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

  • Emanuelle C. Machado
  • José E. O. PessanhaEmail author


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.


Energy function Hamiltonian formalism Transient stability Power systems 



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


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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

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