@article {7153,
	title = {A novel affine arithmetic method to solve optimal power flow problems with uncertainties},
	journal = {IEEE Transactions on Power Systems},
	volume = {29},
	year = {2014},
	pages = {2775-2783},
	abstract = {<p>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.</p><p>\&nbsp;</p>},
	author = {Mehrdad Pirnia and Claudio A Ca{\~n}izares and Kankar Bhattacharya and Alfredo Vaccaro}
}
