SGER: Static Voltage Stability Analysis using Grobner Basis Techniques

电压不稳定现象已被认为是对电力系统安全和可靠性的重大威胁。以前研究电压稳定性的努力是基于数值技术的。虽然这些技术可以有效地在大型电力系统中实施，但它们产生的分析信息很少。另一方面，基于符号代数-几何的方法虽然能够产生与母线电压和负载灵敏度有关的明确分析信息，但由于其计算复杂性很大，因此仅限于非常小的系统。这项工作通过采用混合符号/数值方法来解决可扩展性问题，利用传统的基于潮流和符号代数/几何技术的优势，将静态电压稳定性分析扩展到更大的电力系统。目的是获得母线电压和负载的局部符号灵敏度。这些可用于在此类总线上设计VAR支持装置。研究将进一步集中在系统条件的识别上，在这些条件下，所得到的参数化潮流方程总是可以使用Gröbner基（GB）约简为三角形形式。该项目促进了对多种潮流解决方案的GB降低技术领域的知识和理解，并为大型电力系统的分析（静态）电压稳定性研究提供了理论基础。更广泛的影响所提出的代数-几何技术可以应用于从其他环境中产生的网络中获得分析和理论见解，例如无线通信和传感器网络。如果成功，这项工作将有助于提高美国最关键的基础设施之一——电网的安全性和可靠性。教育计划是将建议的研究技术纳入NDSU的电力系统分析研究生课程。研究结果将通过期刊和会议出版物以及电力工程通讯传播给教育机构，包括由美洲土著学生组成的五个部落社区学院。合作项目的活动将有助于加强非博士学位的研究工作。授予大学。

The phenomenon of voltage (in)stability has been identified as a significant threat to power system security and reliability. Previous research efforts to study voltage stability have been based on numerical techniques. While such techniques can be efficiently implemented on large scale power systems, they yield little analytical information. On the other hand, symbolic algebraic-geometric based methods, while capable of yielding explicit analytical information pertaining to bus voltage and load sensitivities, are limited to very small systems because of their large computational complexity. This effort addresses the scalability issue by adopting a mixed symbolic/numerical approach exploiting the strengths of both conventional power-flow based and symbolic algebraic/geometric techniques to extend static voltage stability analysis on larger power systems. The objective is to obtain local symbolic sensitivities of bus voltage and loads. These can be used in the design of VAR support devices at such buses. The investigation will further focus on the identification of system conditions under which the resulting parameterized power flow equations can always be reduced to triangular form using Gröbner basis (GB) reduction.Intellectual MeritThe project advances the knowledge and understanding in the area of GB reduction techniques for multiple power flow solutions and provides a theoretical foundation to facilitate analytical (static) voltage stability studies in larger power systems. Broader ImpactsThe proposed algebraic-geometric techniques can be applied to obtain analytical and theoretical insights in networks arising from other contexts, for example, wireless communication and sensor networks. If successful, the effort will contribute to improved security and reliability of one of the Nation's most critical infrastructures, the electric power grid. The educational plan is to absorb the proposed research techniques in to a graduate course in power systems analysis at NDSU. The results will be disseminated through journal and conference publications and through a power engineering newsletter to educational institutions including five tribal community colleges comprising Native American students. The Co-PIs activities will serve to enhance research efforts at a non-Ph.D. granting university.