Power flow routing is an emerging control paradigm for the dynamic and responsive control of electric power flows. In this paper, we investigate the design and modelling of the power flow router (PFR) which is a major building block of power flow routing. First, a generic PFR architecture is proposed to encapsulate the desired functions of PFRs. Then, the load flow model of PFRs is developed and incorporated into the optimal power flow (OPF) framework. Based on the load flow model, the control capabilities of PFR, such as decoupled branch power flows and enlarged flow regions, are analysed. With particular attention to available transfer capability (ATC), an OPF study on the standard IEEE benchmark systems with 14, 57, and 118 buses has been performed to show that ATC can be enhanced remarkably by installing the proposed PFRs at some critical buses of the power network.