Point Estimate Schemes to Solve the Probabilistic Power Flow

TLDR

Uncertainty in power systems arises from load demand and generation outages, and point‑estimate methods provide a computationally efficient way to handle such stochastic problems, though prior studies have only considered the two‑point approach. This study evaluates Hong’s four point‑estimate schemes for probabilistic power flow, aiming to assess their behavior under uncertainty. The authors model input random variables with binomial and normal distributions. In IEEE 14‑ and 118‑bus test systems, the schemes outperformed Monte Carlo, with the best performance observed when many continuous and discrete random variables were involved.

Abstract

This paper analyzes the behavior of Hong's point estimate methods to account for uncertainties on the probabilistic power flow problem. This uncertainty may arise from different sources as load demand or generation unit outages. Point estimate methods constitute a remarkable tool to handle stochastic power system problems because good results can be achieved by using the same routines as those corresponding to deterministic problems, while keeping low the computational burden. In previous works related to power systems, only the two-point estimate method has been considered. In this paper, four different Hong's point estimate schemes are presented and tested on the probabilistic power flow problem. Binomial and normal distributions are used to model input random variables. Results for two different case studies, based on the IEEE 14-bus and IEEE 118-bus test systems, respectively, are presented and compared against those obtained from the Monte Carlo simulation. Particularly, this paper shows that the use of the scheme provides the best performance when a high number of random variables, both continuous and discrete, are considered.