# American Institute of Mathematical Sciences

October  2014, 10(4): 1297-1318. doi: 10.3934/jimo.2014.10.1297

## Distributed optimal dispatch of virtual power plant based on ELM transformation

 1 Hunan Province Key Laboratory of Smart Grids Operation and Control, School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China 2 School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China 3 The Centre for Intelligent Electricity Networks, The University of Newcastle, NSW 2308 4 Centre for Intelligent Electricity Networks, The University of Newcastle, Callaghan, NSW 2308, Australia 5 School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW 2006, Australia

Received  August 2013 Revised  January 2014 Published  February 2014

To implement the optimal dispatch of distributed energy resources (DER) in the virtual power plant (VPP), a distributed optimal dispatch method based on ELM (Extreme Learning Machine) transformation is proposed. The joint distribution of maximum available outputs of multiple wind turbines in the VPP is firstly modeled with the Gumbel-Copula function. A VPP optimal dispatch model is then formulated to achieve maximum utilization of renewable energy generation, which can take into account the constraints of electric power network and DERs. Based on the Gumbel-Copula joint distribution, the nonlinear functional relationship between the wind power cost and wind turbine output is approximated using ELM. The approximated functional relationship is then transformed into a set of equality constraints, which can be easily integrated with the optimal dispatch model. To solve the optimal dispatch problem, a distributed primal-dual sub-gradient algorithm is proposed to determine the operational strategies of DERs via local decision making and limited communication between neighbors. Finally, case studies based on the 15-node and the 118-node virtual power plant prove that the proposed method is effective and can achieve identical performance as the centralized dispatch approach.
Citation: Hongming Yang, Dexin Yi, Junhua Zhao, Fengji Luo, Zhaoyang Dong. Distributed optimal dispatch of virtual power plant based on ELM transformation. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1297-1318. doi: 10.3934/jimo.2014.10.1297
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Tam, et al., Data preprocessing and modelling of electronically-controlled automotive engine power performance using kernel principal components analysis and least squares support vector machines, International Journal of Vehicle Systems Modelling and Testing, 3 (2008), 312-330. doi: 10.1504/IJVSMT.2008.025406.  Google Scholar [21] P. K. Wong, Q. S. Xu and C. M. Vong, et al., Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine, IEEE Transactions on Industrial Electronics, 59 (2012), 1988-2001. doi: 10.1109/TIE.2011.2166235.  Google Scholar [22] T. H. Yeh and W. Li, A study on generator capacity for wind turbines under various tower heights and rated wind speeds using weibull distribution, IEEE Transactions on Energy Conversion, 23 (2008), 592-602. doi: 10.1109/TEC.2008.918626.  Google Scholar [23] L. Yu and E. O. Voit, Construction of bivariate s-distributions with copulas, Computational Statistics and Data Analysis, 51 (2006), 1822-1839. doi: 10.1016/j.csda.2005.11.021.  Google Scholar [24] C. Yuen, A. Oudalov and A. Timbus, The provision of frequency control reserves from multiple microgrids, IEEE Transactions on Industrial Electronics, 58 (2011), 173-183. doi: 10.1109/TIE.2010.2041139.  Google Scholar [25] J. H. Zhai, Fuzzy decision tree based on fuzzy-rough technique, Soft Computing, 15 (2011), 1087-1096. doi: 10.1007/s00500-010-0584-0.  Google Scholar [26] J. H. Zhao, F. S. Wen and Z. Y. Dong, et al., Optimal dispatch of electric vehicles and wind power using enhanced particle swarm optimization,, IEEE Transactions on Industrial Informatics, 8 (): 889.  doi: 10.1109/TII.2012.2205398.  Google Scholar

