Geographical Location Optimisation of Wind and Solar Photovoltaic Power Capacity in South Africa Using Mean- Variance Portfolio Theory and Time Series Clustering
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Geographical Location Optimisation of Wind and Solar Photovoltaic Power Capacity in South Africa using Mean- variance Portfolio Theory and Time Series Clustering By Christiaan Johannes Joubert Thesis presented in partial fulfilment of the requirements for the degree Master of Engineering in Electrical Engineering at Stellenbosch University Supervisor: Prof. H.J. Vermeulen Department of Electrical and Electronic Engineering November 2016 Declaration By submitting this thesis/dissertation electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the sole author thereof (save to the extent explicitly otherwise stated), that reproduction and publication thereof by Stellenbosch University will not infringe any third party rights and that I have not previously in its entirety or in part submitted it for obtaining any qualification. C.J. Joubert November 2016 Copyright © 2016 Stellenbosch University All rights reserved i Acknowledgements I would like to thank the following people for their contribution during this project: My study leader, Prof H.J. Vermeulen, for his valuable guidance and inputs throughout my two years at Stellenbosch University. Thanks are also due to Prof H.J. Vermeulen’s family who opened up their home to the crowd of master’s students and their circle of friends on many occasions. My mother, Marina Joubert, father, Stefan Joubert, brother, Peter Joubert, aunt, Juanita Du Toit, grandmother, Irene Du Toit, as well as my late grandparents Pieter du Toit, Chris Joubert and Rita Joubert. To the extent that I have achieved anything in my life it would undoubtedly not have been possible without their unwavering love, sacrifice and support. Yoko Yuan, who showed enormous patience and strength while waiting for two years for me to complete my master’s. All my fellow masters students in room E222, Almero de Villiers, George Blignault, Edwin Mangwende, Vicki Vermeulen and Tielman Nieuwoudt who made my time in Stellenbosch unforgettable. The director of the Centre for Renewable and Sustainable Energy Studies at Stellenbosch University, Prof J.L. Van Niekerk, who awarded me a bursary which enabled me to pursue a master’s degree and switch to a career in renewable energy. Karin Kritzinger, a researcher at the Centre for Renewable and Sustainable Energy Studies at Stellenbosch University, for being a friend and an enthusiastic supporter of my work and future career plans. Dylan Jacklin, an old friend from the residence in Pretoria who joined me in Stellenbosch in 2016 and who made sure that a printed copy of this thesis reached my study leader while I was attending a conference in Malaysia. My industrial mentor, Riaan Smit from Eskom, who patiently listened to my project updates and helped me whenever I needed any data from Eskom. ii Abstract Throughout the world, there is a lot of pressure on governments and electricity utilities to try to mitigate the possible effects of climate change by reducing emissions of greenhouse gases and investing in renewable energy sources. Wind power and solar photovoltaic power represent the bulk of the installed renewable energy capacity. However, these energy sources are stochastic and highly dependent on weather conditions and exhibit marked diurnal and seasonal cyclic behaviour. It follows that power systems with a high penetration of wind and solar power present challenges to grid operators in the sense that renewable power cannot be dispatched on demand as is the case with conventional power generation plants. There are several studies in the literature which investigate the possibility of optimising the location of wind farms so as to reduce the variability of the cumulative wind power output. The majority of these studies employ mean-variance optimisation, which is a quadratic programming method that is used in finance theory to construct efficient share portfolios. Several studies suggest the inclusion of solar photovoltaic power and load profiles in the mean-variance optimisation procedure, but little work has been done to investigate the effects. A problem with the mean-variance optimisation is that it often assigns low capacities to certain sites, with no clear alternatives, which makes part of its solution unfeasible in the face of practical and economic considerations. Time series clustering has been suggested as a possible solution to this problem, but the literature is sparse when it comes to time series clustering implementations combined with mean-variance optimisation. In this investigation, wind power and solar photovoltaic power time series were simulated for a South African case study. An optimal clustering methodology was