Based on the discrete dynamic model， the stability of hardware-in-the-loop simulation（PHILS） of power systems is studied. From the perspective of a numerical approach， the stability of PHILS is determined by the delay system， that PHILS converges to， and the absolute stability of iterations of the discrete dynamic model. Based on delay differential equations（DDEs） theory， the stability of delay system and the discrete dynamic model is analyzed， and the conception of interface stability is proposed. A PHILS experiment of an LC circuit is implemented， and the experimental results verify the conclusions of theoretical analysis.This work is supported by State Grid Corporation of China.