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Developing a Stochastic Optimization Model for Operating the Manitoba Hydro Multi-Reservoir Hydroelectric Power System

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Developing a Stochastic Optimization Model for Operating the Manitoba Hydro Multi-Reservoir Hydroelectric Power System Developing a stochastic optimization model for operating the Manitoba Hydro multi-reservoir hydroelectric power system By Jacob Snell A Thesis submitted to the Faculty of Graduate Studies of The University of Manitoba in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil Engineering University of Manitoba Winnipeg, Manitoba Copyright © 2020 by Jacob Snell Abstract The province of Manitoba generates more than 90% of its electric power from hydroelectric generating stations located in the Nelson-Churchill Rivers basins. Prudent management of the major reservoirs in the system is essential for providing value through economic and reliable electricity. Reservoir managers are challenged by the variability of reservoir inflows, the misalignment of electrical energy demands and seasonality of reservoir inflows, and travel time lags between reservoirs and major generating stations on the Lower Nelson River. This thesis examines some of the challenges of current hydroelectric system management and applies a Sampling Stochastic Dynamic Programming algorithm to the operation of the Manitoba Hydro electric system. Direct consideration of variability and uncertainty of inflows are incorporated in the algorithm by generating a water value function based policy that considers multiple inflow scenarios and inflow scenario transition probabilities derived from conditional probability distributions based on a regression relationship between sequential periods of system inflow. The travel time lag is incorporated into the algorithm directly as a lagged inflow state variable to bridge reservoir release decisions between time periods. Storage values and penalties are incorporated to reflect operating license requirements and to prevent depletion of reserve storage that can lead to infeasibilities in the algorithm. The water value function policy is simulated over 38 historical years of inflow scenarios and compared against historical reservoir operation decisions. Model results show significant improvement in economic values and reductions in energy deficits over historical scenarios but are highly sensitive to the calibration of storage benefit and penalty values. Extensions to the model to use hydrological based inflow models, improving the transition matrix by evaluating alternative hydrological variables, and alternative approaches to the storage benefit and penalty method are discussed. ii Acknowledgements I would like to acknowledge the support, advice, guidance and encouragement from my advisor, Dr. Masoud Asadzadeh, to continue with my masters studies and thesis, and my advisory committee for much of the same. Furthermore, I would like to acknowledge my colleagues at Manitoba Hydro, particularly Mr. Kevin Gawne for his avid support and encouragement in perusing a higher education and development as a professional engineer. Lastly, I would like to thank my wife, Kaitlin, for believing in me and encouraging me along the way. iii Table of Contents Abstract ............................................................................................................................................ii Acknowledgements ......................................................................................................................... iii Table of Contents ............................................................................................................................ iv List of Tables ................................................................................................................................ vi List of Figures............................................................................................................................... vi SI Unit Conversions .......................................................................................................................... x 1. Overview .................................................................................................................................. 1 2. Study Area ............................................................................................................................... 3 2.1. Manitoba Hydro Overview ............................................................................................... 3 2.2. Manitoba Hydro Electric System Description .................................................................. 3 2.2.1. Electric System Economic Dispatch .......................................................................... 6 2.3. Manitoba Hydro Reservoir System .................................................................................. 7 3. Manitoba Hydro Hydroelectric Reservoir System Operation................................................ 13 3.1. Reservoir System Operation Objectives......................................................................... 13 3.2. Inflow Forecasting .......................................................................................................... 14 3.3. EMMA Model ................................................................................................................. 15 3.4. Ideas for Improving Manitoba Hydro Midterm Operations .......................................... 16 4. Review of Multi-Reservoir Operation Optimization Approaches ......................................... 18 4.1. Linear Programming Approaches ................................................................................... 20 4.1.1. Stochastic Linear Programming .............................................................................. 21 4.1.2. Stochastic Linear Programming Applications ......................................................... 23 4.2. Dynamic Programming ................................................................................................... 25 5. Methodology ......................................................................................................................... 30 iv 5.1. Overview ........................................................................................................................ 30 5.2. Dynamic Programming Overview .................................................................................. 30 5.3. Sampling Stochastic Dynamic Problem Description ...................................................... 34 5.3.1. Considerations for Flow Travel Time in the Optimization Model .......................... 35 5.3.2. State Variable Discretization ................................................................................... 36 5.3.3. Subproblem Description ......................................................................................... 37 5.3.4. Water Value Function Approximation .................................................................... 45 5.3.5. Inflow Scenario Selection ........................................................................................ 47 5.3.6. Transition Probability Calculation ........................................................................... 49 5.4. Analysis Setup ................................................................................................................ 50 6. Results and Discussion ........................................................................................................... 55 6.1. Historic Results ............................................................................................................... 55 6.2. “No-Lag” Approach Results ............................................................................................ 56 6.3. ”With-Lag” Case Results ................................................................................................ 64 6.4. Hydrological Results ....................................................................................................... 68 7. Conclusions and Recommendations for Future Work .......................................................... 72 7.1. Summary of Findings ...................................................................................................... 72 7.2. Limitations ...................................................................................................................... 73 7.3. Applications .................................................................................................................... 74 7.4. Recommendations for Future Work .............................................................................. 75 References .................................................................................................................................... 77 Appendix A1: Estimation of the travel time delay in the Manitoba Hydro hydroelectric reservoir system ........................................................................................................................................... 87 Appendix A2: Hydrologic and energy system results from the simulation of historical releases 89 v List of Tables Table 1 - Manitoba Hydro generating station capacity (Manitoba Hydro 2019) ........................... 4 Table 3 – Average annual inflows for the aggregated Long Term Flow Data locations ............... 10 Table 4 – Storage bounds and discretization limits ...................................................................... 37 Table 5 - Outflow limits on modeled lake outlets ........................................................................ 45 Table 6 - Energy deficits from simulated historic operating decisions by flow year .................... 56 Table
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