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.