Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization

Abstract

Rampant integration of renewable resources (e.g., photovoltaic and wind-energy conversion systems) and uncontrollable and elastic loads (e.g., plug-in hybrid electric vehicles) are rapidly transforming power systems. In this environment, an analytic method to quantify the impact of parametric and input uncertainty will be critical to ensure the reliable operation of next-generation power systems. This task is analytically and computationally challenging since power-system dynamics are nonlinear in nature. In this thesis, we present analytic methods to quantify the impact of parametric and input uncertainties for two important applications in power systems: i) uncertainty propagation in power-system differential-algebraic equation model and power flow, and ii) robust stability assessment of power-system dynamics. For the first topic, an optimization-based method is presented to estimate maximum and minimum bounds on state variables while acknowleding worst-case parametric and input uncertainties in the model. The approach leverages a second-order Taylor-series expansion of the states around a nominal (known) solution. Maximum and minimum bounds are then estimated from either Semidefinite relaxation of Quadratically-Constrained Quadratic-Programming or Alternating Direction Method of Multipliers. For the second topic, an analytical method to quantify power systems stability margins while acknowleding uncertainty is presented within the framework of Lyapunov's direct method. It focuses on the algorithmic construction of Lyapunov functions and the estimation of the robust Region-Of-Attraction with Sum-of-Squares optimization problems which can be translated into semidefinite problems. For both topics, numerical case studies are presented for different test systems to demonstrate and validate the proposed methods.