# American Institute of Mathematical Sciences

April  2010, 6(2): 315-331. doi: 10.3934/jimo.2010.6.315

## How to efficiently incorporate facts devices in optimal active power flow model

 1 Universidade Estadual Paulista, Faculdade de Engenharia de Guaratinguetá, Av. Dr. Ariberto Pereira da Cunha, 333, DMA, C.P. 0205, Guaratinguetá, SP, Brazil 2 Applied Mathematics Department, State University of Campinas, Praça Sérgio Buarque de Holanda, 651, C.P. 606, Campinas, SP, Brazil 3 Universidade Estadual Paulista, Faculdade de Engenharia de Ilha Solteira, Departamento de Engenharia Elétrica, Avenida Brasil Centro, 56, C.P. 31, Ilha Solteira, SP, Brazil 4 Electrical and Computer Engineering School, State University of Campinas, Av. Albert Einstein, 400, C.P. 6101, Campinas, SP, Brazil

Received  November 2008 Revised  November 2009 Published  March 2010

This paper presents for the first time how to easily incorporate facts devices in an optimal active power flow model such that an efficient interior-point method may be applied. The optimal active power flow model is based on a network flow approach instead of the traditional nodal formulation that allows the use of an efficiently predictor-corrector interior point method speed up by sparsity exploitation. The mathematical equivalence between the network flow and the nodal models is addressed, as well as the computational advantages of the former considering the solution by interior point methods. The adequacy of the network flow model for representing facts devices is presented and illustrated on a small 5-bus system. The model was implemented using Matlab and its performance was evaluated with the 3,397-bus and 4,075- branch Brazilian power system which show the robustness and efficiency of the formulation proposed. The numerical results also indicate an efficient tool for optimal active power flow that is suitable for incorporating facts devices.
Citation: Anibal T. Azevedo, Aurelio R. L. Oliveira, Marcos J. Rider, Secundino Soares. How to efficiently incorporate facts devices in optimal active power flow model. Journal of Industrial and Management Optimization, 2010, 6 (2) : 315-331. doi: 10.3934/jimo.2010.6.315
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