Power system voltage small-disturbance stability studies based on the power flow equation

This study first studies power system small-disturbance stability at the operating point where the power flow (PF) equation encounters a saddle-node bifurcation. The authors demonstrate that the linearised model of the differential-algebraic equation (DAE) that describes the power system dynamics will have a zero eigenvalue at the equilibrium precisely when the PF Jacobian is singular. Note that the PF equation and DAE models are general ones. This clarifies a point in previous contributions on this relationship. Numerical results for two power system examples are used to demonstrate the theory, and finally the extension of the theory is discussed for the limit-induced bifurcation associated with the PF equation when some generators reach their reactive power limits.

[1]  C. Cañizares.  Conditions for saddle-node bifurcations in AC/DC power systems , 1995 .

[2]  M. Pai,et al.  Power system steady-state stability and the load-flow Jacobian , 1990 .

[3]  Federico Milano,et al.  Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  P. Kundur,et al.  Power system stability and control , 1994 .

[5]  C. W. Taylor.  Power System Voltage Stability , 1993 .

[6]  Antonio J. Conejo,et al.  Electric Energy Systems : Analysis and Operation , 2008 .

[7]  Y. Kataoka,et al.  Voltage stability limit of electric power systems with Generator reactive power constraints considered , 2005, IEEE Transactions on Power Systems.

[8]  Peter W. Sauer,et al.  Power System Dynamics and Stability , 1997 .

[9]  E. Bompard,et al.  A dynamic interpretation of the load-flow Jacobian singularity for voltage stability analysis , 1996 .

[10]  Ian Dobson,et al.  THE IRRELEVANCE OF LOAD DYNAMICS FOR THE LOADING MARGIN TO VOLTAGE COLLAPSE AND ITS SENSITIVITIES , 1994 .

[11]  Claudio A. Canizares,et al.  On the linear profile of indices for the prediction of saddle-node and limit-induced bifurcation points in power systems , 2003 .

[12]  Ian Dobson,et al.  Voltage collapse precipitated by the immediate change in stability when generator reactive power limits are encountered , 1992 .

[13]  H. Sasaki,et al.  A predictor/corrector scheme for obtaining Q-limit points for power flow studies , 2005, IEEE Transactions on Power Systems.

[14]  H. Schättler,et al.  Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability] , 1995 .

[15]  Claudio A. Canizares,et al.  Multiparameter bifurcation analysis of the south Brazilian power system , 2003 .

[16]  P. Kundur,et al.  Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions , 2004, IEEE Transactions on Power Systems.

[17]  Chen Chen,et al.  Novel Techniques for Continuation Method to Calculate the Limit-induced Bifurcation of the Power Flow Equation , 2010 .

[18]  Ian A. Hiskens,et al.  Direct calculation of reactive power limit points , 1996 .

[19]  V. A. Venikov,et al.  Estimation of electrical power system steady-state stability in load flow calculations , 1975, IEEE Transactions on Power Apparatus and Systems.