## Modeling, Simulation, and Control Design for Electro-Mechanical Phenomena in Heterogeneous Power Systems

*MS student Ethan WIlliams with Advisor A. Domínguez-García*

Secure power system operation has become an increasing concern, given the growing penetration of inverted-interfaced renewables. Specifically, with the wide variety of inverter-based resources, it is important to investigate how they interact amongst each other and with synchronous generators. Further, as the modern grid becomes heterogeneous, it is important to design and test control strategies, such as primary and secondary frequency and voltage control, in the context of this resource mix. There are two main issues when studying full-order models: first, high-modeling complexity makes it difficult to gain an analytical system understanding and second, it is computationally expensive. Fortunately, for the purpose of power system control, many of the time scales associated with these models are relatively fast and can be abstracted away with reduced-order models. These are applicable for capturing electro-mechanical phenomena occurring on time scales ranging from tenths of seconds to minutes.

Previously, a reduced-order modeling framework for studying system control in generic power systems with generation from synchronous generators and from grid-forming inverters with virtual synchronous machine control (VSMC), droop control (Droop), and dispatchable virtual oscillator control (dVOC) was developed. A non-linear and linearized model of the generic power system was constructed in MATLAB/Simulink. Since then, 14-bus and 57-bus IEEE case studies have been studied with this tool. In these studies, a transformation technique has been tested which converts differential algebraic equations (DAEs) into an approximate ordinary differential equation (ODE). representation. In Figure 1, generating resource frequencies, bus voltages, and bus active/reactive power injections are shown for a selection of entities within the 57-bus case study. A general external control model was added where multiple strategies have since been implemented. In prior work, a generalized linear-quadradic-regulated optimal controller was developed which can both provide reference tracking for secondary control and augment primary control services. Since then, the ability to directly regulate frequency of Droop and dVOC inverters has been added. As an example, for a four-bus system with a load and different type of resource at each bus, the frequency response of the dVOC inverter with and without augmented primary control for frequency is shown in Figure 2. This research is funded by the Power Systems Engineering Research Center.