The increasing prevalence of distributed energy resources and storage systems requires the future power grid to be flexible, reliable, and capable of seamlessly interfacing with multiple networks. To meet these requirements, authors have proposed a highly controllable network design based on power routers, named the power router grid. A convex Optimal Power Flow (OPF) specifically designed for use on power router grids has recently been developed. This paper enhances this formulation by introducing a set of linear constraints that describe the internal losses of power routers based on a modular multilevel converter model. Additionally, the OPF formulation is expanded in order to consider AC and DC network integration. An investigation of the effects of converter losses in the power router grid operation revealed that power router losses accounted for between 18.2% and 25.6% of the total losses. Furthermore, a comparative analysis between the power router grid and a traditional network assessed whether the power router grid's benefits outweigh the added converter losses. Results indicate that, despite the added converter losses, the power router grid is more efficient than a traditional network in most scenarios, particularly when loads with low power factors are considered.