# Probabilistic Power Flow Calculation using Non-intrusive Low-rank Approximation Method

## TL;DR

This paper introduces a non-intrusive low-rank approximation method for probabilistic power flow analysis, providing accurate results with less computational effort, especially for high-dimensional problems involving renewable energy variability.

## Contribution

The paper presents a novel LRA-based approach that efficiently estimates probabilistic power flow solutions, outperforming traditional methods in high-dimensional scenarios.

## Key findings

- Accurately estimates probabilistic characteristics with less computation.
- Performs well on large-scale power systems like 1354-bus.
- Handles high-dimensional random inputs effectively.

## Abstract

In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, probability density function) of the PPF solutions. This method aims at building up a statistically-equivalent surrogate for the PPF solutions through a small number of power flow evaluations. By exploiting the retained tensor-product form of the univariate polynomial basis, a sequential correction-updating scheme is applied, making the total number of unknowns to be linear rather than exponential to the number of random inputs. Consequently, the LRA method is particularly promising for dealing with high-dimensional problems with a large number of random inputs. Numerical studies on the IEEE 39-bus, 118-bus, and 1354-bus systems show that the proposed method can achieve accurate probabilistic characteristics of the PPF solutions with much less computational effort compared to the Monte Carlo simulations. Even compared to the polynomial chaos expansion method, the LRA method can achieve comparable accuracy, while the LRA method is more capable of handling higher-dimensional problems. Moreover, numerical results reveal that the randomness brought about by the renewable energy resources and loads may inevitably affect the feasibility of dispatch/planning schemes.