The time-delay stability criterion based on the Lyapunov stability theory is commonly used to analyze the time-delay stability of power systems. Owing to the different Lyapunov functions and derivation processes adopted

different stability criteria tend to have different forms

computational efficiency and conservative properties. This paper tries to explain the difference in conservative properties by numerical calculation and a visualization method to provide guidance for seeking better criteria. First

four typical time-delay stability criteria are introduced based on a simple review of the time-delay system model. Furthermore

three kinds of indices reflecting the operational diversity of the power system are introduced by time-delay system simulation data. Then a numerical calculation method for evaluating the conservatism of time-delay stability criteria for power systems is presented. Finally

the application process of the evaluation method is shown by a typical first-order system. The effectiveness of the proposed method in multi-dimensional systems and multi-time-delay scenarios has been validated by a single-generator-infinite-bus system and a WSCC 3-generator 9-bus time-delay system. This work is supported by National Natural Science Foundation of China(No. 51277128)and National High Technology Research and Development Program of China(863 Program)(No. 2015AA050403).