JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2010.6.315 MANAGEMENT OPTIMIZATION Volume 6, Number 2, May 2010 pp. 315–331 HOW TO EFFICIENTLY INCORPORATE FACTS DEVICES IN OPTIMAL ACTIVE POWER FLOW MODEL Anibal T. Azevedo Universidade Estadual Paulista, Faculdade de Engenharia de Guaratinguet´ a Av. Dr. Ariberto Pereira da Cunha, 333, DMA, C.P. 0205 Guaratinguet´ a, SP, Brazil Aurelio R. L. Oliveira Applied Mathematics Department, State University of Campinas Pra¸ ca S´ ergio Buarque de Holanda, 651, C.P. 606 Campinas, SP, Brazil Marcos J. Rider Universidade Estadual Paulista, Faculdade de Engenharia de Ilha Solteira Departamento de Engenharia El´ etrica, Avenida Brasil Centro, 56, C.P. 31 Ilha Solteira, SP, Brazil Secundino Soares Electrical and Computer Engineering School, State University of Campinas Av. Albert Einstein, 400, C.P. 6101 Campinas, SP, Brazil (Communicated by Liqun Qi) Abstract. 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 pre- sented 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. 2000 Mathematics Subject Classification. Primary: 58F15, 58F17; Secondary: 53C35. Key words and phrases. Optimal active power flow, facts devices, network flow model, interior point method. This research was supported in part by the Foundation for the Support of Research of the State of S˜ ao Paulo (FAPESP), by the Brazilian Council for the Development of Science and Technology (CNPq), and by the Superior Level Coordination for Personal Development (CAPES). 315