Effect of Levy type load fluctuations on the stability of single machine infinite bus power systems

Abstract

In this paper, the stochastic excitations in single machine infinite bus power systems have been modeled as alpha-stable Levy processes. Through the simulations of the corresponding stochastic differential equations, we have 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 although it is stable in the sense of probability, it might not be stable in the mean square sense. However, by properly choosing the parameters of Levy type fluctuations the rotor angle stability can be improved in the sense of probability as the beneficience of noise.

Controlling the Rotor Angle Stability of Single Machine Infinite Bus System in the Presence of Wiener and Alpha-Stable Levy Type Power Fluctuations

“…The increase in noisy measurements in feedback controller results in wider con¯dence intervals. As we proposed in [19,20] the imbalance between the mechanical input power and the electrical output power in SMIB system has been modeled by P L ðtÞ ¼ L ðtÞ where is the noise intensity and L ðtÞ is the -stable L evy process. The increments of the L evy process dL ðtÞ¼ : L ðtÞ À L ðsÞ is -stable random variable with S ððt À sÞ 1= ; ; 0Þ for any 0 s < t < 1.…”

Stochastic bifurcation in generalized chua's circuit through alpha-stable levy noise

“…Since the random fluctuations in many real physical phenomena show impulsive and asymmetric characteristics then such an impulsive and asymmetric random fluctuations with heavy-tailed and skewed distributions are modeled by stable non-Gaussian distributions (referred to as alpha-stable (αstable) distributions) [15], [16]. Stochastic α-stable Lévy type dynamical system is more general class of random dynamical systems [17], [18] and its application areas are very wide including the power systems, neural networks, finance, social networks, biological systems [19]- [25]. Bifurcations for a simple nonlinear dynamical system under additive Lévy noises have been analyzed in [26].…”