| In stochastic circuit simulation, parameters are random variables, therefore, the results become random as well. There are many different methods to deal with this issue. In this dissertation, a method using polynomial chaos is introduced, analyzed, implemented and validated. The proposed methodology processes the polynomial chaos expansion to express the random variables and is applied to nodal analysis circuit simulation.;A library of stochastic companion models of circuit elements and power electronic and power system devices including switches, transmission lines and synchronous machines is created in this work. To build stochastic models of devices with discontinuous status in stochastic situations, a novel voltage-step simulation algorithm is induced. To apply this algorithm in practical circuit simulation, a hybrid simulation platform is built.;A polynomial chaos based stochastic SPICE-type circuit simulation is then built based on this library. Comprehensive studies are performed to confirm the validity of the proposed stochastic simulation methodology. The results are tested and compared with those of widely accepted stochastic analysis methods, such as Monte Carlo and root-sum-square.;In this dissertation, only cases with one or two independent random inputs, which are described as Gaussian distributions, are considered. However, the stochastic simulation methodology introduced here could be extended in both dimensionality and types of probability distribution assumed. |
