The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

The loading margin to a saddle-node or fold bifurcation measures the proximity to voltage collapse blackouts of electric power transmission systems. Sensitivities of the loading margin can be used to select controls to avoid voltage collapse. We analytically justify the use of static models to compute loading margins and their sensitivities and explain how the results apply to underlying dynamic models. The relation between fold bifurcations of the static models and saddle-node bifurcations of the underlying dynamic models is clarified.

[1]  Claudio A. Canizares,et al.  Point of collapse and continuation methods for large AC/DC systems , 1993 .

[2]  Eyad H. Abed,et al.  Bifurcations, chaos, and crises in voltage collapse of a model power system , 1994 .

[3]  T. Van Cutsem,et al.  Unified sensitivity analysis of unstable or low voltages caused by load increases or contingencies , 2005, IEEE Transactions on Power Systems.

[4]  R. H. Lasseter,et al.  Re-dispatching generation to increase power system security margin and support low voltage bus , 2000 .

[5]  Ian Dobson,et al.  Towards a theory of voltage collapse in electric power systems , 1989 .

[6]  I. Dobson.  Computing a closest bifurcation instability in multidimensional parameter space , 1993 .

[7]  C. Cañizares.  Calculating optimal system parameters to maximize the distance to saddle-node bifurcations , 1998 .

[8]  V. Ajjarapu,et al.  Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system , 1991 .

[9]  Hsiao-Dong Chiang,et al.  CPFLOW: a practical tool for tracing power system steady-state stationary behavior due to load and generation variations , 1995 .

[10]  Thierry Van Cutsem,et al.  Voltage Stability of Electric Power Systems , 1998 .

[11]  Chih-Wen Liu,et al.  New methods for computing a saddle-node bifurcation point for voltage stability analysis , 1995 .

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

[13]  D. Hill,et al.  Voltage stability indices for stressed power systems , 1993 .

[14]  Hua Li,et al.  Linear and nonlinear methods for contingency analysis in on-line voltage security assessments , 2009, 2009 IEEE Power & Energy Society General Meeting.

[15]  M. Golubitsky,et al.  Stable mappings and their singularities , 1973 .

[16]  Peter W. Sauer,et al.  Dynamic aspects of voltage/power characteristics (multimachine power systems) , 1992 .

[17]  I. Dobson.  Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systems , 1992 .

[18]  Hua Li,et al.  Applying bifurcation Analysis to Determine Optimal Placements of Measurement Devices for Power System Load Modeling , 2008, Int. J. Bifurc. Chaos.

[19]  David J. Hill,et al.  Nonlinear dynamic load models with recovery for voltage stability studies , 1993 .

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

[21]  L. Lu,et al.  Computing an optimum direction in control space to avoid stable node bifurcation and voltage collapse in electric power systems , 1992 .

[22]  B. Gao,et al.  Voltage Stability Evaluation Using Modal Analysis , 1992, IEEE Power Engineering Review.

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

[24]  Fernando L. Alvarado,et al.  Contingency ranking for voltage collapse via sensitivities from a single nose curve , 1999 .

[25]  I. Dobson,et al.  New methods for computing a closest saddle node bifurcation and worst case load power margin for voltage collapse , 1993 .

[26]  H. Okubo,et al.  Multiple time-scale power system dynamic simulation , 1993 .

[27]  F. Alvarado,et al.  Computation of closest bifurcations in power systems , 1994 .

[28]  Robert J. Thomas,et al.  A posturing strategy against voltage instabilities in electric power systems , 1988 .

[29]  J. Hale,et al.  Methods of Bifurcation Theory , 1996 .

[30]  Joe H. Chow,et al.  Dynamic voltage stability analysis of a single machine constant power load system , 1990, 29th IEEE Conference on Decision and Control.

[31]  I. Dobson,et al.  Sensitivity of Transfer Capability Margins with a Fast Formula , 2002, IEEE Power Engineering Review.

[32]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[33]  Venkataramana Ajjarapu,et al.  The continuation power flow: a tool for steady state voltage stability analysis , 1991 .

[34]  K. Iba,et al.  Calculation of critical loading condition with nose curve using homotopy continuation method , 1991 .

[35]  Fernando L. Alvarado,et al.  Sensitivity of the loading margin to voltage collapse with respect to arbitrary parameters , 1997 .

[36]  H. Schättler,et al.  Voltage dynamics: study of a generator with voltage control, transmission, and matched MW load , 1992 .

[37]  Felix F. Wu,et al.  Chaos in a simple power system , 1993 .

[38]  I. Dobson.  Distance to Bifurcation in Multidimensional Parameter Space: Margin Sensitivity and Closest Bifurcations , 2003 .

[39]  Ian Dobson,et al.  Quantifying transmission reliability margin , 2004 .

[40]  F. Alvarado,et al.  Sensitivity of Hopf bifurcations to power system parameters , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[41]  T. Van Cutsem,et al.  Voltage instability: phenomena, countermeasures, and analysis methods , 2000, Proc. IEEE.

[42]  Thomas J. Overbye,et al.  Q-V curve interpretations of energy measures for voltage security , 1994 .

[43]  Thierry Van Cutsem,et al.  Analysis of emergency voltage situations , 1993 .