Your browser does not support JavaScript!

Hybrid modal-balanced truncation method based on power system transfer function energy concepts

Hybrid modal-balanced truncation method based on power system transfer function energy concepts

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
IET Generation, Transmission & Distribution — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The combined use of modal and balanced truncations methods is proposed for model order reductions. To efficiently combine these methods, a stopping criterion based on spectral energy concepts is also proposed. This criterion was implemented into the code of the widely known subspace accelerated dominant pole algorithm (SADPA), designed to compute a set of dominant poles and associated residues of transfer functions from large-scale, sparse, linear descriptor systems. The resulting enhanced SADPA code automatically stops once the computed set of dominant poles and associated residues is sufficient to build a modal reduced order model (ROM) whose energy content approaches that of the complete model within a specified tolerance and considering a frequency window of interest. The number of dominant poles in this set is much smaller than the number of poles of the full system model. Hence, their state-space realisation usually has a small enough dimension for the efficient application of the square root balanced truncation method. This new method, named hybrid modal-balanced truncation, produces ROMs whose order are much smaller than that of the modal ROMs and, most importantly, can also be applied to unstable models.


    1. 1)
    2. 2)
    3. 3)
      • 7. Balakrishnan, V., Su, Q., Koh, C.K.: ‘Efficient balance-and-truncate model reduction for large scale systems’. Proc. of the American Control Conf., Arlington, VA, 25–27 June 2001.
    4. 4)
    5. 5)
    6. 6)
      • 4. Varricchio, S.L., Freitas, F.D., Martins, N., Véliz, F.C.: ‘Computation of dominant poles and residue matrices for multivariable transfer functions of infinite power system models’, to be published in theIEEE Trans. Power Syst.Available at IEEE Xplore Early Access (doi: 10.1109/TPWRS.2014.2336243).
    7. 7)
    8. 8)
    9. 9)
      • 13. Saak, J., Benner, P., Kürschner, P.: ‘A goal-oriented dual LRCF-ADI for balanced truncation’, in F. Breitenecker Troch, I. (Ed.): ‘MATHMOD 2012 – full paper preprint volume’ (Vienna University of Technology, Vienna, Austria, 2012).
    10. 10)
      • 5. Schilders, W.H., van der Vorst, H.A., Rommes, J.: ‘Model order reduction: theory, research aspects and applications’ (Springer-Verlag Heidelberg, 2008).
    11. 11)
      • 11. Huang, C., Zhang, K., Dai, X., Tang, W.: ‘A modified balanced truncation method and its application to model reduction of power system’. IEEE Power and Energy Society General Meeting, 2013, pp. 15.
    12. 12)
    13. 13)
      • 14. Benner, P., Kürschner, P., Saak, J.: ‘An improved numerical method for balanced truncation for symmetric second order systems’, Math. Comput. Model. Dyn. Syst. Methods, Tools Appl. Eng. Relat. Sci., 2013, 19, (6).
    14. 14)
      • 15. Antoulas, A.C.: ‘Approximation of large-scale systems’ (SIAM Publications, 2005).
    15. 15)
    16. 16)
    17. 17)
      • 17. Gomes, S.Jr., Varricchio, S.L., Martins, N., Portela, C.: ‘Results on modal analysis to speed-up electromagnetic transient simulations’. IEEE General Meeting, San Francisco, CA USA, 12–16 June 2005.
    18. 18)
      • 18. Barrachina, S., Benner, P., Quintana-Ortí, E.S., Quintana-Ortí, G.: ‘Parallel algorithms for balanced truncation of large-scale unstable systems’. 44th IEEE Conf. on Decision and Control, Seville, Spain, 2005, pp. 22482253.
    19. 19)
      • 19. Spiegel, M.R., Liu, J.: ‘Mathematical handbook of formulas and tables’ (Mc-Graw-Hill, New York, 1998, 2nd edn.).

Related content

This is a required field
Please enter a valid email address