Wind turbine generators (WTGs) play an important role in renewable power generation. The wind turbine can drive different types of generators and the most commonly used machines are induction generators (IG) and synchronous generators (SG). The hybrid generator (HG) concept has been proposed and has drawn more attention these years, which shows some merits in a flexible terminal voltage, low mass and high efficiency. Since many grid operators require the WTG can participate in the frequency response, many researchers contribute to the schemes or controller designs of WTG systems with traditional IG or SG. However, there are few papers discussing the frequency response from HG based WTG systems. This paper proposes several schemes of HG with battery energy storage systems (BESS) to support the grid frequency and compares their operation performance through simulations, which gives people an insight into the design of HG systems. Based on the results, it can be found that HG systems with the grid-forming control have better performance in frequency support than the system with grid-following control