for the reservoir system and these policies produce a substantial increase of 52% - 57% per year in power production. (U.S Army Corps of Engineers, 1991) published a report that reviews the modeling and analysis approaches for optimization of multiple purpose reservoir system operations. Also, the report summarizes fundamentals of reservoir operation practices and procedures. The report was concluding that the reservoir operations policy changed especially between regions of the country, water management agencies and even between individual reservoirs operated by the same agency in the same river basin. (Wurbs, 1993) collected and arranged a wide range of computer models for estimating reservoir operations under the basis of selecting modeling and analysis method for a specific application depending upon the characteristics of the application. According to state of author this paper is useful for the engineers and water managers to better understand which tools might be most beneficial for their particular reservoir-system analysis applications. (Oliveira & Loucks, 1997) constituted a model to derive the operating policies for multi-reservoir by applying genetic search algorithm. The genetic algorithm uses real-valued vectors containing information needed to define both system release and individual reservoir storage volume targets as functions of total storage in each of multiple within-year periods. The suggested algorithm is applied to example reservoir systems used for water supply and hydropower. They proposed that the genetic algorithm may be a practical and robust way of estimating operating policies for such systems. (Panigrahi & Mujumdar, 2000) applied fuzzy rule system to construct a base model for the single objective Malaprabha irrigation reservoir in Karnataka, India. The model functions based on an ‘if – then’ principle, where the ‘if’ is a vector of fuzzy premises and the ‘then’ is a vector of fuzzy consequences. Reservoir storage, inflow, and demands are used as input variables and the release is output. Moreover, they indicated that the fuzzy rule based on reservoir operation is a [ 10 ]

Chapter Two

Literature Review

simple method because it is eliminating difficult optimization procedures, and linguistic statements such as ‘low inflow’ ‘poor rainfall’ etc., may be instant integrated. (Mousavi, et al., 2005) used dynamic programming fuzzy rule–based (DPFRB) model to get the optimal operation of reservoirs system. Deterministic dynamic programming (DP) model is used to develop the optimal set of inflows, storage volumes, and reservoir releases and then optimal values are used as inputs to a fuzzy rule–based (FRB) model to evaluate the general operating policies. Subsequently, the operating policies are estimated in a simulation model which is robust against the uncertainty of inflows. The results of the study demonstrated that the DPFRB performs well in terms of satisfying the system target performances and computational requirements. (Reddy & Kumar, 2006) used a multi objective evolutionary algorithm (MOEA) to obtain a set of optimal operation policies for a multipurpose realistic reservoir system, namely Bhadra reservoir system, in India. The reservoir is used for irrigation, hydropower generation and serves the downstream water quality requirements. The main objective in multipurpose optimization is to get a number of well distributed optimal solutions along the Pareto front. From the study outcomes, the ability and usefulness of MOEAs for evolving multi-objective reservoir operation policies were appeared. (Ngo, et al., 2007) used optimization techniques to optimize the operation of Hoa-Binh reservoir in Red river basin, Vietnam, by applying of optimization and simulation together with considering hydropower production and downstream flood control. The shuffled complex evolution(SCE) algorithm in the AUTOCAL software was designated for optimization and the problem put focus on the tradeoff between short-term hydropower and flood risk objectives and long-term penalties in terms of aberrations from the optimized rule curves. The results of the study showed that the optimized rule curves significantly improve the reservoir performance to hydropower generation without decreasing the downstream safety

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Chapter Two

Literature Review

opposite flooding. Furthermore, the results displayed that the SCE algorithm is an efficient tool for optimizing complex systems. (Azamathulla, et al., 2008) investigated the growth and compared two models, genetic algorithm (GA) and linear programming (LP), which are practical to real time reservoir operation in an existing chiller reservoir system in Madhya Pradesh, India. They approved that the GA model is more efficient than the LP model and the developed GA model could be applied to more complex problems with little difficulty. (Dhar & Datta, 2008) developed a linked simulation–optimization method to take the optimal operation policy of the reservoir to regulate the downstream water quality requirements, by constructing simulation model and then connecting externally with an optimization algorithm. An elitist genetic algorithm is used as the optimization algorithm and the combined simulation–optimization approach considers a single objective of operation, i.e. minimization of deviation from target storage. The method includes the non-linear relationship between reservoir release and downstream water quality. The solution results obtained are also confirmed by solving the water quality simulation model using the given optimal release rates. (Rani & Moreira, 2010)reviewed the previous articles in which describes simulation, optimization and combined simulation-optimization modelling together and gave an overview of their applications reported in literature. From this survey revealed that in recent years the researchers tried to develop new optimization methodologies, such as using evolutionary algorithms, ANN and fuzzy modelling for optimization of reservoir systems operation. The investigation is outlined, which could be useful for future research and for system administrators to decide a suitable method for application to their systems. (Younis, 2011) applied the technique of discrete differential dynamic programming (DDDP), to take the optimal policy for monthly operation of Mosul dam for 35 years’ time interval in order to minimize the total penalties taken place caused by both releases and storage when exceeded the allowable limit, and find [ 12 ]

Chapter Two

Literature Review

the suitable probability distribution of the values of storage. Then outcomes achieved the lognormal distribution with two parameters was found to be the best distribution to demonstrate the operation curves values. (Younis, et al., 2010) used the discrete differential dynamic programming (DDDP) to find the present and future optimal monthly Mosul reservoir operation policies for the years (2007, 2017, and 2027) in order to satisfy the irrigation requirements of Jazira Irrigation Project and water supply requirements according to different operation states. The results showed that the water deficit existence with the second and third states. For optimization model, the water deficits were distributed over long periods, which aided to minimize the penalty, and the reservoir storages were within the upper and lower operating storage limits. (Zahraie & Hosseini, 2010) constructed a model by integrated optimizationsimulation based on genetic algorithm model (IOSGA) to give the operational policies for the multipurpose Zayandeh-Rud river reservoir system, in central part of Iran. The objective function of the optimization model is considered to be a linear function of reliability (Rel), resiliency (Res), and vulnerability (Vul) of the river reservoir system. For optimization model the genetic algorithm (GA) were used, in which the parameters of reservoir operation policy equations are considered as decision variables. These parameters are expressed in the form of fuzzy numbers to be able to control the variations in releases and in water demands. The results of the study indicated that the developed algorithm can significantly decrease the time and costs of modeling efforts and the run time of the GA model and also improve the general performance of the system in terms of Rel, Res, and maximum vulnerability (VulMax) and the coefficient of efficiency (CE) and standard error (SE). (Al-Taiee, 2011) used the genetic algorithm (GA) to find optimal daily operating rule curve for storage of the Mosul regulating reservoir in Iraq. The objective function is set to minimize the annual sum of squared deviation from the desired downstream release and desired storage volume in the reservoir. Comparing the results of GA model with the actual rule curve and the designed [ 13 ]

Chapter Two

Literature Review

rating curve of the reservoir showed a good agreement and displayed that GAderived policies are promising, competitive and can be successfully used for daily reservoir operation. (Ziaei, et al., 2012) developed combined optimization and simulation models to determine monthly operating rules for the Zayandeh Rud reservoir system in Iran. For this purpose, they used LINGO program to get optimal operation and HEC-ResSim software for modeling of the reservoir. The study results demonstrated that optimizing the operation of Zayandeh Rud reservoir could increase its storage by 88.9% and increase the reliability index of regulated water for all downstream demands by over 10%. Also, the results revealed that the applied methods can efficiently optimize the rule curves for operating the current reservoir in a single-objective framework. (Mythili, et al., 2013) described different approaches for optimizing the reservoir operation to allocate the reservoir water in a proper way for different purposes. The study includes stochastic dynamic programming model for hydroelectric power generation, system dynamic approach model for optimizing the flood control, chance constrained goal programming model for optimizing the multipurpose reservoir, Bayesian stochastic dynamic programming (BSDP) model for optimizing the inflow and storage and finally implicit stochastic model for reservoir yield operation. (Fayaed, et al., 2013) provided an overview of simulation and optimization modeling techniques, which consumed in resolving critical issues with respect to reservoir systems. Optimization methods have shown high efficiency when used with simulation modeling and the combination of the two approaches had given the best results in the reservoir management. Their purpose of this review is to evaluate and analyze the simulation, optimization and combined simulation optimization modeling methods and then to take the perspective for future researchers, system analysts and managers to gain more precise optimal operational system. Also, they suggested, and applied an integrate PSDP-ANN

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Chapter Two

Literature Review

model for reservoir operation, particularly, reservoir system simulation and optimization in order to reach more reliable and robust model. (Taghian, et al., 2014) established a hybrid model for optimizing the conventional rule curves combined with hedging rules to minimize the effects of droughts. To create this model, they used simulation and nested optimization model together, which is developed by incorporating a simple genetic algorithm to the acres reservoir simulation program (ARSP) model. Final results displayed that the coupling of conventional rule curves to hedging rules could improve the operational performance in comparison to applying the rule curve alone. (Fang, et al., 2014) suggested a new rule for storage allocation by considering the target storage curves. Also, they proposed a joint operating rule to improve the operation problems of a multi reservoir system with combined demands and water transfer supply projects. A simulation-optimization model was generated to optimize the strategic points of the water diversion curves, the hedging rule curves and the target storage curves utilizing the improved particle swarm optimization (IPSO) algorithm. They concluded that the proposed joint operating rules can lead to a desirable performance in comparison to other rules and the storage distribution rule based on target storage curves is more operative than the compensation regulation rule. (Devisree & Nowshaja, 2014) applied genetic algorithms (GA) and linear programming (LP) for optimization of multi objective reservoir operation to maximize annual power production and irrigation demands. The study showed the ability of GA as an effective optimization tool for multi objective reservoir operation optimization and the results of GA and LP solution are very close. (Thankachan & B., 2015) utilized standard linear operation policy (SLOP) to achieve an optimal operation plan for the reservoirs in Kuttiadi river basin in India using systems approach. The system had taken as a case study consists of three reservoirs namely; Banasurasagar in Wayanad district, Kakkayam and Peruvannamuzhi in Kozhikode region. The Banasurasagar and Peruvannamuzhi reservoirs always serve the purposes of water supply without occurring water [ 15 ]

Chapter Two

Literature Review

shortage. For Banasurasagar reservoir, irrigation and water supply dependability is found to be 86% while for Peruvanannamuzhi reservoir, it is 77%. The study found that, by utilizing the method, the demand for power generation can be met with 90% reliability and the spill of the reservoir for the rule curve based operation policy for the three reservoirs can be reduced. (Galo, 2015) built three simulation models for operating Bekhma reservoir system on the Great Zab river, Kurdistan Region, Iraq and applied to the period of 1932 to 2004. The study developed the models by using HEC-ReSim software (Model-I), Simulink (Model-II) and Simulink Technique with Fuzzy Logic Controller (Model-III) in MATLAB software. The main objective of this reservoir is generating hydropower. The average monthly river flow discharges are recorded, which have been used in the models for maximizing the hydropower generation. The outcomes of the study revealed that the Model-I and Model-II nearly produce the same average amount of hydropower, whereas the model that integrating the fuzzy logic system (Model-III) had generated the hydropower by an amount of 8.51% more than the two other models. (Ahmadianfar, et al., 2016) attempted to improve the conventional hedging rule to control the changes of rationing factors. Therefore, the combination of a simple fuzzy logic concept with the conventional hedging rule has been suggested to increase the rationing factors flexibility and improves the system operation during severe drought periods. The simulation model was optimized by considering a multi-objective particle swarm optimization (MOPSO) algorithm and for this case Zohre multi-reservoir system chosen for the test of the proposed rule, which is located in Sothern Iran. In the study, the optimization objective had been taken as the minimum of two objectives involving minimum flow of water supply and agriculture demands using modified shortage index (MSI). The solutions of the proposed hedging rule displayed long term and annual MSI values have considerably improved compared to the conventional hedging rule. They concluded that the proposed method is promising and efficient to decrease the water shortage problem. [ 16 ]

Chapter Two

Literature Review

2.3 Previous Operating Dokan Reservoir System Studies Each reservoir has special characteristics according to purposes of construction for supply downstream water demands and geographical information of it. Therefore, for a particular reservoir, it is necessary to use the operating rules which are appropriate to the system of reservoir operation. Here some available previous studies that carried out to simulate and optimize the operation of Dokan reservoir in Kurdistan Region, Iraq. (Rashid, et al., 2007) developed an explicit stochastic optimization model for Dokan reservoir in Kurdistan Region, Iraq. The model was based on dynamic programming, for long-term operation of a large hydropower reservoir, to improve the efficiency of hydroelectric power generation and tradeoff with other conflicting project uses and purposes. The optimal decisions obtained from the study allow to trace several optimal storage guide curves, which are useful to assist decision maker in current operation. (Younis & Thanoon, 2008) found the best optimal daily management and operation policy for Dokan reservoir, by using discrete differential dynamic programming (DDDP) at minimum levels of inflow discharge during the period of 30 years (1965-1995) for maximizing the hydropower generation. The results of the study are compared with the other researches that applied to Dokan reservoir for the same purpose. Results indicated that the total annual hydroelectric power generation for the case under investigation is 1073 MW, i.e., an increase of 93 MW above the monthly operation of 980 MW. Besides, the results revealed that the number of trials required to get the optimal management in the daily operation between 70 and 90 trials, while the trials for optimal management in the case of monthly operation are between 35 and 70. (Ahmed, et al., 2013) developed two models for optimization and simulation the maximum safe (firm) yield for the single reservoir system with permissible deficit. The Dokan reservoir in Kurdistan Region, Iraq was considered as the case study. Linear programming (LP) was used to create the models in which one of them was a full optimization (complete model), and the other was a simplified [ 17 ]

Chapter Two

Literature Review

optimization (yield model). Concluded of the full optimization model provides more accurate representation of system behavior than the yield model because during each year the within-year time period chosen is sufficiently small (month) along the length of the data being analyzed. (Al-Masudi, 2013) estimated the reliability of Dokan reservoir by applying two procedures of capacity-yield and using data generation techniques. These techniques are the probability matrix (Gould) procedure, and the behavior analysis. In the study, vulnerability and resilience, are also measured in the second procedure. The data that used in the study is generated by handling four approaches, namely, Thomas-Fiering model with log-transformation (TF-log), Two-Tier model (TTM), modified Two-Tier model (MTTM) and modified Fragment model (MFM). The data of these models are tested and compared with the historical data. The study concluded that among these four procedures the Thomas-Fiering model with log is the best for generating monthly inflows to Dokan reservoir. 2.4 Summary From all the reviewed published studies and researches in the previous section, the followings can be concluded: 1. Many different types of optimization techniques are used to optimize the reservoirs operation. The techniques, mostly, are dynamic programming, nonlinear programming, linear programming, genetic algorithm, …, etc. 2. Selecting optimization techniques usually changes according to the types of objective functions, linear or nonlinear, single or multi objective and constraints of the system. 3. Moreover, the ability of techniques used to optimize the operation policy of reservoirs varies according to sort of objective function and constraints (linear or nonlinear). 4.

Many different types of approaches are used for simulation of the reservoirs operation.

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Chapter Two

Literature Review

5. Some objectives in reservoir operation system can be optimized (minimize or maximize) such as hydropower generation, discharge releases, deficiency, …, etc. according to the objectives of reservoir. 6. Several computer software are used to simulate reservoir operation like HECReSim, Simulink toolbox, Excel, MIKE, …, etc. 7. Combined simulation-optimization is a new technique has a rapid development in recent years and the most significant simulation technology according to different author. Therefore, the present study focuses on developing models to minimize the deficit in hydropower generation and downstream water demands for Dokan reservoir, by considering constraints to satisfy the minimum water quality requirements, water supply for cities, towns and districts and irrigation water demands in Sulaimani and Kirkuk governorates in Iraq. To optimize the operation system of Dokan reservoir, the combined simulation-optimization model using genetic algorithm (GA) has been investigated. Because the power production is a function of the discharge release through turbines and hydraulic head of water in the reservoir, the objective function and constraints with elevation-storage relationship are nonlinear.

