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In Partial Fulfilment of the Requirements for the Degree of It{Aster of Science

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In Partial Fulfilment of the Requirements for the Degree of It{Aster of Science The University of Manitoba Optimal Operation of a Flood Control Systen by John Nairn MacKenzie A Thesis Submitted to the Faculty of Graduate Studies in Partial Fulfilment of the Requirements for the Degree of It{aster of Science Tl¡-nr+man+ l'ir¡i'l DePdL Llllu.lIL ^.Ê\JI \,-LVI-L FnoinoarinoLtlSrIrçvf rrrð WitIrIulft/võ, nn i nco l\4en i toba Arrmrcf I q7R C)PTiIIAL OPEIIAÏIÛN OT A FLOOD CÛNTRC]L SYSÏËi4 BY JOHN I.IÄIRÎ''J I.4¡CKEI{Z] E A clissertation submiÈted to tåte Facr*lty of Cr*ci".¡aÉe Stuse.åies of' tlre University oá' Munitoba ire partLrl f'uifilln'le¡rt ol' t!re requle'ernemts ol'tlre clegrce ot IIAST TR OF S C I ENC E o,ig78 Fernrissio¡r hus bec¡r gnunted Ëo the t-l¡ì$l,AÊLV ûF Te!U U¡{l\¡¡-:F¿- S¡TV Ol.' h{.4þ]lTO!3"4 tr¡ lenei q¡r s¿:l! copies oü t!¡is cåÈ*;ertati{!r¡" 8o the N,4TltNAL [.N8¡4,ARY ûFr {lA"l\Ai}A to l¡riar¡:*'ilrsr tl¡ls ciissertafio¡r and tr: lend or sell copies of the felnr, und {,JNl'VUåì,5åTY h{lCfì,OFlLh{S tr: pubiish i¡¡r ahsåraet of this rJissert¿¡f ion. The ar¡thor re$erve$ otå:cr publ!c¿¡Èir¡¡r rights, ¿¡¡rJ ¡"¡either the dissertation ncr exÉensive cxtri¡cfs fr¡:nr it mluy h*: gx'int*d eir otl¡er- wise repi:oeíLlced evithout t !¡c uuf l¡o¡''s writËc¡r 3:cnrr ieslr.xr" ACI$IOWLEDffiIvE\TS I would like to e4press my appTeciation to my advisor, Professor G. Booy for his guidance and patience throughout the somewhat long gestation period of this thesis. I would also like to express my appreciation to Mr. P. Flatt of charles Howard and Associates, consulting Engineers, for making avail- able the linear progranrning solution algorithm used in this thesis and his comments regarding the solution algorithm in particular and the linear programning technique in general- I would like to express my most sincere appreciation to my wife, l-1'aLrrv LvrrtJnnmletion - l\4nninrro fnr her Ëll\-U(Jfên..ìrlr^2ocmcnf dBclllurr L @lILfenrl nafPa LlLlrLv ience thrc"^]^^"rLlrr uutslrvuL of the thesis. II onbruol^l TABLE OF CONTENTS Page Acl,noivledgements i I i cf nf Fi or rrpq Vi 1.0 INTRODUCTION 2 1.1 A Flood Control System La 7.2 Sinulation Analysis 3 | ( f lnlrmf 7aT1î\'**-rr furdaj/5_L> 4 7.4 Optimization-Símulation Comparison 5 r.J1 q T'harlrv r-ÌnfimirationvIJur¡ttr¿ l4ode1 Selected in this Tþesis 6 2.0 TTIE ASSINIBOINE RIVER SYSTEM l-U 2.I History 10 2.2 Flood Control Tnvestigations 10 2.3 Shellmouth Reservoir 72 2.4 Assiniboine River Diversion 13 3.O THE GENERAL LINEAR PROGRA}O4ING Ì\4ODEL FOR A FLOOD CONTROL SYSTEM 22 3. 1 The Linear Progranming Tecirnique 22 3.2 The }{odel Descríption 25 3.3 Linear Progrannning }lodel Coirstraints 3.3.7 Physical Constraints 27 3 .3.7.7 Storage Constraints 27 3.3.7.2 Reservoir Mass Balance Constraint 28 111 Table of Contents cont. Ðc'_*Þ: ¡a 3.3.I.3 Reservoir Release Constraint 28 3.3.7.4 Cha:r¡rel Continuity of Storage Constraint 29 3 .3 .1.5 RiParian Constraint 29 3.3.7.6 Diversion Capacity Constraint JU 3.3.1.7 Upper Limit on Diversion Flow Values 30 3.3.2 Coniputational- Constraints 3L 3.3.2.I Peak Discharge Constraint 3L 3.3.2.2 Non-Negativity Constraint 32 3.4 Objective Functíon )L 3.5 Time Dependency of Objective Fr-urctíon at Danage Centres 33 3.6 NonlinearitY 35 3.7 Size of the Linear Progranu.ning Problem 3B 3.7.7 Elinination of Variable Qi^t 38 3.7.2 Elinination of Fixed Valued Variables 39 4.0 ftIE LINEAR PROGRA}MING MODEL APPLIED TO 'IT]E ASSINIBOINE RIVER SYSTM,Í 46 4.7 TLe Assiniboine River lt{odel 46 4.2 Study Operational Rules 47 4.3 Flood Damage Fulctions 4B 4.4 Specific Linear Prograruning }lode1 for the Assjniboine River SYstem 53 4.4.I Physical Constraints 53 4.4.7.I Storage Constraints 53 4.4.7.2 Reservoir Mass Balance Equation 53 4.4.7.3 Reservoir Release Constraint trA Table of Contents cont. T)a¡a 4.4.7.4 Riparian Constraint 54 4.4.L.5 Diversion Capacity Constraint 55 4.4.7.6 Upper Limit on Divcrsion Florv Values 55 4 .4.2 Contputational Constraints 56 4.4.2.1 Peak Discharge Constraint 56 4.5 Sumrmry of Problem Constraints 57 5. 