One means of fulfilling $CO_2$ emission legislation is to downsize engines by boosting their power using turbochargers or mechanical superchargers. This reduces fuel consumption by decreasing the engine displacement. When a turbocharger, which is preferable to a mechanical supercharger in terms of fuel efficiency, is used, there is insufficient availability of exhaust gas energy at low engine speeds, resulting in an unfavorable engine response. Therefore, mechanically driven superchargers have increased in popularity due to their quick response to changing speeds in the transient phase. However, since a mechanical supercharger obtains its driving power from the engine, it is difficult to decrease its fuel consumption. This remains a large negative factor for superchargers, despite their excellent dynamic performance. This study aims to develop a power control concept to improve the fuel economy of a mechanical screw supercharger, which could then be used for engine downsizing.