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CHAPTER THREE THEORETICAL BACKGROUND

Chapter Three

Theoretical Background

Chapter Three Theoretical Background 3.1 Introduction Reservoir operation is a significant part in water resource systems. It involves some control variables that explain the operation policies for guiding a sequence of releases to meet numerous demands from different objectives, such as flood control, hydropower generation and distribution of water to different users. Optimization is the technique used to choose the optimum (maximize or minimize) value among different alternatives, with considering constraints of the system. Optimization tells us what we should do – what the best decision is – that solution is often based on many limiting assumptions. On the other hand, simulation is a process duplicates system’s behaviour to better understanding of it, and any proposed plan for system can be tested through simulation before implemented. Simulation simply addresses ‘what-if’ scenarios – what may occur if a specific scenario is assumed or if a particular decision is made (Loucks, et al., 2005). This chapter provides the basic and principle theories related to the elements of reservoir simulation, optimization and combined simulation-optimization modelling, including data and information processing, objectives, constraints identification, and the details of the modelling process are described in the next sections. 3.2 Reservoir Operation Reservoir operation is a composite problem that includes many decision variables. Conventionally, reservoir operation is based on heuristic procedures, involving rule curves and subjective judgments by the operator. This provides general operation strategies for reservoir release according to the current reservoir level, hydrological conditions, water demands and the time of the year. Reservoir is the most important element of a water resources development system and assists

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Chapter Three

Theoretical Background

in arrangement natural stream-flow thereby adjusting the temporal and spatial availability of water according to human requirements (Al-Taiee, 2011). The water stored can be used for irrigation, domestic and industrial requirements and hydroelectric power production. Rules for operation of a reservoir have to be developed in the planning stage of a project. Later on, these are refined on the basis of real operational skill. For a multi objective reservoir, it is also necessary to optimally distribute the release among purposes. The difficulty of the problem of reservoir operation depends on the range to which the various intended purposes are compatible. Some basic elements of the reservoir operation system are described in the following sections. 3.2.1 Reservoir Operation Policy Each reservoir has a mechanism for operation in which the operating rule curves consist of several control variables, which depend on them for guiding releases to meet the different demands, such as flood control, irrigation demands, hydropower generation and allocate of water for different users. Release from reservoir depending on the level of water in the reservoir, if the elevation of water in the reservoir above the guide curve, then the release will increase to draw down the elevation of water, if the elevation of water in the reservoir below the guide curve, then the release must be decreased to refill the reservoir. For reservoir operation system, the inflow discharge and evaporation rate are required as input variables and the release is required as the output variable. A major difficulty in the operation of reservoirs is the often conflicting and unequal objectives. Therefore, it is necessary to optimize reservoir operation in determining balanced solutions between the conflicting objectives (Ngo, 2006). 3.2.2 Reservoir Storage Zones Total capacity of the reservoir can be distributed into three main parts, which are: active storage, dead storage, and flood control storage. The volume of water between dead and flood control storage is active storage of the reservoir that is used for various purposes of downstream requirements. In other words, it is the

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Chapter Three

Theoretical Background

volume between minimum and normal water levels. Normal water level is the maximum elevation of a reservoir during normal operation. For many reservoirs, the normal water level is the elevation of spillway crest, and the minimum water level is the lowest elevation of the reservoir during normal operation and may be fixed by elevation of the lowest outlet or minimum head required for hydropower generation. Dead storage is the volume of water must be remaining in the reservoir for the purpose of navigation and sediment of the reservoir. While flood control storage is the volume of water between normal water level and maximum water level in the reservoir, when the water level rises above normal operation, this excess storage is surcharge storage and is normally uncontrolled to protect the dam against flooding (Karamouz, et al., 2003). 3.2.3 Hydropower Rules Generated hydropower depends on the discharge which released for turbines and hydraulic head of water. Hydropower rules determine the minimum discharge required to operate the turbines which are working in a specified range of the water head. Therefore, it should be keep the head of water in the reservoir in a high level to increase the production of power. Storage power plants can produce more energy through a relatively high head and less variable discharge (Karamouz, et al., 2003). The power capacity of a hydropower plant is mainly the function of the hydraulic head and discharge release through the turbines. The hydraulic head is the elevation difference the water falls in passing through the plant or to the tail water, whichever elevation difference is less. Project design may focus on either of these variables or both, and on the hydropower plant’s installed capacity. The production of hydroelectric energy during any period at any specific reservoir site is dependent on the installed plant capacity; the flow through the turbines; the average effective productive storage head; the number of hours in the period; the plant factor (the fraction of time that energy is produced); and a constant for

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Chapter Three

Theoretical Background

converting the product of flow, head and plant efficiency to electrical energy (Loucks, et al., 2005). 3.3 Reservoir Simulation Simulation is the process to represent the system behaviour to better understanding of it. Proposed an operating policy for the system can be tested through simulation before applied in real location. When analysing complex systems, the physical model and the mathematical description are difficult, that no solution algorithm can be developed. In many of these cases, no mathematical model is even available, then the only choice to be used is the simulation of the model (Karamouz, et al., 2003). Reservoir simulation contains the continuity (mass balance) equation of reservoir inflows, outflows, and storage fluctuations. Simulation applied when there are only a relatively a small number of alternatives to be evaluated (Loucks, et al., 2005). 3.3.1 Reservoir Simulation Model Components The main components of the reservoir simulation model include inputs, physical relationships and constraints, operating rules, and outputs. Inputs in reservoir simulation are reservoir inflow discharge, evaporation rate, and downstream demands, etc. The relationships and constraints component describe the relationships of physical variables of the system which include reservoir storage-elevation-area relationships, storage continuity relationships, etc. The operating rules consist of release policies and rule curves that explain the operation of the system while the outputs are results of system response from operating the system following known or specified rules and constraints such as the reservoir release for irrigation, hydropower, etc. (Galo, 2015). 3.3.2 Simulink Toolbox of MATLAB Software MATLAB software is a high-level language and interactive environment for numerical computation, visualization, and programming. According to (Goodarzi, et al., 2014) MATLAB or Matrix Laboratory is a robust program it can be [ 23 ]

Chapter Three

Theoretical Background

implemented to construct models and develop different algorithms to solve simple or complex problems. In addition, the applications of MATLAB cover a vast range of areas including; civil engineering, mechanical engineering, signal processing and communications, modeling and simulation, etc. Simulink toolbox in MATLAB is a platform for modelling, simulating, analysing, and dynamical systems. It supports linear and nonlinear systems. This tool is a graphical user interface (GUI) for construction models as block diagrams by using click-and-mouse operations for modelling. This is the main feature of Simulink tool that differs from pervious simulation packages that required formulation of differential equations and difference equation in a language or program (Galo, 2015). Simulink toolbox contains a comprehensive block library of sinks, sources, linear and nonlinear components and connectors that enable customized block to be created. Simulation results can be seen in display blocks during running model, as well as the parameters can be changed to see the effects directly. Output of simulation can be put in the MATLAB workspace for post processing and visualizing. 3.3.3 Reservoir Simulation with Standard Operating Policy (SOP) Standard operating policy (SOP) aims to best meet the demand in each period based on the water availability in that period and it is not based on or derived from any optimization algorithm. According to this rule, if the total water available at a specific period is less than the demand, then all the available water is released. If the available water is more than the demand, however, less than the sum of demand and maximum storage capacity, then release is equal to the demand. On the other hand, if the available storage after meeting the demands exceeds the maximum storage capacity, excess water is released as spill from the reservoir (Mujumdar & Vedula. , 2005) as cited in (Sharma, et al., 2014). Fig. (3-1) shows schematically the description of reservoir simulation with standard operating policy. The figure can be represented as follow: •

Along OA: Release = water available; reservoir will be at minimum storage after release. [ 24 ]

Chapter Three

•

Theoretical Background

Along AB: Release = demand (𝐷); excess water is stored in the reservoir (filling phase).

•

At point A: Reservoir is at minimum storage (𝑆𝑚𝑖𝑛 ) after release.

•

At point B: Reservoir is at full storage (𝑆𝑚𝑎𝑥 ) after release.

•

Along BC: Release = demand + excess of availability over the capacity (spill).

Fig. (3-1): Schematic description of reservoir simulation with standard operating policy (Mujumdar & Vedula. , 2005) as cited in (Sharma, et al., 2014). The values of release, overflow discharge, and storage are determined as follow: 𝑅(𝑡) = 𝐷(𝑡) 𝑖𝑓 𝑆(𝑡) − 𝑆𝑚𝑖𝑛 + 𝑄(𝑡) ≥ 𝐷(𝑡) } 𝑅(𝑡) = 𝑆(𝑡) − 𝑆𝑚𝑖𝑛 + 𝑄(𝑡) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(3-1)

𝑂(𝑡) = (𝑆(𝑡) + 𝑄(𝑡) − 𝐷(𝑡)) − 𝑆𝑚𝑎𝑥 (𝑡) 𝑂(𝑡) = 0

(3-2)

𝑆(𝑡 + 1) = 𝑆(𝑡) + 𝑄(𝑡) − 𝐷(𝑡)

𝑖𝑓 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 } 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(3-3)

Where: 𝑅(𝑡): release during the time 𝑡. [ 25 ]

Chapter Three

Theoretical Background

𝑂(𝑡): overflow discharge during the time 𝑡. 𝐷(𝑡): water demand during the time 𝑡. 𝑄(𝑡): inflow discharge during the time 𝑡. 𝑆(𝑡): storage at the beginning of time 𝑡. 𝑆(𝑡 + 1): storage at the end of time 𝑡. 𝑆𝑚𝑖𝑛 (𝑡): minimum storage at time 𝑡. 𝑆𝑚𝑎𝑥 (𝑡): maximum storage at time 𝑡. 3.4 Nonlinear Optimization Technique Nonlinearity exists in various reservoir system operation problems due to complex relationships among different physical and hydrological variables or because of specific objectives being served by system. Such problems are generally solved by approximating a nonlinear problem to a linear problem or by successive application of linear programming (LP). Besides, dynamic programming can also tackle nonlinearities. However, nonlinear programming (NLP) techniques are used to solve such class of problems (Rani & Moreira, 2010). In nonlinear optimization, an objective function or some of the constraints are nonlinear. Therefore, obtaining the optimal solution is more difficult than the linear programming. For example, normally, hydropower generation problems, reservoir water surface area versus storage relationships and evaporation calculations are nonlinear and pose difficulties in obtaining their solutions (U.S Army Corps of Engineers, 1991). 3.4.1 Multi-Objective Optimization Multi-objective optimization problems represent an important class of realworld optimization problems such as the multipurpose reservoir, which mainly serves hydropower and irrigation as key purposes (Reddy & Kumar, 2006). As mentioned earlier, the main objective of this study is to minimize the deficit in hydropower generation and irrigation demand of Dokan reservoir. By considering the water supply and irrigation demands and water quality constraints, general objective function can be expressed as follows: [ 26 ]

Chapter Three

Theoretical Background 𝑛 2

2

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ (𝑤1 (𝑃𝐶 − 𝐻𝑃(𝑡)) + 𝑤2 (𝐷(𝑡) − 𝑅(𝑡)) )

(3-4)

𝑡=1

Where: 𝐻𝑃(𝑡): hydropower generation (MW) at time 𝑡. 𝐷(𝑡): downstream demand discharge (Mm3/month) at time 𝑡. 𝑅(𝑡): discharge release (Mm3/month) at time 𝑡. 𝑃𝐶: maximum power capacity of turbines (MW). 𝑤1 , 𝑤2 : weight factor for each objective function and their values depend on the consideration of the decision maker. 3.4.2 Optimization Constraints In the optimization of reservoir system operation, there are several constraints which represent limitations on the behaviour and performance of the system. Hereafter, brief descriptions of the constraints that found in the optimization of reservoir system operation: a. Reservoir continuity equation Water balance in the reservoir must be preserved in all stages of optimization. The reservoir continuity equation is considered as the main constraint in this case. Note that in the mass balance as shown in equation (3-3), any losses due to evaporation or seepage have been neglected for Dokan reservoir because the inflows data are obtained by operation balance, and thus the losses are implicitly included. b. Release constraints Release from the reservoir must be less than or equal to the downstream demands, while these demands equal to sum of irrigation, water supply and other demands (municipal, industrial, and hydropower generation), which can be written as: 𝑅𝑚𝑖𝑛 ≤ 𝑅(𝑡) ≤ 𝑅𝑚𝑎𝑥

(3-5)

Where 𝑅𝑚𝑖𝑛 (60 Mm3/month) is the minimum discharge release required for downstream demands and 𝑅𝑚𝑎𝑥 is the maximum capacity of outlet turbines (1218 [ 27 ]

Chapter Three

Theoretical Background

Mm3/month) or maximum demand when it is greater than the capacity of outlet turbines. c. Storage constraints Reservoir storage for any time period should not be greater than the maximum capacity of reservoir and less than dead storage of reservoir and expressed as: 𝑆𝑚𝑖𝑛 ≤ 𝑆(𝑡) ≤ 𝑆𝑚𝑎𝑥 (𝑡)

(3-6)

Where 𝑆𝑚𝑖𝑛 (1400 Mm3) is the minimum storage of reservoir and 𝑆𝑚𝑎𝑥 (𝑡) is the maximum capacity of reservoir at time 𝑡. d. Overflow constraints The overflow constraint takes care of the spills as and when the storage in the reservoir exceeds the maximum capacity of the reservoir. The relevant constraint can be expressed as shown in equation (3-2). e. Head constraints Power plants work in a specified range of water elevation in the reservoir; therefore, the level of water in the reservoir should remain below maximum and above minimum water elevation and its written as: 𝐻𝑚𝑖𝑛 ≤ 𝐻(𝑡) ≤ 𝐻𝑚𝑎𝑥

(3-7)

Where 𝐻𝑚𝑖𝑛 (63 m) and 𝐻𝑚𝑎𝑥 (95 m) are the minimum and maximum net head of water respectively, that can be operate the turbines. f. Hydropower constraints Hydropower must be generated according to the demand in that period and should not be greater than the maximum required of hydropower (capacity of turbines) and this constraint written as: 𝐻𝑃(𝑡) ≤ 𝐻𝑃𝑚𝑎𝑥

(3-8)

In which 𝐻𝑃𝑚𝑎𝑥 (400 MW) is the maximum capacity of turbines that installed in the reservoir hydropower station.

[ 28 ]

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Theoretical Background

3.4.3 Optimization Toolbox of MATLAB Software The Optimization toolbox in MATLAB software is a powerful optimization platform that uses well known algorithms to solve wide ranges of constrained and unconstrained optimization problems (Goodarzi, et al., 2014). The optimization toolbox provides functions for finding parameters that minimize or maximize objective functions while satisfying constraints. Furthermore, it includes solvers for linear programming, mixed-integer linear programming, quadratic programming, nonlinear optimization, and nonlinear least squares. These solvers can be used to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications. For nonlinear optimization model that developed in this study, the solver (𝑓𝑚𝑖𝑛𝑐𝑜𝑛) in optimization toolbox of MATLAB software has been used. 3.5 Dynamic Optimization Technique Dynamic programming (DP) was first introduced by Richard Bellman in 1957 as an optimization procedure for solving multistage decision processes. The most appealing feature of DP algorithm which results in its successful application to reservoir systems optimization is that, a complex multistage problem is decomposed into a series of simple sub problems, which are solved recursively one at a time and that nonlinear problems as well as problems involving stochastic variables may be readily accommodated in the general framework of DP (Rani & Moreira, 2010). The dynamic programming can be represented by the following components (Chow & Rivera, 1974): a. State variables (𝑺𝒊 ): state variable is a set of variables including all the information about the condition of a system at a specific stage and transports information about changing this condition from one stage to the next. For a reservoir operation system, state variable is the volume of water stored in the reservoir at a stage. b. Stage (𝒊): stage is a particular period (point) in a system and most commonly time (monthly, daily, etc.) is the stage which produces the decisions about the system. [ 29 ]

Chapter Three

Theoretical Background

c. Control or decision variables (𝑫𝒊 ): control or decision variables are variables that expressing the controls implemented at a certain stage and convert the state of the system. In the operation of a reservoir system the release of water discharge is considered as a control variable. d. Return variables (𝒓𝒊 ): return variables are scalar variables that measure the total return obtained in each stage; they are a function of decision (𝐷𝑖 ) and state (𝑆𝑖 ) variables, that is: 𝑟𝑖 = 𝑟𝑖 (𝑆𝑖 , 𝐷𝑖 )

𝑖 = 1, 2, … , 𝑁

(3-9)

In which 𝑁 is the total number of stages (648). e. Stage transformation (𝒕𝒊 ): stage transformation is a transformation that expressing each component of the output states (𝑆𝑖−1 ) as a function of the input state (𝑆𝑖 ) and decision (𝐷𝑖 ) corresponding to the stage (𝑖) as shown in Fig. (3-2), that is: 𝑆𝑖−1 = 𝑡𝑖 (𝑆𝑖 , 𝐷𝑖 )

𝑖 = 1, 2, … , 𝑁

(3-10)

Fig. (3-2): Schematic progress of DP computations in a forward algorithm (Fayaed, et al., 2013).

3.5.1 Formulation of DP Model for a Single Reservoir Optimization of multipurpose single reservoir operation is subject to the following requirement: [ 30 ]

Chapter Three

Theoretical Background

a. Objective function: the recursion equation of dynamic programming may be written as: 𝐹𝑖 (𝑆𝑖 ) = 𝑚𝑖𝑛 𝑄𝑖 (𝑆𝑖 , 𝐷𝑖 )

𝑖 = 1, 2, … , 𝑁

(3-11)

𝑄𝑖 (𝑆𝑖 , 𝐷𝑖 ) = 𝑟𝑖 (𝑆𝑖 , 𝐷𝑖 )

𝑖=1

(3-12)

𝑄𝑖 (𝑆𝑖 , 𝐷𝑖 ) = 𝑟𝑖 (𝑆𝑖 , 𝐷𝑖 ) + 𝐹𝑖−1 (𝑆𝑖−1 )

(3-13)

𝑆𝑖−1 = 𝑡𝑖 (𝑆𝑖 , 𝐷𝑖 )

(3-14)

𝑖 = 2, 3, … , 𝑁

Where: 𝐹𝑖 (𝑆𝑖 ): optimal return at stage (𝑖). 𝐹𝑖−1 (𝑆𝑖−1 ): optimal return from the previous stage (𝑖). b. Release constraints: the reservoir release (𝑅𝑖 ) during any particular period should be in the range of feasible releases: 𝑅𝑖 ≤ 𝑆𝑖̅ + 𝑞𝑖 − 𝑆𝑚𝑖𝑛 𝑅𝑚𝑖𝑛 ≤ 𝑅𝑖 ≤ 𝑅𝑚𝑎𝑥

(3-15) 𝑖 = 1, 2, … , 𝑁

(3-16)

Where: 𝑅𝑚𝑎𝑥 : the maximum allowable release during any period. 𝑅𝑚𝑖𝑛 : the minimum allowable release during any period. 𝑆𝑖̅ : the storage at the beginning of 𝑖 𝑡ℎ period. 𝑞𝑖 : the inflow to the reservoir during any period. c. Storage constraint: the storage at the beginning of first period (initial storage) should be a known quantity and for other periods, storage must be less than and greater than maximum and minimum reservoir capacity respectively and expressed as follow: 𝑆𝑚𝑖𝑛 ≤ 𝑆𝑖 ≤ 𝑆𝑚𝑎𝑥 𝑖 = 2, 3, … , 𝑁 or } 𝑆𝑚𝑖𝑛 ≤ 𝑆𝑖 ≤ 𝑚𝑖𝑛 ( 𝑆𝑚𝑎𝑥 , 𝑆𝑖̅ + 𝑞𝑖 − 𝑅𝑚𝑖𝑛 )

(3-17)

d. Continuity equation (mass balance equation): this equation is used to calculate the storage at the end of each period (𝑆𝑖 ) and expressed as: 𝑆𝑖 = (𝑆𝑖̅ + 𝑞𝑖 − 𝑅𝑖 ) ≤ 𝑆𝑚𝑎𝑥

(3-18)

[ 31 ]

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Theoretical Background

Assume the storage at the beginning of (𝑖 + 1)𝑡ℎ period equal to the storage at the end of (𝑖 𝑡ℎ ) period and then: ̅ = 𝑆𝑖 = 𝑆𝑖̅ + 𝑞𝑖 − 𝑅𝑖 𝑆𝑖+1

𝑖 = 1, 2, … , 𝑁

(3-19)

