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Development of multidimensional sequence operation theory with applications to risk evaluation in power system generation scheduling. (English) Zbl 1144.78015

Summary: Sequence operation theory (SOT) is a powerful tool for solving complex probabilistic problems in power system. However, the basic single dimension SOT cannot satisfy the requirement of multi-state and multi-attribute analysis, which is often the case in actual power system practice. To address this problem, multidimensional sequence operation theory (MSOT) is developed. On the basis of previous research, this paper first categorizes the situations by the number of state variables and the number of attribute values, and defines the multidimensional sequence for single state variable and multiple attribute values, as well as the multidimensional sequence for multiple state variables and multiple attribute values. Corresponding to those definitions, four types of operations between two discrete multidimensional sequences are derived respectively. Therefore, the sequence is extended from single dimensional to multidimensional, establishing an integrated theory of multidimensional sequence operation. In particular, the basic single dimension SOT can be viewed as a special case of MSOT with only one state variable and one attribute value. Finally, the paper demonstrates the effectiveness of MSOT through an example of risk evaluation in power system generation scheduling.

MSC:

78A55 Technical applications of optics and electromagnetic theory
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[1] Jing X J, Wang Y C, Tan D L. Artificial coordinating field and its application to motion planning of robots in uncertain dynamic environments. Sci China Ser E-Tech Sci, 2004, 47(5): 577–594 · Zbl 1329.70016 · doi:10.1360/02ye0479
[2] Li Z Y, Peng L H. An exploration of the uncertainty relation satisfied by BP network learning ability and generalization ability. Sci China Ser F-Inf Sci, 2004, 47(2): 137–150 · doi:10.1360/02yf0331
[3] Escudero L F, Fuente J L, Garcia C, et al. Hydropower generation management under uncertainty via scenario analysis and parallel computation. IEEE Trans Power Systems, 1996, 11(2): 683–689 · doi:10.1109/59.496139
[4] Douglas A P, Breipohl A M, Lee F N, et al. Risk due to load forecast uncertainty in short term power system planning. IEEE Trans Power Systems, 1998, 13(4): 1493–1499 · doi:10.1109/59.736296
[5] Contreras J, Conejo A J, De La Torre S. Experience with an electricity market simulation tool. Prod Plan Control, 2003, 14(2): 135–145 · doi:10.1080/0953728031000107671
[6] Ventosa M, Baillo A, Ramos A, et al. Electricity market modeling trends. Energy Policy, 2005, 33(7): 897–913 · doi:10.1016/j.enpol.2003.10.013
[7] Rodriguez C P, Anders G J. Energy price forecasting in the Ontario Competitive Power System Market. IEEE Trans Power Systems, 2004, 19(1): 366–374 · doi:10.1109/TPWRS.2003.821470
[8] Kang C Q, Xia Q, Xiang N D. Sequence operation theory and its application in power system reliability evaluation. Reliability Engineering & System Safety, 2002, 78(2): 101–109 · doi:10.1016/S0951-8320(02)00048-0
[9] Kang C Q, Xia Q, Xiang N D, et al. Sequence Operation Theory and Its Application (in Chinese). Beijing: Tsinghua University Press, 2003. 9–38
[10] Kang C Q, Xia Q, Xiang N D, et al. Sequence-based analysis of probabilistic production cost simulation. Proc CSEE (in Chinese), 2002, 22(4): 8–12
[11] Kang C Q, Bai L C, Xia Q, et al. Incorporating reliability evaluation into the uncertainty analysis of electricity market price. Electric Power Systems Research, 2005, 73(2): 205–215 · doi:10.1016/j.epsr.2004.08.005
[12] Yang G F, Kang C Q, Xu G X, et al. A preliminary investigation on multidimensional sequence operation theory and its application in the analysis on uncertainty of electric demand. Proc CSEE (in Chinese), 2005, 25(25): 12–17
[13] Yang G F. Flexibility evaluation of power grid planning under uncertain marketcConditions. M.S. Dissertation of Tsinghua University (in Chinese), 2005. 15–36
[14] Zhan X Z. Inequalities involving Hadamard products and unitarily invariant norms. Adv Math (in Chinese), 1998, 27(5): 416–422 · Zbl 1054.15503
[15] Charytoniuk W, Chen M S, Kotas P, et al. Demand forecasting in power distribution systems using nonparametric probability density estimation. IEEE Trans Power Systems, 1999, 14(4): 1200–1206 · doi:10.1109/59.801873
[16] Escudero L F, Salmeron J, Paradinas I, et al. SEGEM: A simulation approach for electric generation management. IEEE trans Power Systems, 1998, 13(3): 738–748 · doi:10.1109/59.708575
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