Advertisement

Foundations on the Hamiltonian Energy Balance Method for Power System Transient Stability Analysis: Theory and Simulation

  • Emanuelle C. Machado
  • José E. O. PessanhaEmail author
Article
  • 30 Downloads

Abstract

Significant progress was made in the 1980s and 1990s in the development and application of direct methods in power system transient stability analysis. However, there is still certain mistrust because most of them have been built on heuristics, simplifications and simulations. To build confidence in direct energy methods, a first version of a Hamiltonian energy balance method based on perturbation theory and wave energy function was recently proposed. In this method, the kinetic and potential Hamiltonian energies of the dynamical system are computed in the prefault, fault-on and postfault periods, using the time-independent Schrodinger equation, canonical transformation and calculus of variations. One major disadvantage of the method is that it still does not compute the critical clearing angle (CCA) and the critical clearing time (CCT). In the present paper, earlier and current theoretical concepts built on a preliminary topological characterization of the stable equilibrium energy boundary (also referred to as energy barrier) are used to address this deficiency, resulting in a new version of the Hamiltonian energy balance method that is tested for computing CCA and CCT, providing more accurate results than other methods available in the literature.

Keywords

Energy function Hamiltonian formalism Transient stability Power systems 

Notes

Funding

This work was supported in part by the State of Maranhão Research Foundation (FAPEMA) under Grant BD-01478/19.

References

  1. Chiang, H. D. (2011). Direct methods for stability analysis of electric power systems: Theoretical foundation, BCU methodologies, and applications (1st ed.). Hoboken: Wiley.Google Scholar
  2. Chiang, H. D., Wu, F., & Varaiya, P. (1987). Foundations of direct methods for power system transient stability analysis. IEEE Transactions on Circuits and Systems, 34(2), 160–173.MathSciNetCrossRefGoogle Scholar
  3. Gonzalez, O. (2000). Time integration and discrete Hamiltonian systems. In Journal of nonlinear science mechanics: From theory to computation (pp. 257–275). New York: Springer.CrossRefGoogle Scholar
  4. Kakimoto, N., Ohsawa, Y., & Hayashi, M. (1978). Transient stability analysis of electric power system via lure-type Lyapunov function—part I new critical value for transient stability. IEE J, 98, 63–71.Google Scholar
  5. Krechetnikov, R., & Marsden, J. E. (2007). Dissipation-induced instabilities in finite dimensions. APS Reviews of Modern Physics, 79(2), 519–553.MathSciNetCrossRefGoogle Scholar
  6. Liu, H., Hu, Z., & Song, Y. (2012). Lyapunov-based decentralized excitation control for global asymptotic stability and voltage regulation of multi-machine power systems. IEEE Transactions on Power Systems, 27(4), 2262–2270.CrossRefGoogle Scholar
  7. Liu, Q. J., Sun, Y. Z., Shen, T. L., & Song, Y. H. (2003). Adaptive nonlinear co-ordinated excitation and STATCOM controller based on Hamiltonian structure for multimachine-power-system stability enhancement. In IEE proceedings—control theory and applications (vol. 150, no. 3, pp. 285–294).Google Scholar
  8. Machado, E., & Pessanha, J. E. O. (2019). Hamiltonian energy-balance method for direct analysis of power systems transient stability. IET Generation, Transmission and Distribution, 13(10), 1895–1905.CrossRefGoogle Scholar
  9. Meyer, K., Hall, G., & Offin, D. (2009). Introduction to Hamiltonian dynamical systems and the N-body problem (1st ed.). New York: Springer.CrossRefGoogle Scholar
  10. Owusu-Mireku, R., & Chiang, H.-D. (2018). A direct method for the transient stability analysis of transmission switching events. In Proceedings IEEE PESGM, Portland, pp. 1–5.Google Scholar
  11. Padiyar, K. R. (2008). Power system dynamics stability and control (2nd ed.). Hyderabad: BS Publications.Google Scholar
  12. Pai, M. A. (1982). Energy function analysis for power system stability. Boston: Kluwer Academic Publishers.Google Scholar
  13. Pillco, E. C., & Alberto, L. F. C. (2015). Direct methods for stability assessment of two-time-scale electrical power system models. In 2015 IEEE Eindhoven PowerTech, Eindhoven, pp. 1–6.Google Scholar
  14. Robinett, R. D., III, & Wilson, D. G. (2011). Nonlinear power flow control design: Utilizing exergy, entropy, static and dynamic stability, and Lyapunov analyses (1st ed.). Berlin: Springer.CrossRefGoogle Scholar
  15. Sun, Y. Z., Liu, Q. J., Song, Y. H., & Shen, T. L. (2002). Hamiltonian modelling and nonlinear disturbance attenuation control of TCSC for improving power system stability. IEE Proceedings—Control Theory and Applications, 149(4), 278–284.CrossRefGoogle Scholar
  16. Tang, Y., Li, F., Wang, Q., & Xu, Y. (2018). Hybrid method for power system transient stability prediction based on two-stage computing resources. IET GTD, 12(8), 1697–1703.Google Scholar
  17. Vittal, V. (1992). Transient stability test systems for direct stability methods. IEEE Transactions on Power Systems, 7(1), 37–43.Google Scholar

Copyright information

© Brazilian Society for Automatics--SBA 2019

Authors and Affiliations

  1. 1.GASPSD - Group of Advanced Studies in Power Systems DynamicsFederal University of MaranhaoSão LuísBrazil
  2. 2.FAPEMA - State of Maranhão Research FoundationSão LuísBrazil

Personalised recommendations