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Integration of wind power into grids requires accurate forecasting, however, traditional wind power point forecast errors are unavoidable and they cannot be eliminated due to the highly volatile and uncertain in the chaotic time series of wind power. Unlike point prediction, which conveys no information about the prediction accuracy, probabilistic interval forecasts can provide a range, within which the target will lie with a certain probability, for estimating the potential impacts and risks facing the system operation. Most existing prediction interval (PI) construction methods are often placed after a deterministic forecasting model with or without prior assumptions, this paper propose a novel lower-upper bound estimation approach using extreme learning machine to directly construct PIs for wind power series. Based on the analysis of the interval forecasting error information in training dataset, a new problem formulation is developed in this method to get better PIs. In addition, in order to obtain the global optimal solution of the above model, a quantum bacterial foraging optimization algorithm is proposed by introducing the theory of quantum mechanics into bacteria foraging behavior. The testing results from two real wind farms with different confidence probability and optimization criterion demonstrate the excellent quality of PIs in terms of both reliability and sharpness, which provide a support for the steady operation of power system with wind power integration.
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Keywords:
- chaotic time series /
- probabilistic interval forecasts /
- extreme learning machine /
- quantum bacterial foraging optimization
[1] Jung J, Broadwater R P 2014 Renewable and Sustainable Energy Reviews 31 762
[2] Zhang X Q, Liang J 2012 Acta Phys. Sin. 61 190507 (in Chinese) [张学清, 梁军 2012 61 190507]
[3] Zhang Y 2013 Chin. Phys. B 22 050502
[4] Qu H, Ma W T, Zhao J H, Chen B D 2013 Chin. Phys. Lett. 30 110505
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[6] Liu D W, Guo J B, Huang Y H, Wang W S 2013 Proceeding of the CSEE 33 9 (in Chinese) [刘德伟, 郭剑波, 黄越辉, 王伟胜 2013 中国电机工程学报 33 9]
[7] Wu X S, Zhang B H, Yuan X M, Li G W, Luo G, Zhou Y 2013 Proceeding of the CSEE 33 45 (in Chinese) [吴小珊, 张步涵, 袁小明, 李高望, 罗钢, 周杨 2013 中国电机工程学报 33 45]
[8] Zhang Z S, Sun Y Z, Gao D W, Lin J, Cheng L 2013 IEEE Trans. on Power Systems 28 3114
[9] Jiang R W, Wang J H, Zhang M H, Guan Y P 2013 IEEE Trans. on Power Systems 28 2271
[10] Lange M 2005 J. Sol. Energy Eng. 127 177
[11] Zhou S L, Mao M Q, Shu J H 2011 Proceeding of the CSEE 31 10 (in Chinese)[周松林, 茆美琴, 苏建徽 2011 中国电机工程学报 31 10]
[12] Li Z, Han X S, Yang M, Zhong S M 2011 Automation of Electric Power Systems 35 83 (in Chinese) [李智, 韩学山, 杨明, 钟世民 2011 电力系统自动化 35 83]
[13] Sideratos G, Hatziargyriou N D 2012 IEEE Trans. Power Syst. 27 1788
[14] Jeon J, Taylor J W 2012 J. Amer. Statist. Assoc. 107 66
[15] Bessa R J, Miranda V, Botterud A, Zhou Z, Wang J 2012 Renew. Energy 40 29
[16] Khosravi A, Nahavandi S, Creighton D, Atiya A 2011 IEEE Trans. Neural Networks 22 337
[17] Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[18] Wang X Y, Han M 2012 Acta Phys. Sin. 61 080507 (in Chinese)[王新迎, 韩敏 2012 61 080507]
