In the process of solving the power system time-delay stability via the linear matrix inequality (LMI) criterion

the high dimensions in the dynamic model of power systems may result in the over abundance of unknown variables and unacceptable length of calculation time. In order to surmount this difficulty

this paper initially converts the power system linear model with single time-delay to a state-space model with the input and output component. Furthermore

the extended model is simplified via the well-developed state-space based model reduction method. As a consequence

the quantity of unknown variables will substantially decrease while the system’s crucial dynamic features are reserved. Finally

on the basis of the simplified model

the LMI technique and the parameter transform tool

a new time-delay stability criterion with better performance

is obtained. The proposed method is used in the WSCC 3-machine 9-bus and IEEE 10-machine 39-bus system with single time-delay component

and a comparison of stability margin solving results between the two systems is made with the binary search method. The numerical results indicate that the simplified model of time-delay system generates fewer errors in the calculation of stability margin than those of the model without simplification

but the calculation time is remarkably reduced.