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

电力系统稳态运行与控制的符号代数几何技术

• 批准号: 0424475
• 负责人: Chikaodinaka Nwankpa
• 金额: --
• 依托单位: Drexel University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-15 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0424475&HistoricalAwards=false
• 关键词: Symbolic; Algebraic; Geometry; Techniques; Power

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.

可靠、持续的电能供应对于当今复杂社会的运转至关重要。像2004年8月14日东海岸停电这样的停电表明，尽管计算和通信系统取得了进步，但现代放松管制的电力系统仍然经历着大范围的连锁停电。造成这次停电的人为和软件/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，其中系统负荷和系统拓扑的变化不能解析地表示，但必须通过稳态系统仿真、迭代潮流计算来获得。该项目的目标是将对静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变为对电力系统电压行为作为负荷条件的函数的参数和几何分析的理解。PI建议检验代数理想和几何变量的对偶性，它们表征潮流解的轨迹和安全运行区域的边界。由于所涉及的代数运算非常繁琐且相当复杂，因此将使用符号计算工具来自动执行一些数学推导。为了找到定义变种的多项式的根，PIS建议使用柱面代数分解技术。除了为电力行业开发新的洞察力和新的工具外，PI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。