Kernel Structure Design for Data-Driven Probabilistic Load Flow Studies

In power system analysis, probabilistic load flow (PLF) accounts for uncertainties stemming from power entities such as renewable generation systems and consumer demands. In this paper, we present a Gaussian Process (GP) emulator for enabling data-driven PLF on practical distribution networks (DNs) without requiring knowledge of underlying system parameters. The main novelty of our proposal lies in the kernel design process. An ideal kernel allows for greater efficiency during training and inferencing stages without being subject to common issues that include overfitting to the training dataset and poor accuracies. In this proposal, the kernel selection process is formulated as a bi-level optimization problem. This is a very difficult problem to solve as it is composed of discrete variables and non-convex constraints. We overcome these issues by proposing a best-response strategy refinement process to identify an efficient kernel configuration in an iterative manner. The convergence properties of this iterative algorithm and the approximating capabilities of the resulting GP emulator are established using potential game theoretic constructs, universal approximation theorem and representer theorem. The performance of the proposed emulator is then showcased via comprehensive simulations conducted on practical DNs and comparisons with the state-of-the-art.