To analyze the small disturbance voltage stability of a power system， the Thevenin equivalent circuit is used to represent the section of system seen from a load bus at any point of time， and a third order induction motor model paralleled with a constant impedance dynamic model is used to represent the bus load. The results of small disturbance analysis at equilibrium points on the load bus's PV curve show that the essence of the small disturbance voltage stability of an equivalent system is the steady stability of the induction motor part of a load， and it makes no difference whether the first order model or the third order model is used to represent the induction motor. Based on this finding， a new state index for the small disturbance voltage stability is expressed by an analytical equation which is deduced from the first order model. Calculation results on the IEEE 39-bus system validate the method.