Tail Quantile Estimation of Heteroskedastic Intraday Increases in Peak Electricity Demand

Sigauke, Caston; Verster, Andréhette; Chikobvu, Delson

doi:10.4236/ojs.2012.24054

Cited by 11 publications

(9 citation statements)

References 7 publications

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“…A hybrid model called an autoregressive moving average-exponential generalised autoregressive conditional heteroscedasticity-generalised single Pareto (ARMA-EGARCH-GSP) was developed in [9]. The model was used for estimating extreme quantiles of inter-day increases in peak electricity demand.…”

Section: A Backgroundmentioning

confidence: 99%

Analysis of Extreme Peak Loads Using Point Processes: An Application Using South African Data

2020

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Extreme value modelling of peak load process is critical to the reliable specification of power generation, distribution and maintenance purposes during both peak and off-peak periods. In this study, a frequency assessment of extreme peak electricity demand for the four seasons of the year using South African data for the period, January 1997 to December 2013 is carried out. A point process approach from extreme value theory is proposed as an ingenious extreme value theory approach. The data are made stationary by using a time-varying threshold which has a positive shift factor. The non-linear detrended datasets are then grouped into summer, spring, winter and autumn according to the calendar dates in the Southern Hemisphere. The datasets were declustered to keep the series relatively independent using Ferro and Segers automatic declustering method. A stationary point process model is then fitted to each of the cluster maxima. The modelling framework, which is easily extensible to other peak load parameters, assumes that peak power follows a Poisson point process. The parameters of the developed model are estimated using the maximum likelihood method. Empirical results show that daily peak electricity demand could be experienced approximately 27, 16, 7 and 15 days per year in winter, spring, summer and autumn, respectively. The modelling approach could assist system operators of utility companies in scheduling maintenance of generating units including long term planning. INDEX TERMS Extreme value theory, daily peak electricity demand, peaks-over threshold, maximum likelihood estimation, point process.

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Section: A Backgroundmentioning

confidence: 99%

Analysis of Extreme Peak Loads Using Point Processes: An Application Using South African Data

2020

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“…South African daily peak electricity demand (DPED) data for the period 1 January 2000 to 31 August 2011 was used, where 1 , … , was considered to be a sequence of inter-day changes in peak electricity demand. The increase/decrease in peak demand is relative to the previous day (Sigauke et al, 2012). Let be equal to DPED on day and −1 DPED on day − 1, then the inter-day change, , in peak electricity demand on day , can be defined as in Equation 1.…”

Section: Description Of the Datamentioning

confidence: 99%

“…Modelling daily peak electricity demand using the South African data is discussed in the literature (Sigauke et al, 2012;Sigauke et al, 2013;Verster et al, 2013;among others). Sigauke et al (2012) developed a hybrid model called an autoregressive moving average -exponential generalised autoregressive conditional heteroscedasticity -generalised single Pareto (ARMA-EGARCH-GSP) model for estimating extreme quantiles of inter-day increases in peak electricity demand. It was argued that this modelling approach captures the conditional heteroscedasticity in the data and can be used to estimate extreme tail quantiles of the distribution of the inter-day increases in peak electricity demand.…”

Section: Introductionmentioning

confidence: 99%

Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

Sigauke

Chikobvu

2017

J. energy South. Afr.

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Uncertainty in electricity demand is caused by many factors. Large changes are usually attributed to extreme weather conditions and the general random usage of electricity by consumers. More understanding requires a detailed analysis using a stochastic process approach. This paper presents a Markov chain analysis to determine stationary distributions (steady state probabilities) of large daily changes in peak electricity demand. Such large changes pose challenges to system operators in the scheduling and dispatching of electrical energy to consumers. The analysis used on South African daily peak electricity demand data from 2000 to 2011 and on a simple two-state discrete-time Markov chain modelling framework was adopted to estimate steady-state probabilities of two states: positive inter-day changes (increases) and negative inter-day changes (decreases). This was extended to a three-state Markov chain by distinguishing small positive changes and extreme large positive changes. For the negative changes, a decrease state was defined. Empirical results showed that the steady state probability for an increase was 0.4022 for the two-state problem, giving a return period of 2.5 days. For the three state problem, the steady state probability of an extreme increase was 0.0234 with a return period of 43 days, giving approximately nine days in a year that experience extreme inter-day increases in electricity demand. Such an analysis was found to be important for planning, load shifting, load flow analysis and scheduling of electricity, particularly during peak periods.

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“…For these reasons, the increase of the consumption peak occurrence and intensity are difficult to forecast with statistical models. Different works develop numerical tools to forecast the increase in energy demand peaks, e.g., statistical tools capable to capture unexpected extreme intraday increases by using available statistical records of energy demand [54], parametric models to predict long-term peaks correlated with weather, economic and demographic parameters of a particular area [55] or Bayesian estimation techniques to predict energy consumption peaks in transportation systems [56].The statistical forecast approaches are based on the so-called normal profiles of the statistical parameter, e.g., energy consumption or temperature, which do not account for a possible increase of the peak occurrence and magnitude in the future [57]. Moreover, the multi-parameters time series models accounting for weather-induced effects, daily/weekly/yearly seasonality, special calendar events and in some cases, the variation of GDP and demographics of the geographical areas, provide a more accurate forecast for peak occurrence and magnitude [58]- [60].…”

Section: Energy Demand Peaksmentioning

confidence: 99%

Analysis of robust optimization for decentralized microgrid energy management under uncertainty

Kuznetsova

Ruiz

et al. 2015

International Journal of Electrical Power & Energy Systems

116

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The present paper provides an extended analysis of a microgrid energy management framework based on Robust Optimization (RO). Uncertainties in wind power generation and energy consumption are described in the form of Prediction Intervals (PIs), estimated by a Genetic Algorithm (GA)-trained Neural Network (NN). The framework is tested and exemplified in a microgrid formed by a middle-size train station (TS) with integrated photovoltaic power production system (PV), an urban wind power plant (WPP) and a surrounding residential district (D). The system is described by Agent-Based Modelling (ABM): each stakeholder is modelled as an individual agent, which aims at a specific goal, either of decreasing its expenses from power purchasing or increasing its revenues from power selling. The aim of this paper is to identify which is the uncertainty level associated to the "extreme" conditions upon which robust management decisions perform better than a microgrid management based on expected values. This work shows how the probability of occurrence of some specific uncertain events, e.g., failures of electrical lines and electricity demand and price peaks, highly conditions the reliability and performance indicators of the microgrid under the two optimization approaches: (i) RO based on the PIs of the uncertain parameters and (ii) optimization based on expected values.

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Tail Quantile Estimation of Heteroskedastic Intraday Increases in Peak Electricity Demand

Cited by 11 publications

References 7 publications

Analysis of Extreme Peak Loads Using Point Processes: An Application Using South African Data

Analysis of Extreme Peak Loads Using Point Processes: An Application Using South African Data

Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

Analysis of robust optimization for decentralized microgrid energy management under uncertainty

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