Abstract — Parameters of power system models, in particular load models, are seldom known exactly. Yet dynamic security assessment relies upon simulation of those uncertain models. This paper proposes a computationally feasible approach to assessing the influence of uncertainty in simulations of power system dynamic behaviour. It is shown that trajectory sensitivities can be used to generate accurate first-order approximations of trajectories that arise from perturbed parameter sets. The computational cost of obtaining the sensitivities and perturbed trajectories is minimal. The mathematical structure of the trajectory approximations allows the effects of uncertainty to be quantified and visualized using worst-case analysis and probabilistic approaches. Index Terms — Parameter uncertainty; power system dynamic performance assessment; power system simulation; trajectory sensitivity; load modelling. I.

This thesis introduces a novel application of factor graphs to the domain of analog circuits. It proposes a technique of leveraging factor graphs for performing statistical yield analysis of analog circuits that is much faster than the standard Monte Carlo/Simulation Program With Integrated Circuit Emphasis (SPICE) simulation techniques. We have designed a tool chain to model an analog circuit and its corresponding factor graph and then use a Gaussian message passing approach along the edges of the graph for yield calculation. The tool is also capable of estimating unknown parameters of the circuit given known output statistics through backward message propagation in the factor graph. The tool builds upon the concept of domain-specific modeling leveraged for modeling and interpreting different kinds of analog circuits. Generic Modeling Environment (GME) is used to design modeling environment for analog circuits. It is a configurable tool set that supports creation of domain-specific design environments for different applications. This research has developed a generalized methodology that could be applied towards design automation of different kinds of analog circuits, both linear and nonlinear. The tool has been successfully used to model linear amplifier circuits and a nonlinear Metal Oxide Semiconductor Field Effect Transistor (MOSFET) circuit. The results obtained by Monte Carlo simulationsiv performed on these circuits are used as a reference in the project to compare against the tool’s results. The tool is tested for its efficiency in terms of time and accuracy against the standard results. (104 pages) To my loving family and friends.... v vi