Interconnected converters are used in a variety of applications. This paper describes a complete family of possible structures of interconnected converters considering different connection styles and converter types. The various structures are compared in terms of power sharing capability, mutual effects among interconnected modules, basic control requirements and load characteristics, aiming to provide crucial information to the design of interconnected converters for different application scenarios. As an illustrative example, a two-stage structure including a voltage-source-mode (VSM) converter and two current-source-mode (CSM) converters is presented for driving light-emitting-diodes (LEDs) under high input voltage conditions.