A Novel Affine Arithmetic Method to Solve Optimal Power Flow Problems With Uncertainties

Author

Pirnia, Mehrdad ; Canizares, Claudio A. ; Bhattacharya, Kankar ; Vaccaro, Alfredo

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada

Volume

29

Issue

6

fYear

2014

fDate

Nov. 2014

Firstpage

2775

Lastpage

2783

Abstract

An affine arithmetic (AA) method is proposed in this paper to solve the optimal power flow (OPF) problem with uncertain generation sources. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a probability density function (pdf). The proposed AA-based OPF problem is used to determine the operating margins of the thermal generators in systems with uncertain wind and solar generation dispatch. The AA-based approach is benchmarked against Monte Carlo simulation (MCS) intervals in order to determine its effectiveness. The proposed technique is tested and demonstrated on the IEEE 30-bus system and also a real 1211-bus European system.

Keywords

IEEE standards; Monte Carlo methods; affine transforms; busbars; load flow; power generation dispatch; solar power; wind power; 1211-bus European system; AA-based OPF problem; IEEE 30-bus system; MCS; Monte Carlo simulation; affine arithmetic method; control variable; model error; optimal power flow; pdf; probability density function; solar generation dispatch; thermal generator operating margin determination; uncertain generation source; wind generation dispatch; Chebyshev approximation; Load flow; Mathematical model; Power generation dispatch; Reactive power; Uncertainty; Affine arithmetic; generation uncertainty; interval analysis; optimal power flow;

fLanguage

English

Journal_Title

Power Systems, IEEE Transactions on

Publisher

ieee

ISSN

0885-8950

Type

jour

DOI

10.1109/TPWRS.2014.2316114

Filename

6809857