Power Flow and Fault analysis Using Graph Theory

The power flow and short-circuit algorithms are usually adopted in problems regarding the power system operation and planning. Thus, many authors have been using the Backward-Forward Sweep (BFS) method, due to its simplicity, low computational effort and high accuracy. However, in this method, it is necessary to order all the nodes by layers from the root node to the nodes which are further away from the substation, and this process may be substantially complex depending on the system dimension. Therefore, in this paper, a novel BFS approach was proposed, which uses graph theory to avoid the complex process mentioned before. Furthermore, the graph concepts were also adopted in order to assist in the short-circuit analysis, through the automated computation of the Thevenin equivalent impedance at the faulted node. These procedures were evaluated using the IEEE 13, 34, 37 and 123 node test feeders, and it can be generalized for feeders with higher dimensions. From the results, it is possible to conclude the low computational effort of the proposed method, preserving the high accuracy of the algorithms which achieve the power flow solution and short-circuit current.