  In this work, we propose a non-parametric probabilistic load flow (NP-PLF)
technique based on the Gaussian Process (GP) learning to understand the power
system behavior under uncertainty for better operational decisions. The
technique can provide "semi-explicit" power flow solutions by implementing the
learning and testing steps which map control variables to inputs. The proposed
NP-PLF leverages upon GP upper confidence bound (GP-UCB) sampling algorithm.
The salient features of this NP-PLF method are: i) applicable for power flow
problem having power injection uncertainty with an unknown class of
distribution; ii) providing probabilistic learning bound (PLB) which further
provides control over the error and convergence; iii) capable of handling
intermittent distributed generation as well as load uncertainties, and iv)
applicable to both balanced and unbalanced power flow with different type and
size of power systems. The simulation results performed on the IEEE 30-bus and
IEEE 118-bus system show that the proposed method can learn the voltage
function over the power injection subspace using a small number of training
samples. Further, the testing with different input uncertainty distributions
indicates that complete statistical information can be obtained for the
probabilistic load flow problem with average percentage relative error of order
$10^{-3}$\% on 50000 test points.
