  In this letter, we present a novel Gaussian Process Learning-based
Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and
load uncertainties of arbitrary distribution. The proposed method relies on a
non-parametric Bayesian inference-based uncertainty propagation approach,
called Gaussian Process (GP). We also suggest a new type of sensitivity called
Subspace-wise Sensitivity, using observations on the interpretability of
GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems
show that the proposed method provides reasonably accurate solutions when
compared with Monte-Carlo Simulations (MCS) solutions at different levels of
uncertain renewable penetration as well as load uncertainties, while requiring
much less number of samples and elapsed time.
