  The quasi steady-state (QSS) model tries to reach a good compromise between
accuracy and efficiency in long-term stability analysis. However, the QSS model
is unable to provide correct approximations and stability assessment for the
long-term stability model consistently. In this paper, some numerical examples
in which the QSS model was stable while the long-term stability model underwent
instabilities are presented with analysis in nonlinear system framework. At the
same time, a hybrid model which serves as a remedy to the QSS model is proposed
according to causes for failure of the QSS model and dynamic mechanisms of
long-term instabilities. Numerical examples are given to show that the
developed hybrid model can successfully capture unstable behaviors of the
long-term stability model while the QSS model fails.
