Symbolic Algebraic Geometry Techniques for Power System Steady State Operation and Control

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A reliable, continuous supply of electric energy is essential for thefunctioning of today's complex societies. Power blackouts like theEast-coast blackout on August 14, 2004 demonstrate that despite advancesin computing and communication systems, modern deregulated power systemsstill experience wide-spread cascading outages. One of the underlyingcauses for human and software/algorithmic failure identified for thisblackout is the point-by-point description of a power system operatingstate where a change in system load and system topology can not beanalytically expressed but has to be obtained by steady-state systemsimulation, the iterative load flow computation. It is the objective ofthis project to shift the emphasis and general understanding of steadystate power system operation from a point by point evaluation based oniterative techniques to a parametric and geometric-analyticalunderstanding of power system voltage behavior as a function of loadingconditions. The PIs propose to examine the duality of algebraic ideals andgeometric varieties which characterize the loci of the load flow solutionsand the boundaries of the secure operating regions. Since the involvedalgebraic operations are tedious and quite evolved, symbolic computationaltools will be used to automate some of the mathematical deductions. Inorder to find the roots of polynomials that define the varieties, the PIspropose to use cylindrical algebraic decomposition techniques. In additionto developing new insight and new tools for the power industry it is thePIs desire to inspire and educate a new generation of engineers to ventureinto cross-disciplinary areas of Computational Algebra and PowerEngineering in order to solve problems more efficiently.