EAGER: Collaborative Research: Spatially Continuous Modeling of Power System Oscillations with Renewable Energy Penetration

This project will contribute to modeling and analysis of electric power grid dynamics, developing a methodology that is expected to provide insights into power system dynamics. There is a need for new and powerful analytical tools for predicting the nature of oscillations and dynamics in the power grid. This is especially true given the increasing presence of renewable energy resources (such as wind and solar-based power generating units) whose energy output varies unpredictably. Traditional modeling of power system dynamics is based on discrete component models, but with the rise of renewable energy sources, it has been observed that for large networks, more accurate continuous component models provide better prediction of system oscillations. For example, it becomes useful in these circumstances to use continuous transmission line models, rather than simple buk circuit representations. These continuous models involve partial differential equations (PDEs) instead of the ordinary differential equations (ODEs) that are traditionally used in power grid models. Unfortunately, currently there is little theoretical insight on how these PDE models can be defined over network topologies other than in the case of strings, or how the oscillations arising from the wave equations of these PDE models can be controlled by boundary power system stabilizers (PSS) or flexible AC transmission systems (FACTS), or how these models might change with more wind and solar generation coming in at different points in the system. Therefore, in this project a PDE-based approach for modeling the power grid is proposed, and forms the focus of this proposal. The proposal aims to develop a solid theoretical foundation, which addresses mathematically challenging questions on power system dynamics, stability and control that can be viewed from a completely new and fresh perspective of spatially continuous modeling and model-based control.

The problem of swing dynamics becomes even more important as renewable penetration increases. For example, the US grid is going through a tremendous amount of transmission expansion to connect renewable generation sites more closely to remote load centers. Thus, electrical quantities at buses that were weakly connected before are now becoming much more strongly coupled.The thesis in this project, in contrast, is that when the number of generators is relatively large the fundamental mechanism that produces the phase and frequency oscillations is a continuous one. As a result, accurate and physically oriented methods for mitigating and suppressing these oscillations are better realized through the use of partial differential equations (PDEs). The goals of the project consist of developing a PDE-based approach for modeling the power grid, and more importantly a PDE control methodology that is model-based. These goals have not been explored in much depth in the literature. The few PDE-based modeling methods reported in the literature date back thirty years. No PDE-based control methods have been proposed in the past for the power grid. As such, this project represents a potentially transformative research idea that can be viewed as high-risk, high-payoff. The project goals, when successful, can therefore transform the way in which wide area oscillations are controlled.