Time-domain simulation of transmission line models with multiple stochastic excitations

The paper deals with a technique for assesment of statistical characteristics of stochastic responses in transmission line (TL) models with possible multiple random excitations. The method is based on a theory of stochastic differential equations (SDE), namely a vector linear SDE with an additive noise is formulated. The TL´s model is ready to be used to test various situations at deterministic and/or stochastic excitations in its arbitrary nodes, for example, enabling to cover influences of random disturbances along the TLs. A core of the TL´s model equations relies on its state-variable description, considering also nonuniform TLs if necessary, and excitations are involved via Thévenin equivalents of the sources. To get characteristics of the stochastic responses, sets of stochastic trajectories are statistically processed, while the weak stochastic backward Euler scheme is applied for the numerical solution. This technique is consistent with an Itô stochastic calculus, and preferable if moments of the stochastic process are needed instead of detailed trajectories. All calculations were performed in a Matlab^® language environment.