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.
This paper proposes and tests strategies to accomplish high quality incomplete triangular factors (ILU) preconditioners for iteratively solve the load flow sublinear problem. The process begins constructing the preconditioner over the reordered Jacobian matrix calculated in the first Newton iteration. If the iterative process does not start due to high inaccuracies and/or numerical stability problems emerged during the preconditioner construction, the solution process is restarted and the Jacobian matrix calculated in the first Newton iteration is preprocessed through scaling, nonsymmetric and symmetric (reordered) permutations, leading to a new and better quality preconditioner. Numerical experiments considering two Brazilian power system configurations (2256/3515 buses) operating under adverse conditions (heavy loaded) corroborate the efficiency of such strategies over the preconditioner quality improving the robustness of the iterative solution process. A LU preconditioner and a direct solver for comparison purposes are also considered.
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