The use of small wind power generators remains quite relevant. In particular, they can be efficient for charging batteries in remote locations where there is no centralized power supply (including in the Arctic, Far East, etc.). They can also be used as part of missions to planets with atmospheres. One of the promising design solutions for a small wind power generator with a vertical axis of rotation is a hybrid device. It consists of two wind turbines that have a common axis of rotation: external (Darrieus wind turbine) and internal (Savonius rotor). This scheme represents a compromise between the relatively high power coefficient of the Darrieus turbine and the good startup characteristics the Savonius rotor. It is known that one of the typical battery charging modes is constant current charging. Here we consider a hybrid installation, the generator of which is connected to a current stabilizer. The load is simulated with an active resistance. It is assumed that the generator is a DC generator. A closed mathematical model of the studied system is constructed. The aerodynamic load is described using the quasi-steady approach. It is assumed that the characteristic time of electrical processes is much smaller than the characteristic time of mechanical processes. The influence of load resistance on the behavior of the system is investigated. It is shown that, under certain conditions, several steady modes (up to five) exist in the system. In this case, at least two of them are attracting. Therefore, the hysteresis of the angular speed of the steady mode is possible when the load resistance changes. It should be noted that in a number of situations, an unstable steady mode (which corresponds to a lower angular speed of the turbine than a stable one) may be preferable (for example, to reduce the load on bearings). In this regard, a resistance control strategy has been proposed to ensure stabilization of the unstable stationary regime.