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題名 利用隨機模型訂定電力之最佳契約容量
Determining the Optimal Contract Capacity of Electric Power Based on Stochastic Modeling
作者 游振利
貢獻者 洪英超
游振利
關鍵詞 具飄移項之布朗運動
Ljung-Box檢定
Kolmogorov-Smirnov檢定
電力契約容量最佳化
日期 2015
上傳時間 17-Aug-2015 14:07:10 (UTC+8)
摘要 由於商業、工業和民生各方面大量的用電需求，使得電費在某些季節會特別昂貴。又因為電力的生產和儲存都有限，故電力公司為了能更有效率的分配總電力，要求消費者事先訂定各自用戶的契約容量，做為每個月分配電力的最大標準。對於消費者而言，相較於較高的契約容量，選取較低的契約容量通常負擔的基本電費也較低，但是當用電量超過契約容量時則必須支付高額罰金。因此消費者為了盡可能使長期的用電消費降低，選擇一個合適且最佳的契約容量是很重要的課題。在本文中以隨機模型”具飄移項之布朗運動”作為分析用電量趨勢的模型，並介紹如何做模型的驗證以及參數的估計，接著建構出總電費的期望值估計式以尋找最佳的契約容量。最後，以政治大學的實際用電量資料作為本文的研究實例，並提出選擇契約容量之建議方針。
參考文獻 [1] T.W. Anderson and D.A. Darling (2014). Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes. The Annals of Mathematical Statistics, Vol.23, No.2, pp.193-212

[2] R. Baldick, S. Kolos and S. Tompaidis (2014). Interruptible Electricity Contracts from an Electricity Retailer`s Point of View: Valuation and Optimal Interruption. Operations Research, Vol.54, No.4, pp.627-642

[3] C.W. Cheng, Y.C. Hung and N. Balakrishnan (2014). Generating Beta Random Numbers and Dirichlet Random Vectors in R: The Package rBeta2009. Computational Statistics and Data Analysis, 71, pp.1011-1020

[4] A. Dahl (2010). A Rigorous Introduction to Brownian Motion. Department of Statistics, The University of Chicago.

[5] L. Decreusefond and A.S. Ustunel (1999). Stochastic Analysis of the Fractional Brownian Motion. Potential Analysis, Vol.10, Issue 2,
pp.177-214

[6] J. Felsenstein (1973). Maximum Likelihood Estimation of Evolutionary Trees from Continuous Characters. American Journal of Human Genetics, Vol.25, pp.471-492

[7] L. Harmon, J. Weir, C. Brock, R. Glor, W. Challenger, G. Hunt, R. FitzJohn, M. Pennell, G. Slater, J. Brown, J. Uyeda and J. Eastman (2014). Package ”geiger”.
URL http://cran.r-project.org/web/packages/geiger/geiger.pdf

[8] S. Heydari and A. Siddiqui (2010). Real Options Analysis of Multiple-Exercise Interruptible Load Contracts. Department of Statistical Science, University College London, London, UK.

[9] D.E. Knuth (1971). Optimum binary search trees. Acta Informatica, Vol.1, Issue 1, pp.14-25

[10] F.J. Massey Jr. (2012). The Kolmogorov-Smirnov Test for Goodness of Fit. Journal of the American Statistical Association, Vol.46, Issue 253, pp.68-78

[11] I. Negri and Y. Nishiyama (2008). Goodness of fit test for ergodic diffusion processes. Annals of the Institute of Statistical Mathematics, Vol.61, Issue 4, pp.919-928

[12] S.S. Oren (2001). Integrating real and financial options in demand-side electricity contracts. Decision Support Systems archive, Vol.30, Issue 3, pp.279-288

[13] L. Qi and J. Sun (1993). A nonsmooth version of Newton`s method.
Mathematical Programming, Vol.58, Issue 1-3, pp.353-367

[14] D.S. Stoffer and C.M.C. Toloi (1992). A note on the Ljung-Box-Pierce portmanteau statistic with missing data. Statistics & Probability Letters, Vol.13, Issue 5, pp.391-396

[15] M. Subasi, N. Yildirim and B. Yildiz (2004). An improvement on Fibonacci search method in optimization theory. Applied Mathematics and Computation, Vol.147, Issue 3, pp.893-901

