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

该项目将有助于电网动态的建模和分析，开发一种方法，预计将提供对电力系统动态的见解。有一个新的和强大的分析工具，用于预测电网中的振荡和动态的性质的需要。考虑到可再生能源（如风能和太阳能发电机组）的不断增加，其能源输出的变化是不可预测的，这一点尤其如此。传统的电力系统动态建模是基于离散元件模型，但随着可再生能源的兴起，人们已经观察到，对于大型网络，更准确的连续元件模型提供了更好的预测系统振荡。例如，在这些情况下，使用连续传输线模型而不是简单的布克电路表示变得有用。这些连续模型涉及偏微分方程（PDE），而不是传统上用于电网模型的常微分方程（ODE）。不幸的是，目前几乎没有理论上的见解，这些PDE模型可以如何定义在网络拓扑结构以外的情况下的字符串，或如何从这些PDE模型的波动方程产生的振荡可以由边界电力系统稳定器（PSS）或灵活的交流输电系统（FACTS）控制，或者随着更多的风能和太阳能发电进入系统的不同位置，这些模型会如何变化。因此，在本项目中，提出了一种基于偏微分方程的方法来建模电网，并形成了本提案的重点。该提案旨在建立一个坚实的理论基础，解决电力系统动态、稳定性和控制等数学上具有挑战性的问题，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量的输电扩建，以将可再生能源发电站更紧密地连接到远程负荷中心。因此，以前弱连接的母线上的电量现在变得更加强耦合。相反，本项目的论文是，当发电机的数量相对较大时，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（PDE），可以更好地实现用于减轻和抑制这些振荡的精确和物理导向的方法。该项目的目标包括开发一种基于PDE的方法来建模电网，更重要的是一种基于模型的PDE控制方法。这些目标在文献中没有深入探讨。文献中报道的几种基于偏微分方程的建模方法可以追溯到三十年前。在过去，没有基于偏微分方程的控制方法已经提出了电网。因此，这个项目代表了一个潜在的变革性研究想法，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.