Probabilistic Load-Flow Computation Using Point Estimate Method

TLDR

Uncertainties in bus injections and line parameters are assumed to be estimable or measurable. The study proposes a probabilistic load‑flow algorithm based on a point‑estimate method to quantify uncertainty in load‑flow solutions. The algorithm performs 2m load‑flow calculations for m uncertain parameters, uses the results to compute statistical moments, fits a probability distribution, and can be applied with any existing deterministic load‑flow program. The method’s performance was validated and shown to be comparable to Monte Carlo and combined simulation‑analytical techniques on several IEEE test systems.

Abstract

A new probabilistic load-flow solution algorithm based on an efficient point estimate method is proposed in this paper. It is assumed that the uncertainties of bus injections and line parameters can be estimated or measured. This paper shows how to estimate the corresponding uncertainty in the load-flow solution. The proposed method can be used directly with any existing deterministic load-flow program. For a system with m uncertain parameters, it uses 2m calculations of load flow to calculate the statistical moments of load-flow solution distributions by weighting the value of the solution evaluated at 2m locations. The moments are then used in the probability distribution fitting. Performance of the proposed method is verified and compared with those obtained from Monte Carlo simulation technique and combined simulation and analytical method using several IEEE test systems.