AMPS: Scalable Methods for Real-time Estimation of Power Systems under Uncertainty

美国电网可以说是最复杂的土木工程系统，它正面临着前所未有的挑战，这些挑战来自于新传感技术的出现、大量可再生能源的采用以及智能电网的出现。电力系统运营商依靠估计参数来实时监控电力系统、检测风险、验证技术合规性和制定决策。然而，由于电网的大尺寸和复杂性以及需要实时执行这些任务，该估计问题特别具有挑战性。关于最佳和安全的电网运行的决策关键取决于了解电网的当前参数和状态。本研究将通过开发可扩展的计算方法来解决这些挑战，利用问题结构，并且对于电力系统模型中的不确定性具有鲁棒性。特别是，该项目将致力于确定电力系统模型中最具影响力的参数，并开发数学工具，以有效地从具有量化不确定性的数据中估计电力系统模型参数。该项目将为STEM中代表性不足的群体的学生提供培训机会。贝叶斯反演有助于将数据与基于复杂物理的模型（如电力系统）相结合，以量化模型预测中的不确定性。在电网背景下，贝叶斯反演的算法发展面临着许多根本性的挑战。其中包括反演参数的高维性（源于电网的大小），参数到可观察地图的昂贵和实时评估，以及除了反演参数的不确定性之外的模型不确定性。该项目将开发数学上严格，计算效率高，鲁棒性强的方法，克服数学和计算障碍，解决由不确定的电力系统模型管理的大规模估计问题。特别是，研究人员将建立在现有的最先进的贝叶斯反演算法，并通过使用（i）灵敏度分析来扩展这些算法，以根据其重要性对不确定参数进行分类，（ii）贝叶斯近似误差方法将额外的不确定性纳入电网模型管理的贝叶斯反演问题，（iii）电力系统的替代建模（通过机器学习和降维技术）和（iv）二阶方法和二阶导数信息的近似，以降低求解贝叶斯逆问题时的计算成本。算法、数学发现和开源代码将通过同行评审的期刊论文以及会议和研讨会上的演讲进行传播。该奖项反映了NSF的法定使命，并被认为值得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来获得支持。

The United States power grid, which is arguably the most complex civil engineering system, is facing unprecedented challenges stemming from the advent of new sensing technologies, adoption of large amounts of renewable energy, and emergence of smart grids. Power system operators rely on estimating parameters for monitoring power systems in real-time, detecting risks, verifying technical compliance, and decision-making. However, this estimation problem is particularly challenging due to the large size and complexity of the power grid, as well as the need to perform such tasks in real-time. Decisions about the best and safe power grid operations depend critically on knowing the current parameters and states of the grid. This research will address these challenges by developing computational methods that are scalable, exploit problem structures, and are robust with respect to uncertainties in the power system models. In particular, the project will address identifying the most influential parameters in the power system models and developing mathematical tools to efficiently estimate power system model parameters from data with quantified uncertainties. The project will provide training opportunities for students from underrepresented groups in STEM.Bayesian inversion facilitates the integration of data with complex physics-based models, such as power systems, to quantify the uncertainties in model predictions. The algorithmic developments for Bayesian inversion in the context of power grid, face a number of fundamental challenges. Among those are high-dimensionality of the inversion parameters (stemming from the size of the power grid), expensive and real-time evaluations of the parameter-to-observable maps, and model uncertainty additional to the uncertainty in inversion parameters. The project will develop mathematically rigorous, computationally efficient, and robust methods that overcome mathematical and computational barriers in solving large-scale estimation problems governed by uncertain power system models. In particular, the investigators will build on the existing state-of-the-art for Bayesian inversion algorithms and extend these by using (i) sensitivity analysis to classify the uncertain parameters based on their importance, (ii) the Bayesian approximation error approach to incorporate additional uncertainty into the Bayesian inverse problem governed by power grid models, (iii) surrogate modeling for power systems (via machine learning and dimension reduction techniques) and (iv) second-order methods and approximations of second derivative information to reduce the computational cost when solving the Bayesian inverse problem. The algorithms, mathematical findings, and open-source codes will be disseminated through peer-reviewed journal papers and presentations at conferences and workshops.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.