Increase of the electricity generation and the growth of global electricity consumption lead to an increase in the power fluctuations. In this dissertation, we have proposed a novel approach by modeling these fluctuations as alpha-stable Levy processes. We have focused on the stability analysis and control for stochastic single machine infinite bus system with an emphasis on (1) understanding the effect of impulsive and asymmetric power fluctuations on the rotor angle stability, and (2) developing control rule for synchronism in the presence of Wiener and alpha-stable Levy type power fluctuations. We have investigated the basin stability over the parameter space of mechanical power and damping parameters in the presence of alpha-stable Levy type load fluctuations. The probabilities of returning to the stable equilibrium point have been calculated for different characteristic exponent and skewness parameters of alpha-stable Levy motion to see the effect of impulsive and asymmetric load fluctuations. It has been shown that the impulsiveness and/or asymmetry in the distributions of the load fluctuations can cause the instability of the rotor angle. Hence, the synchronism is lost and the rotor angle despite being stable in the sense of probability, might not be stable in the mean square sense. Furthermore, we have studied the control of the rotor angle stability of single machine infinite bus power system in the presence of Wiener type stochastic fluctuations by minimizing the stochastic sensitivity function. We have also derived an analytical expression for the rotor angle dispersion of single machine infinite bus system in the presence of alpha-stable Levy type power fluctuations. The control rule for the minimization of the rotor angle dispersion has been achieved.