An Energy-Based Approach to Power System Analysis

Power systems are part of the nation’s critical infrastructure and they support several indispensable services of our civilization such as hospitals, transportation systems, and telecommunications. Among the many requirements that power systems need to satisfy, power systems need to ensure that voltages and currents in the power grid are sinusoidal with a synchronous frequency of 50 or 60 Hz. Failure to do so would cause damage in appliances as well as in electrical industrial machinery that were developed under the assumption of sinusoidal voltages and currents with constant frequency. Furthermore, according to the North American Electric Reliability Corporation, frequency divergence of one or more of the generators that supply power to the grid, i.e., loss of synchronization, can lead to vibrations causing serious damage to the generators. As documented in the United States Department of Energy report on the August 14, 2003 blackout in Canada and the Northeast of the United States, frequency swings are the main reason for blackouts to spread across power systems. This makes the preservation of synchronization of generator frequencies one of the most important problems in power systems. This problem is also known as the transient stability problem in the power systems literature.The classical models used to study the transient stability problem implicitly assume that all the generators are rotating at angular velocities close to the synchronous frequency. This assumption is known not to hold in real power systems. A well documented example by the Department of Energy is the final stage of the August 14, 2003 blackout. This makes us question the validity of the existing tools and methods, based on classical assumptions and models, to predict and prevent the spread of blackouts.In this work, we abandon the classical models and replace them with energy-based models derived from first principles that are not subject to hard-to-justify classical assumptions. In addition to eliminate assumptions that are known not to be satisfied, we derive intuitive conditions ensuring the transient stability of power systems. Providing such conditions in theclassical framework with lossy transmission lines is a problem that has remained unsolved for more than sixty years and partial solutions under very restrictive assumptions have only recently been found. This is to be contrasted with the conditions described in this thesis that naturally handle lossy transmission lines. With the help of the insights we gained in the analysis performed in Section 4.3, we design easy-to-implement controllers that solve the transient stability problem in power systems. We also provide a novel way of performing circuit reduction, aiming to reduce the complexity of transmission grid models. Kron reduction, which is performed under steady state assumptions, is the standard circuit reduction technique used in the power systems literature. The novel circuit reduction method described in Section 3.1 shows how to perform Kron reduction for a class of electrical networks without these steady state assumptions