Electric power systems safety is a fundamental aspect of the operation and management of the grid. In order to maintain safety, the power system is operated around a nominal frequency. In fact, large frequency fluctuations can trigger generator relay-protection mechanisms and load shedding, which may further jeopardize network integrity, leading to cascading failures. Without appropriate estimations on the possible consequences resulting from contingency, operational architectures, and control safeguards in place, the likelihood of such events is not negligible, given that the high penetration of non-rotational renewable resources provides less inertia, possibly inducing higher frequency excursions. These observations motivate us in this thesis to develop approximation and control schemes to efficiently estimate the transient-state evolution subject to disturbances and contingencies and further actively mitigate undesired transient frequency deviations.
This thesis first develops methods to efficiently compute the set of disturbances on a power network that do not tip the frequency of each bus and the power flow in each transmission line beyond their respective bounds. For a linearized power network model, we propose a sampling method to provide superset and subset approximations with a desired accuracy of the set of feasible disturbances. We also introduce an error metric to measure the approximation gap and design an algorithm that is able to reduce its value without impacting the complexity of the resulting set approximations.
As a natural follow-up to our on approximating feasible disturbances, we seek to further regulate transient frequency via novel control schemes. With regard to this, this thesis proposes three control strategies that all achieve local stabilization of power networks characterized by nonlinear swing equations and, at the same time, delimit the transient frequencies of targeted buses to a desired safe interval. To handle the coordination of large numbers of resources in an adaptive and scalable fashion, all three controllers can be implemented in an either partially or fully distributed fashion. Specifically, we synthesize the first transient frequency controller by having it satisfy a transient frequency constraint and an asymptotic stability constraint. Benefitting from its structural simplicity, the controller can be implemented in a distributed fashion by merely allowing each controlled bus physically measure the states of neighbors. To reduce the control effort, the second MPC-based controller enables control command cooperation by communication; however, the coordination is limited within a designed range, and the control algorithm is only partially distributed, potentially non-Lipschitz, and not as computationally efficient. The third controller successfully addresses all these issues via a bilayered structure and information exchange with up to 2-hop neighbors.