An overview of approaches for modelling uncertainty in harmonic load-flow

Abstract

Harmonic distortion is a growing problem in all power systems (PS) around the world due to the increasing use of electronic power devices and nonlinear loads (NLL). Several methods have been developed for the computational analysis of PS harmonic load-flow (HLF). These approaches allow harmonic distortion to be estimated at each PS bus when NLLs (the harmonic sources) are distributed throughout a whole network. Some widely accepted deterministic formulations are used in HLF analysis; however, harmonic distortion in PS is a time-varying phenomenon because both linear loads (LL) and NLLs change non-predictably all the time. Moreover, network configuration also varies and such considerations make HLF calculation a mathematical problem which must be able to model the uncertainty associated with input data. Some approaches based on probability theory and others using fuzzy sets and possibility theories have been proposed for modeling such uncertainty. This paper was thus aimed at providing an overview regarding these approaches. The main HLF formulations within probabilistic and possibilistic frameworks have thus been introduced and some numerical comparisons have been made to clarify some concepts raised.