AMPS: Scalable Methods for Real-time Estimation of Power Systems under Uncertainty

The United States power grid, which is arguably the most complex civil engineering system, is facing unprecedented challenges stemming from the advent of new sensing technologies, adoption of large amounts of renewable energy, and emergence of smart grids. Power system operators rely on estimating parameters for monitoring power systems in real-time, detecting risks, verifying technical compliance, and decision-making. However, this estimation problem is particularly challenging due to the large size and complexity of the power grid, as well as the need to perform such tasks in real-time. Decisions about the best and safe power grid operations depend critically on knowing the current parameters and states of the grid. This research will address these challenges by developing computational methods that are scalable, exploit problem structures, and are robust with respect to uncertainties in the power system models. In particular, the project will address identifying the most influential parameters in the power system models and developing mathematical tools to efficiently estimate power system model parameters from data with quantified uncertainties. The project will provide training opportunities for students from underrepresented groups in STEM. Bayesian inversion facilitates the integration of data with complex physics-based models, such as power systems, to quantify the uncertainties in model predictions. The algorithmic developments for Bayesian inversion in the context of power grid, face a number of fundamental challenges. Among those are high-dimensionality of the inversion parameters (stemming from the size of the power grid), expensive and real-time evaluations of the parameter-to-observable maps, and model uncertainty additional to the uncertainty in inversion parameters. The project will develop mathematically rigorous, computationally efficient, and robust methods that overcome mathematical and computational barriers in solving large-scale estimation problems governed by uncertain power system models. In particular, the investigators will build on the existing state-of-the-art for Bayesian inversion algorithms and extend these by using (i) sensitivity analysis to classify the uncertain parameters based on their importance, (ii) the Bayesian approximation error approach to incorporate additional uncertainty into the Bayesian inverse problem governed by power grid models, (iii) surrogate modeling for power systems (via machine learning and dimension reduction techniques) and (iv) second-order methods and approximations of second derivative information to reduce the computational cost when solving the Bayesian inverse problem. The algorithms, mathematical findings, and open-source codes will be disseminated through peer-reviewed journal papers and presentations at conferences and workshops. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.