The brushless doubly-fed machine (BDFM) is a novel type of multi-port electrical machine. Similar to the doubly-fed induction machine (DFIG), it facilitates high-power electromechanical energy conversion using a relatively small converter but eliminates the need for brushes. Existing research has primarily focused on rotary BDFM, leaving a research gap in long stator linear brushless doubly-fed machine (LS-LBDFM). This paper introduces a structural design for LS-LBDFM and provides a concise explanation of its operating principle. It then discusses a simple and convenient method for calculating inductance parameters of LS-LBDFM based on winding functions. Following this, a dynamic model for the LS-LBDFM is developed using a coupled circuit approach. Lastly, the accuracy of this modelling approach is validated through comparison with a finite element model.