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 & Management Optimization, 2010, 6 (2) : 315-331. doi: 10.3934/jimo.2010.6.315
 [1] Xiaojiao Tong, Felix F. Wu, Yongping Zhang, Zheng Yan, Yixin Ni. A semismooth Newton method for solving optimal power flow. Journal of Industrial & Management Optimization, 2007, 3 (3) : 553-567. doi: 10.3934/jimo.2007.3.553 [2] Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670-677. doi: 10.3934/proc.2015.0670 [3] Laurence Guillot, Maïtine Bergounioux. Existence and uniqueness results for the gradient vector flow and geodesic active contours mixed model. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1333-1349. doi: 10.3934/cpaa.2009.8.1333 [4] Fabian Rüffler, Volker Mehrmann, Falk M. Hante. Optimal model switching for gas flow in pipe networks. Networks & Heterogeneous Media, 2018, 13 (4) : 641-661. doi: 10.3934/nhm.2018029 [5] Colm Connaughton, John R. Ockendon. Interactions of point vortices in the Zabusky-McWilliams model with a background flow. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1795-1807. doi: 10.3934/dcdsb.2012.17.1795 [6] Mohamed Benyahia, Massimiliano D. Rosini. A macroscopic traffic model with phase transitions and local point constraints on the flow. Networks & Heterogeneous Media, 2017, 12 (2) : 297-317. doi: 10.3934/nhm.2017013 [7] Kit Yan Chan, Changjun Yu, Kok Lay Teo, Sven Nordholm. Essential issues on solving optimal power flow problems using soft-computing. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 341-351. doi: 10.3934/naco.2014.4.341 [8] R.L. Sheu, M.J. Ting, I.L. Wang. Maximum flow problem in the distribution network. Journal of Industrial & Management Optimization, 2006, 2 (3) : 237-254. doi: 10.3934/jimo.2006.2.237 [9] Theodore Tachim-Medjo. Optimal control of a two-phase flow model with state constraints. Mathematical Control & Related Fields, 2016, 6 (2) : 335-362. doi: 10.3934/mcrf.2016006 [10] K. Domelevo. Well-posedness of a kinetic model of dispersed two-phase flow with point-particles and stability of travelling waves. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 591-607. doi: 10.3934/dcdsb.2002.2.591 [11] Najwa Najib, Norfifah Bachok, Norihan Md Arifin, Fadzilah Md Ali. Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019041 [12] Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255 [13] Chun Zong, Gen Qi Xu. Observability and controllability analysis of blood flow network. Mathematical Control & Related Fields, 2014, 4 (4) : 521-554. doi: 10.3934/mcrf.2014.4.521 [14] Jingxian Sun, Shouchuan Hu. Flow-invariant sets and critical point theory. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 483-496. doi: 10.3934/dcds.2003.9.483 [15] Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019115 [16] Behrouz Kheirfam, Guoqiang Wang. An infeasible full NT-step interior point method for circular optimization. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 171-184. doi: 10.3934/naco.2017011 [17] Stefan Berres, Ricardo Ruiz-Baier, Hartmut Schwandt, Elmer M. Tory. An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks & Heterogeneous Media, 2011, 6 (3) : 401-423. doi: 10.3934/nhm.2011.6.401 [18] T. Tachim Medjo. On the Newton method in robust control of fluid flow. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1201-1222. doi: 10.3934/dcds.2003.9.1201 [19] Artyom Nahapetyan, Panos M. Pardalos. A bilinear relaxation based algorithm for concave piecewise linear network flow problems. Journal of Industrial & Management Optimization, 2007, 3 (1) : 71-85. doi: 10.3934/jimo.2007.3.71 [20] Gunhild A. Reigstad. Numerical network models and entropy principles for isothermal junction flow. Networks & Heterogeneous Media, 2014, 9 (1) : 65-95. doi: 10.3934/nhm.2014.9.65

2018 Impact Factor: 1.025