Non-parametric Probabilistic Load Flow using Gaussian Process Learning

TL;DR

This paper introduces a non-parametric probabilistic load flow method using Gaussian Process learning, capable of handling uncertainties in power systems with high accuracy and efficiency, applicable to various system types and conditions.

Contribution

It presents a novel GP-based NP-PLF technique that manages unknown uncertainty distributions and provides probabilistic bounds, improving operational decision-making in power systems.

Findings

Accurately learns voltage functions with few training samples.

Achieves about 0.001% relative error on 50,000 test points.

Handles diverse uncertainties in different power system configurations.

Abstract

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.