A turbocharger apparatus of an internal combustion engine and method of controlling the same is provided with electrically coupled fully variable turbo-compound capability. The turbocharger includes an exhaust gas turbine and an intake air compressor. A first electric machine coupled to the engine generates electricity and adds power to an output shaft of the engine depending on electricity flow to and from the first electric machine. A second electric machine coupled to the turbine and/or the compressor generates electricity and drives the turbine and/or the compressor depending on electricity flow between the first and the second electric machines. A planetary gearset connects the turbine, the compressor, and the second electric machine, and varies rotational speeds of the turbine, the compressor, and the second electric machine depending on electricity flow between the first and second electric machines to maximize efficiency and power of the engine.