Verbic, GregorCanizares, Claudio A.2025-07-022025-07-022006-11-300885-8950https://doi.org/10.1109/TPWRS.2006.881146https://hdl.handle.net/10012/21944(© 2006 IEEE) Verbic, G., & Canizares, C. A. (2006). Probabilistic optimal power flow in electricity markets based on a two-point estimate method. IEEE Transactions on Power Systems, 21(4), 1883–1893. https://doi.org/10.1109/tpwrs.2006.881146This paper presents an application of a two-point estimate method (2PEM) to account for uncertainties in the optimal power flow (OPF) problem in the context of competitive electricity markets. These uncertainties can be seen as a by-product of the economic pressure that forces market participants to behave in an “unpredictable” manner; hence, probability distributions of locational marginal prices are calculated as a result. Instead of using computationally demanding methods, the proposed approach needs2nruns of the deterministic OPF fornuncertain variables to get the result in terms of the first three moments of the corresponding probability density functions. Another advantage of the 2PEM is that it does not require derivatives of the nonlinear function used in the computation of the probability distributions. The proposed method is tested on a simple three-bus test system and on a more realistic 129-bus test system. Results are compared against more accurate results obtained from MCS. The proposed method demonstrates a high level of accuracy for mean values when compared to the MCS; for standard deviations, the results are better in those cases when the number of uncertain variables is relatively low or when their dispersion is not large.enprobabilistic optimal power flowelectricity marketstwo-point estimate methodprobability distributionuncertaintyArticle10.1109/tpwrs.2006.881146