[19] Gao G Y, Jiang G P 2012 Acta Phys. Sin. 61 040506 (in Chinese)[高光勇, 梁国平 2012 61 040506]
[20] Khosravi A, Nahavandi S 2013 IEEE Trans. Sustainable Energy 4 849
[21] Quan H, Srinivasan D, Khosravi A 2014 IEEE Trans. Neural Netw. Learn. Syst. 25 303
[22] Van den Bergh F, Engelbrecht A P 2002 Proceedings of the IEEE International Conf on Systems, Man and Cybernetics, October 6-9, 2002 p94
[23] Sun J, Feng B, Xu W B 2004 Proceedings of the IEEE Congress on Evolutionary Computation, Dec. 1-3, 2004 p325
[24] Passino K M 2002 IEEE Control Systems Magazine 22 52
[25] Shrestha D L, Solomatine D P 2006 Neural Netw. 19 225
[26] Fang W, Sun J, Xie Z P, Xu W B 2010 Acta Phys. Sin. 59 3686 (in Chinese) [方伟, 孙俊, 谢振平, 须文波 2010 59 3686]
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[1] Jung J, Broadwater R P 2014 Renewable and Sustainable Energy Reviews 31 762
[2] Zhang X Q, Liang J 2012 Acta Phys. Sin. 61 190507 (in Chinese) [张学清, 梁军 2012 61 190507]
[3] Zhang Y 2013 Chin. Phys. B 22 050502
[4] Qu H, Ma W T, Zhao J H, Chen B D 2013 Chin. Phys. Lett. 30 110505
[5] Zhang X Q, Liang J 2013 Acta Phys. Sin. 62 050505 (in Chinese) [张学清, 梁军 2013 62 050505]
[6] Liu D W, Guo J B, Huang Y H, Wang W S 2013 Proceeding of the CSEE 33 9 (in Chinese) [刘德伟, 郭剑波, 黄越辉, 王伟胜 2013 中国电机工程学报 33 9]
[7] Wu X S, Zhang B H, Yuan X M, Li G W, Luo G, Zhou Y 2013 Proceeding of the CSEE 33 45 (in Chinese) [吴小珊, 张步涵, 袁小明, 李高望, 罗钢, 周杨 2013 中国电机工程学报 33 45]
[8] Zhang Z S, Sun Y Z, Gao D W, Lin J, Cheng L 2013 IEEE Trans. on Power Systems 28 3114
[9] Jiang R W, Wang J H, Zhang M H, Guan Y P 2013 IEEE Trans. on Power Systems 28 2271
[10] Lange M 2005 J. Sol. Energy Eng. 127 177
[11] Zhou S L, Mao M Q, Shu J H 2011 Proceeding of the CSEE 31 10 (in Chinese)[周松林, 茆美琴, 苏建徽 2011 中国电机工程学报 31 10]
[12] Li Z, Han X S, Yang M, Zhong S M 2011 Automation of Electric Power Systems 35 83 (in Chinese) [李智, 韩学山, 杨明, 钟世民 2011 电力系统自动化 35 83]
[13] Sideratos G, Hatziargyriou N D 2012 IEEE Trans. Power Syst. 27 1788
[14] Jeon J, Taylor J W 2012 J. Amer. Statist. Assoc. 107 66
[15] Bessa R J, Miranda V, Botterud A, Zhou Z, Wang J 2012 Renew. Energy 40 29
[16] Khosravi A, Nahavandi S, Creighton D, Atiya A 2011 IEEE Trans. Neural Networks 22 337
[17] Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[18] Wang X Y, Han M 2012 Acta Phys. Sin. 61 080507 (in Chinese)[王新迎, 韩敏 2012 61 080507]
[19] Gao G Y, Jiang G P 2012 Acta Phys. Sin. 61 040506 (in Chinese)[高光勇, 梁国平 2012 61 040506]
[20] Khosravi A, Nahavandi S 2013 IEEE Trans. Sustainable Energy 4 849
[21] Quan H, Srinivasan D, Khosravi A 2014 IEEE Trans. Neural Netw. Learn. Syst. 25 303
[22] Van den Bergh F, Engelbrecht A P 2002 Proceedings of the IEEE International Conf on Systems, Man and Cybernetics, October 6-9, 2002 p94
[23] Sun J, Feng B, Xu W B 2004 Proceedings of the IEEE Congress on Evolutionary Computation, Dec. 1-3, 2004 p325
[24] Passino K M 2002 IEEE Control Systems Magazine 22 52
[25] Shrestha D L, Solomatine D P 2006 Neural Netw. 19 225
[26] Fang W, Sun J, Xie Z P, Xu W B 2010 Acta Phys. Sin. 59 3686 (in Chinese) [方伟, 孙俊, 谢振平, 须文波 2010 59 3686]
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