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

Drexel University, Philadelphia PA

Investigators

Abstract

A reliable, continuous supply of electric energy is essential for the functioning of today's complex societies. Power blackouts like the East-coast blackout on August 14, 2004 demonstrate that despite advances in computing and communication systems, modern deregulated power systems still experience wide-spread cascading outages. One of the underlying causes for human and software/algorithmic failure identified for this blackout is the point-by-point description of a power system operating state where a change in system load and system topology can not be analytically expressed but has to be obtained by steady-state system simulation, the iterative load flow computation. It is the objective of this project to shift the emphasis and general understanding of steady state power system operation from a point by point evaluation based on iterative techniques to a parametric and geometric-analytical understanding of power system voltage behavior as a function of loading conditions. The PIs propose to examine the duality of algebraic ideals and geometric varieties which characterize the loci of the load flow solutions and the boundaries of the secure operating regions. Since the involved algebraic operations are tedious and quite evolved, symbolic computational tools will be used to automate some of the mathematical deductions. In order to find the roots of polynomials that define the varieties, the PIs propose to use cylindrical algebraic decomposition techniques. In addition to developing new insight and new tools for the power industry it is the PIs desire to inspire and educate a new generation of engineers to venture into cross-disciplinary areas of Computational Algebra and Power Engineering in order to solve problems more efficiently.