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Successive Linear Programming to The THE UNIVERSITY OF MANITOBA AN APPLICATION OF SUCCESSIVE LINEAR PROGRAMMING TO THE OPTIMIZATION OF AN INTERCONNECTED HYDRO UTILMY OPERATION by @ KARoLI REZNICEK A Thesis Submitted to the Faculfy of Graduate Studies in Partial Fulfillment of the Requirements for the Degree of Master of Science DEPARTMENT OF CTVIL ENGINEERING Winnipeg, Manitoba DECEMBER 1988 Per¡niesion trae been granted L'autorleatlon a êtê accordêe to the Natlonal Llbrary of å la Blbllothèque natlonale Canada to nicrofiln thlg du Canada de nlcrofllner thesls and to lend or eell cette thèse et de prêter ou copies of the filn. de vendre dee exenplairee du f llrn. The author (copyright owner) Lrauteur (tltulaire du drolt has reaerved other d'auteur) ae rêeerve lee pubtication ríghts, and autres droits de publlcatlon; neither the thesie nor nl ta thèee nl de longe extensive extracts from it extraite de celle-cl ne Day be printed or otherwiee doivent être irnprlnês ou reproduced wlthout his/her autrement reprodults BanB aon written perurieeion. autorieatlon écrite. rsBN 0-3L5-5i.576-7 AN APPLICATION OF SUCCESSIVE LINEAR PROGRAMMING TO THE OPTIMIZATION OF AN INTERCONNECTED HYDRO UTILITY OPERATION BY KAROLJ REZNICEK A thesis submirted to the Faculty of craduate studies of the university of Manitoba in partiar furfilrment of the requirenrents of the degree of I'fASTER OF SCIENCE o 1989 Permission has beerr grarìred ro the LIBRARy oF THE UNIVER- S¡TY OF MANITOBA to lend or sell copies of this thesis. ro the NATIONAL LIBRARy oF CANADA to microfìrnr this thesis and to lend or seil copies of the firm, and uNIVERsrry llf ICROFILMS to publish an absrract of this thesis. The author reserves other pubtication rights, a'd neither ttre thesis nor extensive extracts from it may be printed or other- wise reproduced without the author's writte¡l perntissìon. I ACKNOWLEDGMENTS I would like to express my gratitude to all people who provided me with support and understanding while working on this thesis. I am specially indebted to Professor S.P. Simonovic for his advice, guidance and encouragement throughout my studies at the University of Manitoba. I am also thanHul for the valuable comments of Mr AD. Cormie and Mr P.E. Barritt- Flatt during the research which preceded this thesis. My gratitude goes to Professors I.C. Goulter and D.H. Burn for their assistance and suggestiôns pertaining this work. I wish to acknowledge the financial support from Manitoba Hydro, approved by the Research and Development Committee, as well as the availability of Energy Management and Maintenance Analysis program and Manitoba Hydro data. I would also like to thank Mr. J.C. Grygier and Mr. J.R. Stedinger for providing me with the code of the Successive Linear Programming model developed at Cornell University. I am grateful to my fellow graduate students in water resources at the university of Manitoba for being sincere friends and encouraging my work. Special thanlis goes to Wendy Seversen for helping me to edit and arrange this work. Finally, I deeply appreciate the help and understanding of my parents throughout my studies. 1l ABSTRACT The operation planning of a hydro-electric utility is a complex problem involving decisions about reservoir releases, energy supplies and many other production related problems during a certain planning period. Mathematical modelling (simulation and optimization techniques) is widely used to aid the decision making process. This work presents a deterministic Linear Programming (LP) based optimization model. The objective is to maximize the energy erport benefits of the utility, while minimizing the costs of satisffing the domestic power demand over the planning period. For the specified reservoir inflow and power demand scheme, decisions about the energy production, e4port and import have to be made for each time step. An iterative algorithm named EMSLP (Energy Management by Successive Linear Programming) was developed to solve the optimization problem. The EMSLP algorithm has two iteration levels: at the first level a stable solution is sought, and at the second the interior of the feasible region is searched to improve the objective function whenever its value decreases. The EMSLP algorithm has been tested using the Manitoba Hydro system data. To evaluate the performance of the algorithm a comparative study has been made with the EMMA (Energy Management and Maintenance Analysis) program used in the Manitoba Hydro practice. The results of the comparison have shown a number of advantages of the EMSLP algorithm. lu TABLE OF CONTENTS PAGE Acknowledgements Abstract Table of Contents List of Tables List of Figures Chapter 1: Introduction 1..1. Problem Statement 1,.2 The Concept of Successive Linear Programing 1,.3 Modelling approximations Chapter 