This paper puts forward a new practical voltage source converter (VSC) based AC-DC converter model suitable for conducting power flow assessment of multi-terminal VSC-based high-voltage direct current (VSC-MTDC) systems. The model uses an advanced method to handle the operational limits and control modes of VSCs into the power flow formulation. The new model is incorporated into a unified framework encompassing AC and DC power grids and is solved by using the Newton-Raphson method to enable quadratically convergent iterative solutions. The use of complementarity constraints, together with the Fischer-Burmeister function, is proposed to enable the seamless incorporation of operational control modes of VSC and automatic enforcement of any converter’s operational limits that become violated during the iterative solution process. Thus, a dedicated process for checking limits is no longer required. Furthermore, all existing relationships between the VSC control laws and their operational limits are considered directly during the solution of the power flow problem. The applicability of the new model is demonstrated with numerical examples using various multi-terminal AC-DC transmission networks, one of which is a utility-sized power system.