Random load fluctuations and collapse probability of a power system operating near codimension 1 saddle-node bifurcation

For a power system operating in the vicinity of the power transfer limit of its transmission system, effect of stochastic fluctuations of power loads can become critical as a sufficiently strong such fluctuation may activate voltage instability and lead to a large scale collapse of the system. Considering the effect of these stochastic fluctuations near a codimension 1 saddle-node bifurcation, we explicitly calculate the autocorrelation function of the state vector and show how its behavior explains the phenomenon of critical slowing-down often observed for power systems on the threshold of blackout. We also estimate the collapse probability/mean clearing time for the power system and construct a new indicator function signaling the proximity to a large scale collapse. The new indicator function is easy to estimate in real time using data from PMU and SCADA information about power load fluctuations on the nodes of the grid. We discuss control strategies leading to the minimization of the collapse probability.

[1]  Thomas J. Overbye,et al.  An energy based security measure for assessing vulnerability to voltage collapse , 1990 .

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

[3]  Costas D. Vournas,et al.  Power System Voltage Stability , 2015, Encyclopedia of Systems and Control.

[4]  A. Bergen,et al.  A security measure for random load disturbances in nonlinear power system models , 1987 .

[5]  A.R. Bergen,et al.  A Structure Preserving Model for Power System Stability Analysis , 1981, IEEE Transactions on Power Apparatus and Systems.

[6]  K. R. Padiyar,et al.  ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY , 1990 .

[7]  Claudio A. Caiiizares.  ON BIFURCATIONS, VOLTAGE COLLAPSE AND LOAD MODELING , 1995 .

[8]  T. Baldwin,et al.  Power system observability with minimal phasor measurement placement , 1993 .

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

[10]  Chika O. Nwankpa,et al.  A stochastic based voltage collapse indicator , 1993 .

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

[12]  Eric Hirst,et al.  Costs for electric-power ancillary services , 1996 .

[13]  Janusz Bialek,et al.  Power System Dynamics: Stability and Control , 2008 .

[14]  Christopher M. Danforth,et al.  Predicting critical transitions from time series synchrophasor data , 2013, PES 2013.

[15]  S. Redner.  A guide to first-passage processes , 2001 .

[16]  I. Kamwa,et al.  Causes of the 2003 major grid blackouts in North America and Europe, and recommended means to improve system dynamic performance , 2005, IEEE Transactions on Power Systems.

[17]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[18]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[19]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[20]  F. Milano,et al.  An open source power system analysis toolbox , 2005, 2006 IEEE Power Engineering Society General Meeting.

[21]  R. Fischl,et al.  Local bifurcation in power systems: theory, computation, and application , 1995, Proc. IEEE.

[22]  Seth Blumsack,et al.  Topological Models and Critical Slowing down: Two Approaches to Power System Blackout Risk Analysis , 2011, 2011 44th Hawaii International Conference on System Sciences.

[23]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .