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Wind Energy Forecasts in Calculation of Expected Energy Not Served

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Wind Energy Forecasts in Calculation of Expected Energy Not Served WIND ENERGY FORECASTS IN CALCULATION OF EXPECTED ENERGY NOT SERVED By Richard Sun Bachelor of Applied Science and Engineering, University of Toronto 2011 A thesis presented to Ryerson University in partial fulfillment of the requirements of the degree Master of Applied Science in the program Electrical and Computer Engineering Toronto, Ontario, Canada, 2014 ©Richard Sun 2014 AUTHOR'S DECLARATION FOR ELECTRONIC SUBMISSION OF A THESIS I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I authorize Ryerson University to lend this thesis to other institutions or individuals for the purpose of scholarly research I further authorize Ryerson University to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. I understand that my thesis may be made electronically available to the public. ii Wind Energy Forecasts In Calculation of Expected Energy Not Served Master of Applied Science 2014 Richard Sun Electrical and Computer Engineering Ryerson University ABSTRACT The stochastic nature of wind energy generation introduces uncertainties and risk in generation schedules computed using optimal power flow (OPF). This risk is quantified as expected energy not served (EENS) and computed via an error distribution found for each hourly forecast. This thesis produces an accurate method of estimating EENS that is also suitable for real-time OPF calculation. This thesis examines two statistical predictive models used to forecast hourly production of wind energy generators (WEGs), Markov chain model, and auto-regressive moving-average (ARMA) model, and their effects on EENS. Persistence model is used as a benchmark for comparison. For persistence and ARMA models, both Gaussian and Cauchy error distributions are used to compute EENS via a closed-form solution that reduces computational complexity.. Markov chain and ARMA both provide accurate forecasts of WEG power generation though Markov Chain model performs significantly better. The Markov chain model also produces the most accurate EENS estimate of the three models. iii ACKNOWLEDGEMENTS I would like to express my sincere gratitude and appreciation for my supervisors, Dr. Bala Venkatesh and Dr. Soosan Beheshti. Their support, patience, and guidance have been instrumental to this research and their insight and knowledge have been invaluable to my own personal development. I would also like to express my gratitude for the endless encouragement given by my parents who are a constant inspiration and an object lesson that hard work is the key to achieving anything worth having. Finally, I would like to thank my instructors and colleagues at Ryerson University and especially members of the Centre for Urban Energy for providing a wonderful working environment throughout this research. iv TABLE OF CONTENTS 1. Introduction ................................................................................................................................................... 1 1.1. Introduction ..................................................................................................................... 1 1.2. Survey of Recent Work in WEG Forecasting and EENS ............................................... 1 1.3. Objective ......................................................................................................................... 2 1.4. Chapter-wise Introduction .............................................................................................. 3 1.5. Chapter Summary ........................................................................................................... 3 2. Theory ............................................................................................................................................................ 4 2.1. EENS Overview .......................................................................................................... 6 2.2. Persistence Model (Used as a benchmark) ..................................................................... 8 2.2.1. Theoretical Background .......................................................................................... 8 2.2.2. Methodology ........................................................................................................... 8 2.2.3. Probability Density Function .................................................................................. 9 2.2.4. Calculating EENS ................................................................................................. 12 2.3. Markov Chain Model .................................................................................................... 15 2.3.1. Theoretical Background ........................................................................................ 15 2.3.2. Methodology ......................................................................................................... 19 2.3.3. Probability Density Function ................................................................................ 19 2.3.4. Calculating EENS ................................................................................................. 20 2.4. ARMA Model ............................................................................................................... 20 2.4.1. Theoretical Background ........................................................................................ 20 2.4.2. Model Order .......................................................................................................... 22 2.4.3. Coefficient Determination .................................................................................... 23 2.4.4. Methodology ......................................................................................................... 23 2.4.5. Probability Density Function ................................................................................ 24 2.4.6. Calculating EENS ................................................................................................. 24 3. Results and Discussion ............................................................................................................................. 25 3.1. Data ............................................................................................................................... 25 3.2. Amaranth Wind Farm ................................................................................................... 25 3.2.1. Comparing Forecast Error..................................................................................... 25 3.2.2. Comparing EENS.................................................................................................. 31 3.3. Wolfe Island Wind Farm .............................................................................................. 38 3.3.1. Comparing Forecast Error..................................................................................... 38 3.3.2. Comparing EENS..................................................................................................... i 3.4. ERCOT System-wide.................................................................................................... 48 3.4.1. Comparing Forecast Error..................................................................................... 48 3.4.2. Comparing EENS.................................................................................................. 54 3.4.3. Comparison with Previous Work .......................................................................... 55 4. Conclusions ................................................................................................................................................ 57 5. Appendix ..................................................................................................................................................... 59 5.1.1. Amaranth Wind Farm Raw Data .......................................................................... 59 5.1.1.1. Training Data ........................................................................................................ 59 5.1.1.2. Validation Data ..................................................................................................... 65 5.1.2. Wolfe Island Wind Farm Raw Data ...................................................................... 67 v 5.1.2.1. Training Data ........................................................................................................ 67 5.1.2.2. Validation Data ..................................................................................................... 74 5.1.3. ERCOT System-wide Raw Data ........................................................................... 75 5.1.3.1. Training Data ........................................................................................................ 75 5.1.3.2. Validation Data ..................................................................................................... 77 5.2. Forecasted Data ......................................................................................................... 78 5.2.1. Amaranth Wind Farm Forecasted Data ................................................................ 78 5.2.2. Wolfe Island Wind Farm Forecasted Data ............................................................ 88 5.2.3. ERCOT System-wide Forecasted Data ................................................................
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