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 (GUâs).
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 GUâs 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ufs/oai:etd.uovs.ac.za:etd-11162007-075128 |
| Date | 16 November 2007 |
| Creators | Micali, V |
| Contributors | Prof DJ de Waal |
| Publisher | University of the Free State |
| Source Sets | South African National ETD Portal |
| Language | en-uk |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.uovs.ac.za//theses/available/etd-11162007-075128/restricted/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University Free State or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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