Analytical Probabilistic Power Flow Approximation Using Invertible Neural Networks

TL;DR

This paper introduces an invertible neural network-based analytical probabilistic power flow method that accurately models voltage distributions without relying on Monte Carlo simulations, improving efficiency and precision.

Contribution

It presents a novel framework using invertible neural networks to directly approximate voltage distributions in probabilistic power flow, eliminating the need for Monte Carlo simulations.

Findings

Achieves high accuracy in power flow estimation.

Provides efficient analytical voltage distribution approximations.

Outperforms existing methods in numerical studies.

Abstract

Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC) based power flow (PF) simulations or simplified analytical approximations. While MC approaches are computationally intensive and demand substantial data storage, analytical approximations often compromise accuracy. In this paper, we propose a novel analytical PPF framework that eliminates the dependence on MC-based PF simulations and, in principle, enables an approximation of the analytical form of arbitrary voltage distributions. The core idea is to learn an explicit and invertible mapping between stochastic power injections and system voltages using invertible neural networks (INNs). By leveraging the Change of Variable Theorem, the proposed framework facilitates direct approximation of the analytical form of voltage probability distributions without repeated PF computations. Extensive numerical studies demonstrate that the proposed framework achieves state-of-the-art performance both as a high-accuracy PF solver and as an efficient analytical PPF estimator.