Non-parametric probabilistic load flow using Gaussian process learning

Highlights: • Novel non-parametric probabilistic load flow for uncertain power injections. • No need of information about the type of uncertainty distribution. • A semi-explicit form of power flow solutions. • Accurate statistical information on power flow. • Probabilistic learning bound (PLB) for convergence criteria. The load flow problem is fundamental to characterize the equilibrium behavior of a power system. Uncertain power injections such as those due to demand variations and intermittent renewable resources will change the system's equilibrium unexpectedly, and thus potentially jeopardizing the system's reliability and stability. Understanding load flow solutions under uncertainty becomes imperative to ensure the seamless operation of a power system. 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" form of load flow solutions by implementing the learning and testing steps that 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. 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 an average percentage relative error of the order of $10^{-3}$% on 50,000 test points.