Collaborative Research: AMPS: Robust Failure Probability Minimization for Grid Operational Planning with Non-Gaussian Uncertainties

2020年，电力行业在所有经济部门的碳排放量中占第二大份额。可再生能源，特别是风能和太阳能，对电网脱碳和确保国家未来的繁荣和福利至关重要。然而，由于其固有的和不可避免的间歇性和可变性，可再生能源在国家能源结构中的成功整合对日常电网运营构成了根本性的挑战。如果不能在规划过程中考虑到这种不确定性，将导致服务中断和电网不稳定，从而不仅危及脱碳目标的实现，还会影响系统的可靠性。该项目为电网运行规划开发新一代数学方法、计算机模型和算法，准确、系统地考虑到可再生能源不确定性的非常态和多模态性质，以及控制电网的非线性和通常反直觉的物理定律。该项目的方法和计算机实施将有利于电力部门以及更广泛的能源部门，包括那些专门从事电力系统软件的私营公司和供应商，并为各种规划工具提供信息。该项目通过培训本科和研究生STEM学生在能源系统优化和电网运行基础方面的知识，进一步影响教育和更广泛的社会，从而使他们能够运用他们的分析技能来设计更环保和经济高效的未来能源系统。该项目提供了一种通用的方法，包括新的数学模型、理论和算法，以系统地解释可再生能源预测的非高斯误差分布，这是最基本的电力系统规划问题之一，称为交流最优潮流。在电力负荷和可再生能源预测中的非高斯误差的一般处理以前在电网规划中没有考虑过，尽管在数据中已经显示出来。该项目通过开发一种在非高斯概率约束下进行优化的新方法，严格地集成了这种情况下的风险和不确定性。这是通过利用高斯混合模型的可表征性和可分析性，以及通过设计足够模块化的算法来实现的，这些算法允许当前被证明可以很好地处理高斯误差的方法，只需稍加修改即可重用。该方法的通用性有望在更广泛的机会约束优化领域激发新的算法，包括约束受高斯混合不确定性影响的非线性非凸问题。该项目还通过设计新的非高斯模糊集严格解释了混合模型参数的错误说明，这些模糊集以前没有被研究过，但有可能发现具有改进样本外性能和可靠性的鲁棒网络工作点。该项目使用真实的效用数据来指导模型验证和实验，并为系统操作员提供了一套实用的建议，以促进所开发方法的采用。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。

The electric power industry accounted for the second-largest portion of all carbon emissions across economic sectors in 2020. Renewable energy resources, particularly wind and solar, are critical to decarbonizing the grid and ensuring the nation's future prosperity and welfare. However, because of their inherent and unavoidable intermittency and variability, successful integration of renewable energy resources in the nation's energy mix poses fundamental challenges for day-to-day grid operations. Failure to account for this uncertainty during planning can result in loss of service and grid de-stabilization, thus jeopardizing not only the achievement of decarbonization targets but also system reliability. This project develops the next generation of mathematical methods, computer models, and algorithms for grid operational planning, which accurately and systematically take into account the non-normal and multi-modal nature of renewable uncertainty, as well as the nonlinear and often counter-intuitive physical laws that govern electric power networks. The project's methods and computer implementations shall benefit and inform diverse planning tools, both within the electric power sector as well as the broader energy sector, including those of private companies and vendors who specialize in power systems software. The project further impacts education and the broader society by training undergraduate and graduate STEM students in energy systems optimization and the foundations of electric power grid operations, thereby enabling them to apply their analytical skills to design more environmentally- and economically-efficient future energy systems.The project contributes a general methodology, including new mathematical models, theory, and algorithms, to systematically account for non-Gaussian error distributions of renewable energy forecasts, in one of the most fundamental power system planning problems called AC Optimal Power Flow. A general treatment of non-Gaussian errors in electric load and renewable energy forecasts has not been considered before in grid planning, despite being exhibited in data. The project rigorously integrates risk and uncertainty in this context by developing a novel methodology for optimization under non-Gaussian probabilistic constraints. This is achieved by exploiting the representability and analyticity of Gaussian mixture models and by designing algorithms that are modular enough to allow current methods which are proven to work well for Gaussian errors to be reusable with only minor modifications. The generality of the approach is expected to spur new algorithms in the broader field of chance-constrained optimization, including nonlinear nonconvex problems whose constraints are affected by Gaussian mixture uncertainties. The project also rigorously accounts for misspecification of the mixture model parameters by designing novel non-Gaussian ambiguity sets, which have not been studied before but have the potential to enable the discovery of robust network operating points with improved out-of-sample performance and reliability. The project uses real utility data to guide model validation and experimentation and also provides a set of practical recommendations for system operators to facilitate the adoption of the developed methods.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.