  The future electric grid will consist of significant penetration of renewable
and distributed generation that is likely to create a homogenous transmission
and distribution (T&D) system, requiring tools that can model and robustly
simulate the combined T&D networks. Existing tools use disparate models and
formulations for simulation of transmission versus distribution grids and
solving for the steady-state solution of the combined T&D networks often lacks
convergence robustness and scalability to large systems. In this paper, we show
that modeling both the T&D grid elements in terms of currents and voltages
using an equivalent circuit framework enables simulation of combined positive
sequence networks of the transmission grids with three-phase networks of the
distribution grids without loss of generality. We further demonstrate that we
can ensure robust convergence for these resulting large-scale complex T&D
systems when the circuit simulation methods are applied to them. Our results
illustrate robust convergence of combined T&D networks using a direct
Newton-Raphson solver on a single machine for smaller sized systems and using a
parallel Gauss-Seidel-Newton solver on multiple machines for larger sized
systems with greater than million nodes.
