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

可靠、持续的电力供应对当今复杂社会的运转至关重要。2004年8月14日发生在美国东海岸的停电事件表明，尽管计算机和通信系统有了进步，但解除管制的现代电力系统仍然会出现大范围的连锁停电。人为和软件/算法故障的根本原因之一是对电力系统运行状态的逐点描述，其中系统负载和系统拓扑的变化不能解析表达，但必须通过稳态系统仿真，迭代负载流计算来获得。该项目的目标是将对稳态电力系统运行的重点和一般理解从基于迭代技术的逐点评估转移到对电力系统电压行为作为负载条件函数的参数化和几何解析理解。pi建议检查表征负载流解的轨迹和安全操作区域边界的代数理想和几何变异的对偶性。由于所涉及的代数运算繁琐且相当复杂，因此将使用符号计算工具来自动化一些数学推导。为了找到定义变量的多项式的根，他们建议使用圆柱代数分解技术。除了为电力行业开发新的见解和新工具外，pis还希望激励和教育新一代工程师冒险进入计算代数和电力工程的跨学科领域，以便更有效地解决问题。

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.