Sparsity-oriented method for swift steady-state solution of large-scale power systems using a discrete equivalent model

This paper presents the application of a time-domain (TD) method for the solution of equations of discrete equivalent models. This approach consists in the substitution of a discrete equivalent Norton model (DNEM) for electric components, which allows obtaining a reduction through companion-circuit branches. The companion-circuit branch is obtained from numerical integration methods, e.g. backward Euler (BE) and trapezoidal rule (TR). This formulation is based on companion-circuit analysis (CCA). The CCA is of general application regardless of the size of the system and consists of algebraic equations, whose solution can be obtained by sparse matrix factorization using a LU decomposition process. The efficiency of the sparse CCA BE -LU and CCA TR -LU methods is demonstrated through the determination of the periodic steady-state solution in power systems of varying scales, including small, medium and large-scale, which may be operating under different conditions such as the presence of faults or harmonic distortion. These methods can deliver fast and accurate computational solutions, and by comparing their performance with the results obtained through the PSCAD/EMTDC ^® simulator, their reliability in delivering the solution can be verified.