Risk Assessment of Power Systems to Extreme Events using Polynomial-Chaos-based Methods

现代电力系统包含许多不确定性，这些不确定性是由随机负荷变化、可再生能源变化以及发电机组、线路和变压器的随机停电引起的。因此，它们面临着越来越大的连锁故障风险，导致大规模停电。对于大型系统，现有方法的计算负担过大，限制了它们在评估拓扑和功率注入不确定情况下的级联故障风险时的实用性。为了应对这些挑战，本文将采用多项式混沌方法和不确定性量化理论来建立一个新的电力系统极端事件风险评估框架。开发的框架将加强电力系统规划、运营、在线监测以及本地和全球控制。此外，不确定性量化方法可以推广到许多其他工程领域，如飞机设计和控制、车辆和列车控制等，为控制和设计程序提供很大的改进。开发的框架将在两个实际电力系统上进行验证，即巴西南部电力系统和弗吉尼亚电力公司500千伏输电系统。该项目还包含对STEM（科学、技术、工程和数学）领域感兴趣的K-12学生、本科生和研究生的综合教育议程。目前，基于蒙特卡罗的方法被广泛应用于电力系统规划和运行中。这些方法对于本提案中感兴趣的问题的计算负担非常高。本课题将基于多项式混沌方法和不确定性量化理论，建立一种新的极端事件和大不确定性电力系统风险评估框架。具体而言，我们的建议将旨在1)设计一种新的基于多项式混沌的算法，该算法可以处理随机输入假设的任意概率分布，同时在短时间和长时间模拟中提供准确的结果；2)当所开发的算法应用于具有高维不确定输入的高度非线性系统时，提供快速的计算速度。这是通过启动一种混合方法来对非常高维的数据进行降维来实现的，该方法包括两个步骤。第一步，采用基于核的主成分分析（PCA）得到中间降维结果。在第二步中，我们使用方差分析（ANOVA）或切片逆回归来获得更活跃的中心子空间。此外，将启动基于场景的多元素多项式混沌展开来处理系统拓扑变化。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。

Modern power systems involve numerous uncertainties induced by random load variations, renewable energy variations, and random outages of generating units, lines, and transformers. As a result, they have been subject to an increasing risk of cascading failures leading to large-scale blackouts. The computational burden current methods is prohibitively large for large-scale systems, restricting their practicability when assessing the risk of cascading failures under topology and power injection uncertainties. To address these challenges, this proposal will resort to polynomial-chaos methods and uncertainty quantification theory to develop a new risk assessment framework for power systems subject to extreme events. The developed framework will enhance power system planning, operations, online monitoring and local and global controls. Besides, the uncertainty quantification methods can be generalized to provide great improvement in the control and design procedures of many other engineering fields, such as aircraft design and control, vehicle and train control, among others. The developed framework will be validated on two real power systems, namely the Southern Brazil power system and the Dominion Virginia Power 500-KV transmission system. The project also contains an integrated educational agenda for K-12 students, undergraduates and graduate students who are interested in the STEM (Science Technology Engineering and Mathematics) area.Currently, Monte-Carlo-based methods are widely used in power system planning and operation. The computational burden of these methods for the problem of interest in this proposal is very high. In this project, a new risk assessment framework for power systems subject to extreme events and large uncertainties will be developed based on polynomial-chaos methods and uncertainty quantification theory. Specifically, our proposal will aim to 1) designing a new polynomial chaos-based algorithm that can handle arbitrary probability distributions assumed for the random inputs while providing accurate results for both short-time and long-time simulations, and 2) providing fast calculation speed when the developed algorithm is applied to a highly nonlinear system subject to high-dimensional uncertain inputs. This is achieved by initiating a hybrid approach to conduct dimension reduction for very high-dimension data, which consists of two steps. In the first step, a kernel-based principle component analysis (PCA) is applied to obtain intermediate dimension reduction results. In the second step, we use an analysis of variance (ANOVA) or sliced-inverse-regression to obtain a more active central subspace. Furthermore, scenario-based multi-element polynomial chaos expansion to handle system topology changes will be initiated.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.