在代数流形上寻找到达电压崩溃点的最短路径
Searching for the Shortest Path to the Point of Voltage Collapse on the Algebraic Manifold
摘要：
电压失稳是造成电力系统大停电的主要原因之一。可再生能源集成、分布式能源和需求响应等新兴技术可能会给全系统电压稳定性分析带来显著的不确定性。本文首先总结了各种已知的电压失稳机理，然后重点研究了一类由代数流形的奇异曲面引起的电压失稳。我们认为，并证明，这一类可以包括动态和静态电压不稳定性。为了确定到电压崩溃点的最小距离，在代数流形上提出了一种新的公式。该公式被进一步转换成一个最优控制框架，用于识别流形上具有最小距离的路径。对不同电力系统测试用例的流形进行了全面的数值研究，结果表明，所提出的方法在动态模型和静态模型下都能得到到流形上奇异曲面的局部最短路径。仿真结果表明，该方法可以识别比最小欧氏距离相关的路径更短的路径。此外，所提出的方法总是定位正确的路径结束于正确的奇异表面，这是负责电压不稳定，而欧几里得距离公式可以错误地找到解决方案错误的奇异表面。广泛的潜在应用，使用所提出的方法进行了讨论。
英文摘要：
Voltage instability is one of the main causes of power system blackouts. Emerging technologies such as renewable energy integration, distributed energy resources and demand responses may introduce significant uncertainties in analyzing of system-wide voltage stability. This paper starts with summarizing different known voltage instability mechanisms, and then focuses on a class of voltage instability which is induced by the singular surface of the algebraic manifold. We argue and demonstrate that this class can include both dynamic and static voltage instabilities. To determine the minimum distance to the point of voltage collapse, a new formulation is proposed on the algebraic manifold. This formulation is further converted into an optimal control framework for identifying the path with minimum distance on the manifold. Comprehensive numerical studies are conducted on some manifolds of different power system test cases and demonstrate that the proposed method yields candidates for the local shortest paths to the singular surface on the manifold for both the dynamic model and the static model. Simulations show that the proposed method can identify shorter paths on the manifold than the paths associated with the minimum Euclidean distances. Furthermore, the proposed method always locates the right path ending at the correct singular surface which is responsible for the voltage instability; while the Euclidean distance formulation can mistakenly find solutions on the wrong singular surface. A broad range of potential applications using the proposed method are also discussed.
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