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The objective function in OPF can take on different forms relating to active or reactive power quantities that we wish to either minimise or maximise. For example we may wish to minimise transmission losses or minimise real power generation costs on a power network.
Other power flow solution methods like stochastic optimization incorporate the uncertainty found in modeling power systems by using the probability distributions of certain variables whose exact values are not known. When uncertainties in the constraints are present, such as for dynamic line ratings, chance constrained optimization can be used where the probability of violating a constraint is limited to a certain value<ref>Giraldo, Juan S., Juan Camilo López, Jhon A. Castrillon, Marcos J. Rider, and Carlos A. Castro. "Probabilistic OPF model for unbalanced three-phase electrical distribution systems considering robust constraints." IEEE Transactions on Power Systems 34, no. 5 (2019): 3443-3454. https://doi.org/10.1109/TPWRS.2019.2909404</ref>. Another technique to model variability is the [[Monte Carlo method]], in which different combinations of inputs and resulting outputs are considered based on the probability of their occurrence in the real world. This method can be applied to simulations for system security and unit commitment risk, and it is increasingly being used to model probabilistic load flow with renewable and/or distributed generation.<ref>Banerjee, Binayak, and Syed Islam. "Modelling and Simulation of Power Systems." Smart Power Systems and Renewable Energy System Integration. By Dilan Jayaweera. Vol. 57. Cham: Springer International, 2016. 15-26. Studies in Systems, Decision and Control. Springer Link. Web. 22 Nov. 2016. <nowiki>http://link.springer.com/book/10.1007%2F978-3-319-30427-4</nowiki></ref>
==Models of competitive behavior==
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