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

这个项目将有助于电网动态的建模和分析，开发一种方法，有望为电力系统动态提供见解。需要新的和强大的分析工具来预测电网中的振荡和动态的性质。鉴于可再生能源(如风能和太阳能发电机组)的存在日益增多，情况尤其如此，它们的能量输出变化不可预测。传统的电力系统动力学建模是基于离散分量模型的，但随着可再生能源的兴起，人们已经观察到，对于大型网络，更准确的连续分量模型可以更好地预测系统振荡。例如，在这些情况下，使用连续传输线模型而不是简单的Buk电路表示法变得很有用。这些连续模型涉及的是偏微分方程组(PDE)，而不是传统上用于电网模型的常微分方程组(ODE)。遗憾的是，目前对于如何在网络拓扑结构上定义这些PDE模型而不是在串的情况下，或者这些PDE模型的波动方程产生的振荡如何通过边界电力系统稳定器(PSS)或灵活交流输电系统(FACTS)来控制，或者这些模型如何随着更多的风能和太阳能发电进入系统的不同点而改变，目前几乎没有理论上的见解。因此，在本项目中，提出了一种基于偏微分方程的电网建模方法，并形成了本方案的重点。该提案旨在建立坚实的理论基础，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角度来看待。随着可再生能源普及率的增加，摆动动力学问题变得更加重要。例如，美国电网正在经历巨大的输电扩张，以更紧密地将可再生发电站点连接到偏远的负荷中心。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，本项目的主题是，当发电机数量相对较大时，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组(PDE)可以更好地实现减轻和抑制这些振荡的精确和面向物理的方法。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。这些目标在文献中没有得到太深入的探讨。文献中报道的为数不多的基于偏微分方程的建模方法可以追溯到30年前。过去还没有人提出基于偏微分方程的电网控制方法。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.