Quantifying South Africa’s sulphur dioxide emission efficiency in coal-powered electricity generation by fitting the three-parameter log-logistic distribution
DOI:
https://doi.org/10.17159/2413-3051/2017/v28i1a1530Keywords:
emission, Eskom, log logistic distribution, goodness of fit, sulphur dioxide, Burr-type distributionAbstract
This paper fits the three-parameter log-logistic (3LL) distribution to sulphur dioxide (SO2) monthly emissions in kilograms per gigawatt hour (kg/GWh) and in milligrams per cubic nano metre (mg/Nm3), at 13 of Eskom’s coal fired power-generating stations in South Africa. The aim is to quantify and describe the emission of sulphur dioxide at these stations using a statistical distribution, and to also estimate the probabilities of extreme emissions and exceedances (emissions above a certain threshold). Using the 3LL distribution is proposed as such a distribution. The log-logistic distribution is a special form of a Burr-type distribution. Various goodness-of-fit measures, including the Kolmogorov Smirnov, the Anderson Darling and some graphical tests, are employed to test if the 3LL distribution is a good fit to the data. The maximum likelihood method is used to estimate the parameters. The distribution fit is important as it then becomes possible to quantify and manage the SO2 emissions effectively. The 3LL distribution, which is compared with three other distributions, gave the best overall fit to most of the power stations.
Keywords: emission, Eskom, log logistic distribution, goodness of fit, sulphur dioxide, Burr-type distribution
Highlights- Quantification of SO2 emissions in terms of a statistical distribution
- Calculating the probability of SO2 emissions exceeding certain specified limits
- Ranking power stations in terms of SO2 emissions efficiency
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References
Abbas, K.; Alamgir.; Khan, S.A.; Ali, A.; Khan, D.M.; Khalil, U. 2012. Statistical analysis of wind speed da-ta in Pakistan. World Applied Sciences Journal 18(11): 1533–1539.
Ashkar, F. and Mahdi, S. 2003. Comparison of two fit-ting methods for log–logistic. Water Resources Re-search 39(8): SWC 7.1–SWC 7.8
Balakrishnan, N. and Malik, H.J. 1987. Best linear unbiased estimation of the location and scale parameters of the log–logistic distribution. Communication in statistics A: Theory and Methods 16: 3477–95.
Beirlant, J., Goegebeur, Y., Teugels J., De Waal, D. and Ferro C. 2004. Statistics of extremes. West Sussex: John Willey & Sons.
Brown, S. 2011. Measures of shape: Skewness and kurtosis. Available online at: http://web.ipac.caltec.edu/staff/fmasci/home/statistics_refs/SkewStatSignif.pdf.
Burr, I. 1942. Cumulative frequency functions. Annals of Mathematical Statistics. 13(2): 215–232.
Eskom. 2011. Eskom emission monitoring. Available online at: http://www.wonderware.co.za/content/Eskom%20Emission%20Monitoring.pdf.
Eskom. 2012. Kusile and Medupi coal–fired power sta-tions under construction. Available online at: http://www.eskom.co.za/OurCompany/SustainableDevelop-ment/ClimateChangeCOP17/Documents/Kusile_and_Medupi_coal–fired_power_stations_under_construction.pdf.
Eskom. 2012. Climate change COP 17 fact sheet. Avail-able online at: http://www.eskom.co.za/OurCompany/SustainableDevelop-ment/ClimateChangeCOP17/Documents/Air_quality_and_climate_change.pdf.
Evans, D.L., Drew, J.H. and Leemis, L.M. 2008. The distribution of the Kolmogorov–Smirnov, Cramer–von Mises and Anderson–Darling tests statistics for exceptional populations with estimated parameters. Communication in Statistics–Simulation and Computation 37: 1396–1421.
Georgopoulos, G.P. and Seinfeld H.J. 1982. Statistical distributions of air pollutant concentrations. Environmental Science and Technology 16(7): 401A–416A.
Hadley, A. and Toumi, R. 2003. Assessing changes to the probability distribution of sulphur dioxide in the UK using lognormal model. Atmospheric Environment 37: 1461–1474.
Mielke, P.W., & Johnson, E.S. 1973. Three parameter Kappa distribution maximum likelihood estimates and likelihood ratio tests. Monthly Weather Review 101, 701–709.
Mitchell, B. 1971. A comparison of Chi Square and Kolmogorov–Smirnov tests. Area 3(4): 237–241. Available online at: https://www.jstor.org/stable/ 20000590?seq=1#fndtn–page_scan_tab_contents
Rumburg, B., Alldredge, R. and Claiborn, C. 2001. Statistical distributions of particulate matter and error associated with sampling frequency. Atmospheric En-vironment 35: 2907–20.
Seifeld, J.H. and Pandis, S.N., 1998. Atmospheric chem-istry and physics: From air pollution to climate change. New York: Wiley.
Singh, V.P., Gou, H. and Yu, F.X., 1993. Parameter estimation for 3–parameter log–logistic distribution (LLD3) by Pome. Stochastic Hydrology and Hydraulics 7: 163–177.
Smith, L.R. 1989. Extreme value analysis of environ-mental time series: An application to trend detection in ground–level ozone. Statistical Science 44: 367–393.
Tiku, M.L. and Suresh, R.P. 1992. A new method of estimation for location and scale parameters. Journal of Statistical Planning and Inference 30: 281–292.
Wingo, D.R. (Metrica). 1993. Maximum likelihood methods for fitting the Burr Type XII distribution to multiply (progressively) censored Life Data. 40: 203–210. doi:10.1007/BF02613681.
Zaharim, A., Najid, S.K., Razali, A.M. and Sopian, K. 2009. Analysing Malaysian wind speed data using statistical distribution. Proceedings of the 4th IASME/WSEAS International Conference on Energy and Environment, Cambridge, UK.
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