The following steps are the procedure used to solve the DP recursive equation: 1. Starting with 𝑖 = 1, 𝑟𝑖 (𝑆𝑖 , 𝐷𝑖 ) is calculated and then 𝐹𝑖 (𝑆𝑖 ) is obtained by using equation (3-12) and (3-11), all values of 𝐹𝑖 (𝑆𝑖 ) and 𝐷𝑖 (𝑆𝑖 ) are then stored. 2. Assuming 𝑖 = 𝑖 + 1, 𝑟𝑖 (𝑆𝑖 , 𝐷𝑖 ) is calculated and 𝐹𝑖 (𝑆𝑖 ) is obtained from equation (3-13) and (3-11), all values of 𝐹𝑖 (𝑆𝑖 ) and 𝐷𝑖 (𝑆𝑖 ) are then stored. The values of 𝐹𝑖−1 (𝑆𝑖 ) then can be discarded. 3. Step 2 is repeated for 𝑖 = 3, 4, … , 𝑁 until 𝐹𝑁 (𝑆𝑁 ) is obtained. 4. At stage 𝑖 = 𝑁, the optimal state 𝑆𝑁∗ is found by obtaining the optimal return from the 𝑁 stage system, 𝐹𝑁 (𝑆𝑁∗ ), using the following equation: 𝐹𝑁 (𝑆𝑁∗ ) = 𝑚𝑖𝑛 𝐹𝑁 (𝑆𝑁 )

(3-20)

and the optimal decision is computed from: 𝐷𝑁∗ = 𝐷𝑁 (𝑆𝑁∗ )

(3-21)

5. Both the optimal state, 𝑆𝑖∗ (𝑖 = 𝑁 − 1, 𝑁 − 2, … , 1) and the optimal decision 𝐷𝑖∗ (𝑖 = 𝑁 − 1, 𝑁 − 2, … , 1) are calculated by the following equations: ∗ ∗ 𝑆𝑖∗ = 𝑡𝑖+1 (𝑆𝑖+1 , 𝐷𝑖+1 )

(3-22)

𝐷𝑖∗ = 𝐷𝑖 (𝑆𝑖∗ )

(3-23)

𝑖 = 𝑁 − 1, 𝑁 − 2, … , 1

3.5.2 Discrete Differential Dynamic Programming (DDDP) The discrete differential dynamic programming (DDDP) was used as the program for optimization of reservoir operation by (Heidari, et al., 1971). The DDDP uses the concept of increments for state variables in an iterative procedure by which the DP recursive equation may be solved within a restricted set of quantized values of the state variables. It has all the required characteristics of the [ 32 ]

Chapter Three

Theoretical Background

conventional dynamic programming computational procedure and it is necessary less computational time requirements. In order to understand and formulate the discrete differential dynamic programming (DDDP), (Chow & Rivera, 1974) were explained the following terms as shown in Fig. (3-3): 1. Corridor: is the collection of restricted quantized values of the state variables at all the stages. The composition of corridors changes from one iteration to the next in such a way as to obtain convergence of the algorithm toward the optimal solution for the entire set of quantized values of the state variables. 2. Trajectory: is the path of the iterations through a corridor. Trajectory is either initial trial or optimal: a. Initial trial trajectory: it is the series of transformation of the state vector throughout the entire period 𝑁 of system analysis. It is feasible if satisfies all constrained imposed on the system. The initial trajectory is the first approximation of the optimal trajectory. b. Optimal trajectory: it is the trajectory which takes the optimal solution of the system inside the corridor.

Fig. (3-3): Concepts description of corridor, corridor width, trial and optimal trajectory in DDDP (Heidari, et al., 1971). Trial trajectory in DDDP method is the series of feasible state vector (𝑆𝑖 ) which satisfying equation (3-22) determines the decision vector (𝐷𝑖 ) called the trial policy which satisfies equation (3-23). The total return caused by trial [ 33 ]

Chapter Three

Theoretical Background

trajectory and policy from each stage within the corridor can be computed by introducing the value of an admissible state vector (𝑆𝑖 ) and decision vector (𝐷𝑖 ) in to dynamic programming recursive equation. The value of state sub-domain (𝑆𝑖 ) is calculated by adding a set of incremental (∆𝑠(𝑘, 𝑖)) to the state vector (𝑆𝑖̅ ) of the initial trial trajectory or optimal trajectory of the last iteration as shown in Fig. (3-4), that is: 𝑆𝑖 = 𝑆𝑖̅ + ∆𝑠(𝑘 , 𝑖)

𝑖 = 1,2, … , 𝑁

𝑘 = 1, 2, …

(3-24)

In which 𝑘 is the total number of assumed increments and ∆s is the maximum deviation allowed from the initial trial trajectory or optimal trajectory of the last iteration. It should be noted that one value of ∆𝑠(𝑘, 𝑖) must be zero since the trial trajectory is always in the sub-domain (Heidari, et al., 1971). There must be at least 3 increments ∆𝑠(𝑘, 𝑖), one of which must be equal to zero, the second less than zero and the third must be greater than zero.

Fig. (3-4): Sub-domain of discrete differential dynamic programming (DDDP) computations (Heidari, et al., 1971).

[ 34 ]

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Theoretical Background

The following steps are the procedure used in the discrete differential dynamic programming (DDDP) computations: 1. Choose the initial trial trajectory 𝑆𝑖̅ , (𝑖 = 1, 2, … , 𝑁) and these state vector must satisfy the following equations: 𝑆𝑖 ∈ 𝑆𝑆𝑖

(3-25)

𝐷𝑖 ∈ 𝐷𝐷𝑖

(3-26)

Where 𝑆𝑆𝑖 is a set of admissible states of stage 𝑖 and 𝐷𝐷𝑖 is a set of admissible decisions at stage 𝑖. 2. Select the maximum deviate (∆𝑠) allowed from the initial trial trajectory, to define the corridor (𝐶𝑗 ), then the state sub-domain (𝑆𝑖 ) becomes: 𝑆𝑖̅ + ∆𝑠(𝑖) (3-27) 𝑆𝑖 = { 𝑆𝑖̅ 𝑆𝑖̅ − ∆𝑠(𝑖) Use only state sub-domain in the next step which satisfy equations (3-25) and (3-26). 3. Use state sub-domain (𝑆𝑖 ) to find the optimal total of the return (𝐹𝑖∗ ) in corridor by using the DP recursive equation (3-11), then compute the optimal trajectory (𝑆𝑖∗ ). ∗ 4. Let 𝐹𝑖−1 = 𝐹𝑖∗ and 𝑆𝑖 = 𝑆𝑖∗ then repeat step (2) and (3). ∗ ∗ 5. If ((𝐹𝑖∗ − 𝐹𝑖−1 ) > 𝜆) then go to step (4) or if ((𝐹𝑖∗ − 𝐹𝑖−1 ) < 𝜆 and if ∗ (∆𝑠⁄𝑆𝑚𝑎𝑥 ) > 𝛾 then ∆𝑠 = ∆𝑠/2 and go back to step (4). If (𝐹𝑖∗ − 𝐹𝑖−1 )≤𝜆

and if (∆𝑠⁄𝑆𝑚𝑎𝑥 ) ≤ 𝛾 then stop iteration. Where 𝜆 and 𝛾 are the convergence parameters and have been used as 𝛾 = 0.1 and 𝜆 = 0.001 (Chow & Rivera, 1974). 3.6 Combined Simulation-Optimization Approach Some system analysis models are used to determine optimum operation for reservoirs such as simulation models, optimization models, and hybrid of simulation and optimization models. Simulation-optimization can be defined as the process of finding the best input variable values from among all possibilities [ 35 ]

Chapter Three

Theoretical Background

without explicitly evaluating each possibility (Carson & Maria, 1997). According to different authors, simulation-optimization is the most significant simulation technology in the last years. Recently, there has been a rapid development of simulation-optimization. There are lots of methods suggested for simulation optimization. The major simulation optimization methods are displayed in Fig. (3-5). The Heuristic methods represent the latest developments in the field of direct search methods (requiring only function values) frequently used for simulation optimization. The heuristic search algorithms provide good and reasonably fast results on a wide variety of problems. Authors mention at least a few important heuristic algorithms. These include genetic algorithms, evolutionary strategies, simulated annealing, simplex search and tabu search (Carson & Maria, 1997). Therefore, in the present study, genetic algorithm was used for optimization in the combined simulation optimization model.

Gradient Based Search Methods

Finite Difference Estimation Perturbation Analysis (PA)

Stochastic Optimization

Response Surface Methodology Simulation Optimization Methods

Likelihood Ratio Estimators (LR) Frequency Domain Experemints (FDE) Genetic Algorithm (GA) Tabu Search (TS)

Heuristic Methods

Evolutionary Strategies (ES) Simulated Annealing (SA)

A-Teams Importance Sampling Statistical Methods

Multiple Comparison Ranking and Selection

Fig. (3-5): Important methods of simulation optimization (S-O) (Carson & Maria, 1997). [ 36 ]

Chapter Three

Theoretical Background

According to state, for water resources planning and management, it is a lot of time useful to use together optimization and simulation modeling. Simulation without optimization required extra time to simulate the model due to the availability of a large number of possible alternatives. Therefore, it is necessary to use optimization approach not as a way to find the best solution, but to define a relatively small number of good alternatives that can later be tested, evaluated, and improved by means of simulation. Process of using optimization to decrease the large number of plans and policies to a few that can then be simulated and better evaluated is often called preliminary screening (Loucks, et al., 2005). Fig. (3-6) shows the general framework of simulation-optimization modeling approach for reservoir system operation.

Fig. (3-6): General framework of simulation-optimization modelling approach for reservoir operation (Fayaed, et al., 2013) .

[ 37 ]

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Theoretical Background

3.6.1 General Steps of Simulation-Optimization Simulation-optimization generally works as the following steps which are described in (Waller, 2006) as cited in (Hrcka, et al., 2014): 1. An initial set of parameter values is selected and one or more replication experiment is carried out with these values. 2. The results are obtained from the simulation runs and then the optimization module chooses another parameter set to try. 3. The new values are set and the next experiment set is run. 4. Steps 2 and 3 are repeated until either the algorithm is stopped manually or a set of defined finishing conditions are met. 3.6.2 Genetic Algorithm (GA) Genetic algorithms are random or probable optimization search methods used to determine the optimum values of the parameters or decision-variables of existing models (Loucks, et al., 2005). This algorithm contains several iterations of the operation in each iteration (generation) creates populations that tend to obtain better results. The genetic algorithm process can end when there is no significant change in the values of the best solution that has been found. Usually, the genetic algorithm (GA) requires the following three heuristic processes (Montaseri, et al., 2015): a. Random reproduction: the algorithm begins its search through a certain initial random point, known as population. Any member of the population that defines a solution for a given problem is called a chromosome. Chromosomes develop in iterations (generation). In genetic algorithm, a chromosome consists of several genes that change the parental features to the children. b. Crossover: the crossover operator constitutes one or more chromosomes of parents to generate their children. Also, it is the most significant genetic operator. Evolutionary operators such as roulette wheel and selection process can be noted as the rule of parental selection for construction of next generation’s population. According to this rule, each chromosome, based on

[ 38 ]

Chapter Three

Theoretical Background

its fitness function value, distributes a particular surface area of the roulette wheel. c. Mutation: the mutation operator can produce random changes in one or more genes in one or more chromosomes. The fitness of each string is often estimated based on the objective functions and the constraints. A usual way is to add a penalty term to the objective function if any chromosome becomes not feasible by violating one or more constraints. Pairs of chromosomes are made randomly, and they are then subjected to certain genetic manipulations that change the genes in the parent chromosomes. A typical procedure is the crossover, which swaps a part of the genetic information contained in the two chromosomes. Usually a substring portion is designated randomly in the chromosomes, and the genes within that substring are replaced. In this manner, new offspring are generated to exchange the parent chromosomes. There is no guarantee that the new pairs of chromosomes will be better than the parent chromosomes. To overcome this problem, mutations are allowed to occur which reverse one or more genes in a chromosome (Karamouz, et al., 2003). This algorithm guides a population towards an optimal point, trying to get a set of solutions that either maximizes or minimizes the value of objective function of those solution values. A number of populations of solutions may take better results of the objective function, others may not. In each generation, the best result of all populations of solutions should be kept. The ones that develop its value play a greater role in the generation of new populations of solutions than those that do not. All different set of solutions includes the values of all the parameters or variables whose optimum results are being sought. These solutions are expressed as strings of values. The genetic algorithm process includes the following steps (Melanie, 1999): 1. Start with a randomly generated population of chromosomes (candidate solutions to a problem).

[ 39 ]

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Theoretical Background

2. Evaluate the fitness of each chromosome in the population by calculate the value of objective function. 3. Choose a pair of parent chromosomes from the existing population, the probability of selection being an increasing function of fitness. Selection is done "with replacement," meaning that the same chromosome can be selected more than once to become a parent. 4. Cross over the pair at a randomly selected point (chosen with uniform probability) to produce two offspring. If no crossover takes place, form two offspring that are exact copies of their respective parents. 5. Mutate the two offspring at each locus with probability (the mutation probability or mutation rate), and place the resulting chromosomes in the new population. 6. Replace the current population with the new population. 7. Repeat steps 2-6 until the number of generations is met or convergence criteria is satisfied. 8. Solution (Best Chromosomes). 3.7 Reservoir Operation Policy Performance Criteria One of the most significant stage in simulation and optimization model building of reservoir operation is evaluating the reservoir operation policy performance. The performance criteria or indices that aid the planner to classify the status of a system as satisfactory or unsatisfactory outputs should be defined. While, suitable descriptions for the performance indices depend on the problem and objectives of planning, some basic concepts are similar. Also, assessing the performance of an evaluating system is the final step in the application of simulation and optimization models for river–reservoir systems planning and management (Karamouz, et al., 2003). There are three main criteria that used for evaluating the performance of reservoir operation systems and also useful to evaluate and rank different alternative plans or policies. These criteria are reliability, resilience, and vulnerability as described below: [ 40 ]

Chapter Three

Theoretical Background

3.7.1 Reliability Reliability index (𝑅𝑒𝑙) is the best indicator which defined as the probability that the system output is satisfactory or the probability that the system will not fail in a given period (Ziaei, et al., 2012). Reliability can also be defined as the probability of providing a specific percentage of water for demand in the given time period (Hashimoto, et al., 1982). In the present study, time reliability expressed as percent value of the months in which deficit is less than predefined threshold (20%). The reliability index for examining the reservoir operation system performance is calculated as follow: 𝑅𝑒𝑙 =

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑛𝑡ℎ𝑠 𝑤𝑖𝑡ℎ 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑠𝑢𝑝𝑝𝑙𝑦 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑛𝑡ℎ𝑠

(3-28)

3.7.2 Resilience Resilience (𝑅𝑒𝑠) describes how quickly a system is likely to recover or bounce back from failure, once failure has occurred (Hashimoto, et al., 1982). According to state (Kjeldsen & Rosbjerg, 2004) resilience is equal to the inverse of the mean value of the time that the system spends in an unsatisfactory state as shown below: 𝑀

𝑅𝑒𝑠 = [

−1

1 ∑ 𝑑(𝑗)] 𝑀

(3-29)

𝑗=1

In which, 𝑑(𝑗) is the duration of the 𝑗𝑡ℎ failure event and 𝑀 is the total number of failure events. 3.7.3 Vulnerability Vulnerability (𝑉𝑢𝑙) is defined as the severity of failure event and was simplified by (Kjeldsen & Rosbjerg, 2004) as the mean value of the deficit events. It is given as: 𝑀

1 𝑉𝑢𝑙 = ∑ 𝑣(𝑗) 𝑀

(3-30)

𝑗=1

Where 𝑣(𝑗) represents the deficit volume of the failure event.

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CHAPTER FOUR METHODOLOGY AND MODELS BUILDING

Chapter Four

Methodology and Models Building

Chapter Four Methodology and Models Building 4.1 Introduction Each reservoir has a special policy for working, which consists of particular operating rules and depends on the storage and water elevation in the reservoir. Several methods are used for investigating reservoir operation models to define optimum operation policy for reservoirs such as: simulation models; optimization models; and hybrid of simulation and optimization models. In addition, during the past many techniques were suggested to deal with the hard task of optimal operation of reservoirs systems. Specification of the reservoir operation plan to efficiently manage available water is a complex problem since it contains random hydrologic events. Several attempts have been made to improve this problem using optimization and simulation models (Jain & Singh, 2003). Simulation models are used for mimicking the physical process of operating reservoir system and not operative in suggesting optimal policies. Hence simulation results provide a detailed description of how systems reply to, or are affected by, planning and design solutions, or sets of solutions. Optimization techniques can be applied to decide the best sequence of releases, when known a hydrological input series to the system, that minimizes the losses or maximizes the benefits (Wurbs, 1993). Determination of optimal strategies needs formulation and solution of optimization models. Applied optimization technique to reduce the range of designs and policies required in simulation and complexity estimation is often called preliminary screening (Loucks, et al., 2005). This chapter discusses the characteristics, inflow discharge series, downstream demands and storage-elevation relationship of Dokan reservoir in Kurdistan Region / Iraq. Furthermore, describes the process of building several types of models used for simulation and optimization of the reservoir operation. The models that have been built in this study are:

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1. A simulation model by applying standard operation policy (SOP) has been developed using the Simulink toolbox in MATLAB software. 2. A nonlinear optimization model by applying nonlinear optimization technique to minimize the deficit in power generation and irrigation demand has been developed using the Optimization toolbox in MATLAB software. 3. An optimization model by applying discrete differential dynamic programming (DDDP) optimization technique to minimize the deficit in power generation and irrigation demand. A MATLAB code has been written for executing this model. 4. Developed a combined simulation-optimization model by utilizing the genetic algorithm (GA) as optimization technique. A MATLAB code has been written for executing this model. For all aforementioned model types, water supply, irrigation demand and minimum water required constraints have been considered. 4.2 Study Area Description The concept of building dams in Iraq started in the first half of the 20 th century to protect Baghdad, the capital, and other major cities from flooding. Dokan dam is one of the big dams which was built in 1959 on the Lesser Zab river (Al-Ansari, 2013). The dam is located about approximately 295 km north of Baghdad and 67 km north-west of Sulaimani city, Kurdistan Region, Iraq. The dam site is located at Latitude 35°57'15" N and Longitude 44°57'10" E near to the city of Ranya, Kurdistan Region, Iraq as shown in Fig. (4-1). The design of the dam was carried out by the Binnie & Partners, British engineering company and it was constructed between 1954 and 1959 as a multipurpose dam to provide water for irrigation and hydroelectric power generation. In addition, it was constructed for the storage of excess water contained at the top of Lesser Zab river and its branches to take advantage of the water and launch when necessary in times of summer drought periods for areas south of the reservoir, which suffer from deficiencies, particularly for irrigation purposes such as the Hawijah, Kirkuk and Koya irrigation projects. The dam type [ 43 ]

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is a concrete arch dam abutted by gravity monoliths and the primary inflow is from the Lesser Zab river (Wikipedia, 2015).

