Pirnia, MehrdadCanizares, Claudio A.Bhattacharya, KankarVaccaro, Alfredo2025-07-312025-07-312014-05-020885-89501558-0679https://doi.org/10.1109/TPWRS.2014.2316114https://hdl.handle.net/10012/22075(© 2014 IEEE) Pirnia, M., Canizares, C. A., Bhattacharya, K., & Vaccaro, A. (2014). A novel affine arithmetic method to solve optimal power flow problems with uncertainties. IEEE Transactions on Power Systems, 29(6), 2775–2783. https://doi.org/10.1109/tpwrs.2014.2316114An 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.enoptimal power flowgeneration uncertaintyaffine arithmeticinterval analysisArticle10.1109/tpwrs.2014.2316114