Abstract Insufficient control flexibility in multi-terminal HVDC (MT-HVDC) grids is an important motivation to install suitable power electronic-based DC power flow controller (PFC)s to ensure grid controllability, security, and reliability. This article proposes a new static power injection model (PIM) for those (interline) DC-PFCs to enable DC power flow (PF) studies and ease integration of the PFCs in the power system analysis softwares within the well-accepted Newton–Raphson (NR) solver-based framework. HVDC lines shunt conductances are also taken in to account in this newly developed paradigm. For this purpose, the IDC-PFC, as well as other MT-HVDC grid physical/control state variables are modified in cooperation to attain predefined control objective(s). Furthermore, a novel general routine (solution procedure) is proposed to handle several system physical/control limitations during the NR-based DC PF problem solution. Static/dynamic simulations are executed on an eight-bus test MT-HVDC grid to show/confirm the accuracy, effective performance, and excellent convergence property of the proposed IDC-PFC model, NR-based DC PF solver, and technical constraints handling routine. In this situation, it is proved that the original structure and symmetry of the admittance matrix can still be kept, and a few modifications are needed to be done in the Jacobin matrix.