SGER: Static Voltage Stability Analysis using Grobner Basis Techniques

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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.