This paper introduces a hybrid real-time simulation platform based on CPU and FPGA. Compared with the off-the-shelf power system real-time simulation system, it offers both wide time scale simulation and high simulation accuracy. The multi-time scale model can perform electromechanical-electromagnetic transient hybrid simulation, which can be applied to the research of power systems with high renewable energy penetration. The power electronic converter models are built on the Typhoon platform with FPGA as the core computing unit while the power grid is implemented in the spaceR platform. Due to the intrinsic discrete nature of the real-time simulation system, a new type of delay is introduced in the simulation model. When studying the stability of grid-connected inverters in weak grids, the delay will bring an impact that cannot be ignored on the simulation platform. Therefore, based on the classical impedance-based stability criterion, we analyze the influence of this new delay type on the system in this paper with the support from the real-time simulation verification.