# Formulations

## Abstract Models

PowerModelsDistribution.LPUBFDiagModelType

LinDist3Flow per Arnold et al. (2016), using vector variables for power, voltage and current

D. B. Arnold, M. Sankur, R. Dobbe, K. Brady, D. S. Callaway and A. Von Meier, "Optimal dispatch of reactive power for voltage regulation and balancing in unbalanced distribution systems," 2016 IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, 2016, pp. 1-5, doi: 10.1109/PESGM.2016.7741261.

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## Power Models

PowerModelsDistribution.ACPUPowerModelType

AC power flow Model with polar bus voltage variables. The seminal reference of AC OPF:

@article{carpentier1962contribution,
title={Contribution to the economic dispatch problem},
author={Carpentier, J},
journal={Bulletin de la Societe Francoise des Electriciens},
volume={3},
number={8},
pages={431--447},
year={1962}
}

History and discussion:

@techreport{Cain2012,
author = {Cain, Mary B and {O' Neill}, Richard P and Castillo, Anya},
title = {{History of optimal power flow and Models}},
year = {2012}
pages = {1--36},
url = {https://www.ferc.gov/industries/electric/indus-act/market-planning/opf-papers/acopf-1-history-Model-testing.pdf}
}
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PowerModelsDistribution.ACRUPowerModelType

AC power flow Model with rectangular bus voltage variables.

@techreport{Cain2012,
author = {Cain, Mary B and {O' Neill}, Richard P and Castillo, Anya},
pages = {1--36},
title = {{History of optimal power flow and Models}},
url = {https://www.ferc.gov/industries/electric/indus-act/market-planning/opf-papers/acopf-1-history-Model-testing.pdf}
year = {2012}
}
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PowerModelsDistribution.IVRUPowerModelType

Current voltage formulation of AC OPF. The formulation uses rectangular coordinates for both current and voltage. Note that, even though Kirchhoff's circuit laws are linear in current and voltage, this formulation is nonconvex due to constants power loads/generators and apparent power limits.

@techreport{ONeill2012,
author = {{O' Neill}, Richard P and Castillo, Anya and Cain, Mary B},
pages = {1--18},
title = {{The IV formulation and linear approximations of the ac optimal power flow problem}},
year = {2012}
}

Applicable to problem formulations with _iv in the name.

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PowerModelsDistribution.DCPUPowerModelType

Linearized 'DC' power flow Model with polar voltage variables. This model is a basic linear active-power-only approximation, which uses branch susceptance values br_b = -br_x / (br_x^2 + br_x^2) for determining the network phase angles. Furthermore, transformer parameters such as tap ratios and phase shifts are not considered as part of this model. It is important to note that it is also common for active-power-only approximations to use 1/br_x for determining the network phase angles, instead of the br_b value that is used here. Small discrepancies in solutions should be expected when comparing active-power-only approximations across multiple tools.

@ARTICLE{4956966,
author={B. Stott and J. Jardim and O. Alsac},
journal={IEEE Transactions on Power Systems},
title={DC Power Flow Revisited},
year={2009},
month={Aug},
volume={24},
number={3},
pages={1290-1300},
doi={10.1109/TPWRS.2009.2021235},
ISSN={0885-8950}
}
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