This paper obtains the mathematical model of a single machine infinite bus power system using the idea of parameter identifications. Because the noise is considered in parameter identification process, the model reflects the real system more exactly. On the base of the identified model this paper also presents a discrete automatic voltage regulator by minimum variance control principles. In order to avoid the static error, we combine discrete minimum variance control with continuous integral control and get very satisfactory effects. This proposed control strategy is very easy to realize. The simulation results show that in every case the dynamic qualities of the proposed control strategy are incomparably superior to that of the conventional PI regulator, which means the proposed control strategy has great practical values.