Journal of Electrical Engineering and Technology

The Korean Institute of Electrical Engineers (대한전기학회)
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An Improved Poincaré-like Carleman Linearization Approach for Power System Nonlinear Analysis

  • Wang, Zhou-Qiang (Dept. of Electrical Engineering, Sichuan Engineering Technical College (SCETC)) ;
  • Huang, Qi (Sichuan Provincial Key Lab of Power System Wide-area Measurement and Control, University of Electronic Science and Technology of China (UESTC)) ;
  • Zhang, Chang-Hua (Sichuan Provincial Key Lab of Power System Wide-area Measurement and Control, University of Electronic Science and Technology of China (UESTC))
  • Received : 2012.07.14
  • Accepted : 2012.10.09
  • Published : 2013.03.01
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Abstract

In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincar$\acute{e}$ transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.

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References

  1. J. J. Sanchez-Gasca, V. Vittal, M. J. Gibbard et al, "Inclusion of higher order terms for small-signal (modal) Analysis: committee report-task force on assessing the need to include higher order terms for small-signal (modal) analysis," IEEE Trans. Power Systems, Vol. 20, No. 4, pp. 1886-1904 , Nov. 2005. https://doi.org/10.1109/TPWRS.2005.858029
  2. Huang Qi, Wang Zhouqiang, Zhang Changhua, "The third order analytical solution of power systems based on normal form," Journal of UESTC, Vol. 38, No. 6, pp. 957-961, Nov. 2009.
  3. H. M. Shanechi,, N. Pariz, and E. Vaahedi, "General nonlinear modal representation of large scale power systems," IEEE Trans. Power Systems, Vol. 18, No. 3, pp. 1103-1109, August 2003. https://doi.org/10.1109/TPWRS.2003.814883
  4. Krzysztof Kowalski, Willi-Hans Steeb, Nonlinear Dynamical Systems and Carleman Linearization: Singapore: World Scientific Publishing Co. Pt. Ltd., 1991, p. 75-94.
  5. Filippo Cacace, Valerio Cusimano, Alfredo Germani, "An efficient approach to the design of observers for continuous-time systems with discrete-time measurements," The 50th IEEE Conference on Decision and Control and European Control Conference (CDCECC), December 12-15, 2011, Orlando, FL, USA.
  6. J. Arroyo, E. Barocio, R. Betancourt, and A. R. Messina, "A bilinear analysis technique for detection and quantification of nonlinear Quantification of Nonlinear Modal Interaction," IEEE Power Engineering Society General Meeting, June 18-22, 2006, Montreal Quebec, Canada.
  7. V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, 2nd ed: New York: Springer-Verlag, 2004, p. 180-221
  8. Zhang Xianda, Modern Signal Processing .2nd edition. Beijing: Tsinghua University Press, 2006, pp. 119- 125
  9. Shu Hongchun, Application of signal processing in electrical engineering: Beijing Science Press, 2009
  10. P. Kundur. Power System Stability and Control: McGraw-Hill, 1994. p. 732.
  11. Z. Wu, X. Zhou, "Power System Analysis Software Package (PSASP)-an integrated power system analysis tool," Proc. International Conference on Power System Technology, Vol.1, 1998, pp: 7-11.
  12. Wang Xifan, Modem power system analysis: Beijing Science Press, 2003, p. 326-327.

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