On the use of extreme value theory in energy markets
| dc.contributor.advisor | De Waal, D. | |
| dc.contributor.author | Micali, V. | |
| dc.date.accessioned | 2016-01-13T09:05:32Z | |
| dc.date.available | 2016-01-13T09:05:32Z | |
| dc.date.copyright | 2007-05-09 | |
| dc.date.issued | 2007-05-09 | |
| dc.date.submitted | 2007-04-09 | |
| dc.description.abstract | English: The thesis intent is to provide a set of statistical methodologies in the field of Extreme Value Theory (EVT) with a particular application to energy losses, in Gigawatt-hours (GWh) experienced by electrical generating units (GU’s). Due to the complexity of the energy market, the thesis focuses on the volume loss only and does not expand into the price, cost or mixes thereof (although the strong relationship between volume and price is acknowledged by some initial work on the energy price [SMP] is provided in Appendix B) Hence, occurrences of excessive unexpected energy losses incurred by these GU’s formulate the problem. Exploratory Data Analysis (EDA) structures the data and attempts at giving an indication on the categorisation of the excessive losses. The size of the GU failure is also investigated from an aggregated perspective to relate to the Generation System. Here the effect of concomitant variables (such as the Load Factor imposed by the market) is emphasised. Cluster Analysis (2-Way Joining) provided an initial categorising technique. EDA highlights the shortfall of a scientific approach to determine the answer to the question at when is a large loss sufficiently large that it affects the System. The usage of EVT shows that the GWh Losses tend to behave as a variable in the Fréchet domain of attraction. The Block Maxima (BM) and Peak-Over-Threshold (POT), the latter as semi and full parametric, methods are investigated. The POT methodologies are both applicable. Of particular interest is the Q-Q plots results on the semiparametric POT method, which yielded results that fit the data satisfactorily (pp 55-56). The Generalised Pareto Distribution (GPD) models well the tail of the GWh Losses above a threshold under the POT full parametric method. Different methodologies were explored in determining the parameters of the GPD. The method of 3-LM (linear combinations of Probability Weighted Moments) is used to arrive at initial estimates of the GPD parameters. A GPD is finally parameterised for the GWh Losses above 766 GWh. The Bayesian philosophy is also utilised in this thesis as it provides a predictive distribution of (high quantiles) the large GWh Losses. Results are found in this part of the thesis in so far that it utilises the ratio of the Mean Excess Function (the expectation of a loss above a certain threshold) over its probability of exceeding the threshold as an indicator to establish the minimum of this ratio. The technique was developed for the GPD by using the Fisher Information Matrix (FIM) and the Delta-Method. Prediction of high quantiles were done by using Markov Chain Monte Carlo (MCMC) and eliciting the GPD Maximal Data Information (MDI) prior. The last EVT methodology investigated in the thesis is the one that uses the Dirichlet process and the method of Negative Differential Entropy (NDE). The thesis also opened new areas of pertinent research. | en_ZA |
| dc.description.abstract | Afrikaans: metodologië in die veld van Ekstreme Waarde Teorie te voorsien met ’n besonderse aanwending van verlore energie in Gigawatt-ure en wat ondervind is deur elektries-ontwikkelde eenhede. As gevolg van die kompleksiteit van die energiemark, fokus die skripsie alleenlik op die volume verlies en nie op die pryskostes of die verhouding daarvan nie, alhoewel die sterk verhouding tussen volume en prys erken word aan die beginstadium van werk op die energieprys wat in Aanhangsel B voorsien word. Hierna word verspreiding van buitensporige onverwagte verlore energie deur hierdie ontwikkelde eenhede blootgestel wat die probleem formuleer. Verkennende data ontleding struktureer die data en pogings om ’n aanduiding te gee op die kategorisering van die oormatige verliese. Die grootte van die mislukte ontwikkelde eenheid is ook ondersoek vanuit ’n gesamentlike perspektief om die Opwekkingstelsel in verband te bring. Hier word die effek van gepaardgaande veranderlikes (soos wat die Gelaaide Faktor deur die mark voorgeskryf word) beklemtoon. Bondelontleding (2-Way Joining) het ’n aanvanklike kategorieserings tegniek voorsien. Verkennende data-ontleding lig die gebrek aan ’n wetenskaplike benadering uit om die antwoord op die vraag te bepaal wanneer ’n groot verlies grootgenoeg is om die Stelsel te beïnvloed. Die gebuik van Ekstreemwaarde-teorie toon dat die GW-ure verliese geneig is om as ’n veranderlike in te tree in die Fréchet gebied. Die Blok-Maksima en “Peak-Over Threshold” (POT) metodes, laasgenoemde as half en vol parametriese metodes, is ondersoek. Die POT metodologië is beide bruikbaar. Uit besonderse belangstelling lewer die QQ voorstellings van die half parametriese POT metode, goeie resultate. Die Veralgemeende Paretoverdeling (GPD) modeleer die stert van GWh-verliese bokant a drempelwaarde onder POT goed. Verskillende metodologië was ondersoek deur die bepaling van parameters van die GPD. Die metode van 3-LM (lineêr kombinasies van die Waarskynlikheid-Geweegde-Momente-metode ) is gebruik as `n eerste skatting van die GPD parameters. ’n GPD is finaal geparameteriseerd vir die GW-ure verliese bo 766 GW-ure. Die Bayes-filisofie is ook gebruik in hierdie skripsie en voorsien ’n voorspellingsfunksie van (hoë kwantiele) van groot GW-ure verliese. Nuwe werk is in hierdie gedeelte van die skripsie gedoen in soverre dit die gebruik van die verhouding van die gemiddelde-oorskrydingsfunksie relatief tot `n oorskrydingswaarskynlikheid as ’n aanwysing om die minimum van hierdie verhouding te vestig. Die tegniek was ontwikkel vir die GPD deur die Fisher-informasiematriks en die Delta-metode te gebruik. Voorspelling van hoë kwantiele is deur die gebruik van MCMC gedoen en die MDI prior vir die GPD is gebruik. Die laaste Ekstreemwaarde metodologie wat in die skripsie ondersoek is, is die een wat die Dirichlet proses en die metode van Negatiewe-Afgeleide-Entropie gebruik. Die skripsie open ook nuwe areas vir gepaste navorsing. | af |
| dc.identifier.uri | http://hdl.handle.net/11660/2178 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | University of the Free State | en_ZA |
| dc.rights.holder | University of the Free State | en_ZA |
| dc.subject | Thesis (Ph.D. (Mathematical Statistics))--University of the Free State, 2007 | en_ZA |
| dc.subject | Extreme value theory | en_ZA |
| dc.subject | Mathematical statistics | en_ZA |
| dc.subject | Cluster Analysis (2-Way Joining) | en_ZA |
| dc.subject | Plots | en_ZA |
| dc.subject | Q-Q | en_ZA |
| dc.subject | Generalised Pareto Distribution | en_ZA |
| dc.subject | GPD Fisher Information Matrix | en_ZA |
| dc.subject | GPD Jeffreys’ Prior | en_ZA |
| dc.subject | Gigawatthours Losses | en_ZA |
| dc.subject | Extreme Value Theory | en_ZA |
| dc.subject | Energy Markets | en_ZA |
| dc.title | On the use of extreme value theory in energy markets | en_ZA |
| dc.type | Thesis | en_ZA |