Differential Geometry Methods in Electric Energy Systems with Distributed Renewable Energy Resources

In recent years extreme weather conditions such as serious floods in China and Europe, long-lasting wild fires in America and Australia, extreme winter cyclones in the southern part of the U.S., and extreme heat in the Arctic circle occurred more frequently than often, suggesting a prelude of the potential global climate change. To prevent, or at least alleviate, the devastating consequences of abrupt climate change, the world has reached a consensus of reducing the carbon emission from human activities. Efforts include re-electrifying traditional industry, promoting electric vehicles in transportation systems, and replacing the fossil fuels with the renewable energy in the electric power generation. These revolutions depend heavily on the reliability and resiliency of the electric energy systems. However, due to the intermittent feature and the large spatial dispersion of the renewable energy, the near future electric energy systems are expected to work at a huge number of different modes with frequent changes. This situation brings a great complexity challenge to the traditional operational methods which heavily rely on good predictions and a few typical system changing directions.

In this talk, we will discuss how to apply differential geometry methods to dealing with the complexity challenge introduced by the distributed renewable energy resources. Specifically, we will focus on the long-term voltage stability problem. An introduction to the traditional voltage stability analysis methods will be summarized at first. Then, we will demonstrate and visualize the drawbacks of the traditional methods based on the Euclidean metric distance formulation. To cope with these drawbacks, we re-establish the voltage stability analysis and computations on the manifold through an optimal control framework and differential geometry methods, and illustrate its accuracy in predicting the shortest voltage collapse path. A computationally efficient approximation will be further discussed to further validate the applicability of our proposed framework in large-scale implementations. Finally, some new research observations based on curvature tensors will be presented and compared.