Matrix decompositions-based approach to Z-bus matrix building process for radial distribution systems

In this study, a novel Z-bus matrix-building algorithm based on graph theory is proposed as an alternative method for radial distribution systems. The proposed algorithm is based on the branch-path incidence matrix K of a radial distribution network as opposed to a traditional Z-bus building algorithm and inverse Y-bus matrix with lower and upper triangular matrix (LU) method. Advantages of the proposed algorithm include fewer logical judgments, less execution time, and suitability for computing-aided analyses. The algorithm possessed potential for applications in all power system analyses related to a Z-bus impedance matrix including power flow analysis, short circuit fault current analysis, and harmonic power flow analysis. Four standard IEEE test systems and random test systems are selected to demonstrate the superiority of the proposed method with respect to execution times. The results indicate that the proposed algorithm exhibited a performance that exceeded those of other methods, particularly with respect to large-scale unbalanced radial distribution systems with hybrids of single, two-phase, and three-phase elements and nodes.