SGER: Static Voltage Stability Analysis using Grobner Basis Techniques

电压失稳现象已被确认为对电力系统安全性和可靠性的重大威胁。以前的研究工作，研究电压稳定性一直是基于数值技术。虽然这种技术可以有效地实现大规模的电力系统，他们产生很少的分析信息。另一方面，符号代数几何为基础的方法，而能够产生明确的分析信息有关的总线电压和负载的灵敏度，是有限的，因为它们的大计算复杂性非常小的系统。这一努力解决了可扩展性问题，采用混合的符号/数值方法，利用传统的基于潮流和符号代数/几何技术的优势，扩展静态电压稳定性分析较大的电力系统。其目的是获得当地的符号灵敏度的母线电压和负荷。这些可以用于在这样的总线上的VAR支持设备的设计。研究将进一步集中于系统条件的识别，在该条件下，所得到的参数化潮流方程总是可以使用Gröbner基（GB）约简简化为三角形形式。智力价值该项目推进了对GB约简技术领域的知识和理解，用于多个潮流解，并提供了理论基础，以便于分析（静态）大型电力系统的电压稳定性研究。更广泛的影响所提出的代数几何技术可以应用于获得分析和理论的见解，在网络中产生的其他情况下，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国家最重要的基础设施之一，电网的安全性和可靠性。教育计划是吸收拟议的研究技术在研究生课程在电力系统分析在NDSU。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所部落社区学院。Co-PI活动将有助于加强非博士研究工作。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.