0 COIPUTATIONAL TECFil{IQUES 77 5.1 Ïte ComPuter lt{odel 77 5.2 lt{atrix Generator 77 5.3 Thc Liucar Plogramning Solution Algorithm 79 5 .4 'Ihe RePort Writer 79 6.0 RESULTS B2 6.1 The Optirriization }4ode1 BZ 6.2 Discr-rssion of Results 84 6.3 Model Run Cost B6 6 .4 Surnurary Conclus ions B7 APPENDIX A 100 APPENDIX B L46 BIBLIORAPFry 1s8 LIS'I OF FIüMES Þa oa II-1 Assiniboine River Drainage Basín 77 II-2 Shellnouth Reservoir, Location 1B II-'3 Assiniboine River Díversion, Location 19 II=4 Assiniboine River Diversion, Layout Details 20 III.1 Sanple Linear Progranirning Problent 47 III=2 Hypothetical River Basin System 42 III-5 Definítion of Tine periods used in Aria11'sis A7 III-4 Scparable Programning Example Figure 44 IV-1 Assiniboine River Drainage Basin IV-2 l\ratcr Sur-vey of Canada Streamflow Gauging Locations in the Study Area 64 IV-3 Discharge Damage Relationship - Assiniboine Rir¡er at Russell 65 IV-4 Discharge Damagc Relationship - Assiniboine River al- Ir{iniota 66 n^*^ n^1^+: TV- 5 Di sclrarse UcLllldgv^^ L l-uj^*^llio l>.--r - Assiniboine River AL Þ- ^f'-Ld Brandon 67 a1- IV-6 Discharge Damage Relationship - Assiniboine River dL Pnrt:oe le Prairie 68 IV-7 Discharge Damage Relationship - Assiniboine River Diversion ov rr--^-^ Tr^1^+;'^-^hin TV-B Discharp-e----- ò- lJdllidgE r\Uf d Ll-\-rlI>rrrlr - /Ass'inìboine LJJ !rrruvri River !{oodino1 er¡ 70 V1 List of Figures coqt_. T)c ra IV-9 Discharge Damage fte1atíonsìlip - Assiniboine Ríver at l\Tinnipeg /I ry-10 Elevation.Ðisc]-iarge Relationsliip Shellmouth Reservoir 72 W-11 Elevation=storage Rclationship Shcllmouth Reservoir 73 IV-72 Outflow-storage Relationship Shellmouth Resen'oir 74 IV=13 Schematic Repr-esentation of Assiniboiire River Basin 75 W-1 Natural and Optimal Flow Values, Russell BB VÍ-2 Natural and Optimal Flow Val.ues, tr{iniota 89 VI-3 Natural and Optimal Flor.^¡ Values, Blandon 90 VI-4 Natural and Optimal Flow Values, Portage 1a Prairie 91 VI-S Natural arrd Optimal Florv Values, I"leadingley ^a 'l{imipeg Vi - 6 Natural and Optinal Flow Values , VI-7 Optimal Shellmouth Reservoir Operating Schedule 94 VI-8 Optinal Assiniboine River Divelsion Operating Schedule 95 \iI-9 Output fr'om Report lfriter 96 VI-10 Output from RePort l\rriter 97 VI-11 Output from Rcport j\'riter 98 vii 1.0 INIRODUCTION OPTIMAL OPERATION OF A FLOOD CONTROL SYSTEM 1.0 INTRODUCTION 1.1 A Flood Control SYstem Two kinds of flood control works may be actively operated in order to alleviate flood danage, reservoirs and diversiors. Reservoirs reduce flood damage by storing flood waters and releasing them at a later date so as to reduce the peak of the flood wave and lengthen its duration. Diversions sinply divert flood waters away to an area less prone to flood damage. An operable flood control system as discussed in this thesis is composed of reservoirs and diversions in addition to passive flood con- trol rvorks such as dykes. The object of operation of any flood control system is to minimlze flood damage. This requirement defines the optimal operating schedule for each of the system components. The degree of complexity of the op- timal operation of a flood control systeilì is deternined by the nr¡rber of flood control reseryoirs and/or diversions which conrprise the system for each flood control component requires its oirrn operating schedule. Since the operating schedules of the components of the system may be hi-ghly inter-related it may be appreciated that the difficulty in arriving at optinal operating schedules increases very rapidly as the ru.mber of com- ponents of the flood control systen increases. The opti-mal operating procedure is based on anticipated florvs. The r:ncertainty in forecasting flows therefore adds a degree of r.rncertaintY to the optimal operating procedure. It need not add to the complexity of the analysis if the rincertainty itself is not a factor in the objec- tive of the system oPeration. 2 In this thesis all flow values have been treated as being determin- istic and no allowance for stochastic variation has been included. Stochastic variation of flow values could be addressed by mearìs of new estinates of flow values which would then be subject to another analysis. In an operational flood control context this might take the form of a high, best and low estimate of systen in flows with each estimate re- quiring a separate analysis. In this manner any stochastic variation in flow estimates can be partially addressed within the deterministic frame- work of the model constructed in a nanner acceptable for operational flood control ÐurDoses, 7.2 Sinrulation Analysis Sinrulation analysis is a conmonly accepted method of arrivi¡rg at an operating schedule for a flood control systen. In a simulation analysis, the river system is modelled so that movement in time and space of river flows throughout the river basin may be simulated.
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