Fig. (4-1): Location of the Dokan dam and reservoir on Lesser Zab river in Iraq (Google Earth, 2016). Dokan reservoir is surrounded by mountains of Sara and Quasar to the southeast, Assos to the north-east, Kosrat to the south-west and Barda Rash to the northwest. There is a gorge that extends from the Turba village to Bemusha village. This gorge separates the larger northern part of the reservoir in Bitwen plain from the small southern part of the reservoir near Dokan dam. Villages and towns with agricultural lands, such as Rania, Chwar Qurna, and Qala Dza, surround the reservoir, with the densest populations and agricultural development to the northwest of the large reservoir (Ararat, et al., 2009) as cited in (Abdullah, 2016). Start of storage in Dokan reservoir is in the month of January until May, in which in

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this period the volume of water stored more than the volume of water released from the reservoir (Talab, 2013). The reservoir is controlled by two spillways, both located on the left bank of the reservoir. The service spillway, discussed to as the gated spillway, has three vertical gates, each closing an orifice with a clear opening of 10 m high by 6.8 m wide. The orifices discharge into a short steep chute connecting to a tunnel with 11 m diameter and free outlet set about 50 m above the river in the gorge downstream of the dam. The gated spillway crest is set 14.5 m under the normal top water level of the reservoir. The maximum capacity of the gated spillway is 2,450 m³/s. The emergency spillway is a circular 40.26 m diameter bell mouth (Morning Glory) spillway with its crest set at the normal top water level of the reservoir. The bell mouth discharges via a vertical 12.5 m diameter drop shaft into a tunnel of 10.2 m diameter. At its downstream end, the tunnel is steel lined, decreasing in diameter to 9.9 m and inclined both 30º upwards and 47º in a downstream direction for a free discharge into the river gorge. The maximum capacity of the emergency spillway is 1,860 m³/s. Furthermore, releases can be made through two irrigation outlets that are fed by a tunnel passing below the dam on the right bank. This tunnel bifurcates below the crest of the dam, where each 2.29 m diameter steel lined tunnels can be closed by emergency gates lowered from the dam crest. Each of these tunnels connects to a steel conduit with a butterfly guard valve and flow is regulated by a hollowjet discharge valve with a maximum capacity of 120 m³/s each at full reservoir level. Five further steel conduits of 3.65 m diameter were constructed through the arch section of the dam. Each of these can be closed by an emergency gate lowered from the dam crest and each conduit leads to a guard valve and 80 MW turbine unit in the main power station sited at the dam toe (Anon., 2006). The relevant data of Dokan dam and reservoir and its appurtenant structures are summarised in Table (4-1).

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Table (4-1): Characteristics of Dokan dam and reservoir (Dokan Dam Directorate, 2015). Dam and Spillways Cylindrical arch with gravity abutments 116.5 m 360 m 6.2 m 34.3 m 370,000 m3 516 m 2 No. Service: Tunnel Emergency: Bell-mouth Service: 2,450 m3/s Emergency: 1,860 m3/s 2 No., maximum capacity: 120 m³/s for each at full reservoir level

Type of dam Height Length Crest width Base width Volume Crest elevation Spillways Type of spillway Spillway capacity Irrigation outlet

Reservoir Capacity at El. 511.00 Active capacity Dead Storage Volume Surface area at level 511 m Normal elevation Maximum elevation Minimum hydropower operating level

6,800,000,000 m3 6,100,000,000 m3 700,000,000 m3 270 km2 511 m 515 m 479 m

Hydrology 11690 km2

Catchment area Mean annual catchment precipitation Design inflow

850 mm 13,300 m³/s Power Station

Hydraulic head Turbines Installed capacity

95 m (rated) 5 x 80 MW Francis-type [2] 400 MW

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4.3 Collection and Processing Data collection and processing are the significant part of the first stage of building the reservoir operation models. Data collection is a very demanding job which needs thorough planning, hard work, patience, perseverance and more to be able to complete the task successfully. Data collection starts with determining what kind of data necessary, after that need gathered the data. Based on the availability of data, decisions need to be made about the gathering of additional hydro meteorological data, water demand and quality data as well as demographic, economic, and ecological information. The data collection process needs recognizing the sources of data, exploration of these sources, inquiries about other appropriate data sources, assessment of data quality, and computerization of data for processing. Due to the high level of computerization and modem means of information spreading, the data collection is a simpler exercise in developed countries. But in several countries, most of the data are still in the manuscript form and are distributed in various branches of a data collection agency (Jain & Singh, 2003). Commonly no data record is available in a central office and it may be necessary to visit each branch office and copy and computerize the data. Also, there may not be a common format for storing the data and the quality and reliability may widely change from agency to agency and sometimes across the same agency. Therefore, adequate time and funds should be allocated for the purpose of data collection. 4.3.1 Inflow Time Series of Dokan Reservoir Inflow to reservoirs is generally calculated at hydro climatic stations placed on streams entering the rivers and reservoirs and other control points. In some of the reservoirs, the inflow is estimated by the water balance in the reservoir using the actual release records on an hourly or daily basis. Inflow to the reservoir is one of the most important sources of uncertainty in development of operating policies for a system. In a system approach to reservoir operation and modeling, it is preferable to have a long record of stream flows that includes worst-case scenarios of droughts and floods experienced during the historical record [ 47 ]

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(Karamouz, et al., 2003). From the available data in the Dokan dam directorate, the average annual rainfall in the station of Dokan Dam is 739 mm for the period 1958-2011. Additionally, inflow discharge of the reservoir is formed from numerous small rivers, which are the south-western tributary of upper Lesser Zab and the rivers are the following: 1. Sewail river which has two tributaries Shalar and Qislaja. 2. Joga soor river which has only one tributary called Mawakan. These two tributaries, Sewail and Jaga soor combine together contributing Qala jolan river and drain to Lesser Zab river near the Iraq–Iranian border. There are several other small rivers at northern part of this watershed drain directly to Dokan reservoir such as; Hizob, Qashan, Dara-siw, Sulana and Zarawa (Talab, 2013). In this study, monthly inflow discharges into Dokan reservoir of dam site gauge station over the period (1958-2011) were used for developing the simulation and optimization models. The inflows data of Dokan dam gage station are obtained by operation balance, and hence the losses are implicitly included. Fig. (4-2) shows the monthly inflow time series data that available in Dokan dam directorate for the period October, 1958 to September, 2011. The maximum and minimum values of inflow discharges are 1510 m3/s in March, 1988 and 9 m3/s in September, 2008 respectively. While, the average monthly multiannual data is about 186 m3/s. 1600

Inflow (m3/s)

1400 1200 1000 800 600 400 200 0 1960

1970

1980

1990

2000

2010

Year

Fig. (4-2): Monthly inflow discharges into Dokan reservoir for the period October, 1958 to September, 2011. [ 48 ]

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4.3.2 Testing for Outlier Data Outlier data is the data usually higher or lower than the normal range of time series data. These data should be deleted after detection because, they can affect the number and values of statistical parameters calculated from the data. Processes for treating outliers require judgment include both mathematical and hydrologic considerations. For determination of outlier data, each sample data can be tested with the Bulletin 17B detection method as discussed by the following steps (McCuen, 1998): 1. To determine the high outlier data, that is: 𝑦𝐻 = 𝑦̅ + 𝑘0 . 𝑆𝑦

(4-1)

Where: 𝑦𝐻 : The high outlier threshold in log unit. 𝑦̅: The logarithmic mean of the series data. 𝑘0 : Frequency factor for outlier detection, regarding to the number of inflow data (648) in the present study, the value of 𝑘0 is 3.148 (McCuen, 1998). 𝑆𝑦 : Logarithmic standard deviation. 2. To determine low outlier data, that is: 𝑦𝐿 = 𝑦̅ − 𝑘0 . 𝑆𝑦

(4-2)

Where 𝑦𝐿 is the low outlier threshold in log unit. If any logarithms of the data are greater than the high outlier threshold (𝑦𝐻 ) or smaller than the low outlier threshold (𝑦𝐿 ) then can be considered as outlier data. In the present study, the estimated statistical parameters are shown in Table (4-2). The results of outlier test display that there is no outlier data for inflow time series of Dokan reservoir.

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Table ( 4-2): Statistical parameters to determine high and low outlier data. Statistical Parameters

Quantity

𝑦̅ 𝑆𝑦 𝑦𝐻 𝑦𝐿 𝑘0 𝑛

2.084 0.41 3.373 0.794 3.148 648

4.3.3 Downstream Water Demands Water conveyance for the different sector (domestic use, agriculture, industrial …etc.) is one of the important purposes of reservoir systems. The highest of water demand may occur in months during which inflows are at a minimum such as in the middle of summer. The main purpose of water resources modeling is to develop strategies for water distribution in a manner that demands can be reached with proper certainty. Thus, to manage a system, it is important to be able to define the current and projected water use fluctuations and variations. Water demands change from year to year and month to month. Many physical, economic, social, and political reasons for these changes can be recognized. In latest years, substantial climatic changes have been observed in several parts of the world, involving more intense floods, greater precipitation, and even unusual droughts in some regions. In many parts of the world these variations have significantly affected the water demands (Karamouz, et al., 2003). The water requirements for different uses in the downstream of Dokan reservoir are explained in the following sections. 4.3.3.1 Water Supply Domestic water uses cover residential (apartments and houses), commercial (stores and businesses), institutional (hospitals and schools), industrial, and other water uses (firefighting, swimming pools, park watering). In most river basins, the domestic or municipal demand will be small compared to the demand for

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irrigation. However, given the importance of this demand for human health and economic developments, it is often given first priority (Loucks, et al., 2005). The Dokan reservoir is one of the main sources of water supply for domestic use of Kurdistan Region, Iraq particularly to the provinces of Sulaimani, Kirkuk and around of them. For this purpose, water requirements are about 400000 m3/day for Sulaimani province (Sulaimani Water Directorate, 2015) and 288000 m3/day for Kirkuk province (Kirkuk Water Directorate, 2015). 4.3.3.2 Irrigation Water Demand Water requirement for agricultural is defined as the amount of water that required for growing crops and crop water demand is usually measured in terms of evapotranspiration. The amount of evapotranspiration depends on meteorological factors such as temperature, relative humidity, wind, radiation, number of daylight hours, precipitation, …, and field factors like soil moisture and surface properties. Agriculture already accounts for about 70% of water consumption worldwide (Karamouz, et al., 2003). Water consumption for agriculture sector in Iraq according to the recent evaluations is 85% of the total water withdrawal (Al-Ansari & Knutsson, 2011). The amount of water that is utilized for irrigation purpose (water withdrawal for irrigation) mostly exceeds the water requirement for this purpose caused by substantial losses during supply, distribution and application. A sufficient water supply is the essential factor for plant growth. When rainfall is not sufficient, the plants must receive additional water from irrigation. Regulated deficit in irrigation is one way of maximizing water use efficiency for higher yields per unit of irrigation water applied. Irrigation demands are consumptive and only a small portion of the water supplied is available to the system as return flow. These requirements have direct relationship with rainfall in the command area. Irrigation requirements are seasonal in nature and the variation mostly depends on cropping patterns in the command area. In general, demands will be lesser during the wet season and large during summer months. The average annual demands remain more or less steady [ 51 ]

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unless there is increase in the command area or large variation in the cropping pattern. The safety against droughts depends on the available water in the reservoir and hence it is required to keep as much water in storage as possible consistent with current demands (Jain & Singh, 2003). Most agricultural parts in the world depend on rain as the major source of water. During dry periods, extra water may be provided through irrigation systems. In semi-arid and arid countries, irrigation is an absolute requirement to support agricultural production. Dokan reservoir is provided water for agriculture land about 182500 hectares for Kirkuk, Hawija and Adhaim irrigation project (Kirkuk Water Resources Directorate, 2016). Table (4-3) shows the irrigation water requirement for the irrigation projects that constructed on Lesser Zab river at downstream of Dokan reservoir (Harza Engineering Company, et al., 1963). Furthermore, Klesa irrigation project is a new project in Koya, Sulaimani, Kurdistan Region, Iraq that involving about 7000 hectare of agriculture land. The water requirement of this project for irrigation is displayed in Table (4-3), (Koya Water Resources Directorate, 2016) 4.3.3.3 Environmental Flow Calculation for Reservoir Downstream Environmental flows are defined as the minimum flow requires to remaining habitats. Environmental flows may include elements from the full range of flow conditions which describe long term average flows, variability of flows including low flows and irregular flooding events (Environment ACT, 1999). Therefore, providing adequate water to protect the aquatic, biological, and aesthetic values of a stream and to preserve existing fisheries is an important constraint in river– reservoir systems planning and operation. To calculate the minimum flow requirement some different methods are used in countries. In this study to estimate environmental flow for Dokan reservoir, hydrological method which uses daily or monthly flow to determine environmental flow has been used. It can be used to calculate minimum flow in the stream with/without gauging station. It can also be applied easily in the planning stage of the water resources development project.

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Tennant (Montana) method (1976) is the most common method applied worldwide and has been used by at least 25 countries (Tharme, 2003). This method uses a percentage of mean annual flow to describe situations of flow related to fishery, wildlife, recreation and environmental resources. The method calculates the minimum flow requirement in a stream by taking 10 % of the mean annual flow. Depending on this method, the minimum release to downstream, from Dokan reservoir, in each month will be 15 m3/s.

Table (4-3): Downstream water demands for different uses of Dokan reservoir.

Month

Irrigation Requirement (million m3) (Kirkuk, Hawija, Klesa Adhaim Project Projects)

Sulaimani Domestic Use (106 m3)

Kirkuk Domestic Use (106 m3)

Environmental Flow Requirement (106 m3)

Total Water Demand (106 m3)

January

184.81

0.12

12.4

8.93

40.18

246.44

February

202.95

0.80

11.6

8.35

37.58

261.28

March

326.76

3.16

12.4

8.93

40.18

391.43

April

316.22

7.19

12

8.64

38.88

382.93

May

286.59

8.94

12.4

8.93

40.18

357.04

June

409.54

7.98

12

8.64

38.88

477.04

July

444.61

8.58

12.4

8.93

40.18

514.70

August

417.83

9.85

12.4

8.93

40.18

489.19

September

243.65

8.56

12

8.64

38.88

311.73

October

227.66

5.26

12.4

8.93

40.18

294.43

November

274.75

3.40

12

8.64

38.88

337.67

December

206.24

0.51

12.4

8.93

40.18

268.26

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4.3.4 Storage-Elevation Relationships Storage capacity is the most important physical characteristic of reservoirs and can be calculated for each level of water from the topographic map of the site. An area-volume-elevation curve can be created by applying the area surrounded with each interval in the reservoir site and summation of the increments of storage below each level. This curve can be used in selection of total capacity for reservoir and reservoir operation optimization (Karamouz, et al., 2003). From the area-volume-elevation relationships, storage and surface area of water can be determined for any elevation of water surface in the reservoir above sea level. For Dokan reservoir, the following relationship between storage and elevation of water surface was derived from the available data display in Table (4-4) by quadratic regression (Dokan Dam Directorate, 2015): ℎ = −0.0000007 ∗ 𝑆 2 + 0.0118 ∗ 𝑆 + 464.01

(4-3)

In which ℎ is the elevation of water surface above sea level (m) and 𝑆 is the storage volume in the reservoir (million m3).

Table (4-4): Storage-elevation relationship of Dokan reservoir. No. 1 2 3 4 5 6 7 8 9 10

Elevation (m) 470 474 478.11 480.5 484 486 488 490.03 492.01 494.06

Storage (106 m3) 741.5 969.1 1262 1463 1802 2022 2262 2529 2810 3126

No. 11 12 13 14 15 16 17 18 19

[ 54 ]

Elevation (m) 496.01 498.04 500.04 502.1 504.1 506.4 508.04 510.75 512.36

Storage (106 m3) 3450 3813 4197 4619 5055 5590 5991 6695 7135

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Methodology and Models Building

4.3.5 Flood Control Operation Rule Sometimes flood control is the main objective of reservoir building since flood control reservoir protects the downstream areas of the reservoir from the damages due to flood events. While, absolute protection from dangerous floods is not economically suitable. A flood control reservoir reduces the flood damage and it is also called the flood protection or flood mitigation reservoir. The flood storage capacity of a reservoir is one of the main components of several flood control systems. For this purpose, part of the active storage of a reservoir is kept empty to store potential floods and after that inflow to the reservoir reduces gradually release excess water at rates not exceeding the capacity of the downstream river (Karamouz, et al., 2003). The requirement of storage space for flood control is in conflict with the requirements for conservation needs. The conservation requirements, such as water supply and hydropower generation, require the storage space to be full while the flood control aspect requires the availability of empty storage space (Jain & Singh, 2003). One of the important aims of Dokan reservoir was to protect Baghdad city, the capital, and other major cities from flooding. During the flood season (September to April), the storage volume in the reservoir should be lowered below 6800 million m3 according to flood control operation rule. Table (4-5) shows the maximum allowable reservoir storage for different months throughout the year (Harza Engineering Company, et al., 1963).

Table (4-5): Flood control operation rule of Dokan reservoir.

No.

Month

1 2 3 4 5 6

January February March April May June

Storage (Month End) (106 m3) 5320 5320 5870 6580 6800 6800

No.

