This paper demonstrates the convergence of the integrated AC-DC power-flow algorithm as affected by the selection of different base values for the DC quantities and adoption of different control strategies for the DC link. For power-flow modeling of integrated AC-DC systems, the base values of the various DC quantities can be defined in several ways, giving rise to different sets of per-unit system equations. It is observed that different per-unit system models affect the convergence of the power-flow algorithm differently. In a similar manner, the control strategy adopted for the DC link also affects the power-flow convergence. The sequential method is used to solve the DC variables in the Newton Raphson (NR) power flow model, where AC and DC systems are solved separately and are coupled by injecting an equivalent amount of real and reactive power at the terminal AC buses. Now, for a majority of the possible control strategies, the equivalent real and reactive power injections at the concerned buses can be computed a-priori and are independent of the NR iterative loop. However, for a few of the control strategies, the equivalent reactive power injections cannot be computed a-priori and need to be computed in every NR iteration. This affects the performance of the iterative process. Two different per-unit system models and six typical control strategies are taken into consideration. This is validated by numerous case studies conducted on the IEEE 118-bus and 300-bus test systems.