The Transactions of the Korean Institute of Electrical Engineers A (대한전기학회논문지:전력기술부문A)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Hessenberg Method for Small Signal Stability Analysis of Large Power Systems

대규모 전력계통의 미소신호 안정도 해석을 위한 Hessenberg법

  • Published : 2000.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents the Hessenberg method, a new sparsity-based small signal stability analysis program for large interconnected power systems. The Hessenberg method as well as the Arnoldi method computes the partial eigen-solution of large systems. However, the Hessenberg method with pivoting is numerically very stable comparable to the Householder method and thus re-orthogonalization of the krylov vectors is not required. The fractional transformation with a complex shift is used to compute the modes around the shift point. If only the dominant electromechanical oscillation modes are of concern, the modes can be computed fast with the shift point determined by Fourier transforming the time simulation results for transient stability analysis, if available. The program has been successfully tested on the New England 10-machine 39-bus system and Korea Electric Power Co. (KEPCO) system in the year of 2000, which is comprised of 791-bus, 1575-branch, and 215-machines. The method is so efficient that CPU time for computing five eigenvalues of the KEPCO system is 3.4 sec by a PC with 400 MHz Pentium IIprocessor.

Keywords

References

  1. S. Zelingher, B. Shperling, J. D. Mounford, and R. J. Koessler, 'Analytical Studies for Thyristor- Controlled Series Compensation in New York State, Part Ⅱ Dynamic Stability Analysis', Proc. of FACTS Conference 2, pp. 2.1-15~32, Dec. 1992
  2. N. Martins, etc all 'Retuning Stabilizers for the North-South Brazilian Interconnection', 1999 IEEE PES Summer Meeting, pp. 58-67, Edmonton, 18-22 July 1999 https://doi.org/10.1109/PESS.1999.784325
  3. G. Angelidis, A. Semlyen, 'Improved Methodologies for the Calculation of Critical Eigenvalues in Small Signal Stability Analysis', IEEE/PES Summer Meeting, July 1995
  4. EPRI, Phase Ⅱ : Frequency Domain Analysis of Low Frequency Analysis Oscillations in Large Power System, Vol.2, Final Report EPRI EL-2348, 1982
  5. N. Martins, H. Pinto, L. Lima, 'Efficient Methods for Finding Transfer Function Zeros of Power Systems', IEEE Trans. on Power Systems, Vol. 7, No. 3, pp. 1350-1361, August 1992 https://doi.org/10.1109/59.207354
  6. D. Y. Wang, G. J. Rogers, B. Porreta, and P. Kundur, 'Eigenvalue Analysis of Very Large Power Systems', IEEE Trans. on Power Systems, Vol. PWRS-3, May 1988 https://doi.org/10.1109/59.192898
  7. L. Wang, A. Semlyen, 'Application of Sparse Eigenvalue Techniques to the Small Signal Stability Analysis of Large Power Systems', IEEE Trans. on Power Systems, Vol. PWRS-5, No. 2, pp. 635-642, May 1990 https://doi.org/10.1109/59.54575
  8. L. Wang, 'Eigenvalue Analysis of Large Power Systems', Ph. D Thesis, Toronto University, 1991, pp. 14-35, 50-54
  9. N. Uchida and T. Nagao, 'A New Eigen-Analysis Method of Steady State Stability Studies for Large Power Systems: S Matrix Method', IEEE Trans. on Power Systems, Vol. PWRS-3, No. 2, pp. 706-714, May 1988 https://doi.org/10.1109/59.192926
  10. H. K. Nam, K. S. Shim, and C. J. Moon, 'Modal Analysis of Large Scale Power System Using Hessenberg Process', Trans. of KIEE, Vol. 42, No. 10, 1993, pp. 53-63
  11. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965, pp. 377-392
  12. PTI, PSS/E Program Application Guide VolumeⅡ, Ver 24, pp. 13-1 13-13
  13. H. K. Nam, Y. K. Kim, K. S. Shim, K. Y. Lee, 'A New Eigen-sensitivity Theory of Augmented Matrix and Its Applications to Power System Stability Analysis', accepted for publication in IEEE Trans. on Power Systems, PE-464-PWRS-0-02, 1999