Month

7 8 9 10 11 12

July August September October November December

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Storage (Month End) (106 m3) 6800 6800 5970 5320 5320 5320

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Methodology and Models Building

4.4 Hydropower Generation The hydroelectric power generation is a non-consumptive use of water since after passage through the power plant the same water can again be utilized for other downstream users. Due to this feature, hydroelectric projects are mostly multipurpose. It is estimated that one quarter of the electrical energy produced in the world is from hydropower. Main advantages of hydropower generation are as follows (Jain & Singh, 2003): 1. This is a renewable source of energy, the sun being the prime mover of water cycle. As no payment is made for the input, the production is free from inflation. 2. The hydropower plants do not necessitate much expenditure on account of operation and maintenance, and have a long life. 3. The hydropower production does not pollute the environment; no warmness is created and no dangerous gases are released. 4. The hydropower power plants work at a very high efficiency (up to 90%). Power production is a major objective of water resources growth in several rivers–reservoir systems. In hydropower station, energy is produced when water of a sufficient head runs electric turbines and produces electricity (Karamouz, et al., 2003). Power station of Dokan reservoir consists of 5 Francis type turbines and maximum power generation capacity of each is 80 MW. The Power station became fully operational in 1979 and working at net heads between 63 and 95 m, with discharges of 50-111 m3/s and minimum hydropower operating level is 479 m (Rashid, et al., 2007). The reservoir is operated to obtain as much hydropower as possible inside the constraints of the downstream demands. For this purpose, a regulation for hydropower generation has been developed in this study based on the characteristics of the turbines, flood control curve and the minimum downstream discharge requirement. Power generation can be calculated by following equation:

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𝑒. 𝛾. 𝑅𝑡 . 𝐻𝑡 𝐻𝑃𝑡 = 1000 } 𝑜𝑟 𝐻𝑃𝑡 = 𝐾. 𝑅𝑡 . 𝐻𝑡

(4-4)

Where: 𝐻𝑡 : Average net head (m) above turbines at time 𝑡. 𝑅𝑡 : Discharge release through turbines (Mm3/month) at time 𝑡. 𝐻𝑃𝑡 : Hydropower generation (MW) at time 𝑡. 𝐾: Constant of hydropower equation (0.0031). γ: Specific weight of water (9810 N/m3). 𝑒: Overall efficiency which is 0.8 for the turbines of Dokan power station. By knowing the elevation of water surface (ℎ) from equation (4-3) the net head (𝐻𝑡 ) above turbines can be calculated as follows: 𝐻𝑡 = ℎ − 𝑙𝑏

(4-5)

In which 𝑙𝑏 is the bed level of turbines which is equal to 415 m for Dokan power station. Then the equation (4-4) becomes: 𝐻𝑃𝑡 = 0.0031((−0.0000007𝑆𝑡2 + 0.0118𝑆𝑡 + 464.01) − 415)×𝑅𝑡

(4-6)

4.5 Reservoir Operation Constraints There are several constraints should be considered in the building of simulation and optimization models for operation of Dokan reservoir system which can be summarized as follow: 1. The first priority demands in the Dokan reservoir are domestic, industrial, and environmental, and should be fully supplied in the planning horizon. In other words, the minimum allowed release of the dam must supply the total needs of the mentioned priorities in each month. The constraint in this case is: 𝑅𝑒 + 𝑅𝑤 ≤ 𝑅𝑖 ≤ 𝑅𝑚𝑎𝑥

(4-7)

Where 𝑅𝑒 is the environmental flow requirement and 𝑅𝑤 is the water supply requirement for domestic and industrial uses.

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2. The minimum reservoir capacity is 1400 million m3 for each month and maximum capacity of the reservoir should not exceed the flood control storage operation rule at each month. The starting month for optimization is January and the Dokan reservoir storage is almost around 2000 million m3 in this month, therefore, the initial storage (𝑆𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ) assumed to be 2000 million m3. 4.6 Building the Models In the current study, as mentioned earlier, three different techniques were used to optimize and simulate the operation of Dokan reservoir system. Depending on these techniques, four models which are SOP, NLP, DDDP, and SO have been built. The models analyse the behaviour of Dokan reservoir system using a monthly time series data for a total of 648 time periods, starting from January 1958 to December 2011. The initial storage value was specified as the storage volume of January 1958, and then the storages were calculated based on given inputs of historical inflows, domestic and industrial demands, irrigation demands, and maximum storage capacity. Moreover, after satisfying all the demands, the excess releases are recorded as spills or overflows. The description and explanation of the models that built in this study are found in the following sections. 4.6.1 Model-I: Simulation Model The simulation model is operated according to physical relation and a series of operation rules to simulate new situation and system behaviour based a specified rule. In the present study, Simulink toolbox in MATLAB software was used to design a simulation model for Dokan reservoir system based on standard operation policy (SOP). The results of the simulation model were evaluated by computing various performance measures such as reliability, resilience and vulnerability. Fig. (4-3) shows the simulation flowchart that developed for Dokan reservoir system based on SOP. Simulink includes a comprehensive block library of other [ 58 ]

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toolboxes. Once the required blocks have dragged to the new model window, the in-ports and out-ports of the adjacent blocks can join to create a block-diagram as desired. A double-click on each block in the model leads to open a dialog box, in which the block's parameters can be set (Ashish Tewari, 2002). Simulation can be started after defining a model, either from Simulink menus or by entering commands in MATLAB’s command window. Using display blocks provided, the simulation result can be seen while the simulation is running. The simulation results can be put in the MATLAB work space for post processing and visualization. In the present study, the described blocks that are necessary to build the simulation model are shown in Table (4-6). The Simulink layout model for Dokan reservoir system under SOP is shown in Fig. (4-4).

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Fig. (4-3): Flowchart of simulation with standard operating policy (SOP). [ 60 ]

Chapter Four

Methodology and Models Building

Table (4-6): Descriptions of the Simulink blocks that used in the SOP Model building (MATLAB 2013: Simulink Library Browser). Block Figure

Block Name

Description

Repeating Sequence Stair

The repeating sequence stair block outputs and repeats a stair sequence to define the input signal (inflow series, discharge release) for the model.

Sum

The sum block performs addition or subtraction on its inputs. This block can add or subtract scalar, vector, or matrix inputs. It can also collapse the elements of a signal.

Switch

The switch block passes through the first input or the third input based on the value of the second input.

Scope

The scope block displays inputs signals with respect to simulation time.

Product

The product block performs multiplication or division of inputs.

Gain

The gain block multiplies the input by a constant value (gain).

Constant

The constant block generates a real or complex constant value.

The unit delay block holds and delays its input by Unit Delay the sample period you specify (initial storage in the model). Function Block

The function block applies the specified mathematical expression to its input (change storage to elevation in the model).

Out Port

The out-port blocks are the links from a system to a destination outside the system.

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Fig. (4-4): Simulink model layout based on the standard operation policy (SOP) for Dokan reservoir system. [ 62 ]

Chapter Four

Methodology and Models Building

4.6.2 Model–II: Optimization Models In the present study, the second technique used to analyse the behaviour of Dokan reservoir system using a monthly time series data is optimization. The nonlinear programming (NLP) and discrete differential dynamic programming (DDDP) optimization methods were used for optimization the operation of the reservoir. As for SOP model, the basic input to the optimization models is the historical observed monthly inflow data for the period (January, 1958 to December, 2011). The outputs of the models are release from reservoir, reservoir storage, reservoir water level, and generated electrical power. 4.6.2.1 Model–II-a: Nonlinear Programming Optimization Model To apply the nonlinear programming optimization (NLP) model, several different values of weight factors, 𝑤1 , 𝑤2 (see Eq. 3-4) between (0-1) should be tested and then selected. In the present study, for analyzing the results of the developed models, five sets of weight factors have been selected as follow: set 1 (𝑤1 = 0 , 𝑤2 = 1), set 2 (𝑤1 = 0.2 , 𝑤2 = 0.8), set 3 (𝑤1 = 0.5 , 𝑤2 = 0.5), set 4 (𝑤1 = 0.8 , 𝑤2 = 0.2) and set 5 (𝑤1 = 1 , 𝑤2 = 0). In which 𝑤1 represents the weight factor of first objective function (minimize the deficit in hydropower production) and 𝑤2 represents the weight factor of the second objective function (minimize the deficit in irrigation demand). The first set (𝑤1 = 0 , 𝑤2 = 1) is reduce the objective function only to minimize the deficit in irrigation demand while the last set (𝑤1 = 1 , 𝑤2 = 0) is reduce the objective function only to minimize the deficit in hydropower generation. The solver (𝑓𝑚𝑖𝑛𝑐𝑜𝑛) in Optimization toolbox of MATLAB software (version 8.1) is commonly used to solve nonlinear optimization problems. Optimization toolbox includes many solvers which is capable of modeling all systems (large or small) for linear and non-linear problems. This Optimization toolbox allows a user to quickly input the model formulation, assess the correctness or appropriateness of the formulation based on the solution, quickly make minor modifications to the formulation, and repeat the process. Therefore, [ 63 ]

Chapter Four

Methodology and Models Building

it has been applied for building and solving the nonlinear optimization model for Dokan reservoir throughout this study. To find the minimum value of objective function by applying the constrained nonlinear optimization techniques can be using (𝑓𝑚𝑖𝑛𝑐𝑜𝑛) solver of MATLAB software in the following forms (Goodarzi, et al., 2014): 1.

𝑥 = 𝑓𝑚𝑖𝑛𝑐𝑜𝑛(𝑓𝑢𝑛, 𝑥0 , 𝐴, 𝑏), find the minimum of function 𝑓(𝑥) which is described by the term (fun) at starting point 𝑥0 and subject to linear inequality 𝐴𝑥 ≤ 𝑏.

2.

𝑥 = 𝑓𝑚𝑖𝑛𝑐𝑜𝑛(𝑓𝑢𝑛, 𝑥0 , 𝐴, 𝑏, 𝐴𝑒𝑞, 𝑏𝑒𝑞), find the minimum of function 𝑓(𝑥), described by term (fun), at starting point 𝑥0 and subject to linear inequality 𝐴𝑥 ≤ 𝑏 and linear equality 𝐴𝑒𝑞 𝑥 = 𝑏𝑒𝑞.

3. 𝑥 = 𝑓𝑚𝑖𝑛𝑐𝑜𝑛(𝑓𝑢𝑛, 𝑥0 , 𝐴, 𝑏, 𝐴𝑒𝑞, 𝑏𝑒𝑞, 𝑙𝑏, 𝑢𝑏), find the minimum of function 𝑓(𝑥) at starting point 𝑥0 and subject to linear inequality 𝐴𝑥 ≤ 𝑏 and linear equality 𝐴𝑒𝑞 𝑥 = 𝑏𝑒𝑞 with the lower and upper bounds 𝑙𝑏 and 𝑢𝑏, respectively. 4.

[𝑥, 𝑓𝑣𝑎𝑙] = 𝑓𝑚𝑖𝑛𝑐𝑜𝑛(𝑓𝑢𝑛, 𝑥0 , 𝐴, 𝑏), return the minimum of function 𝑓(𝑥) at the solution point x subject to linear inequality 𝐴𝑥 ≤ 𝑏.

5. [𝑥, 𝑓𝑣𝑎𝑙] = 𝑓𝑚𝑖𝑛𝑐𝑜𝑛(𝑓𝑢𝑛, 𝑥0 , 𝐴, 𝑏, 𝐴𝑒𝑞, 𝑏𝑒𝑞), return the minimum of function 𝑓(𝑥) at the solution point 𝑥 subject to linear inequality 𝐴𝑥 ≤ 𝑏 and linear equality 𝐴𝑒𝑞 𝑥 = 𝑏𝑒𝑞. 6. [𝑥, 𝑓𝑣𝑎𝑙] = 𝑓𝑚𝑖𝑛𝑐𝑜𝑛(𝑓𝑢𝑛, 𝑥0 , 𝐴, 𝑏, 𝐴𝑒𝑞, 𝑏𝑒𝑞, 𝑙𝑏, 𝑢𝑏), return the minimum of function 𝑓(𝑥) at the solution point 𝑥 subject to linear inequality 𝐴𝑥 ≤ 𝑏 and linear equality 𝐴𝑒𝑞 𝑥 = 𝑏𝑒𝑞 with the lower and upper bounds 𝑙𝑏 and 𝑢𝑏, respectively. On the other hand, to simulate the reservoir operation, the input data for the simulation model are inflow, elevation-storage relationship, downstream demands, physical characteristics of the reservoir, and series of optimized discharge releases. Fig. (4-5) shows the Simulink model layout for Dokan reservoir system based on the optimized results of NLP optimization model.

[ 64 ]

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Fig. (4-5): Simulink model layout based on the optimized results of NLP optimization model for Dokan reservoir system. [ 65 ]

Chapter Four

Methodology and Models Building

4.6.2.2 Model-II-b: Dynamic Programming Optimization Model Using traditional dynamic programing with the use of high speed digital computers to optimize operating policies of multiple unit and multiple purpose water resource systems has two major difficulties: memory requirements and computer time requirements. To simplify the difficulties considerably, an iterative method called discrete differential dynamic programming (DDDP) were presented (Heidari, et al., 1971). The optimization process method starts with an initial trial trajectory satisfying a specific set of initial and final conditions and much time is spent to find the feasible initial trial trajectory, which is a difficult task especially in a complex system. At the end of each iteration step a locally improved trajectory is obtained and used as the trial trajectory in the next step. In the present study, to apply the DDDP optimization model for Dokan reservoir operation process, the initial storage (2000 million m3) in January, 1958 and monthly inflow series during the past 54 years (January, 1958 to December, 2011) were used. The solution improvement for Dokan reservoir optimization had become very small after about 50 iterations and slight differences of convergences among each run were recognized after about 120 iterations. The optimum results of objective function were obtained at the iteration number 32. As mentioned in the nonlinear optimization model (NLP), the optimum values of discharge releases determined from DDDP model were utilized in the Simulink of MATLAB software to simulate the reservoir operation. The input data for the simulation model are inflow, elevation-storage relationship, downstream demands, physical characteristics of the reservoir, and series of optimized discharge releases from DDDP model. Fig. (4-6) shows the Simulink model layout for Dokan reservoir system based on the optimized results of DDDP optimization model.

[ 66 ]

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Methodology and Models Building

Fig. (4-6): Simulink model layout based on the optimized results of DDDP optimization model for Dokan reservoir system. [ 67 ]

Chapter Four

Methodology and Models Building

4.6.3 Model-III: Combined Simulation-Optimization Model The combined simulation-optimization model uses a repetition process to generate inputs to the simulation model then the results would be used by the optimization model to search the optimal solution. The solution of the optimization model will lead to better or more appropriate input for the simulation model and this repetition process continues so that the final optimal solution is achieved (Montaseri, et al., 2015). In the present study, the optimization model by applying genetic algorithm is linked to the external simulation model with using Simulink toolbox of MATLAB software to develop the simulationoptimization model. To apply the genetic algorithm in reservoir operation model, the parameters should be selected after a thorough sensitivity analysis by changing each of the parameters. In water resources applications, a larger population helps to maintain greater diversity but, it involves considerable computational time requirement (Al-Taiee, 2011). Obtaining optimum population size is very important in the applied of genetic algorithm. Therefore, in the present study, different population sizes have been considered. A population size of 300 gives the optimum fitness value as shown in Fig. (4-7). Toward optimality have become very small after about 200 generation and there are slight differences of convergences among the runs after about 8000 generations as shown in Fig. (4-8). Therefore, a population size of 300 and a maximum generation number of 8000 have been chosen to run the S-O model in this study. The second important parameter for genetic operator chosen is crossover probability (𝑝𝑐). Its effect on the system performance is studied by varying the probability of crossover from 0.5 to 0.9 with an increment of 0.05 and adopting the obtained optimal population of 300. The results show that 0.5 is optimum value for crossover probability which takes the minimum fitness value as shown in Fig. (4-9). Also, a mutation probability (pm) of 0.001 was selected and the total number of decision variables of the model is 648, which is equal to the dimension

[ 68 ]

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Methodology and Models Building

of the problem. The result obtained by the created genetic program is not always similar because of the difference in initial population, since the GA creates initial population randomly.

Fig. (4-7): Fitness values versus population size of GA for Dokan reservoir.

Fig. (4-8): Fitness values versus number of generation of GA for Dokan reservoir. [ 69 ]

Chapter Four

Methodology and Models Building

Fig. (4-9): Fitness value for various crossover probability of GA for Dokan reservoir. Using MATLAB code for applying genetic algorithm provides full control on the genetic operations such as population, cross over and mutation, and also gives more freedom in developing constraints and penalty methods. In the program code, the initial population is generated randomly and the user can specify the size of population. Moreover, real value coding is used and the fitness function is evaluated by penalty methods. The selection process is done by a random selection method and single point crossover is carried out because it is easy to code in MATLAB software. By running the model, for the parameter set in each trial, the simulation model is used to evaluate the performance of the system with respect to different objectives. Then, the parameter set is modified toward optimality by using the optimization algorithm. The process is continued until one of the criteria for termination is satisfied as follow: 1. Maximum number of generations. 2. Convergence in objective function space.

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Note that the optimal solution for the current study is achieved when the deficiency in hydropower production and irrigation demand is minimized. The flowchart and Simulink layout of the combined simulation-optimization model for Dokan reservoir system are shown in Fig. (4-10) and Fig. (4-11) respectively.

Fig. (4-10): Flow chart of S-O model based on the genetic algorithm (GA). [ 71 ]

Chapter Four

Methodology and Models Building

Fig. (4-11): Simulink model layout based on combined simulation-optimization (S-O) model for Dokan reservoir system. [ 72 ]

CHAPTER FIVE RESULTS AND DISCUSSIONS

Chapter Five

Results and Discussions

Chapter Five Results and Discussions 5.1 Introduction The results that obtained in the present study by applying the developed models for operating the Dokan reservoir are viewed and discussed in detail in this chapter. Also, some performance criteria such as the reliability, resilience and vulnerability of reservoir operation are represented for developed models. In this study, three types of reservoir modelling; simulation, optimization and combine simulation-optimization model have been developed and each of them fed with the same actual inflow data and constraints for the period (1958-2011). As well as, a comparative study based on the results of the developed models has been carried considering the irrigation water supply, performance evaluation, energy construction, release through turbines, storage of reservoir, spillway release controlling and monthly hydropower operation policies. 5.2 Developed Models The simulation model (Model-I) based on standard operation policy (SOP) was run for a period of 54 years, i.e. 648 months starting from January 1958 to December 2011, for which the historical data were available. The initial storage value was specified as the storage volume of January 1958, and then the storages were calculated based on given inputs of historical inflows, environmental and domestic demands, irrigation demands and maximum storage capacity. Also, the optimization models (Model-II-a and Model-II-b), based on the NLP and DDDP respectively, were developed to minimize the deficit in hydropower production and irrigation demand for Dokan reservoir system by considering the constraints of reservoir operation. The difficult task in DDDP is determining the initial trial trajectory which is should be satisfied a specific set of initial and final conditions and much time is expended to find the feasible initial trial trajectory. At the end of each iteration step a locally improved trajectory is obtained and used as the trial trajectory in the next step as shown in Fig. (5-1). In spite of trial and iteration [ 73 ]

Chapter Five

Results and Discussions

procedure of the DDDP optimization model it needs less computer running time than NLP optimization model. Iteration 1

Average monthly storage (Mm3)

8000

Upper boundary Trial trajectory Lower boundary

7000

Optimal trajectory 6000

5000

4000

3000

2000

1

2

3

4

5

6

7 Months

8

9

10

11

12

Iteration 32 6500 Upper boundary Trial trajectory Lower boundary Optimal trajectory

Average monthly storage (Mm3)

6000

5500

5000

4500

4000

3500

1

2

3

4

5

6

7 Months

8

9

10

11

12

Fig. (5-1): Convergence initial trial trajectory to optimal trajectory through optimization iterations of DDDP method. [ 74 ]

Chapter Five

Results and Discussions

Moreover, combined simulation-optimization model (Model-III) as a new technique in recent years was developed based on the genetic algorithm (GA) as an optimization technique. As NLP optimization model, the CPU time required to run the simulation-optimization model is one of the limitations of this model due to linking to the external simulation model. The running time depends on the number of generations and population size used in the model. 5.3 Discharge Release for Downstream Demands The present study focuses on developing models that provide priorities for different sectors of demands with a manner that, first fulfilling domestic, industrial and environmental water demands, and then meeting irrigation demands. Fig. (5-2) and Fig. (5-3) show the discharge release for Dokan reservoir system operation during the period (1958-2011) and first year of operation (1958) respectively. The results demonstrate that the system operation on the basis of simulation model (Model-I) has a significant difference from the other developed models to determine the optimum discharge release. Table (5-1) shows characteristics of discharge releases for downstream demands in the proposed models.

