Computational Methods for Mixed-Integer Programs in Power Systems

该项目的目标是为电力系统的优化运行设计可证明有效的计算方法，并促进其向可持续系统的转变。由于电力系统是由数以万计的设备通过物理基础设施相互连接的大规模互联网络，电力运营商定期解决一系列高度复杂的优化问题，以便能够运行这些系统。一个主要的电力优化问题是机组组合(UC)，它优化了参与的发电机的生产计划，是美国电力市场的支柱，每年的价值超过3000亿美元。此外，新出现的最优输电切换(OTS)问题能够通过共同优化基础设施中的资源之间的相互作用来进一步改善电力系统的运行。由于这些问题是高度非线性的，成熟的优化算法不能有效地一致地解决它们，并且存在重大缺陷。该项目旨在解决迫切需要开发有效的技术，能够在更短的时间范围内以更高的精度解决更大的功率优化问题，与当前的能力相比。该项目利用真实世界系统的底层结构，为功率优化问题开发定制的计算技术，具有强大的理论和实践保障。由于其他混合整数功率问题在数学上类似于UC和OTS的组合，因此重点讨论UC问题(在系统的节点上具有二进制变量)和OTS问题(在系统的链路上具有二进制变量)。所提出的方法依赖于图论、圆锥优化、有效不等式、舍入技术、惩罚方法、分枝定界技术、稳健优化和代数几何的高级主题。该项目将推动非线性电力优化领域的发展，其研究结果将对电网的能源管理系统产生重大影响，从而带来重大的资金节约和环境效益。该项目有大量的外展项目，对“儿童工程”和“工程师无国界”项目以及培养本科生研究、MS学生的工程领导能力、研究生课程丰富和不同社会之间知识的交叉培养的教育活动做出了贡献。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。

The goal of this project is to design provably efficient computational methods for the optimal operation of power systems and to facilitate their transformation into sustainable systems. Since power systems are large-scale interconnected networks with tens of thousands of devices connected to one another via a physical infrastructure, power operators periodically solve a series of highly complex optimization problems to be able to run these systems. One major power optimization problem is unit commitment (UC), which optimizes the production schedules of the participating generators and is the backbone of the US electricity market with the value exceeding $300B annually. In addition, the emerging problem of optimal transmission switching (OTS) enables a further improvement of power systems operation by co-optimizing the interactions among the resources in the infrastructure. Since these problems are highly nonlinear, well-established optimization algorithms cannot efficiently solve them consistently and suffer from major drawbacks. This project aims to address the pressing need to develop effective techniques that are able to solve much larger power optimization problems on a much shorter time scale with a higher accuracy, compared to the current capabilities. This project leverages the underlying structures of real-world systems to develop customized computational techniques for power optimization problems with strong theoretical and practical guarantees. The focus is on the UC problem (with binary variables at the nodes of the system) and the OTS problem (with binary variables on the links of the system), since other mixed-integer power problems mathematically resemble a combination of UC and OTS. The proposed approach relies on advanced topics in graph theory, conic optimization, valid inequalities, rounding techniques, penalization methods, branch-and-bound techniques, robust optimization, and algebraic geometry. This project will advance the area of nonlinear power optimization, and its findings will significantly impact the energy management systems of power grids leading to major monetary savings and environmental benefits. This project has substantial outreach components with contributions to the programs "Engineering for Kids" and "Engineers without Borders," as well as educational activities to foster undergraduate research, engineering leadership for MS students, graduate curriculum enrichment, and cross fertilization of knowledge among different societies.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.