  With the increased penetrations of distributed energy resources (DERs), the
need for integrated transmission and distribution system analysis (T&D) is
imperative. This paper presents an integrated unbalanced T&D analysis framework
using an iteratively coupled co-simulation approach. The unbalanced T&D systems
are solved separately using dedicated solvers. An iterative approach is
developed for T&D interface coupling and to ensure convergence of the boundary
variables. To do so, analytical expressions governing the T&D interface are
obtained. First-order and second-order convergent methods using the Fixed-point
iteration (FPI) method and Newton's method, respectively are proposed to solve
the system of nonlinear T&D interface equations. The proposed framework is
tested using an integrated T&D system model comprised of a 9-bus IEEE
transmission test system integrated with a real-world 6000-bus distribution
test system. The results show that the proposed framework can model the impacts
of system unbalance and increased demand variability on integrated T&D systems
and converges during stressed system conditions. As expected, Newton's method
converges faster with a fewer number of iterations as compared to the FPI
method and the improvements are more pronounced during high levels of system
unbalance and high loading conditions.