700

Model-I Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

Discharge release (m3/s)

600 500 400 300 200 100 0

0

100

200

300 400 Time (Month)

500

600

Fig. (5-2): Models outputs of discharge release for Dokan reservoir during the period (1958-2011). [ 75 ]

Chapter Five

Results and Discussions Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

Discharge release (m3/s)

250 200 150 100 50 0

1

2

3

4

5

6 7 Time (Month)

8

9

10

11

12

Fig. (5-3): Models outputs of discharge release for Dokan reservoir during the first year of operation (1958). The actual and models’ outputs of average monthly discharge releases for Dokan reservoir are presented in Fig. (5-4). It is noted that for the actual operation state, the deficiency was occurred during the months of March to June because of the high discharge releases in summer months for the purpose of power production. On the other hand, the simulation model (Model-I) shows more discharge releases during the flood season because the SOP aims to best meet the demand in each period based on the water availability in that period. In this way, the shortage in irrigation demand is occurred during the dry season. From the results, it is observed that the lowest level of discharge release for downstream of the reservoir was recorded in the simulation model (Model-I) because of the discharge release based on SOP method is depends on the current available water in the reservoir. Therefore, when the available water is less than the downstream demands the SOP method do not save water in the reservoir for the months that has low inflow discharge and it causes increase the severity of failure events and extra discharge is released through spillway of the reservoir during the flood season.

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Table (5-1): characteristics of discharge releases for downstream demands in the proposed models. Models

Maximum Discharge Release (m3/s)

Average Discharge Release (m3/s)

Minimum Discharge Release (m3/s)

Model-II-a (NLP)

Model-II-b (DDDP)

Model-III (S-O)

1

465.8

469.89

465.44

0.2

0.8

469.91

462.96

469.24

0.5

0.5

469.91

462.96

469.77

0.8

0.2

469.91

469.91

469.59

1

0

469.91

469.91

466.41

0

1

188.94

188.94

188.94

0.2

0.8

188.94

188.94

188.94

0.5

0.5

188.94

188.94

188.93

0.8

0.2

188.94

188.94

188.93

1

0

188.94

188.78

188.94

0

1

55.72

59.29

36.42

0.2

0.8

55.76

38.97

31.99

0.5

0.5

49.75

38.26

37.54

0.8

0.2

23.15

23.59

23.9

1

0

23.15

23.59

24.79

𝑤1

𝑤2

0

Model-I (SOP)

469.91

181.24

11.02

Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O) Demand Actual

400

Discharge release (m3/s)

350 300 250 200 150 100 50 Jan.

Feb.

Mar.

Apr.

May

Jun. Jul. Months

Aug.

Sep.

Oct.

Nov.

Dec.

Fig. (5-4): Actual and models outputs of average monthly discharge release for Dokan reservoir. [ 77 ]

Chapter Five

Results and Discussions

Furthermore, average discharge releases of the reservoir operation period are nearly equal for all the applied models and do not change for all different weighted factors of objectives. While, the minimum discharge changed with using different weights of objective functions, in a manner that the discharge release is decreased to the minimum level of downstream requirements, especially for the first year of reservoir operation, by increasing the value of weight factor for the power objective (𝑤1 ) in order to rise the water surface elevation in the reservoir to generate more hydropower. In addition, the outcomes of the developed models display that the discharge releases based on NLP (Model-II-a) and S-O (Model-III) models are very close, in contrast with the results of the DDDP (Model-II-b) model that lesser discharge is released to the downstream in order to remain the reservoir storage at a high level to generate more hydropower. 5.3.1 Deficit in Downstream Demands Deficiency is occurred when the discharge release cannot satisfy the downstream demands and the monthly deficits during the operation of Dokan reservoir are presented in Fig. (5-5). From the figure, it can be observed that the most deficits of the developed models were occurred during the first and last 18 years of operation (1958-1962 and 1999-2011) i.e., about 33% of the time horizon. This pattern shows that there has been an extensive use of water in the region upstream of the dam during the last decade and subsequently the inflow discharge was decreased in that period. The highest value of deficit was recorded with the operation of SOP simulation model (Model-I). In this model, sometimes the minimum requirement for environmental flow and domestic use cannot be satisfied. Although, it has minimum deficit events along the time period of reservoir operation. On the other hand, the NLP optimization model (Model-II-a) has more events with a little deficit in the downstream release whereas the combined simulation-optimization using GA model (Model-III) has greater deficits comparing with the other models. [ 78 ]

Chapter Five

Results and Discussions

300 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O) Actual

Deficit in Release (m3/s)

250

200

150

100

50

0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-5): Monthly deficit in downstream demands of proposed models and actual operation for Dokan reservoir. The objectives of the developed models are minimization of deficits in irrigation and hydropower generation. Table (5-2) represents the characteristics of deficit months in Dokan reservoir operation based on the proposed models and historical operation. The number of deficit months changes with the different weight factors of objectives. The two objectives are mutually conflicting objectives, in a manner the one that tries for minimization of the irrigation deficits, requires more water to be released to satisfy irrigation demands and the other tries to maximize hydropower production, requiring higher level of storage in the reservoir to produce more power. In contrast, from the applied models the historical operation has the greater deficit events throughout the time period of reservoir operation and the deficiency in the range (0.16-167.07 m3/s), the deficiency is during (292 months) out of the (648 months) operation period.

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Results and Discussions

Table (5-2): Characteristics of deficit months in Dokan reservoir operation based on the proposed models and actual operation. Models

Average deficit in discharge release (m3/s)

Maximum deficit in discharge release (m3/s)

Minimum deficit in discharge release (m3/s)

No. of deficit events

Percentage of deficit events (%)

Model-II-a (NLP)

Model-II-b (DDDP)

Model-III (S-O)

1

20.08

19.56

26.86

0.2

0.8

14.04

21.46

19.31

0.5

0.5

17.15

24.88

25.72

0.8

0.2

28.06

29.99

42.73

1

0

46.42

46.15

61.67

0

1

43.06

40.1

112.9

0.2

0.8

41.82

56.81

118.95

0.5

0.5

48.65

61.62

136.83

0.8

0.2

85.26

91.76

139.12

1

0

148.93

149.32

164.62

0

1

0.13

0.83

0.38

0.2

0.8

0.11

0.2

0.25

0.5

0.5

0.11

0.2

0.14

0.8

0.2

0.15

0.2

0.76

1

0

1.39

0.24

0.65

0

1

159

152

125

0.2

0.8

263

166

225

0.5

0.5

261

176

256

0.8

0.2

233

205

234

1

0

185

163

234

0

1

24.54

23.46

19.29

0.2

0.8

40.59

25.62

34.72

0.5

0.5

40.28

27.16

39.51

0.8

0.2

35.96

31.64

36.11

1

0

28.55

25.15

36.11

𝑤1

𝑤2

0

Actual

64.57

167.07

0.16

292

45.06

Model-I (SOP)

78.8

180.98

1.41

45

6.94

[ 80 ]

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Results and Discussions

5.3.2 Performance Criteria of Reservoir System The operational status of water resources systems can be classified as satisfactory, unsatisfactory, or failed. Hence, performance criteria can be defined as the indicator for evaluating the performance of reservoir operation systems and also useful to evaluate and rank different alternative plans or policies. In this study, the reliability, resilience and vulnerability criterion were used to analyse and compare the results of the suggested models. According to the results of all the proposed models, water supply for domestic, industrial and environmental flow can be satisfied without any deficits in all 648 months, except the simulation (SOP) model (Model-I) has 10 months of shortage. On the other hand, the results reveal that water allocated for the agricultural sector cannot satisfy all demands. Hence, the number of failure months in irrigation demand can be calculated based on Natural Resources Conservation Service (NRCS) practice to use the 80 percent of irrigation demand as a minimum criterion (USDA NRCS, 2009). The calculated number of critical failure months and performance indices of discharge release by considering 80% supply of downstream agricultural demand in all months are shown in Table (5-3). The higher reliability for irrigation demand and dangerous deficit events in irrigation and water quality requirement was recorded in the simulation (SOP) model (Model-I). While, the reliabilities of irrigation demand based on optimization models (Model-II-a and Model-II-b) are very close and the combined simulation-optimization (S-O) model (Model-III) provided more reliability and resilience than the optimization models. The reliability and resilience values are varying with the different weight factors of objective functions. Irrigation reliability in the optimization models was decreased with increasing the weight factors of hydropower objective function and vice versa because of, increase the reliability of irrigation demand requires more discharge released for the downstream and it is conflicting with the hydropower objectives

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Results and Discussions

that required less discharge release for the downstream to protect the water surface elevation at a high level in the reservoir. Furthermore, the maximum and minimum vulnerabilities were recorded in the simulation model (Model-I) and the NLP optimization model (Model-II-a) respectively and this represents the severity of failure events for irrigation demand. By comparing the results of discharge releases for all the developed models with the actual discharge release for Dokan reservoir system, it is observed that the actual status has the most failure events in irrigation and minimum downstream requirements. Also, high vulnerability was occurred in the actual operation status which increases the risk of deficiencies in irrigation and water supply demand.

Table (5-3): Performance criteria of proposed models for downstream discharge release. Models No. of months with deficit in irrigation demand greater than 20%

Reliability

Resilience

Vulnerability (Mm3)

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Actual

Model-I (SOP)

240

40

0.63

0.94

0.25

0.23

133.36

169.71

[ 82 ]

Model-II-a (NLP)

Model-II-b (DDDP)

Model-III (S-O)

63 67 91 104 117 0.9 0.9 0.86 0.84 0.82 0.15 0.19 0.08 0.05 0.21 23.75 25.88 31.09 68.1 104.09

56 62 77 101 106 0.91 0.9 0.88 0.84 0.83 0.19 0.47 0.34 0.04 0.17 20.98 45.29 52.16 70.85 104.14

59 59 118 149 188 0.91 0.91 0.82 0.77 0.71 0.58 0.58 0.45 0.5 0.56 65.15 59.33 48.47 88.43 130.14

Chapter Five

Results and Discussions

5.4 Hydropower Generation From the results of developed models appeared that the average monthly hydropower generation in the DDDP optimization model (Model-II-b) is greater than the other models while the maximum power that can be produced was obtained in the SOP simulation model (Model-I). In other words, optimization process minimizes hydropower deficits and it causes less reduction rates of power generation when compared to the deficits obtained with simulation based on the standard operating policies. Table (5-4) and Table (5-5) show the characteristics of hydropower and energy generation respectively of the developed models.

Table (5-4): Characteristics of hydropower generation of the proposed models. Models

Average monthly power produced (MW)

Maximum monthly power produced (MW)

Minimum monthly power produced (MW)

No. of months’ power production halted

Model-I (SOP)

Model-II-a Model-II-b (NLP) (DDDP)

Model-III (S-O)

𝑤1

𝑤2

0

1

115.36

114.29

127.93

0.2

0.8

134.84

134.94

133.24

0.5

0.5

135.93

135.92

134.79

0.8

0.2

137.38

137.57

135.48

1

0

137.86

138.01

135.24

0

1

359.28

362.34

359.78

0.2

0.8

346.84

351.5

361.2

0.5

0.5

346.84

351.5

362.97

0.8

0.2

346.84

342.83

363.04

1

0

346.84

341.89

360.35

0

1

33.1

35.28

0

0.2

0.8

34.37

24.77

0

0.5

0.5

0

0

0

0.8

0.2

0

0

0

1

0

0

0

0

0

1

0

0

5

0.2

0.8

0

0

1

0.5

0.5

1

9

5

0.8

0.2

6

9

21

1

0

13

13

43

130.85

364.83

0

25

[ 83 ]

Chapter Five

Results and Discussions

Table (5-5): Characteristics of monthly energy production of the proposed models. Models

Average energy generated per month (MWh)

Maximum energy generated per month (MWh)

Minimum energy generated per month (MWh)

Model-II-a (NLP)

Model-II-b (DDDP)

Model-III (S-O)

1

83059.2

82288.8

92109.6

0.2

0.8

97084.8

97156.8

95932.8

0.5

0.5

97869.6

97862.4

97048.8

0.8

0.2

98913.6

99050.4

97545.6

1

0

99259.2

99367.2

97372.8

0

1

258681.6

260884.8

259041.6

0.2

0.8

249724.8

253080

260064

0.5

0.5

249724.8

253080

261338.4

0.8

0.2

249724.8

246837.6

261388.8

1

0

249724.8

246160.8

259452

0

1

23832

25401.6

0

0.2

0.8

24746.4

17834.4

0

0.5

0.5

0

0

0

0.8

0.2

0

0

0

1

0

0

0

0

𝑤1

𝑤2

0

Model-I (SOP)

94212

262677.6

0

The results of applied models exhibit most numbers of months that power generation is halted (25 months) occurred in the SOP simulation model (ModelI) due to the discharge release through turbines is less than the minimum discharge (50 m3/s) required for hydropower generation. Fig. (5-6) and Fig. (5-7) show the monthly hydropower generation of the proposed models during the period (19582011) and first year of operation (1958) respectively. While, for other models the number of failure months for power generation rises directly with increase the weight factor of hydropower generation objective function. In addition, the higher production of hydropower was generated during summer months (May to September). In other words, the production of hydropower is proportional with the downstream demands except for SOP simulation model (Model-I) which has a greater generated power during the winter season. [ 84 ]

Chapter Five

Results and Discussions

600 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

Power generated (MW)

500 400 300 200 100 0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-6): Monthly generated power of the proposed models for Dokan reservoir system during the period (1958-2011). 160 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

Power generated (MW)

140 120 100 80 60 40 20 1

2

3

4

5

6 7 Time (Month)

8

9

10

11

12

Fig. (5-7): Monthly generated power of the proposed models for Dokan reservoir system during the first year of operation (1958). The average monthly hydropower generation of the proposed models for Dokan power station was observed throughout the period (1995-2011) as shown in the Fig. (5-8). The figure demonstrates that the actual operation system has a lower power generation comparing with the results of the developed models especially during the wet season and so on the lowest and highest power was produced in the months of April and August respectively. Moreover, considering [ 85 ]

Chapter Five

Results and Discussions

the weight factors (𝑤1 = 0.8, 𝑤2 = 0.2), the annual production of hydropower for the period (1995-2011) can be increased by 24.9, 30.64, 31.16 and 26.46% more than the actual hydropower production when the models, Model-I (SOP), Model-II-a (NLP), Model-II-b (DDDP) and Model-III (GA) are applied respectively. Hence, it can be said that the system operation with any of the proposed models is better than the actual operation of the reservoir system.

200

Model-I(SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O) Actual

Power generated (MW)

180 160 140 120 100 80 60 40 Jan.

Feb.

Mar.

Apr.

May

Jun. Jul. Months

Aug.

Sep.

Oct.

Nov.

Dec.

Fig. (5-8): Average monthly power generation of the proposed models for Dokan reservoir system. When the reservoir water level is between the lower and upper limits, discharge release through turbines between the minimum (50 m3/s) and maximum (470 m3/s) is required for hydropower generation. The water that is released through turbines can also be used for supplying downstream demands. If the discharge is less than the minimum required for hydropower generation, then the released will be through the bottom outlets for the purpose of irrigation and other demands. The average monthly discharge release through turbines for different months can be derived from the series of discharge releases along the operation time period as shown in Table (5-6).

[ 86 ]

Chapter Five

Results and Discussions

Table (5-6): Average monthly discharge releases through turbines of the proposed models for Dokan reservoir system. Models

January

February

March

April

May

June

July

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Model-I (SOP)

143.92

236.98

213.11

222.47

188.63

193.14

183.90

Model-II-a (NLP) 154.16 170.07 170.13 172.3 182.12 189.24 193.83 195.16 197.29 206.05 209.76 191.48 191.1 189.27 183.42 197.73 196.14 196.07 194.39 191.92 187.91 181.80 181.99 182.27 184.11 220.87 200.52 198.75 192.9 177.61 225.64 198.97 197.04 190.72 173.22

Model-II-b (DDDP) 158.58 156.93 154.71 161.05 169.51 201.87 180.00 179.06 177.64 184.94 225.88 193.48 188.67 187.78 184.12 214.25 200.94 198.82 200.55 197.96 203.02 194.93 193.86 193.35 195.96 234.24 209.35 209.43 204.02 193.97 220.53 208.40 210.86 202.38 189.86

Model-III (S-O) 148.85 149.64 170.12 170.53 182.56 173.65 178.67 181.25 192.46 208.38 191.47 186.16 195.85 201.61 161.16 194.84 194.30 202.45 188.35 187.95 183.11 186.67 190.02 183.14 181.37 221.95 214.07 198.07 196.85 186.29 231.18 219.39 202.97 192.15 178.96

Models

August

September

October

November

December

Average monthly discharge release (m3/s)

[ 87 ]

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Model-I (SOP)

172.34

134.70

176.55

132.30

132.01

177.5

Model-II-a (NLP) 214.64 195.11 193.88 189.06 177.08 163.12 177.51 178.17 180.97 188.72 146.02 173.41 174.27 178.75 188.63 176.74 180.76 181.07 183.03 184.73 144.99 171.41 172.51 175.97 184.81 185.90 185.92 185.85 185.58 185.20

Model-II-b (DDDP) 197.11 206.51 206.61 202.49 195.50 155.18 189.59 192.55 200.17 208.55 125.27 150.90 153.02 155.80 157.70 157.54 175.88 175.48 172.26 170.31 138.24 161.52 160.62 166.10 171.75 185.98 185.7 185.31 185.3 185.01

Model-III (S-O) 203.11 204.79 206.56 188.73 181.13 181.41 175.60 170.61 163.13 175.24 158.83 171.45 167 171.27 179.49 180.11 184.88 181.74 199.87 202.53 158.16 164.26 159.59 168.02 177.62 185.56 185.82 185.52 184.68 183.56

Chapter Five

Results and Discussions

Based on the SOP simulation model (Model-I) the discharge release through turbines during the months of February to April is more than the discharge of other models during the same period. While, after the month of May, discharge release is decreasing in a manner that sometimes would be less than the minimum water requirement for downstream (environmental flow). The most of times that the power generation is halted between the months of September to December. Average monthly discharge release through turbines for Dokan reservoir based on proposed models is shown in Fig. (5-9). As it is clear, the pattern of monthly discharge releases through turbines according to the results of optimization (Model-II-a, Model-II-b) and combined simulation-optimization (Model-III) models is different from the pattern of simulation model (Model-I) since, the standard operating policy (SOP) aims to best meet the demand in each period based on the water availability in that period. While, the optimization techniques are searched to find the optimum operation policy throughout the time period of reservoir operation.

