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

该项目将有助于电网动力学的建模和分析，开发一种有望提供电力系统动力学见解的方法。需要一种新的、功能强大的分析工具来预测电网中振荡和动态的性质。考虑到可再生能源（如风能和太阳能发电机组）的不断增加，其能量输出变化难以预测，这一点尤其正确。传统的电力系统动力学建模是基于离散组件模型的，但随着可再生能源的兴起，人们发现对于大型电网，更精确的连续组件模型可以更好地预测系统的振荡。例如，在这种情况下，使用连续传输线模型而不是简单的批量电路表示就变得很有用。这些连续模型涉及偏微分方程（PDEs），而不是传统上用于电网模型的常微分方程（ode）。不幸的是，目前几乎没有关于这些PDE模型如何在网络拓扑上定义的理论见解，而不是在弦的情况下，或者这些PDE模型的波动方程如何由边界电力系统稳定器（PSS）或灵活的交流传输系统（FACTS）控制，或者这些模型如何随着更多的风能和太阳能发电在系统的不同点进入而变化。因此，本课题提出了一种基于pde的电网建模方法，并构成了本课题的重点。该提案旨在建立一个坚实的理论基础，以解决电力系统动力学，稳定性和控制方面的数学挑战问题，这些问题可以从空间连续建模和基于模型的控制的全新视角来看待。随着可再生能源渗透率的增加，摇摆动力学问题变得更加重要。例如，美国电网正在进行大规模的输电扩展，以将可再生能源发电站点更紧密地连接到远程负荷中心。因此，以前弱连接的总线上的电量现在变得更加强耦合。与此相反，本项目的论文认为，当发电机数量较大时，产生相位和频率振荡的基本机制是连续的。因此，通过使用偏微分方程（PDEs），可以更好地实现精确和物理定向的减轻和抑制这些振荡的方法。该项目的目标包括开发一种基于PDE的电网建模方法，更重要的是开发一种基于模型的PDE控制方法。这些目标在文献中还没有深入探讨。文献中报道的少数基于pde的建模方法可以追溯到30年前。过去没有针对电网提出基于pde的控制方法。因此，这个项目代表了一个潜在的变革性研究理念，可以被视为高风险，高回报。因此，项目目标一旦成功，就可以改变控制广域振荡的方式。

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.