AMPS: Uncertainty Quantification for Stochastic Analysis of Electrical Power Networks

电网的可靠运行是现代工业国家的关键组成部分。 未能保持电网的可靠性会导致重大的社会、国家安全问题和环境成本。 随着诸如风能、太阳能、电池等间歇性电源的不断增加的使用，沿着出现新类型的中断，电网的整体可靠性和稳定性受到威胁。 拟议的研究将对理解这些间歇性电源的电网稳定性产生影响。这可以在建模的基础上显著节省成本，并对环境产生直接的积极影响，以及更稳定的公民社会和经济。随着间歇性（随机）发电机（风能，太阳能，电池等）的不断增加，发电机的数量也在不断增加。和负载，很难在保持可靠性和安全性的同时将这些功率波动整合到电网中。这是一个困难的问题-特别是它是高维的，非高斯的，并且用当前的计算资源来获得足够的预测精度是不可行的。 该项目的目的是数学上严格的数值方法的发展，用于计算的高维感兴趣的量（QoI）的潮流的统计。特别是，调查人员提出：i）推导出随机分析规律的电力潮流的拓扑结构的电网，发电和负载的不确定性，以帮助估计稀疏网格类型的方法的收敛速度。 ii）发展一种适合于电网拓扑随机规律性的多层稀疏网格再生核方法。这种方法将被用来计算随机（暂态）潮流的统计。 iii）如果资源允许，作为非常大维度问题的替代缓解策略，研究人员提出了将QoI分为非线性（大偏差）和线性（小偏差）分量的分割方法。高维的小偏差近似的扰动方法与最多的二次计算成本的维度。对大偏差采用多层稀疏网格再生核方法进行逼近。 这项工作提出了显着改善的国家的最先进的高维UQ方法，适用于拓扑结构，如电网。这是一个非常相关的主题，因为UQ方法在电网中的应用和理论尚处于起步阶段。美国国家科学院去年的一份报告强调了这一问题目前的重要性。

The reliable functioning of the electric power grid forms a critical part of a modern industrial country. The failure to maintain the reliability of the grid leads to significant societal, national security problems and environmental costs. With the ever-increasing use of intermittent power sources such as wind, solar, battery, along with new types of disruptions that are arising, the overall reliability and stability of the electric grid is threatened. The proposed research will have an impact on understanding the stability of the electric grid given these intermittent power sources. This can lead to significant cost savings based on modeling, in addition to a direct positive impact on the environment, and a more stable civil society as well as economy.With the ever-increasing presence of intermittent (stochastic) generators (wind, solar, battery, etc.) and loads, it is difficult to integrate these power fluctuations into an electric grid while maintaining reliability and safety. This is a hard problem - in particular it is high dimensional, non-Gaussian, and it is not feasible with current computational resources to obtain sufficient predictive accuracy. The aim of this project is the development of mathematically rigorous numerical methods for computing the statistics of a high dimensional Quantity of Interest (QoI) of the power flow. In particular, the investigators propose: i) To derive stochastic analytic regularity of the power flow with respect to the topology of the electric grid, power generation and load uncertainties to help estimate convergence rates of sparse grid type methods. ii) To develop a multi-level sparse grid reproducing kernel method that is adapted to the stochastic regularity of the electric grid topology. This method will be used to compute the statistics of the stochastic (transient) power flow. iii) If resources permit, as an alternative mitigation strategy for very large dimensional problems, the investigators propose a splitting method of the QoI into non-linear (large deviation) and linear (small deviation) components. The high dimensional small deviations are approximated with a perturbation method with at most quadratic computational cost in dimension. The large deviations are approximated with a multi-level sparse grid reproducing kernel method. This work proposes to significantly improve the state of the art in high dimensional UQ methods that are adapted to topologies such as those of the electric grid. This is a very relevant topic since the the application and theory of UQ methods to electric grids are in their infancy. A National Academy of Sciences report from last year underscores the current importance of this issue.