The electricity demand and thus the amount of transmitted power are continuously growing in recent year while extensions of transmission systems have kept relatively slow. These results in larger stress of transmission systems that are operated much closer to stability boundaries than ever. This creates a demand for tools allowing very accurate and rapid monitoring of power system voltage stability margin with regard to load demand. This paper deals with applying quasi-steady-state analysis to study long term voltage stability problems resulting from small disturbances or load increase. The long term evolution is traced by successive equilibrium points, hence offering a good compromise between efficiency and accuracy. First a simple case is discussed, where only static load model is adopted and long term load restoration is considered by OLTC tap changing, then load models with long term restoration is dealt. The novel approach provides good convergence when system approaches the critical point by choosing continuation parameter. The accurate load demand margin and high simulation speed are also achieved at the same time. Numerical results are illustrated on a test system.