The rapid development of renewable sources has significantly increased interdependencies between electricity networks of all voltage levels, leading to bidirectional flows between transmission and distribution networks, and requiring analysis of Integrated Transmission-Distribution (ITD) network. The interconnectivity is further amplified by additional coupling with electricity, gas, heat and hydrogen networks, on both national and regional levels. Moreover, installation of solar, wind and storage on customers’ premises has indicated that residential networks need to be included in the overall integrated model, called Integrated Transmission-Distribution-Residential (ITDR) network. The main goal of the paper is to develop a general model of the ITD/ITDR networks and to solve the power-flow problem on large-scale networks in an efficient way. The general model includes three-phase transmission and multi-phase distribution models, as well as accurate control strategies for traditional and electronically coupled electricity resources. The proposed model is solved via novel single-threaded power flow procedure, which incorporates new network elements’ models and the developed algorithm for integrated power flow calculations in different domains. This is further improved by developing a multi-threaded approach. Analyses on a small-scale ITD network have shown that single- and multi-threaded approaches are, respectively, (1.5–4) and (2–5) times faster compared to the state-of-the-art procedures. As network size increases, the efficiency of the proposed multi-threaded procedure becomes more pronounced compared to the single-threaded one (up to 2.39 times).