Data-Driven Stochastic AC-OPF using Gaussian Processes
Mile Mitrovic
The thesis focuses on developing a data-driven algorithm, based on machine
learning, to solve the stochastic alternating current (AC) chance-constrained
(CC) Optimal Power Flow (OPF) problem. Although the AC CC-OPF problem has been
successful in academic circles, it is highly nonlinear and computationally
demanding, which limits its practical impact. The proposed approach aims to
address this limitation and demonstrate its empirical efficiency through
applications to multiple IEEE test cases. To solve the non-convex and
computationally challenging CC AC-OPF problem, the proposed approach relies on
a machine learning Gaussian process regression (GPR) model. The full Gaussian
process (GP) approach is capable of learning a simple yet non-convex
data-driven approximation to the AC power flow equations that can incorporate
uncertain inputs. The proposed approach uses various approximations for
GP-uncertainty propagation. The full GP CC-OPF approach exhibits highly
competitive and promising results, outperforming the state-of-the-art
sample-based chance constraint approaches. To further improve the robustness
and complexity/accuracy trade-off of the full GP CC-OPF, a fast data-driven
setup is proposed. This setup relies on the sparse and hybrid Gaussian
processes (GP) framework to model the power flow equations with input
uncertainty.