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

AMPS：现代电力系统中随机不确定性管理的最优传输算法

• 批准号: 1923278
• 负责人: Abhishek Halder
• 金额: $ 27.98万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1923278&HistoricalAwards=false
• 关键词: AMPS; Optimal; Transport; Algorithms; Stochastic

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.

20世纪遗留下来的电网在过去20年里经历了变革性的变化--行业放松管制导致电力市场竞争，可再生能源的深度渗透以减少碳足迹，大规模部署传感器，如相量测量单元和智能电表，实现前所未有的监控能力，并利用灵活的需求响应负载来实时闭合回路。这些新的因素在电力系统中引入了显著的异质不确定性，要求未来电网不仅要对这些不确定性具有弹性，而且在可能的情况下还要动态地控制这些不确定性。这一研究项目将提供一套新颖的数学算法和数值工具箱来传播和控制建模为复杂互联电力系统动态下的时变联合概率密度函数的随机不确定性。本研究项目中的理论和算法将对电力系统中的多种应用产生影响，包括随机负荷扰动和间歇可再生发电下的暂态稳定分析，以及控制器的设计，以在有限范围内引导状态概率密度函数，以在不确定情况下获得期望的暂态性能。随之而来的是，数学框架将具有足够的通用性，适用于任何大型非线性振荡器网络中的系综级别预测和控制，在系统生物学和机器人学中具有潜在的应用。总体而言，拟议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仿真的视角。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度，而轨迹级别的非线性导致非高斯性，从而需要非参数计算。例如，在存在随机可再生能源以及初始条件和参数存在不确定性的情况下进行暂态稳定分析，需要可扩展但严格的预测算法，这些算法不会受到“维度灾难”的影响。该研究将利用最优质量传输的涌现理论和薛定谔电桥，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。该项目将开发的算法将避免空间离散化或函数近似，而是通过概率加权散乱点云演化在概率密度函数流形上使用新的近邻递归--这是主要研究人员最近开发的一种方法。由此产生的算法将能够处理数千台互联发电机和负载的实时随机模拟。这项研究将通过具体利用电力系统动力学中的结构非线性，为应用概率、优化和控制理论的下一代算法工具的开发做出贡献。从工程的角度来看，这项研究将催化电力系统随机动力学和控制仿真的颠覆性创新，并使用允许快速扩散的通用数值工具箱。该项目将通过整合课堂研究和外联活动，帮助加州大学圣克鲁斯分校建立首席研究员在教育方面的领导地位。这项研究产生的软件工具箱将通过GitHub发布。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Finite Horizon Density Steering for Multi-input State Feedback Linearizable Systems

多输入状态反馈线性化系统的有限水平密度控制

• DOI: 10.23919/acc45564.2020.9147847
• 发表时间: 2020
• 期刊: Proceedings of the 2020 American Control Conference
• 作者: Caluya, Kenneth F.;Halder, Abhishek
• 通讯作者: Halder, Abhishek

Stochastic Uncertainty Propagation in Power System Dynamics Using Measure-Valued Proximal Recursions

• DOI: 10.1109/tpwrs.2022.3217267
• 发表时间: 2021-08
• 期刊: IEEE Transactions on Power Systems
• 影响因子: 6.6
• 作者: A. Halder;Kenneth F. Caluya;Pegah Ojaghi;Xinbo Geng

Reflected Schrödinger Bridge: Density Control with Path Constraints

反射薛定谔桥：具有路径约束的密度控制

• DOI: 10.23919/acc50511.2021.9482813
• 发表时间: 2021
• 期刊: 2021 American Control Conference (ACC
• 作者: Caluya, Kenneth F.;Halder, Abhishek
• 通讯作者: Halder, Abhishek

Gradient Flow Algorithms for Density Propagation in Stochastic Systems

• DOI: 10.1109/tac.2019.2951348
• 发表时间: 2020-10-01
• 期刊: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• 影响因子: 6.8
• 作者: Caluya, Kenneth F.;Halder, Abhishek
• 通讯作者: Halder, Abhishek