Optimization of the operation of multireservoir systems, a Great Lakes case study

To solve reservoir operation problerns it is necessary to take into account thai natural processes nich as inflows, groundwater contribution, evaporaîion, rainfdl, m o f f which are the inputs to the system, are uncertain events. The methods here proposed consider the stochasticity of the inputs. The uncertaiaty of events like evaporation, rainfall, groundwater contribution, ninoff, is incorporated in eittier the net inflows or the net basin supplies. In order to recognize the intrinsic stochastic features of the naturai inputs and take them into consideration explicitly, Stochastic Dynamc Programming is wployed to generate long-tenn opmation policies. Because of the well-known "curse of dimensionali~", that can affect the optimization of large systems, the technique Multi-Level ApproWnate Aggregation/Decomposition Stochastic Dynemic ProgrammiDg (MAM-SDP) Methodotogy is anployed. The performance of this technique can be enhaaced by using the suggesteâ altemate approximation to the conditional distribution of the releases fim die reservoh. So far, MAMSDP perfoms physicd diagnosis to determine the aggregation scheme. A mtsns of applyuig Principal Componcnts Analysis is presented, therefore adding a d i f f m t perspective to solving the problem, i.e., statistical decomposition, This work also aims at obtalliing the relationship performance of the system vasus its respective variance. To this effect, an d o n of the Expected Rctum-Variance of Retum Rule was developed, applied to a multistage decision type of problem. This technique was d e d Two-Pass Mean-Variance Approadi. The algorithm for doing so is describeû It was possi'blc to show a signifiçant range of pedo~ll~illces and the variances associated with them for the operation of resewoir systems. This work ench with the application of the techniques above rnmtimcd to a r d case study. In i~ an altemaîe closeû-loop type opaanon policy is presented for the North American Grwt Lakes. These policies and those fhm the Two-Pass Meamvariance Approach are then compared with the ones obtained fiom a simpMed mode1 of the actuai operation, baxd on heuristics. Two sets of synthetic Net Basin Supplies for the five lakes an stded, genQBting two différent sets of release policies. I have a great deal of gratitude to so many people that enurnerate ail of them wouid be very difficult because I fear being unfair to quite a few. They supported me under diverse circumstances and during different periods of time but 1 was always vay forninate to be able to count on them. They were professors, colleagues and fiends an4 direçtly or indirectly, 1 own the completion of this Ph.D. Program to them. 1 thank my supervisor, Dr. K. Pomarabalam for his support, encouragemen& and guidance. I never forget his ht advice, ''Ge your han& duty! ", and 1 admit that 1 foiîowed it throughout these years at the University of Waterloo. Many thanks to Dr. A. Bogobowicz, who was my CO-supervisor during the early stages of my work. Also, 1 would like to dLank Dr. P. Calamai, Dr. K. Hipel, Dr. W. Lennox, and Dr. A. Singh, membm of the Examining Cornmittee, for their carefùl readiag of the diesis and most valuable crîticimi. My especial gratitude belongs to Dr. C. -L. Chiu, the externai examiner, for his cornments, suggestions and the opportunity to share a Linle of his expaieme. The author acknowledgcs the scholarship provided by the agacy of the Minisûy of Education of B n d , "Conselho Nacional de Descnvolvimmto Cientifiço e Tecnol6gico". 1 "11 always renieniber the early support provided by Dr. Ricardo M. Barcia, fiom the inciustriai Engineering Department of the F e d d University of Santa Catarha. Environment Canada, in the pason of Senior Eng. David Fay, helped me obtain crucial information for my case stuây. My sincere appreciation to 1 the members of the Systems Design Department especiaüy Sue Gooding, Annette Dietrich, Carol Kenctrick, and Heathcr Hngoq who assistecl me diiring the Program. Last but not least, 1 would like to express my deepesi gratinide to my fsmily for their love and mcunditional support Dedicated to Beatriz, Cloris, José, and tuha 3.6. 2 Test Results . 13 1 3.6. 3 Multiple Reservoir Syszems . 136 3.7 SrJMMARY . 143 4 . 1 ~ O D U C T I O N . 146 4.2 GREAT LAKES REGION . 150 4.2. 1 Geographic &scription anà climare . 150 4.2. 2 HHoIogic BacRground . 153 4.3 GREAT ~ K E S WATER LEVELS AND ROWS VAUTION . 154 4 3.1 Hycirologic &ta . 157 43.2 Basi's-~f~omparison. 162 43.3 Reguhtion Plim . 163 4.4 D ~ O N OF THE PROBLEM . 173 4.5 AGGREGATION SCHEME . 176 4.6 VALIDA~ON OF THE SIMULATION MODEL . 177 . 4.6. 1 Resultsjor the Simulation of the Great Lakes Operation as defined by the IJC 178 4.7 COMPARATIVE RESULTS . 185 4.7. 1 IJC 's Operation vs . Sieaày-State Optirnization using Aggregatîon . 185 4.8 STEADY-STATE OFTMEATION USNG AGGREGATION AND THE PROPOSED METHoDOLOGY. TWO-PASS MEAN-VARIANCE APPROACH . 198 48.1 Results with the Proposed MethodoIo@ . 198 48.2 mole System Collst'dered . 199 48.3 Lake O n m o Comidered Independent . 203 4.9 S W Y . 206 5 . CONCLUSIONS AND FURTEER RESEARCH . 207 . REFERENCES . 215 APPENDIX -4 O NORTH AMER~CAN OREAT LAKES C A S S N D Y . 226 APPENDIX B . JUSTIFICATION FOR THE METHODOLOOY EMPLOYED . 244 APPENDIX C . INPUT DATA TO T E GREAT LAKES CASE NWDY . 247 APPENDIX D . TRANSmON PROBABUTIES FOR THE NBS . 264 AETENDfX F O GREAT LAKES OUiFLûWS . 2 9 9 TABLE 2.3.1. HEIURCHICAL MODEL STRUCTURE FOR A MULTJPLE RESERVOIR HYDROELECTRIC SYSTEh4 . 53 TABLE 3 . 1 D I S C R ~ T I O N OF PROBABILITIES FOR THE DJFLOWS . 83 TABLE 3 . 2 AVERAGE M o r n y INFLOW AND REIUW COEFFICIENTS . 84 TABLE 3 . 3 hhWMJM AND MINMUh4 M o r n y STORAGE CAPAC~Y AND MAXMUM AND MINIMUM RELEASES FROM THE RESERVOIR . 84 TABLE 3. 4 MEAN AND STANDARD ~ T I O N OF NA TURAL. ~NFLOW TO &SERVOIR 1 . 87 TABLE 3 . 5 ACTIVE STORAGES FOR PROBLEMS I AND 2 . 87 TABLE 3 O 6 AVERAGE VALUES FOR THE lNnOWS PER MONTH IN UNITS OF VOLUME . 91 TABLE 3 . 7 MAXIMUM ADMISSIBLE STORAGE CAPACITES OF THE RESERVOIRS PER MONTH IN UNITS OF V o L W . 9 2 TABLE 3 . 8 MAXlMUM ADMISSIBLE RELEASES FROM THE RESERVOIRS PER MONTH IN LINïI'S OF VOLUME 9 2 . TABLE 3 . 9 RETURN DUE TO POWER GENEFUION PER UNIT OF VOLUME RELEASED PER RESERVOIR AND . PER MONTH (COEFFICIENT c) 9 3 . TABLE 3 . 1 O CASE 1 M A . S D P (WKH ADNSTMENT OF REUSE POLICIES) . 1 O3 . TABLE 3. 1 1 CASE 2 TURGEON METHOD (NO AIINSTMENT