AMPS: Optimal Transport Algorithms for Stochastic Uncertainty Management in Modern Power Systems

20世纪遗留的电网在过去二十年中经历了转型变化——行业放松管制导致了竞争激烈的电力市场，可再生能源的深入渗透减少了碳足迹，相量测量单元和智能电表等传感器的大规模部署实现了前所未有的监测能力，并利用灵活的负载进行需求响应以实时闭环。这些新因素在电力系统中引入了重大的异构不确定性，要求未来的电网不仅要对这些不确定性具有弹性，而且要在可能的情况下动态地引导这些不确定性。本研究项目将提供一套新颖的数学算法和数值工具箱，以传播和控制受复杂互联电力系统动态影响的随机不确定性模型为时变联合概率密度函数。本研究项目所开发的理论和算法将对电力系统的多种应用产生影响，包括随机负荷扰动下的暂态稳定性分析和间歇性可再生能源发电，以及在有限水平上引导状态概率密度函数以实现不确定条件下所需暂态性能的控制器设计。同时，数学框架将是通用的，足以适用于任何大型非线性振荡器网络的集成级预测和控制，在系统生物学和机器人技术中具有潜在的应用。总的来说，提出的科学活动将显著改变如何对相互关联的不确定非线性系统进行数学分析和可扩展模拟的观点。通常，用于实际电力系统仿真的联合概率密度函数具有高维支持，并且轨迹级非线性导致非高斯性，因此需要非参数计算。例如，在随机可再生能源和初始条件和参数的不确定性存在下的瞬态稳定性分析需要可扩展但严格的预测算法，这些算法不会受到“维数诅咒”的影响。本研究将利用新兴的最优质量传递理论和薛定谔桥理论，实现电力系统仿真中联合概率密度函数的快速预测和有限时间最小努力控制。在这个项目中开发的算法将避免空间离散化或函数逼近，而是通过概率加权分散点云进化在概率密度函数的流形上使用新的近端递推——这是首席研究员最近开发的一种方法。由此产生的算法将能够处理具有数千个相互连接的发电机和负载的实时随机模拟。本研究将通过特别利用电力系统动力学中的结构非线性，促进应用概率、优化和控制理论融合的下一代算法工具的发展。从工程的角度来看，这项研究将促进电力系统随机动力学和控制仿真的颠覆性创新，并提供一个通用的数字工具箱，允许快速扩散。该项目将通过整合课堂研究和外展活动，帮助加州大学圣克鲁斯分校的首席研究员在教育方面建立领导地位。本研究的软件工具箱将通过GitHub发布。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The legacy power grid of the twentieth century has undergone transformational changes in the last two decades -- industry deregulation leading to competitive electricity markets, deep penetration of renewables for reducing the carbon footprint, large scale deployment of sensors such as phasor measurement units and smart meters enabling unprecedented monitoring capabilities and utilizing flexible loads for demand response to close the loop in real-time. These new elements have introduced significant heterogeneous uncertainties in the power systems, requiring the future grid to be not only resilient against these uncertainties, but also to dynamically steer these uncertainties when possible. This research project will deliver a set of novel mathematical algorithms and numerical toolbox to propagate and control the stochastic uncertainties modeled as time-varying joint probability density functions subject to complex interconnected power systems dynamics. The theory and algorithms to be developed in this research project will have impact on multiple applications in power systems including the transient stability analysis under stochastic load perturbations and intermittent renewable generation, as well as the design of controller to steer the state probability density function over finite horizon to achieve desired transient performance under uncertainties. Concomitantly, the mathematical framework will be generic enough to be applicable for ensemble-level prediction and control in any large network of nonlinear oscillators, with potential applications in systems biology, and robotics. Overall, the proposed scientific activities will significantly shift the perspective on how the mathematical analysis and scalable simulation of interconnected uncertain nonlinear systems can be done. Typically, the joint probability density functions of interest for realistic power systems simulation have high dimensional support, and trajectory-level nonlinearities induce non-Gaussianity, thereby requiring non-parametric computation. For example, transient stability analysis in the presence of stochastic renewables, and uncertainties in the initial conditions and parameters requires scalable yet rigorous predictive algorithms that do not suffer from the "curse-of-dimensionality". The proposed research will enable fast prediction and finite-time minimum effort control of joint probability density functions in power systems simulation by harnessing the emergent theory of optimal mass transport and Schrodinger bridge. The algorithms to be developed in this project will avoid spatial discretization or function approximation, and instead use the novel proximal recursions on the manifold of probability density functions via probability weighted scattered point cloud evolution -- an approach the principal investigator has recently developed. The resulting algorithms will be able to handle real-time stochastic simulation with thousands of interconnected generators and loads. This research will contribute to the development of next-generation algorithmic tools at the confluence of applied probability, optimization and control theory by specifically exploiting the structural nonlinearities in power systems dynamics. From an engineering perspective, this research will catalyze disruptive innovation on power systems stochastic dynamics and control simulation with a general-purpose numerical toolbox permitting rapid proliferation. The project will help build the principal investigator's leadership in education at the University of California Santa Cruz by integrating the research in classrooms and outreach activities. Software toolbox resulting from this research will be released via GitHub.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.