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

Non-parametric Probabilistic Load Flow using Gaussian Process Learning