Robust Matrix Free Power Flow Algorithm for Solving T&D Systems

A new approach to system computations, Graph Trace Analysis (GTA), is applied to the power flow problem. A matrix free GTA power flow algorithm that solves unbalanced, three-phase transmission, substations, and multi-phase distribution, all in the same model, is presented. GTA traces are used to combine both Gauss-Seidel (GS) and continuation methods into a GTA algorithm. Testing circuits are used to demonstrate the capability of the new GTA power flow, and solutions are compared and/or verified against Newton-Raphson and forward/backward sweep based power flow algorithms. The comparisons include convergence characteristics for steady-state voltage stability analysis. It is shown that the computational complexity of GS-GTA grows linearly with the size of the model.