Deep-quantile-regression-based surrogate model for joint chance-constrained optimal power flow with renewable generation

TL;DR

This paper introduces a learning-based surrogate model for joint chance-constrained optimal power flow that does not rely on network parameters, using deep quantile regression and data augmentation to handle renewable generation uncertainties.

Contribution

It develops a novel surrogate modeling approach using deep quantile regression to reformulate joint chance constraints without requiring network parameters.

Findings

Achieves high feasibility and optimality in test systems.

Eliminates the need for accurate network parameters.

Enhances prediction accuracy through data augmentation and calibration.

Abstract

Joint chance-constrained optimal power flow (JCC-OPF) is a promising tool to manage uncertainties from distributed renewable generation. However, most existing works are based on power flow equations, which require accurate network parameters that may be unobservable in many distribution systems. To address this issue, this paper proposes a learning-based surrogate model for JCC-OPF with renewable generation. This model equivalently converts joint chance constraints in quantile-based forms and introduces deep quantile regression to replicate them, in which a multi-layer perceptron (MLP) is trained with a special loss function to predict the quantile of constraint violations. Another MLP is trained to predict the expected power loss. Then, the JCC-OPF can be formulated without network parameters by reformulating these two MLPs into mixed-integer linear constraints. To further improve its performance, two pre-processing steps, i.e., data augmentation and calibration, are developed. The former trains a simulator to generate more training samples for enhancing the prediction accuracy of MLPs. The latter designs a positive parameter to calibrate the predictions of MLPs so that the feasibility of solutions can be guaranteed. Numerical experiments based on the IEEE 33- and 123-bus systems validate that the proposed model can achieve desirable feasibility and optimality simultaneously with no need for network parameters.