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##### References:
 [1] N. Br, An Introduction to Copulas, New York: Springer, 2005, 7-48. doi: 10.1007/0-387-28678-0.  Google Scholar [2] D. S. Callaway and I. A. Hiskens, Achieving controllability of electric loads, Proceedings of the IEEE, 99 (2011), 184-199. doi: 10.1109/JPROC.2010.2081652.  Google Scholar [3] N. Celika, Energy output estimation for small-scale wind power generators using weibull-representative wind data, Journal of Wind Engineering and Industrial Aerodynamics, 91 (2003), 693-707. doi: 10.1016/S0167-6105(02)00471-3.  Google Scholar [4] M. Grabisch, The representation of importance and interaction of features by fuzzy measures, Pattern Recognition Letters, 17 (1996), 567-575. doi: 10.1016/0167-8655(96)00020-7.  Google Scholar [5] J. Hetzer, D. C. Yu and K. Bhattarai, An economic dispatch model incorporating wind power, IEEE Transactions on Energy Conversion, 23 (2008), 603-611. doi: 10.1109/TEC.2007.914171.  Google Scholar [6] M. Hofert, Sampling archimedean copulas, Computational Statistics and Data Analysis, vol. 52 (2008), 5163-5174. doi: 10.1016/j.csda.2008.05.019.  Google Scholar [7] G. B. Huang, Q. Y. Zhu and K. Z. Mao, et al., Can threshold networks be trained directly, IEEE Transactions on Circuits and Systems II: Express Briefs, 53 (2006), 187-191. doi: 10.1109/TCSII.2005.857540.  Google Scholar [8] G. B. Huang, Q. Y. Zhu and C. K. Siew, Extreme learning machine: Theory and applications, Neurocomputing, 70 (2006), 489-501. doi: 10.1016/j.neucom.2005.12.126.  Google Scholar [9] N. S. Jens, Wind Energy Systems: Optimising Design and Construction for Safe and Reliable Operation, Woodhead Publishing, 2001. doi: 10.1533/9781857090638.  Google Scholar [10] I. Kuzle, M. Zdrilic and H. 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Martinez, On distributed convex optimization under inequality and equality constraints, IEEE Transactions on Automatic Control, 57 (2012), 151-164. doi: 10.1109/TAC.2011.2167817.  Google Scholar [14] G. Papaefthymiou and D. Kurowicka, Using copulas for modeling stochastic dependence in power system uncertainty analysis, IEEE Transactions on Power Systems, 24 (2009), 40-49. doi: 10.1109/TPWRS.2008.2004728.  Google Scholar [15] D. Pudjianto, C. Ramsay and G. Strbac, Virtual power plant and system integration of distributed energy resources, IET Renewable Power Generation, 1 (2007), 10-16. doi: 10.1049/iet-rpg:20060023.  Google Scholar [16] B. C. Ummels, M. Gibescu and E. Pelgrum, et al., Impacts of wind power on thermal generation unit commitment and dispatch, IEEE Transactions on Energy Conversion, 22 (2007), 44-51. doi: 10.1109/TEC.2006.889616.  Google Scholar [17] C. M. Vong, P. K. Wong and L. M. Tam, et al., Ignition pattern analysis for automotive engine trouble diagnosis using wavelet packet transform and support vector machines, Chinese Journal of Mechanical Engineering, 24 (2011), 870-878. doi: 10.3901/CJME.2011.05.870.  Google Scholar [18] X. Z. Wang, A. X. Chen and H. M. Feng, Upper integral network with extreme learning mechanism, Neurocomputing, 74 (2011), 2520-2525. doi: 10.1016/j.neucom.2010.12.034.  Google Scholar [19] Z. Y. Wang, K. S. Leung and J. K. George, Applying fuzzy measures and nonlinear integrals in data mining, Fuzzy Sets and Systems, 156 (2005), 371-380. doi: 10.1016/j.fss.2005.05.034.  Google Scholar [20] P. K. Wong, C. M. Vong and L. M. Tam, et al., Data preprocessing and modelling of electronically-controlled automotive engine power performance using kernel principal components analysis and least squares support vector machines, International Journal of Vehicle Systems Modelling and Testing, 3 (2008), 312-330. doi: 10.1504/IJVSMT.2008.025406.  Google Scholar [21] P. K. Wong, Q. S. Xu and C. M. Vong, et al., Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine, IEEE Transactions on Industrial Electronics, 59 (2012), 1988-2001. doi: 10.1109/TIE.2011.2166235.  Google Scholar [22] T. H. Yeh and W. Li, A study on generator capacity for wind turbines under various tower heights and rated wind speeds using weibull distribution, IEEE Transactions on Energy Conversion, 23 (2008), 592-602. doi: 10.1109/TEC.2008.918626.  Google Scholar [23] L. Yu and E. O. Voit, Construction of bivariate s-distributions with copulas, Computational Statistics and Data Analysis, 51 (2006), 1822-1839. doi: 10.1016/j.csda.2005.11.021.  Google Scholar [24] C. Yuen, A. Oudalov and A. Timbus, The provision of frequency control reserves from multiple microgrids, IEEE Transactions on Industrial Electronics, 58 (2011), 173-183. doi: 10.1109/TIE.2010.2041139.  Google Scholar [25] J. H. Zhai, Fuzzy decision tree based on fuzzy-rough technique, Soft Computing, 15 (2011), 1087-1096. doi: 10.1007/s00500-010-0584-0.  Google Scholar [26] J. H. Zhao, F. S. Wen and Z. Y. Dong, et al., Optimal dispatch of electric vehicles and wind power using enhanced particle swarm optimization,, IEEE Transactions on Industrial Informatics, 8 (): 889.  doi: 10.1109/TII.2012.2205398.  Google Scholar
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