280 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

Release through turbines (m3/s)

260 240 220 200 180 160 140 120 Jan.

Feb.

Mar.

Apr.

May

Jun. Jul. Months

Aug.

Sep.

Oct.

Nov.

Dec.

Fig. (5-9): Average monthly discharge releases through turbines of the proposed models for Dokan reservoir system.

[ 89 ]

Chapter Five

Results and Discussions

5.5 Reservoir Storage Generally, reservoir storage should serve the two conflicting objectives in the current study, which are the discharge release for the downstream demands and at the same time it should be filled to provide hydraulic head to the hydropower turbines hence, the solution should be the balanced storage between the objectives. From the characteristics of reservoir storage in Table (5-7) which is obtained by applying the proposed models appear that the monthly average storage of reservoir in the DDDP optimization model (Model-II-b) is more than the storage volume of other proposed models. Additionally, all the proposed models have the same maximum storage, while the minimum storage changes with using different weight factors of objectives. On the other hand, the number of months that the reservoir storage is full for SOP simulation model (Model-I) is more than the other models. At the same time, the model has a minimum reservoir storage for the most of operation time period because the operation of reservoir with standard operation policy (SOP) depends on the available water in the reservoir, if greater than the downstream demands then excess water is saved in the reservoir. Furthermore, the average storage of reservoir with the number of months that reservoir is full was increased directly by increasing the weights of hydropower objective (𝑤1 ) because of hydropower generating depends on the hydraulic head of water in the reservoir and the discharge released through turbines. Therefore, discharge release through turbines at a high level of water in the reservoir increases the production of hydropower. In other means, increased storage allows dam administrators to allocate water based on priorities and decrease deficiencies in drought seasons. The variation of storage in the reservoir throughout 54 years and first year of operation by running the mentioned models are displayed in Fig. (5-10) and Fig. (5-11) respectively. As it is clear from the figure that the storage volume pattern of reservoir along the operation time period for the SOP simulation model (Model-I) is different from the other models because the standard operating policy [ 90 ]

Chapter Five

Results and Discussions

(SOP) aims to best meet the demand in each period based on the water availability in that period. While, the optimization techniques are searched to find the optimum operation policy throughout the time period of reservoir operation.

Table (5-7): Characteristics of reservoir storage of the proposed models for Dokan reservoir. Models

Average storage of reservoir (Mm3)

Maximum storage of reservoir (Mm3)

Minimum storage of reservoir (Mm3)

No. of months’ reservoir is full

Percentage of months’ reservoir is full

No. of months’ reservoir is minimum

percentage of months’ reservoir is minimum

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Model-I (SOP)

4842.48

6800

1400

204

31.48

45

6.94

[ 91 ]

Model-II-a (NLP) 2792.03 4754.26 4899.81 5187.62 5382.32 6794.44 6800 6800 6800 6800 1400 1400 1400 1410.48 1410.49 0 38 39 42 47 0 5.86 6.02 6.48 7.25 2 2 1 0 0 0.31 0.31 0.15 0 0

Model-II-b (DDDP) 2751.09 4744.44 4934.42 5216.99 5373.95 6698.03 6800 6800 6800 6800 1400 1400 1400 1497.27 1612.71 4 64 76 71 87 0.62 9.88 11.73 10.96 13.43 81 5 2 0 0 12.5 0.77 0.31 0 0

Model-III (S-O) 3952.77 4521.58 4744.71 4996.34 5155.4 6800 6800 6800 6800 6800 1400 1400 1400 1400 1401.03 10 10 10 12 7 1.54 1.54 1.54 1.85 1.08 1 1 1 1 0 0.15 0.15 0.15 0.15 0

Chapter Five

Results and Discussions

10000 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

9000

Reservoir storage (Mm3)

8000 7000 6000 5000 4000 3000 2000 1000 0

100

200

300 Time (Month)

400

500

600

Fig. (5-10): Monthly reservoir storages of the proposed models for Dokan reservoir system during the period (1958-2011). 4000 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

Reservoir storage (Mm3)

3500 3000 2500 2000 1500 1000 1

2

3

4

5

6 7 Time (Month)

8

9

10

11

12

Fig. (5-11): Monthly reservoir storages of the proposed models for Dokan reservoir system during the first year of operation (1958).

5.6 Spillway Discharge Discharge over the spillway is caused by the water level to rise above normal water level. This excess storage is surcharge storage and is normally uncontrolled. Monthly overflow (spill) discharge at the reservoir along the time horizon is presented in Fig. (5-12). [ 92 ]

Chapter Five

Results and Discussions

From the results of the developed models it is appeared that the spill occurred only in the SOP simulation (Model-I) and DDDP optimization (Model-II-b) models. The discharge release through spillway occurred between the months of March to May due to high inflow in that period. Table (5-8) represents the characteristics of uncontrolled releases through spillway of the proposed models. Also, it can be observed that the spill did not occur during the last decade. This could be an indicator that the inflow to the reservoir has been decreased either due to the change in climate or due to new constructions that might have been built in the reaches of the river upstream of the dam. Furthermore, combined simulation-optimization (Model-III) and NLP optimization (Model-II-a) models indicate that the spillway has not operated during all the period of operation time and that because the releases for all months are less than the maximum capacity of the power station. Therefore, all releases are passed through the turbines and used to generate electric power. In other words, these models provide an improvement in the reservoir operation in terms of increasing storage volumes, ensuring reliable releases, and decrease in spill events comparing to the other developed models.

Spillway discharge (m3/s)

1000 Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

800

600

400

200

0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-12): Discharge releases through spillway of the proposed models for Dokan reservoir during the period (1958-2011).

[ 93 ]

Chapter Five

Results and Discussions

Table (5-8): Characteristics of uncontrolled releases through spillway of the proposed models. Models

No. of months’ spillway operating

Average spillway release (m3/s)

Maximum spillway release (m3/s)

Minimum spillway release (m3/s)

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Model-I (SOP)

21

237.56

878.25

2.4

Model-II-a (NLP) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Model-II-b (DDDP) 0 0 0 3 2 0 0 0 9.73 52.47 0 0 0 17.31 74.36 0 0 0 5.56 30.58

Model-III (S-O) 0 4 5 7 0 0 0.28 0.92 0.47 0 0 0.53 2.03 1.46 0 0 0.12 0.14 0.13 0

5.7 Elevation of Reservoir Water The spillway crest usually is designated as the normal water level for reservoir operation and the target water level in the reservoir should be kept below the flood control level in order to provide sufficient storage for flood cutting. Therefore, when water level rises above normal operation, this excess storage is surcharge storage and is normally uncontrolled to protect the dam against flooding. Also, when the water level in the reservoir is below the minimum operating level, hydropower generation is halted. Monthly water surface elevation in the Dokan reservoir throughout time period of operation is shown in Fig. (5-13). In this figure, it can be noted that the reservoir has a lower water level during the first and last years of operation, due to climate changes and decreased inflow discharge in that periods.

[ 94 ]

Chapter Five

Results and Discussions

Moreover, the average monthly elevation of water surface in the reservoir is extracted from the results of 648 months for each model. It can be said that the average water levels in the reservoir are very close based on the two optimization models (Model-II-a, Model-II-b). On the other hand, the elevation of water surface in the reservoir for combined simulation-optimization (S-O) model (Model-III) is nearly (1.0) m below the water elevation of other models. This state appears the powerful of NLP and DDDP optimization methods to find the optimal solution for the objectives of this study. Monthly operation rule curves in terms of water elevation in Dokan reservoir for the proposed models are shown in Table (5-9) and Fig. (5-14). As it is clear from the results, the maximum elevations of water surface in Dokan reservoir are recorded in the month of May for the SOP simulation model. In contrast, from the results of other suggested models, the maximum elevations of water are occurred in the month of June. It means that, in the optimization methods the maximum elevation of water in the reservoir is lagged one month in order to save more water in the reservoir for the months that have low inflow rate i.e. months of the season of summer.

Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

525 520

Water elevation (m)

515 510 505 500 495 490 485 480 475 0

100

200

300 Time (Month)

400

500

600

Fig. (5-13): Monthly water surface elevation of the proposed models for Dokan reservoir system during the period (1958-2011).

[ 95 ]

Chapter Five

Results and Discussions

Table (5-9): Average monthly water surface elevation of the proposed models for Dokan reservoir. Models

January

February

March

April

May

June

July

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Model-I (SOP)

500.89

501.55

503.58

505.64

506.36

505.54

504.27

Model-II-a (NLP) 484.88 498.81 499.99 501.93 503.05 485.61 499.13 500.26 502.07 503.02 487.58 500.47 501.53 503.23 504.02 491.99 503.91 504.91 506.51 507.27 496.51 506.68 507.59 509.06 509.75 498.09 507.60 508.46 509.85 510.50 496.43 506.76 507.69 509.24 510.07

Model-II-b (DDDP) 485.37 498.88 500.22 502.16 503.10 485.90 499.34 500.67 502.42 503.23 487.46 500.79 502.06 503.72 504.40 491.60 504.15 505.4 506.93 507.55 495.92 506.86 508.01 509.37 509.94 497.29 507.67 508.77 510.08 510.60 495.44 506.80 507.96 509.41 510.07

Model-III (S-O) 493.31 497.26 499.26 500.90 501.71 494.07 497.94 499.54 501.09 501.67 495.90 499.51 501.02 502.37 502.69 499.94 503.18 504.47 505.57 506.39 503.46 506.15 507.22 508.36 509.02 504.61 507.07 508.04 509.21 509.81 503.34 506.1 507.22 508.54 509.28

Models

August

September

October

November

December

Average monthly discharge release (m3/s)

[ 96 ]

𝑤1

𝑤2

0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1 0 0.2 0.5 0.8 1

1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0 1 0.8 0.5 0.2 0

Model-I (SOP)

502.86

501.93

500.50

499.96

500.13

502.77

Model-II-a (NLP) 493.64 505.33 506.35 508.11 509.20 490.56 503.63 504.74 506.71 508.02 488.44 502.10 503.25 505.27 506.57 486.51 500.48 501.65 503.67 504.90 484.71 499.16 500.36 502.41 503.64 490.41 502.84 503.9 505.67 506.67

Model-II-b (DDDP) 492.71 505.31 506.52 508.21 509.06 489.92 503.48 504.78 506.67 507.69 487.87 501.79 503.11 504.99 505.97 486.40 500.40 501.71 503.63 504.61 485.04 499.11 500.47 502.49 503.51 490.08 502.88 504.14 505.84 506.64

Model-III (S-O) 501.13 504.40 505.79 507.35 508.25 498.90 502.43 503.97 505.80 506.86 496.87 500.73 502.47 504.47 505.44 495.05 498.96 500.87 502.87 503.79 493.51 497.49 499.51 501.29 502.18 498.34 501.77 503.28 504.82 505.59

Chapter Five

Results and Discussions

Average water elevation (m)

510

Model-I (SOP) Model-II-a (NLP) Model-II-b (DDDP) Model-III (S-O)

508 506 504 502 500 498 496 Jan.

Feb.

Mar.

Apr.

May

Jun. Jul. Months

Aug.

Sep.

Oct.

Nov.

Dec.

Fig. (5-14): Average monthly water surface elevation of the proposed models for Dokan reservoir.

5.8 Sensitivity Analysis of Models Sensitivity analysis is the technique used to describe how much model output values are affected by changes in model input values. It is the investigation of the importance of imprecision or uncertainty in model inputs in a decision-making or modelling process (Loucks, et al., 2005). Usually water demand for different sectors in any particular month is varying from year to year caused by meteorological and climate changes as well as changes in crop patterns, irrigation practice, etc. In the present study, the series of downstream demands for Dokan reservoir throughout different years of operation (1958-2011) is not available. Therefore, to demonstrate the effect of varying demands along different years of reservoir operation on the outputs of developed models, the downstream demands were assumed to change randomly between 80-120% of the estimated downstream demands. For this purpose, the DDDP optimization (Model-II-b) model and combined simulation-optimization (S-O) model (Model-III) has been applied to get the discharge releases and power generation for variable demand status and then compared with the constant demand state. Table (5-10) represents the characteristics and performance criteria of discharge release based on variable and constant demand status for weight factors of 𝑤1 = 0.2 and 𝑤2 = 0.8. [ 97 ]

Chapter Five

Results and Discussions

The results of DDDP optimization model (Model-II-b) demonstrate that the discharge release at most times is directly changed with the same or less than the amount of varying downstream demands. In addition, the performance indices; reliability, resilience and vulnerability of discharge releases were decreased, compared to the constant demand status. While, the discharge releases for combined simulation-optimization (S-O) model (Model-III) for the variable demand state show there is a significant change compared with the constant demand state and a greater deficit in discharge releases as a result of vulnerability increasing. The series of discharge releases for variable and constant demand states for DDDP optimization (Model-II-b) and combined simulationoptimization (Model-III) models are shown in Fig. (5-15) and Fig. (5-16) respectively.

Table (5-10): Characteristics and performance criteria of discharge releases based on variable and constant demand states. Variable Demand Models

Constant Demand

Model-II-b (DDDP)

Model-III (S-O)

Model-II-b (DDDP)

Model-III (S-O)

Maximum discharge release (m3/s)

467.46

467.03

462.96

469.24

Average discharge release (m3/s)

188.94

188.91

188.94

188.94

Minimum discharge release (m3/s)

38.97

28.41

38.97

31.99

Reliability

0.88

0.88

0.9

0.91

Resilience

0.3

0.61

0.47

0.58

Vulnerability (Mm3)

32.05

64.53

45.29

59.33

[ 98 ]

Chapter Five

Results and Discussions

600 Variable demand Constant demand

Discharge release (m3/s)

500

400

300

200

100

0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-15): Discharge releases of DDDP optimization model (Model-II-b) for Dokan reservoir system during the period (1958-2011). 600 Variable demand Constant demand

Discharge release (m3/s)

500

400

300

200

100

0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-16): Discharge releases of simulation-optimization (S-O) model (ModelIII) for Dokan reservoir system during the period (1958-2011). Furthermore, although some events of power failure (power production halted) were recorded in the results of the DDDP optimization model (Model-IIb), there is no significant change in the production of hydropower by using variable demands. Table (5-11) represents the characteristics of hydropower generation for variable and constant demand states for weight factors of 𝑤1 = 0.2 and 𝑤2 = 0.8. On the other hand, the maximum and average values of [ 99 ]

Chapter Five

Results and Discussions

hydropower generation for variable demand state are reduced for combined simulation-optimization (S-O) model (Model-III). The patterns of power production throughout reservoir operation for variable demand state are shown in Fig. (5-17) and Fig. (5-18) for DDDP optimization (Model-II-b) and combined simulation-optimization (Model-III) models respectively.

Table (5-11): Characteristics of power generation for variable and constant demand states. Variable Demand Models

Model-II-b (DDDP)

Model-III (S-O)

Average monthly power produced (MW)

134.66

Maximum monthly power produced (MW)

Constant Demand Model-III Model-II-b (DDDP)

(S-O)

132.47

134.94

133.24

351.5

355.8

351.5

361.2

Minimum monthly power produced (MW)

0

0

24.77

0

No. of months’ power production halted

6

4

0

1

500 Variable demand Constant demand

450

Power generated (MW)

400 350 300 250 200 150 100 50 0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-17): Power generation of DDDP optimization model (Model-II-b) for Dokan reservoir system during the period (1958-2011). [ 100 ]

Chapter Five

Results and Discussions

500 Variable demand 450

Constant demand

Power generated (MW)

400 350 300 250 200 150 100 50 0

0

100

200

300 Time (Month)

400

500

600

Fig. (5-18): Power generation of simulation-optimization (S-O) model (ModelIII) for Dokan reservoir system during the period (1958-2011).

5.9 Selection of Best Model The suitability of any model in this study is measured based on which of the models has the better results for the performance criteria in a manner that always fulfils the minimum water requirements for downstream (environmental flow and domestic use) and provides a higher reliability and resilience with lower vulnerability of irrigation demand. On the other hand, hydropower generation is the second objective of the Dokan reservoir system hence, increasing hydropower production is one of the important aims of the present study. In this way, by considering the first priority of objectives, the proposed models with weight factors of 𝑤1 = 0.2 and 𝑤2 = 0.8 give better results to satisfy downstream demands. Whereas, the SOP simulation model (Model-I) has a hazardous deficit in irrigation and minimum downstream demands with lower power production. Also, NLP optimization (Model-II-a) and combined simulation-optimization (Model-III) models have a low resilience and higher vulnerability (cause higher severity of failure events) respectively. While, unlike other models, the DDDP optimization model (Model-II-b) provides high reliability with more power generation at the same time. Moreover, it can be easily applied for solving the nonlinear and multi objective problems with less [ 101 ]

Chapter Five

Results and Discussions

computational time requirements. Hence, among the proposed models, the DDDP optimization model (Model-II-b) can be selected as the best model for operating the Dokan reservoir system.

