CONTROL, ORDER REDUCTION, AND IDENTIFICATION OF NONLINEAR DIFFERENTIAL-ALGEBRIC MODELS OF RENEWABLES-HEAVY POWER SYSTEMS

Abstract

Power systems are transitioning toward a greener and more sustainable future through the widespread installation of renewable energy resources (RERs). These RERs, primarily wind and solar-based, are connected to the grid using advanced electronics and converter-based technologies. However, the uncertain, intermittent, and volatile nature of RERs has introduced unprecedented challenges, complicating the secure and reliable operation of modern power systems. Fortunately, the rapid advancements in phasor measurement units (PMUs) and remote-control technologies offer significant opportunities to address these issues. PMUs provide high-resolution, real-time snapshots of voltage and current measurements, which can be utilized for online control and health monitoring of power networks. To design realtime control and monitoring (i.e., state estimation) algorithms, the consideration of an appropriate dynamic model is crucial. This model captures the electromechanical transients of power systems, detailing the time-evolution of critical physical quantities like frequencies, generator rotor angles, and voltages. Typically, this model is derived from nonlinear differential-algebraic equations (NDAE) that integrate generator dynamics with power flow equations. Ideally, real-time control and state monitoring algorithms implemented in control centers should consider the complete NDAE model of power systems, incorporating detailed models of synchronous machines and RERs. However, current literature often oversimplifies the NDAE model through linearization and neglects essential algebraic constraints that describe the relationship between generator dynamics and loads. Using a linearized model to study power system dynamics sacrifices accuracy, as it only considers system behavior around a specific equilibrium point. Consequently, the performance and stability of linearization-based estimators and controllers are limited to that point. Given the increasing complexity and uncertainty of electrical grids due to the aggressive deployment of RERs, it is crucial to account for the full NDAE model and the detailed dynamics of synchronous machines and RERs in control and estimation algorithms. Such comprehensive algorithms would ensure the stable and safe operation of future power systems in real time. To that end, the main objectives of this dissertation are to: (1) develop techniques to effectively capture renewables, loads uncertainties, and grid dynamics; (2) build general theory for state/output feedback control and dynamic-algebraic state estimation for the complete NDAE representation of power system with high penetration of advanced power-electronics based RERs and composite loads dynamics; (3) pave a way for realtime and data-driven control/monitoring via model order reduction and system identification for the complete NDAE power system models; (4) design computationally efficient algorithms that can be implemented in the power systems control center for wide-area monitoring and control.