Collaborative Research: Improving Power Grids Weather Resilience through Model-free Dimension Reduction and Stochastic Search for Optimal Hardening

恶劣天气是美国停电的首要原因，导致巨大的经济和社会损失。鉴于提前几天的天气预报，加强输电线可以显著缓解连锁愤怒的风险，缩短恢复电力的时间，从而提高电网的耐候性。由于时间和/或预算等资源限制，确定具有这些限制的最优强化计划非常重要。考虑到电网上的大量电力线，寻找最优的电力线硬化子集是具有挑战性的。本文研究了一种具有实用约束的最优强化方案的搜索方法。该方法利用统计学中的高维数据分析和运筹学中随机模拟的离散优化方法，在优化电网强化方案、降低恶劣天气下的连锁停电风险等方面取得了基础理论和算法上的进展。由于电网具有广泛的经济和社会重要性，该研究对国家的福利和安全具有更广泛的影响，本项目开发了一种无模型降维方法，通过仿真提高离散优化的计算效率，通过优化电力线硬化来提高电网的耐候性。降维方法根据输电线路与电网断开造成的功率损失对输电线路的子集进行排序。该方法不需要假设线损与所有考虑的线路组合之间建立特定的统计联合模型，只利用线路组合的边际信息，因此对硬化规划具有普遍的适用性。然后提出了一种新的随机搜索算法，该算法利用降维能力，在资源受限的情况下减小了有效搜索空间的大小，以应对恶劣天气条件。为了提高计算效率，随机搜索算法首先使用信息丰富的高斯混合来融合降维结果，同时获得渐近收敛，并利用降维结果构造分层抽样分布。无模型降维和随机搜索算法通常适用于各种其他学科，例如，保护其他关键民用基础设施，如公路网。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。

Severe weather is the leading cause of power outages in the United States, leading to tremendous economic and social costs. Given days-ahead weather forecasts, hardening power lines can significantly mitigate cascading outrage risks, shorten the time to restore electricity, and therefore improve power grids weather resilience. Due to resource constraints, such as time and/or budget, it is important to identify the optimal hardening plan with the constraints. Given the large number of power lines on the grids, searching for the optimal subset of power lines of hardening is challenging. In this research, a novel searching approach for optimal hardening plan with practical constraints is studied. The method takes the advantages of high-dimensional data analysis from statistics and discrete optimization via stochastic simulation from operations research and makes fundamental theoretical and algorithmic advances to optimize power grids hardening plans and reduce cascading power outage risks in severe weather. Because of the broad economic and societal importance of power grids, the research has broader impact on the welfare and security of the country.This project develops a model-free dimension reduction method to improve the computational efficiency of discrete optimization via simulation for improving power grids weather resilience through optimal power line hardening. The dimension reduction method ranks the subsets of the transmission lines according to power loss caused by their disconnection from power grids. The new method does not need to assume a specific statistical joint model between power loss and all considered line combinations and only uses the marginal information of the line combinations, and thus are generally applicable for hardening planning. A new stochastic search algorithm that exploits the dimension reduction capability is then proposed to reduce the size of the effective search space given resource constraints when preparing for severe weather conditions. To improve computational efficiency, the stochastic search algorithm uses an informative Gaussian mixture prior to incorporate dimension reduction results while achieving asymptotical convergence and constructs a hierarchical sampling distribution using dimension reduction results. The model-free dimension reduction and stochastic search algorithm are generally applicable to a variety of other disciplines, e.g., the protection of other critical civil infrastructures such as road networks.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.