This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.<\/p>\r\n","references":"[1]\tN.R. Shivakumar and A. Jain, \"A review of power system dynamic state estimation techniques,\u201d in Power Syst. Technology and IEEE Power India Conf., New Delhi, India, 2008, pp.1\u20136.\r\n[2]\tR. Neela and P. Aravindhababu, \"A new decoupling strategy for power system state estimation,\u201d Int. J. of Energy Convers. and Management, vol.50, pp.2047\u20132051, 2009.\r\n[3]\tA. Thabet, S. Chniba, D. Gaetan, M. Boutayeb and M.N. Abdelkrim, \"Power systems load \ufb02ow and state estimation: Modified methods and evaluation of stability and speeds computing.\u201d Int. Rev. of Electr. Eng., vol.5, pp.1110\u20131118, 2010.\r\n[4]\tE. Scholtz, \"Observer based monitors and distributed wave controllers for electromechanical disturbances in power systems,\u201d Ph.D. dissertation, Massachusetts Institute Technology, USA, 2004.\r\n[5]\tM.A. Pai, P.W. Sauer, B.C. Lesieutre and R. Adapa, \"Structural stability in power systems-effect of load models,\u201d IEEE Trans. on Power Syst., vol.10, pp.609\u2013615, 1995.\r\n[6]\tC.J. Dafis, \"An observbility formulation for nonlinear power systems modeled as differential algebraic systems,\u201d Ph.D. dissertation, Drexel university, PA, USA, 2005.\r\n[7]\tA.S. Debes and R.E. Larson, \"A dynamic estimator for tracking the state of a power system.\u201d IEEE Trans. on Power App. And Syst., vol.89, pp.1670\u20131678, 1970.\r\n[8]\tJ. Aslund and E. Frisk, \"An observer for nonlinear differential-algebraic systems,\u201d Autmatica, vol.42, pp.959\u2013965, 2006.\r\n[9]\tT. Wichmann, \"Simplification of nonlinear DAE systems with index tacking,\u201d in European Conf. on Circuit Theory and Design, Espoo, Finland, 2001, pp.173\u2013176.\r\n[10]\tR. Nikoukhah, A. Willsky and B. Levy, \"Kalman filtering and riccati equations for descriptor systems,\u201d IEEE Trans. on Autom. Control, vol.37, pp.1325\u20131342, 1992.\r\n[11]\tM.F. Isabel and F.P. Barbosa, \"Square root filter algorithm for dynamic state estimation of electric power systems,\u201d in Electrotechnical Conference, 7th Mediterranean, Antalya, Turkey, 1994, pp.877\u2013880.\r\n[12]\tK. Shih and S. Huang, \"Application of a robust algorithm for dynamic state estimation of a power system.\u201d IEEE Trans. on Power Syst., vol.17, pp.141\u2013147, 2002.\r\n[13]\tK.Yu, N. Watson and J. Arrillaga, \"An adaptive Kalman filter for dynamic harmonic state estimation and harmonic injection tracking,\u201d IEEE Trans. on Power Delivery, vol.20, pp.1577\u20131584, 2005.\r\n[14]\tH. Ma and A. Grigis, \"Identification and tracking of harmonic sources in a power system using Kalman filter,\u201d IEEE Trans. on Power Delivery, vol.11, pp.1659\u20131665, 1996.\r\n[15]\tH. Beids and G. Heydt, \"Dynamic state estimation of power system harmonics using kalman filter methodology,\u201d IEEE Trans. on Power Delivery, vol.6, pp.1663\u20131670, 1991.\r\n[16]\tF. Chowdhury, J. Christensen and J. Aravena, \"Power system fault detection and state estimation using Kalman filter with hypothesis testing,\u201d IEEE Trans. on Power Delivery, vol.6, pp.1025\u20131030, 1991.\r\n[17]\tRoytelman and S. Shahidehpour, \"State estimation for electric power distribution systems in quasi real-time conditions,\u201d IEEE Trans. on Power Delivery, vol.8, pp.2009\u20132015, 1993.\r\n[18]\tB.W. Gordon, \"Dynamic sliding manifolds for realization of high index differential-algebraic systems,\u201d Asian J. of Control, vol.5, pp.454\u2013466, 2003.\r\n[19]\tD.C. Tarraf and H.H. Asada, \"On the nature and stability of differential-algebraic systems,\u201d in Proc. American Control Conf., Anchorage, USA, 2002, pp.3546\u20133551.\r\n[20]\tM. Eremia, J. Trecat and A. Germond, \"R\u00e9seaux \u00e9lectriques: Aspects Actuels, 2nd ed. Bucuresti, EdituraTehnica, 2000.\r\n[21]\tD. Karlsson and D.J. Hill, \"Modelling and identification of nonlinear dynamic loads in power systems,\u201d IEEE Trans. on Power Syst., vol.9, pp.157\u2013166, 1994.\r\n[22]\tK. Judd, \"Nonlinear state estimation in distinguishable states and the extended Kalman filter,\u201d Physica D: Nonlinear Phenomena, vol.183, pp.273\u2013281,2003.\r\n[23]\tV.M. Becerra, P.D. Roberts and G.W. Griffiths, \"Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations,\u201d Control Eng. Practice, vol.9, pp.267\u2013281, 2001.\r\n[24]\tM. Boutayeb and C. Aubry, \"A strong tracking extended Kalman observer for nonlinear discrete-time systems,\u201d IEEE Trans. on Autom. Control, vol.44, pp.1550\u20131556, 1999.\r\n[25]\tM. Boutayeb, \"Identification of nonlinear systems in the presence of unknown but bounded disturbances,\u201d IEEE Trans. on Autom. Control, vol.45, pp.1503\u20131507, 2000.\r\n[26]\tY. Song and J. Grizzle, \"The extended kalman filter as a local asymptotic observer for non linear discrete-time systems,\u201d J. of Math. Syst. Estimation and Control, vol.5, pp. 59\u201378, 1995.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 74, 2013"}