identified for the simulated renewable power time series and the results of the clustering procedure was used as an input in a mean-variance optimisation procedure that was adapted to include wind power, solar photovoltaic power and load profiles. The complete optimisation methodology has been studied in four case studies using clearly defined key performance indicators. The results of the case studies are a clear indication of the potential of methodology to optimally distribute wind power and solar photovoltaic power capacity that could reduce the adverse impacts on the conventional generation capacity that are typically associated with large penetrations of renewable power capacity. iii Opsomming Regoor die wêreld is daar 'n baie druk op regerings en elektrisiteitmaatskappye om te probeer om die moontlike gevolge van klimaatsverandering te versag deur die vrystelling van kweekhuisgasse te verminder en te belê in hernubare energiebronne. Windkrag en fotovoltaïese sonkrag verteenwoordig die grootste deel van die geïnstalleerde kapasiteit van hernubare energie. Maar hierdie energiebronne is stogastiese en baie afhanklik van weerstoestande en toon duidelike daaglikse en seisoenale sikliese gedrag. Dit volg dus dat kragstelsels met 'n hoë penetrasie van wind- en sonkrag ’n uitdaging verteenwoordig aan kragstelseloperateurs in die sin dat hernubare krag nie kan gewek word op aanvraag soos in die geval van konvensionele kragopwekkingstasies nie. Daar is verskeie studies in die literatuur wat die moontlikheid ondersoek van die optimering van die ligging van windplase ten einde die wisselvalligheid van die kumulatiewe windkraglewering te verminder. Die meerderheid van hierdie studies gebruik sogenaamde gemiddelde-variansie optimering, wat ’n kwadratiese programmeringmetode is wat gebruik word in die finansiële teorie om doeltreffende aandeleportefeuljes te bou. Verskeie studies dui na die insluiting van fotovoltaïese sonkrag en vragprofiele in die gemiddelde-variansie optimering proses, maar min werk gedoen is om die gevolge te ondersoek. ’n Probleem met die gemiddelde-variansie optimering is dat dit dikwels lae kapasiteite toeken aan sekere plekke, met geen duidelike alternatiewe nie, wat deel van die oplossing ondoenlik maak in die aangesig van praktiese en ekonomiese oorwegings. Tydreeks-groepering is voorgestel as ’n moontlike oplossing vir hierdie probleem, maar die literatuur is yl wanneer dit kom by die implementerings van tydreeksgroeperings, gekombineer met gemiddelde-variansie optimering. In hierdie ondersoek is windkrag- en fotovoltaïese sonkrag-tydreekse gesimuleer vir ’n Suid- Afrikaanse gevallestudie. ’n Optimale groeperingsmetode is geïdentifiseer vir die gesimuleerde hernubare krag-tydreekse en die resultate van die groeperingsprosedure is gebruik as ’n inset in ’n gemiddelde-variansie optimeringsproses wat aangepas is om windkrag, fotovoltaïese sonkrag en vragprofiele in te sluit. Die volledige optimeringsmetode is ondersoek in vier gevallestudies met behulp van duidelik gedefinieerde sleutel prestasie-aanwysers. Die resultate van die gevallestudies is ’n duidelike aanduiding van die potensiaal van die metode om windkrag- en fotovoltaïese sonkragkapasiteit te versprei, wat die negatiewe impak op die konvensionele opwekkingskapasiteit, wat tipies geassosieer word met ’n groot hoeveelhede hernubare krag kapasiteit, kan verminder. iv Table of Contents Declaration ......................................................................................................................................................... i Acknowledgements ........................................................................................................................................... ii Abstract ............................................................................................................................................................ iii Opsomming ...................................................................................................................................................... iv Table of Contents .............................................................................................................................................. v List of Figures.................................................................................................................................................... x List of Tables .................................................................................................................................................. xiv 1 Project motivation and project description ................................................................................................. 1 1.1 Introduction .......................................................................................................................................