The Interline Power Flow Controller (IPFC) is one of the latest generation flexible AC (FACTS) transmission controllers used to control the power flows of multiple transmission lines. This paper presents a mathematical model of IPFC, called power injection model (PIM). This model is incorporated in the Newton Raphson (NR) power flow algorithm to study the power flow control in the transmission lines in which the IPFC is placed. A program has been written in MATLAB to extend the conventional NR algorithm based on this model.