General and simplified computation of fault flow and contribution of distributed sources in unbalanced distribution networks

In this paper, the application of a comprehensive augmented nodal matrix formulation to the multiphase fault analysis of unbalanced distribution systems is demonstrated. The solution technique results in a sparse matrix which can be rapidly solved by employing sparse LU factorization algorithms. The augmented matrix fully respects the actual circuit components of distribution systems and eliminates the necessity of pre- and post-processing in the implementation of the algorithm. For example, protective devices that exist in the network are not eliminated but they are represented with benign switches in the matrix. Network devices including transmission lines, cables and transformers can all be modeled in phase domain with their respective physical quantities. The fault conditions including short circuit and open conductor faults are represented with switches by adding the switch equations to the bottom of the augmented matrix which has a dynamic allocation structure. Although the presented solution is of general nature and can encompass networks from transmission level to meshed secondary distribution grids, the examples are rather concentrated on distribution systems where multiphase analysis is more common and desirable due to unbalanced network components.