In order to pre-validate control strategies of wind energy conversion system (WECS), wind turbine simulators (WTS) are usually adopted to simulate the output characteristic of field wind turbines (WT) in the laboratory. Since the moment inertia of WTS is smaller than that of a practical WT, an inertia emulation scheme has been applied in WTS to replicate the dynamic behavior of real WT. In this paper, an instability phenomenon of the WTS with the inertia emulation scheme is investigated. By modeling of torque compensation loop based on discrete difference equations and analyzing its time-domain response, the instability of the WTS is interpreted and the stability condition of the system is proposed and theoretically proved. Finally, the simulations as well as experimental results verify the stability condition.