Equivalent Circuit Formulation based Framework for Probabilistic Power System Analysis

The Equivalent Circuit Formulation (ECF) was found to enable robust Power System analysis by formulating Power System problems in terms of their true state variables and further applying circuit simulation methods for their robust solution. This thesis describes the theoretical background to formulate equivalent circuit problems for three different Power System analyses: AC Power Flow analysis, an optimization algorithm to identify Power Flow feasibility, and an optimization-based linear State Estimation (SE) algorithm. We further discuss the design and implementation of a prototype ECF based Power System
simulator SUGAR (Simulation with Unified Grid Analyses and Renewables) in C++ that is able to solve the aforementioned analyses effectively. Furthermore, we utilize this implementation to build a framework for probabilistic Power System analyses using a Monte Carlo-based algorithm. We propose a continuation method that effectively and robustly solves Monte Carlo samples given a reference solution, which enables probabilistic Power Flow analysis on models up to continental interconnection-sized systems. In addition, we implement variable correlations within and between models, and propose a probabilistic generation control algorithm. After comparing our linear State Estimation algorithm that incorporates linear models for
PMU and RTU measurements to a traditional WLS estimator, we propose a probabilistic approach
to State Estimation utilizing this algorithm. We further demonstrate the feasibility of such an approach and present probabilistic SE studies including network uncertainties. Finally, we propose an approach to identify “true”-grid states by a Monte Carlo-based stochastic optimization.