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This paper presents a development of program in long-term dynamic stability. The long-term voltage instability is caused by reactive-power reserves. The reactive-power reserve problems are especially determined by over-excitation limiter (OXL) and under load tap changer (ULTC), etc., which are the power device having a few to 10's minutes of time periods. The previous method estimating long-term voltage stability is the full-time domain simulation. The full time simulation methods can compute the exact results, but it may take an amount of time to simulate. And it may have the numerical error in long-term time scale. Thus, the alternative methods to calculate the appropriate results are needed. This paper deals with the long-term voltage stability using quasi-steady-state (QSS) analysis. QSS can provide good results and improve the speed of simulation. This fast time simulation method (QSS) assumes that the short-term dynamics or transient stability are stable after the contingency and can be replaced by their equilibrium equations. The concept of singular perturbation is applied on focus on long-term dynamics.