Swift steady-state solution of large-scale power systems including PV sources using discrete models

This study presents an approach to efficiently solve the periodic steady-state solutions of power systems, ranging from small to large-scale, incorporating photovoltaic (PV) sources within the time-domain framework. The proposed methodology integrates discrete equivalent modeling, numerical integration techniques, and linear equation system solution. The trapezoidal rule (TR) numerical integration method is coupled with companion-circuit analysis to establish the CCA<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TR</inf> technique. By leveraging this approach, a matrix relationship is formulated, primarily comprising a sparse and symmetric equivalent conductance matrix. Taking advantage the sparsity of this matrix, a sparse matrix LU decomposition process is employed, resulting in the development of the sparse CCA<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TR</inf>-LU method. This method is then applied to analyze various power systems, particularly centered on scenarios involving harmonic distortion induced by the PV source integration. To evaluate its efficacy, the performance of the sparse method is assessed in terms of CPU time, computational complexity, and accuracy, and compared against to the results obtained using the PSCAD/EMTDC<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> simulator.