Gaussian Process Learning-Based Probabilistic Optimal Power Flow

Abstract

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 nonparametric 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 and load uncertainties. The proposed method requires a lesser number of samples and elapsed time. The non-parametric nature of the proposed method is manifested by testing uncertain injections that follow various distributions in the 118-bus system. The low error value results verify the proposed method's capability of working with different types of input uncertainty distributions.

A Framework for Analytical Power Flow Solution Using Gaussian Process Learning

“…Further, [22], [23] are time series forecasting works which is the first frontier where GP was applied in power system being a supervised learning tool. The works [24]- [27] are the ones where GP is directly used to learn a particular input-output relationship as a black-box, without exploring the major possibilities of analysis, except in [24] where attempts have been made to exploit interpretability of GP and provide understanding about results. Further, the work [24] uses GP to perform uncertainty quantification (UQ) for ACOPF.…”

“…The works [24]- [27] are the ones where GP is directly used to learn a particular input-output relationship as a black-box, without exploring the major possibilities of analysis, except in [24] where attempts have been made to exploit interpretability of GP and provide understanding about results. Further, the work [24] uses GP to perform uncertainty quantification (UQ) for ACOPF. That work's objective is limited to exploit the non-parametric nature of GP for efficient UQ.…”

Optimal Steady-State Voltage Control Using Gaussian Process Learning

“…These two features, prior and interpretability, make GPR very useful for learning the physical models such as power flow relationships. In the power system applications, GPR is used for wind power forecast [23], small-signal stability [24], demand forecast [25], and probabilistic optimal power flow [26].…”

State-Aware Stochastic Optimal Power Flow

“…The same can also be interpreted as non-parametric affine policy. For details of ACOPF learning via GP, see [24].…”

“…Now, we employ the linear covariance function to learn an optimal set-point p g i as an affine function of the uncertain load ξ, i.e., p g i (ξ) . The learning mechanism is similar to the one used recently in [24]. The core concept in designing affine policy is to learn the optimal generation setpoints using GP regression with linear covariance function and then obtain the standard affine form with sensitivity and intercept coefficients.…”