  Combined Transmission and Distribution Systems (CoTDS) simulation for power
systems requires development of algorithms and software that are numerically
stable and at the same time accurately simulate dynamic events that can occur
in practical systems. The dynamic behavior of transmission and distribution
systems are vastly different, especially with the increased deployment of
distribution generation. The time scales of simulation can be orders of
magnitude apart making the combined simulation extremely challenging. This has
led to increased research in applying co-simulation techniques for integrated
simulation of the two systems. In this paper, a rigorous mathematical analysis
on convergence of numerical methods in co-simulation is presented. Two methods
for co-simulation of CoTDS are proposed using parallel and series computation
of the transmission system and distribution systems. Both these co-simulation
methods are validated against total system simulation in a single time-domain
simulation environment. The series computation co-simulation method is shown to
have better numerical stability at larger integration time steps. The series
computation co-simulation method is additionally validated against commercial
EMTP software and the results show remarkable correspondence.