[ 102 ]

CHAPTER SIX CONCLUTIONS AND RECOMMENDATIONS

Chapter Six

Conclusions and Recommendations

Chapter Six Conclusions and Recommendations 6.1 Introduction In the current study, four models are proposed to increase the efficiency of the Dokan reservoir operation system in terms of hydropower generation and water supply for downstream uses. These models are one traditional simulation model (Model-I) based on SOP, two optimization models, NLP (Model-II-a) and DDDP (Model-II-b) and one combined simulation-optimization (S-O) model (Model-III) as a new technique using Simulink and GA. The outcomes of the study, and recommendations for future studies are presented in the following sections. 6.2 Conclusions From the results of simulation, optimization and combined simulation optimization developed models in the present study; the following facts were observed and concluded: 1. Study results demonstrate that the applied models can efficiently optimize the hydropower production and decrease the deficit in downstream irrigation demands for Dokan reservoir operation system. 2. According to Dokan reservoir releases based on the developed models show that about 80% of failure events in irrigation demand occurred during the last 13 years from 1999 to 2011. This pattern displays that there has been an increased extensive use of water in the region upstream of the dam during the last decade. This could be an indicator that the inflows into the Dokan reservoir have been decreased either due to the change in climate or due to new constructions that might have been built in the reaches of the river upstream of the dam. 3. Hydropower generation is the main objective of the Dokan reservoir. Hence, this reservoir is an important source of electrical power generation for Kurdistan Region, Iraq. Based on hydropower generation results of the [ 103 ]

Chapter Six

Conclusions and Recommendations

developed models during the period of 1995-2011 it has been found that the total annual hydropower generation between 1280 MW and 1344 MW with an increase about 25 % to 31 % more than the production of actual system operation, which is 1025 MW. 4. Results appear that the reservoir operation with each of the suggested models can increase the reliability of irrigation demand from 0.66 of real operation of the reservoir to above 0.9. 5. Minimizing the deficit in irrigation demand and power generation is mutually conflicting objectives, in a manner the one that tries for minimization of the irrigation deficits requires more water to be released to satisfy irrigation demands and the other tries to maximize hydropower production requires higher level of storage in the reservoir to produce more power. 6. The output of the DDDP optimization model (Model-II-b) based on varied downstream demand shows that the discharge release and hydropower generation is directly changed by the same or less than the percentage of varying demands. 7. Comparing the results of all implemented models shows that the operation of DDDP optimization model (Model-II-a) can produce more hydropower than the other models. Also, it has better solution to satisfy the downstream demands with lesser computational time to reach the optimal solution. 6.3 Recommendations The following recommendations were found to provide a guidance for further studies: 1. It is important to continue studying to develop the combined simulationoptimization model for Dokan reservoir system by using other techniques such as Tabu Search (TS), Simulated Annealing (SA), Evolutionary Strategies (ES), …, etc., which may give better results than the results of GA in this study. 2. Most of the indicators show that the inflow discharge to Dokan reservoir has decreased due to climate changes and restriction on the upstream of the [ 104 ]

Chapter Six

Conclusions and Recommendations

reservoir. Therefore, it is recommended to develop new models to demonstrate the effects of using modern irrigation methods in order to decrease the deficiency in the downstream demands of Dokan reservoir as an alternative in the future. 3. To determine the optimum strategy for future reservoir operation, it is recommended to predict the inflow discharge for future months and then the developed models can be applied.

[ 105 ]

REFERENCES

References

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Kjeldsen, T. R. & Rosbjerg, D., 2004. Choice of reliability, resilience and vulnerability estimators for risk assessments of water resources systems. Hydrological Sciences–Journal–des Sciences Hydrologiques, October, 49(5), pp. 755-767. Koya Water Resources Directorate (2016). Loucks, D. P. et al., 2005. Water Resources Systems planning and Management: An introduction to methods, models and applications. Paris: UNESCO. McCuen, R. H., 1998. Hydrologic Analysis and Design. 2nd ed. New Jersey: Pearson Prentice Hall. Melanie, M., 1999. An Introduction to Genetic Algorithms. Fifth printing ed. London: Massachusetts Institute of Technology. Montaseri, M., Afshar, M. H. & Bozorg-Haddad, O., 2015. Development of Simulation-Optimization Model (MUSIC-GA) for Urban Stormwater Management. Water Resour Manage, October, 29(13), p. 4649–4665. Mousavi, S. J., Ponnambalam, K. & Karray, F., 2005. Reservoir Operation Using a Dynamic Programming Fuzzy Rule–Based Approach. Water Resources Management, October, 19(5), p. 655–672. Mujumdar, P. P. & Vedula. , S., 2005. Water Resources Systems. New Delhi: Tata McGraw-Hill Education. Mythili, B., Devi, U. G., Raviteja, A. & Kumar, P. S., 2013. Study of optimizing techniques of reservoir operation. International Journal of Engineering Research and General Science, August.1(1). Ngo, L. L., 2006. Optimising reservoir operation: A case study of the Hoa Binh reservoir, Vietnam. Bygningstorvet, Building 115,Technical University of Denmark: Institute of Environment & Resources. Ngo, L. L., Madsen, H. & Rosbjerg, D., 2007. Simulation and optimisation modelling approach for operation of the Hoa Binh reservoir, Vietnam. Journal of Hydrology, 336(3-4), p. 269– 281. Oliveira, R. & Loucks, D. . P., 1997. Operating rules for multireservoir system. Water resources research, April, 33(4), pp. 839-852. [ 109 ]

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[Online]

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‫اخلالصة‬ ‫إن نظام تشغيل الخزانات هو جزء أساسي من إدارة موارد المياه وان كل خزان له سياسة‬ ‫خاصة للتشغيل‪ .‬ان المحاكاة واألمثلية هما تقنيتان مختلفتان في عملية التشغيل ألي خزان‪.‬‬ ‫لذلك‪ ،‬تهدف هذه الدراسة إلى تطوير نموذج محاكاة جنبا إلى جنب مع نموذج األمثلية (‪)S-O‬‬ ‫كت قنية جديدة استخدمت في السنوات األخيرة للحد من العجز في توليد الطاقة الكهرومائية‬ ‫والمتطلبات المائية للري في نظام خزان دوكان في إقليم كوردستان العراق‪ .‬لقد تم تطوير هذا‬ ‫النموذج بالجمع بين األداة )‪ (SIMULINK‬والخوارزمية الجينية (‪ )GA‬كتقنيتين للمحاكاة‬ ‫واألمثلية على التوالي‪.‬‬ ‫ولغرض المقارنة‪ ،‬فقد تم بناء نموذج محاكاة تقليدية (نموذج‪ )I-‬استنادا إلى سياسة‬ ‫التشغيل القياسية (‪ )SOP‬باستخدام أداة )‪ (SIMULINK‬في برنامج ‪MATLAB‬‬ ‫ونموذجين لألمثلية (نموذج‪ a-II-‬ونموذج‪ )b-II-‬باستخدام البرمجة غير الخطية (‪)NLP‬‬ ‫والبرمجة التفضيلية المنفصلة الديناميكية (‪ )DDDP‬على التوالي‪ .‬تم في هذه الدراسة‪ ،‬استخدام‬ ‫ثالثة معايير لتقييم األداء؛ وهي الموثوقية (‪ ،)Reliability‬والمرونة (‪)Resiliency‬‬ ‫والحساسية (‪ )Vulnerability‬لمقارنة وتقييم األداء للنماذج المستخدمة‪.‬‬ ‫تم تشغيل النماذج المقترحة باستخدام البيانات الشهرية لمدة ‪ 54‬عاما‪ ،‬أي ‪ 648‬شهرا تبدأ‬ ‫من كانون الثاني ‪ 1958‬إلى كانون االول ‪ .2011‬وأشارت النتائج إلى أن النموذج ‪SOP‬‬ ‫(نموذج‪ )I-‬ذا هامش مخاطرة عالي في حساب العجز في متطلبات الحد األدنى‪ ،‬على الرغم‬ ‫من الدرجة العالية من الموثوقية في تجهيز متطلبات الري (‪ .)0.94‬كما ان النماذج األخرى؛‬ ‫البرمجة غير الخطية (نموذج‪ ،)a-II-‬البرمجة التفضيلية المنفصلة الديناميكية (نموذج‪)b-II-‬‬ ‫و )‪( (S-O‬نموذج‪ )III-‬ومن خالل استخدام المعامالت الوزنية (‪ )w1 = 0.2‬و (‪)w2 = 0.8‬‬ ‫لديها تقريبا نفس الموثوقية للكهرباء والري‪ 0.90 ،0.90 ،‬و‪ 0.91‬على التوالي‪.‬‬ ‫عالوة على ذلك‪ ،‬فقد بينت النتائج مرونة منخفضة لنموذج البرمجة غير الخطية (نموذج‪-‬‬ ‫‪ )a-II‬ووجود حساسية شديدة لنموذج ‪( S-O‬نموذج‪ )III-‬الذي يتسبب بمخاطرة عالية لحدوث‬ ‫الفشل‪ .‬وباإلضافة إلى ذلك‪ ،‬وللفترة الممتدة ‪ ،2011-1995‬فان اإلنتاج السنوي من الطاقة‬ ‫الكهرومائية هي ‪ 1280‬ميغاواط‪ 1339 ،‬ميغاواط‪ 1344 ،‬ميغاواط و‪ 1296‬ميغاواط بزيادة‬

‫قدرها ‪ ٪31.16 ،٪30.64 ،٪24.9‬و‪ ٪26.46‬أكثر من إنتاج الطاقة الكهرومائية الفعلي‬ ‫(‪ 1025‬ميغاواط) للنماذج ‪( SOP‬نموذج‪( NLP ،)I-‬نموذج‪( DDDP ،)a-II-‬نموذج‪)b-II-‬‬ ‫و‪( S-O‬نموذج‪ )III-‬على التوالي‪.‬‬ ‫وأخيرا‪ ،‬فإن االستنتاجات تشير إلى أن النموذج األمثل هو ‪( DDDP‬نموذج‪ )b-II-‬حيث‬ ‫يوفر الموثوقية العالية‪ ،‬فضال عن المزيد من توليد الطاقة في نفس الوقت‪ .‬هذا النموذج يمكن‬ ‫تطبيقه بسهولة أكبر في حل المسائل غير الخطية ومتعددة األغراض مع وقت أقل للحسابات‪.‬‬

‫وزارة التعليم العالي والبحث العلمي‬ ‫جامعة السليمانية‬ ‫عمادة كلية اهلندسة‬ ‫قسم هندسة الري‬

‫منوذج حماكاة ‪-‬املثلى لنظام‬ ‫التشغيل يف خزان دوكان‬ ‫أطروحة‬ ‫مقدمة اىل عمادة كلية اهلندسة‪/‬جامعة السليمانية‬ ‫كجزء من متطلبات نيل درجة املاجستري‬ ‫يف هندسة املوارد املائية‬ ‫من قبل‬ ‫لقمان صابر عثمان‬ ‫بكالوريوس هندسة الري ‪2012 -‬‬ ‫باشراف‬ ‫د‪ .‬حكمت مصطفى إبراهيم‬

‫نيسان ‪ 2017‬ميالدية‬

‫نوروز ‪ 2717‬كردي‬

‫رجب ‪ 1438‬هجرية‬

‫ثوخـتـــة‬ ‫سیستهمی كاركردنی بهنداو بهشێكی بنچینهییه له بهڕێوهبردنی سهرچاوه ئاویهكان وه‬ ‫ههر بهنداوێك سیاسهتێكی تایبهتی ههیه بۆ ئیشپێكردنی‪ .‬لهبهرئهوه‪ ،‬پێویسته پالنیكی گونجاو‬ ‫دابمهزرێنرێت بۆ كارپێكردنی بهنداوهكه‪.‬سیمیولهیشن (‪ )Simulation‬وئاپتیمیزهیشن‬ ‫(‪ )Optimization‬دوو ڕێگهی جیاوازن له پرۆسهی كاركردنی ههر بهنداوێكدا‪ .‬لهبهرئهوه‪،‬‬ ‫ئامانجی ئهم توێژینهوه بریتیه له دروستكردنی نمونهیهك به تێكهڵكردنی ههردوو ڕێگهكه‬ ‫پێكهوه )‪ (combined simulation-optimization‬وهك ڕێگهیهكی نوێ لهم ساڵه تازانهدا‬ ‫بۆ كهمكردنهوهی بڕی كهمبوون (‪ )deficit‬له بهرههمی ووزهی كارهبا و پێویستیاتی ئاو بۆ‬ ‫ئاودێری بۆ سیستهمی بهنداوی دوكان له ههرێمی كوردستان‪ ،‬عێراق‪ .‬نمونهكه بهرههمهێنرا‬ ‫به تێكهڵكردنی ‪ Simulink‬وپڕۆگرامی )‪ genetic algorithm (GA‬وهك ڕێگهیهك بۆ‬ ‫سیمیولهیشن (‪ )Simulation‬وئاپتیمیزهیشن (‪ )Optimization‬بهدوای یهكدا‪.‬‬ ‫به مهبهستی بهراوردكردن وه بهڕهچاوكردنی یاسای كاركردنی بهنداوهكان‪ ،‬سێ‬ ‫نمونهی تر بهرههم هێنرا‪ .‬یهكێ لهم نمونانه بریتیه له شێوازێكی نمونهی كۆن (‪)Model-I‬‬

‫لهسهر بنهمای كاركردنی )‪ Standard Operating Policy (SOP‬به بهكارهێنانی‬ ‫‪ Simulink toolbox‬له پڕۆگرامی ‪ MATLAB‬دا‪ ،‬لهگهڵ دووجۆری تری جیاواز‪(Model-‬‬

‫)‪ II-a and Model-II-b‬له نمونهی ئاپتیمیزهیشن (‪ )Optimization‬به بهكارهێنانی ڕێگهی‬ ‫)‪(NLP‬‬

‫‪programming‬‬

‫‪nonlinear‬‬

‫و ‪dynamic‬‬

‫‪differential‬‬

‫‪discrete‬‬

‫)‪ programming (DDDP‬بهدوای یهكدا‪ .‬لهم توێژینهوهیهدا سێ پێوانه جێبهجێكراوه‬ ‫ئهوانیش؛ ‪ resilience ،reliability‬و‪ vulnerability‬بۆبهراوردكردن وخهماڵندنی نمونه‬ ‫دروستكراوهكان‪.‬‬ ‫نمونه پێشنیاز كراوهكان جێبهجێكراون بۆ ماوهی ‪ 54‬ساڵ به بهكارهێنانی ماوهی‬ ‫مانگانه كه دهكاته ‪ 648‬مانگ كه دهست پێدهكات به كانوونی دووهمی ‪ 1958‬بۆكانوونی‬ ‫یهكهمی ‪ .2011‬ئهنجامهكان ئهوه دهردهخهن كه نمونهی )‪ SOP (Model-I‬ماوهی‬

‫مهترسیداری ههیه لهبڕی كهمبوون (‪ )deficit‬بۆ كهمترین بڕی پێویستیاتی ئاوی خوارووی‬ ‫بهنداوهكه‪ ،‬ههرچهنده‪ ،‬بههای ‪ reliability‬بهرزه (‪ .)0.94‬ههروهها نمونهكانی تر؛ ‪NLP‬‬

‫)‪ DDDP (Model-II-b) ،(Model-II-a‬وه )‪ S-O (Model-III‬بهڕهچاوكردنی نرخی‬ ‫كۆلكهی )‪ (𝑤1 = 0.2‬وه )‪ (𝑤2 = 0.8‬بهنزیككراوهیی ههمان ‪ reliability‬یان ههیه‪،0.90 ،‬‬ ‫‪0.90‬و‪ 0.91‬بهدوای یهكدا‪ .‬سهرهڕای ئهوهش‪ ،‬ئهنجامهكان نیشانی ئهدهن كه نمونهی ‪NLP‬‬

‫)‪ (Model-II-a‬بههای پێوانهی ‪ resilience‬كهمه وه نمونهی )‪ S-O (Model-III‬نرخی‬ ‫پێوانهی ‪ vulnerability‬بهرزه كهدهبێتههۆی زیاتركردنی مهترسی له بڕی كهمبووندا‬ ‫(‪ .)deficit‬لهگهڵ ئهوهشدا‪ ،‬لهماوهی كاركردنی ‪ 1995‬بۆ ‪ ،2011‬تێكڕای سااڵنهی بهرههم‬ ‫هێنانی وزهی كارهبا بهڕهچاوكردنی نرخی كۆلكهی )‪ (𝑤1 = 0.8‬وه )‪ (𝑤2 = 0.2‬بریتیه له‬ ‫‪ 1344 MW ،1339 MW ،1280 MW‬وه ‪ 1296 MW‬بهزیادكردنی ‪30.64 ،24.9 %‬‬

‫‪ 31.16 % ،%‬وه ‪ 26.46 %‬زیاتر لهبهرههمی وزهی كارهبای ڕاستهقینه )‪ (1025 MW‬بۆ‬ ‫نمونهكانی )‪ DDDP (Model-II-b) ،NLP (Model-II-a) ،SOP (Model-I‬وه ‪S-O‬‬

‫)‪ (Model-III‬یهك بهدوای یهك‪.‬‬ ‫لهكۆتایدا‪ ،‬دهرئهنجامهكان ئهوهیان پیشاندا كه نمونهی ئاپتیمیزهیشنی ‪DDDP‬‬ ‫)‪ (Model-II-b‬بههایهكی بهرزی ههیه بۆ پێوانهی ‪ reliability‬وه ههروهها بهرههمی وزهی‬ ‫زیاتره‪ .‬نمونهكه دهتوانرێ بهئاسانی جێبهجێ بكرێت بۆحهلكردنی حاڵهتی ‪nonlinear‬‬ ‫وزیاترله ئامانجێك )‪ (multi objective‬بهخهرجكردنی كاتێكی كهم‪.‬‬

‫وةزارةتي خويَندني باالَ وتويَذينةوةي زانسيت‬ ‫زانكوَي سليَماني‬ ‫كؤليَجى ئةندازياري‬ ‫بةشي ئةندازياري ئاوديَري‬

‫نمونهی سیمیولهیشن‪-‬ئاپتیمیزهیشن بۆ‬ ‫ئیش كردنی سیستهمی بهنداوی دوكان‬ ‫ماستةرنامةيةكة‬ ‫ثيشكةشكراوة بؤ كؤليَجى ئةندازياري ‪ /‬زانكوَي سليَماني‬ ‫وةك بةشيَك لة ثيَداويسيت يةكاني بة دةستهيَناني ثلةي ماستةر‬ ‫لة ئةندازياري سةرضاوةكاني ئاو دا‬ ‫لةاليةن‬

‫لقمان صابر عثمان‬ ‫بةكالوريوس لة ئةندازياري ئاوديَري دا ‪2012 -‬‬

‫بة سةرثةرشتيكردني‬

‫د‪ .‬حكمت مصطفى ابراهيم‬

‫نيسان ‪ 2017‬زايين‬

‫نةوروَز ‪ 2717‬كوردي‬

‫رةجةب ‪ 1438‬كؤضي‬