[16] C.H. Tsaia, J. Kolibala and M. Li (2010). The golden section search algorithm for finding a good shape parameter for meshless collocation methods. Engineering Analysis with Boundary Elements, Vol.34, Issue 8, pp.738-746
描述 碩士
國立政治大學
統計研究所
102354028
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102354028
資料類型 thesis
dc.contributor.advisor 洪英超zh_TW
dc.contributor.author (Authors) 游振利zh_TW
dc.creator (作者) 游振利zh_TW
dc.date (日期) 2015en_US
dc.date.accessioned 17-Aug-2015 14:07:10 (UTC+8)-
dc.date.available 17-Aug-2015 14:07:10 (UTC+8)-
dc.date.issued (上傳時間) 17-Aug-2015 14:07:10 (UTC+8)-
dc.identifier (Other Identifiers) G0102354028en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/77550-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 102354028zh_TW
dc.description.abstract (摘要) 由於商業、工業和民生各方面大量的用電需求，使得電費在某些季節會特別昂貴。又因為電力的生產和儲存都有限，故電力公司為了能更有效率的分配總電力，要求消費者事先訂定各自用戶的契約容量，做為每個月分配電力的最大標準。對於消費者而言，相較於較高的契約容量，選取較低的契約容量通常負擔的基本電費也較低，但是當用電量超過契約容量時則必須支付高額罰金。因此消費者為了盡可能使長期的用電消費降低，選擇一個合適且最佳的契約容量是很重要的課題。在本文中以隨機模型”具飄移項之布朗運動”作為分析用電量趨勢的模型，並介紹如何做模型的驗證以及參數的估計，接著建構出總電費的期望值估計式以尋找最佳的契約容量。最後，以政治大學的實際用電量資料作為本文的研究實例，並提出選擇契約容量之建議方針。zh_TW
dc.description.tableofcontents 第一章 導論 1
第二章 布朗運動之參數估計與模型檢定 3
第一節 布朗運動模型(BROWNIAN MOTION) 3
第二節 具飄移項的布朗運動模型(BROWNIAN MOTION WITH DRIFT) 5
第三節 具飄移項布朗運動模型之參數估計 6
第四節 布朗運動模型之驗證 7
第三章 訂定電力最佳契約容量問題 10
第一節 最佳化問題描述 10
第二節 以布朗運動模型擬定最佳策略 12
第四章 實例研究 19
第五章 總結與討論 25
參考文獻 27		zh_TW
dc.format.extent 752042 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102354028en_US
dc.subject (關鍵詞) 具飄移項之布朗運動zh_TW
dc.subject (關鍵詞) Ljung-Box檢定zh_TW
dc.subject (關鍵詞) Kolmogorov-Smirnov檢定zh_TW
dc.subject (關鍵詞) 電力契約容量最佳化zh_TW
dc.title (題名) 利用隨機模型訂定電力之最佳契約容量zh_TW
dc.title (題名) Determining the Optimal Contract Capacity of Electric Power Based on Stochastic Modelingen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] T.W. Anderson and D.A. Darling (2014). Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes. The Annals of Mathematical Statistics, Vol.23, No.2, pp.193-212

[2] R. Baldick, S. Kolos and S. Tompaidis (2014). Interruptible Electricity Contracts from an Electricity Retailer`s Point of View: Valuation and Optimal Interruption. Operations Research, Vol.54, No.4, pp.627-642

[3] C.W. Cheng, Y.C. Hung and N. Balakrishnan (2014). Generating Beta Random Numbers and Dirichlet Random Vectors in R: The Package rBeta2009. Computational Statistics and Data Analysis, 71, pp.1011-1020

[4] A. Dahl (2010). A Rigorous Introduction to Brownian Motion. Department of Statistics, The University of Chicago.

[5] L. Decreusefond and A.S. Ustunel (1999). Stochastic Analysis of the Fractional Brownian Motion. Potential Analysis, Vol.10, Issue 2,
pp.177-214

[6] J. Felsenstein (1973). Maximum Likelihood Estimation of Evolutionary Trees from Continuous Characters. American Journal of Human Genetics, Vol.25, pp.471-492

[7] L. Harmon, J. Weir, C. Brock, R. Glor, W. Challenger, G. Hunt, R. FitzJohn, M. Pennell, G. Slater, J. Brown, J. Uyeda and J. Eastman (2014). Package ”geiger”.
URL http://cran.r-project.org/web/packages/geiger/geiger.pdf

[8] S. Heydari and A. Siddiqui (2010). Real Options Analysis of Multiple-Exercise Interruptible Load Contracts. Department of Statistical Science, University College London, London, UK.

[9] D.E. Knuth (1971). Optimum binary search trees. Acta Informatica, Vol.1, Issue 1, pp.14-25

[10] F.J. Massey Jr. (2012). The Kolmogorov-Smirnov Test for Goodness of Fit. Journal of the American Statistical Association, Vol.46, Issue 253, pp.68-78

[11] I. Negri and Y. Nishiyama (2008). Goodness of fit test for ergodic diffusion processes. Annals of the Institute of Statistical Mathematics, Vol.61, Issue 4, pp.919-928

[12] S.S. Oren (2001). Integrating real and financial options in demand-side electricity contracts. Decision Support Systems archive, Vol.30, Issue 3, pp.279-288

[13] L. Qi and J. Sun (1993). A nonsmooth version of Newton`s method.
Mathematical Programming, Vol.58, Issue 1-3, pp.353-367

[14] D.S. Stoffer and C.M.C. Toloi (1992). A note on the Ljung-Box-Pierce portmanteau statistic with missing data. Statistics & Probability Letters, Vol.13, Issue 5, pp.391-396

[15] M. Subasi, N. Yildirim and B. Yildiz (2004). An improvement on Fibonacci search method in optimization theory. Applied Mathematics and Computation, Vol.147, Issue 3, pp.893-901

[16] C.H. Tsaia, J. Kolibala and M. Li (2010). The golden section search algorithm for finding a good shape parameter for meshless collocation methods. Engineering Analysis with Boundary Elements, Vol.34, Issue 8, pp.738-746		zh_TW