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Center for Nonlinear Studies |
The ongoing democratization of energy is creating a high degree of operational uncertainty in electrical distribution networks. To combat this uncertainty, advanced Uncertainty Quantification (UQ) tools can be used to characterize the forecasted operational state of a network via probabilistic power flow (PPF) analysis. Such UQ tools, though, often suffer from the dreaded curse of dimensionality, requiring thousands of power flow solves in order to characterize the parameters inside the resulting UQ models. In massive distribution networks, with three unbalanced phases and tens of thousands of state variables, sequential power flow solves can become a serious computational bottleneck. This talk develops a computationally efficient algorithm which speeds up the PPF problem by leveraging a variety of tools from numerical linear algebra. These tools, grounded in fast matrix inversion techniques and a dynamic projection-based model order reduction scheme, allow us to solve the PPF problem an order of magnitude faster than the traditional Newton method applied to a full order model. Along the way, we will highlight how the selection and application of tools from numerical linear algebra benefit greatly from a thorough understanding of the underlying problem and its physical characteristics.
Host: Carleton Coffrin