2: Review of Previous Work 6 2.I Mathematical Modelling Applied to Hydro Power 6 Generation 2.1,.1, Dynamic Programming 7 2.1,.2 Nonlinear Programming 13 2.1..3 Simulation 15 2.2 Linear Programming Applications 1,6 2.2.1 Deterministic Models 18 2.2.2 Stochastic Models ¿J 2.3 Description of the EMMA Program of Manitoba Hydro 25 2.4 Description of the Successive Linear Programming Model 39 of J. Grygier lv PAGE Chapter 3: Energy Management by Successive Linear Programming 50 3.L The Problem Formulation 50 3.1.1 The Constraint Set 52 3.1,.2 The Objective Function 56 3.2 The EMSLP Algorithm 58 Chapter 4: Evaluation of EMSLP 63 4.1 The Case Study 63 4.2 The Results of Comparison with EMMA 67 4.2.1, Final Storage Value Variation 68 4.2.2 System Load Variation 68 4.2.3 Release Limit Variation 76 Chapter 5: Conclusions 92 5.1 Discussion of EMSLP-EMMA Comparison Results 92 5.2 Developments of the EMSLP Research 95 5.3 Differences between EMSLP and Grygier's SLP Model 95 5.4 Directions of Future Research 96 Appendix A: Notation 98 Appendix B: Bibliography 100 Appendix C: Tables of the Case Study Results 105 PAGE Appendix D: The Fortran Program of EMSLP Applied ro the Case 112 Study D.1, Program Structure 112 D.2 Variables 1,1,4 D.3 Input Data 120 D.4 Program Execution 121, D.5 Output Report 126 Appendix E: Source Code t28 Appendix F: Sample Input and Output File 178 vl LIST OF TABLES PAGE Table 1. The discretized load duration curve data 65 Table 2. The inflow scheme 65 Table 3. The energy price structure 65 Table C-1. EMSLP results for varying storage benefits 106 Table C-2. EMMA results for varying storage benefits 107 Table C-3. EMSLP results for varying system demand 108 Table C-4. EMMA results for varying system demand 1,09 Table C-5. EMSLP results for varying release limits 1.10 Table C-6. EMMA results for varying release limits 1,1.1 vlt LIST OF FIGURES PAGE Figure 1. Load duration curve modelling 31 Figure 2. EMMA flowchart 38 Figure 3. Flowchart of the SLP algorithm (Gry$er, 1983) 47 Figure 4. EMSLP flowchart 60 Figure 5. Schematic Illustration of the Case Study 64 Figure 6. Comparison of reservoir levels for $3600Æ(CFS-day 69 ending storage value Figure 7. Comparison of reservoir levels for $4000Æ(CFS-day 70 ending storage value Figure 8. Comparison of reservoir levels for $4200Æ(CFS-day 71 ending storage value Figure 9. Comparison of reservoir levels for $45O0iKCFS-day 72 ending storage value Figure 10. Comparison of reservoir levels for $4600Æ(CFS-day 73 ending storage value Figure LL. Comparison of reservoir levels for $4700Æ(CFS-day 74 ending storage value viii PAGE Figure 12. Comparison of reservoir levels for $4800Æ(CFS-day 75 ending storage value Figure L3. Comparison of reservoir levels for system load equa I 77 to 0.3 times the original load Figure L4. Comparison of reservoir levels for system load equal 78 to 0.5 times the original load Figure 15. Comparison of reservoir levels for system load equal 79 to 0.8 times the original load Figure 16. Comparison of reservoir levels for system load equal 80 to 1.0 times the original load Figure L7. Comparison of reservoir levels for system load equal 81 to l-.5 times the original load Figure L8. Comparison of reservoir levels for system load equal 82 to 2.0 times the original load Figure 19. Comparison of reservoir levels for a release limit of 84 5.67 mslsec Figure 20. Comparison of reservoi¡ levels for a release limit of 85 8.57 m3lsec Figure 21. Comparison of reservoir levels for a release limit of 86 11.35 m%ec ü PAGE Figwe 22. comparison of reservoir levels for a release rimit of 87 74.19 ms/sec Figure 23. comparison of reservoir levels for a rerease rimit of 88 19.86 m%ec Figure 24. Normalized objective function difference for storage 89 value variation Figure 25. Normalized objective function difference for load 90 variation Figure 26. Normalized objective function difference for release 91 limit variation 1. CHAPTER 1. INTRODUCTION The optimization of hydro power production (in broader sense reservoir operation) has been a problem addressed by many researchers in the past three decades. Due to the complexity of the problem none of the numerous optimization techniques could model all the pertinent characteristics of a reservoir system operation (multiple-reservoirs, multiple time-periods, stochastic inflows, and nonseparable objective functions). However, this does not mean that there were no successful applications of operations research techniques to the problem. For real world problems, some simplifications are required to take into account the characteristics of the reservoir system, the available data, and the modelling goal. The simplified problem can be successfully modelled. The model can be used for planning and operation purposes keeping in mind the assumptions made.
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