Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory

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dc.contributor.advisorSigauke, C.
dc.contributor.advisorFyei, K. A.
dc.contributor.authorBoano - Danquah, Jerry
dc.date2018
dc.date.accessioned2018-10-05T07:28:32Z
dc.date.available2018-10-05T07:28:32Z
dc.date.issued2018-09-21
dc.descriptionMSc (Statistics)
dc.descriptionDepartment of Statistics
dc.description.abstractDaily peak electricity data from ESKOM, South African power utility company for the period, January 1997 to December 2013 consisting of 6209 observations were used in this dissertation. Since 1994, the increased electricity demand has led to sustainability issues in South Africa. In addition, the electricity demand continues to rise everyday due to a variety of driving factors. Considering this, if the electricity generating capacity in South Africa does not show potential signs of meeting the country’s demands in the subsequent years, this may have a significant impact on the national grid causing it to operate in a risky and vulnerable state, leading to disturbances, such as load shedding as experienced during the past few years. In particular, it is of greater interest to have sufficient information about the extreme value of the stochastic load process in time for proper planning, designing the generation and distribution system, and the storage devices as these would ensure efficiency in the electrical energy in order to maintain discipline in the grid systems. More importantly, electricity is an important commodity used mainly as a source of energy in industrial, residential and commercial sectors. Effective monitoring of electricity demand is of great importance because demand that exceeds maximum power generated will lead to power outage and load shedding. It is in the light of this that the study seeks to assess the frequency of occurrence of extreme peak electricity demand in order to come up with a full electricity demand distribution capable of managing uncertainties in the grid system. In order to achieve stationarity in the daily peak electricity demand (DPED), we apply a penalized regression cubic smoothing spline to ensure the data is non-linearly detrended. The R package “evmix” is used to estimate the thresholds using the bounded corrected kernel density plot. The non-linear detrended datasets were divided into summer, spring, winter and autumn according to the calender dates in the Southern Hemisphere for frequency analysis. The data is declustered using Ferro and Segers automatic declustering method. The cluster maxima is extracted using the R package “evd”. We fit Poisson GPD and stationary point process to the cluster maxima and the intensity function of the point process which measures the frequency of occurrence of the daily peak electricity demand per year is calculated for each dataset. The formal goodness-of-fit test based on Cramer-Von Mises statistics and Anderson-Darling statistics supported the null hypothesis that each dataset follow Poisson GPD (σ, ξ) at 5 percent level of significance. The modelling framework, which is easily extensible to other peak load parameters, is based on the assumption that peak power follows a Poisson process. The parameters of the developed i models were estimated using the Maximum Likelihood. The usual asymptotic properties underlying the Poisson GPD were satisfied by the model.en_US
dc.description.sponsorshipNRFen_US
dc.format.extent1 online resource xvi, 122 leaves : color illustrations)
dc.identifier.apacitationBoano - Danquah, J. (2018). <i>Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory</i>. (). . Retrieved from http://hdl.handle.net/11602/1209en_ZA
dc.identifier.chicagocitationBoano - Danquah, Jerry. <i>"Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory."</i> ., , 2018. http://hdl.handle.net/11602/1209en_ZA
dc.identifier.citationBoano-Danquah, Jerry (2018) Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory, University of Venda, South Africa.<http://hdl.handle.net/11602/1209>.
dc.identifier.ris TY - Dissertation AU - Boano - Danquah, Jerry AB - Daily peak electricity data from ESKOM, South African power utility company for the period, January 1997 to December 2013 consisting of 6209 observations were used in this dissertation. Since 1994, the increased electricity demand has led to sustainability issues in South Africa. In addition, the electricity demand continues to rise everyday due to a variety of driving factors. Considering this, if the electricity generating capacity in South Africa does not show potential signs of meeting the country’s demands in the subsequent years, this may have a significant impact on the national grid causing it to operate in a risky and vulnerable state, leading to disturbances, such as load shedding as experienced during the past few years. In particular, it is of greater interest to have sufficient information about the extreme value of the stochastic load process in time for proper planning, designing the generation and distribution system, and the storage devices as these would ensure efficiency in the electrical energy in order to maintain discipline in the grid systems. More importantly, electricity is an important commodity used mainly as a source of energy in industrial, residential and commercial sectors. Effective monitoring of electricity demand is of great importance because demand that exceeds maximum power generated will lead to power outage and load shedding. It is in the light of this that the study seeks to assess the frequency of occurrence of extreme peak electricity demand in order to come up with a full electricity demand distribution capable of managing uncertainties in the grid system. In order to achieve stationarity in the daily peak electricity demand (DPED), we apply a penalized regression cubic smoothing spline to ensure the data is non-linearly detrended. The R package “evmix” is used to estimate the thresholds using the bounded corrected kernel density plot. The non-linear detrended datasets were divided into summer, spring, winter and autumn according to the calender dates in the Southern Hemisphere for frequency analysis. The data is declustered using Ferro and Segers automatic declustering method. The cluster maxima is extracted using the R package “evd”. We fit Poisson GPD and stationary point process to the cluster maxima and the intensity function of the point process which measures the frequency of occurrence of the daily peak electricity demand per year is calculated for each dataset. The formal goodness-of-fit test based on Cramer-Von Mises statistics and Anderson-Darling statistics supported the null hypothesis that each dataset follow Poisson GPD (σ, ξ) at 5 percent level of significance. The modelling framework, which is easily extensible to other peak load parameters, is based on the assumption that peak power follows a Poisson process. The parameters of the developed i models were estimated using the Maximum Likelihood. The usual asymptotic properties underlying the Poisson GPD were satisfied by the model. DA - 2018-09-21 DB - ResearchSpace DP - Univen KW - Extreme Value Theory (EVT) KW - Daily Peak Electricity (DPED) KW - Peaks-Over - Thresholds (POT) KW - Poisson (GPD) KW - Maximum Likelihood Estimation (MLE) LK - https://univendspace.univen.ac.za PY - 2018 T1 - Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory TI - Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory UR - http://hdl.handle.net/11602/1209 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11602/1209
dc.identifier.vancouvercitationBoano - Danquah J. Stochastic Modelling of Daily Peak Electricity Demand Using Value Theory. []. , 2018 [cited yyyy month dd]. Available from: http://hdl.handle.net/11602/1209en_ZA
dc.language.isoenen_US
dc.subjectExtreme Value Theory (EVT)en_US
dc.subjectUCTDen_ZA
dc.subjectPeaks-Over - Thresholds (POT)en_US
dc.subjectPoisson (GPD)en_US
dc.subjectMaximum Likelihood Estimation (MLE)en_US
dc.subject.ddc333.790968
dc.subject.lcshPower resources -- South Africa
dc.subject.lcshElectric power consumption -- South Africa
dc.subject.lcshDemand-side management (Electric utilities) -- South Africa
dc.subject.lcshEnergy consumption -- South Africa
dc.subject.lcshStochastic processes -- South Africa
dc.subject.lcshElectric power -- South Africa
dc.subject.lcshElectric utilities -- South Africa
dc.subject.lcshElectric industries -- South Africa
dc.titleStochastic Modelling of Daily Peak Electricity Demand Using Value Theoryen_US
dc.typeDissertationen_US
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