@article{pir-can-bha-vac-14-aa-powflow,
  author = {Pirnia, Mehrdad and Ca{\~n}izares, Claudio A. and Bhattacharya, Kankar and Vaccaro, Alfredo},
  title = {A Novel Affine Arithmetic Method to Solve Optimal Power Flow Problems With Uncertainties}, 
  journal = {IEEE Transactions on Power Systems}, 
  year = 2014,
  volume = {29},
  number = {6},
  pages = {2775-2783},
  doi = {10.1109/TPWRS.2014.2316114},
  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.}
}