The voltage stability is an essential security concern when a system is operating in peak load hours or subjected to an N-1 contingency. Among various voltage stability indices, Local Thevenin Index (LTI) has been a popular one, but mostly applied to the measurement-based framework. The reason is that it requires significant computing effort if applied to model-based approach, even though the model-based LTI calculation can provide more accurate results. In this paper, a new model-based LTI calculation is proposed using graph-computing-based power flow calculation, which is fast enough to fully utilize the advantage of model-based LTI. Then, when the voltage stability index of one or multiple buses exceeds the security limit, a demand response scheme is activated to increase the voltage security margin at the lowest cost. The simulation study of a thousand-level-bus system verifies the computation accuracy and efficiency of the proposed model-based LTI. It also demonstrates that the demand response action can enhance the system security effectively. Thus, the proposed work has advantages if applied to a large-scale Energy Management System (EMS). INDEX TERMS Power system security, voltage stability monitoring, voltage stability index, graph computing, demand response, security enhancement, local Thevenin index.