  Robust simulation is essential for reliable operation and planning of
transmission and distribution power grids. At present, disparate methods exist
for steady-state analysis of the transmission (power flow) and distribution
power grid (three-phase power flow). Due to the non-linear nature of the
problem, it is difficult for alternating current (AC) power flow and
three-phase power flow analyses to ensure convergence to the correct physical
solution, particularly from arbitrary initial conditions, or when evaluating a
change (e.g. contingency) in the grid. In this paper, we describe our
equivalent circuit formulation approach with current and voltage variables that
models both the positive sequence network of the transmission grid and
three-phase network of the distribution grid without loss of generality. The
proposed circuit models and formalism enable the extension and application of
circuit simulation techniques to solve for the steady-state solution with
excellent robustness of convergence. Examples for positive sequence
transmission and three-phase distribution systems, including actual 75k+ nodes
Eastern Interconnection transmission test cases and 8k+ nodes taxonomy
distribution test cases, are solved from arbitrary initial guesses to
demonstrate the efficacy of our approach.
