Uncertainty Quantification in Dynamic Simulations of Large-scale Power System Models using the High-Order Probabilistic Collocation Method on Sparse Grids

This paper proposes a probabilistic collocation method (PCM) to quantify the uncertainties with dynamic simulations in power systems. The appraoch was tested on a single-machine-infinite-bus system and the over 15,000 -bus Western Electricity Coordinating Council (WECC) system. Comparing to classic Monte-Carlo (MC) method, the proposed PCM applies the Smolyak algorithm to reduce the number of simulations that have to be performed. Therefore, the computational cost can be greatly reduced using PCM. The algorithm and procedures are described in the paper. Comparison was made with MC method on the single machine as well as the WECC system. The simulation results shows that using PCM only a small number of sparse grid points need to be sampled even when dealing with systems with a relatively large number of uncertain parameters. PCM is, therefore, computationally more efficient than MC method.

[1]  A. Monticelli.  State estimation in electric power systems : a generalized approach , 1999 .

[2]  S. Julier,et al.  A General Method for Approximating Nonlinear Transformations of Probability Distributions , 1996 .

[3]  R. Caflisch,et al.  Quasi-Monte Carlo integration , 1995 .

[4]  Malcolm Irving,et al.  Analysis of confidence bounds in power system state estimation with uncertainty in both measurements and parameters , 2006 .

[5]  Xiu Yang,et al.  Adaptive ANOVA decomposition of stochastic incompressible and compressible flows , 2012, J. Comput. Phys..

[6]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[7]  A. Monticelli,et al.  Electric power system state estimation , 2000, Proceedings of the IEEE.

[8]  D. Kosterev,et al.  A new thermal governor modeling approach in the WECC , 2003 .

[9]  Daniel M. Tartakovsky,et al.  Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids , 2010, J. Comput. Phys..

[10]  R. Cools,et al.  Monomial cubature rules since “Stroud”: a compilation , 1993 .

[11]  Shubha Pandit,et al.  Power System State Estimation , 2002 .

[12]  R. Cools.  Monomial cubature rules since “Stroud”: a compilation—part 2 , 1999 .

[13]  A. K. AL-Othman,et al.  A fuzzy state estimator based on uncertain measurements , 2009 .

[14]  Dongbin Xiu,et al.  High-Order Collocation Methods for Differential Equations with Random Inputs , 2005, SIAM J. Sci. Comput..

[15]  George Em Karniadakis,et al.  Generalized polynomial chaos and random oscillators , 2004 .

[16]  D. Kosterev,et al.  Load modeling in power system studies: WECC progress update , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[17]  C. W. Taylor,et al.  Model validation for the August 10, 1996 WSCC system outage , 1999 .

[18]  E. Kyriakides,et al.  Calculating confidence intervals in parameter estimation: a case study , 2006, IEEE Transactions on Power Delivery.

[19]  D. Kosterev,et al.  An Interim Dynamic Induction Motor Model for Stability Studies in the WSCC , 2002, IEEE Power Engineering Review.

[20]  K. Strunz,et al.  Stochastic Polynomial-Chaos-Based Average Model of Twelve-Pulse Diode Rectifier for Aircraft Applications , 2006, 2006 IEEE Workshops on Computers in Power Electronics.

[21]  M.A. Pai,et al.  Bounding uncertainty in power system dynamic simulations , 2000, 2000 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.00CH37077).

[22]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[23]  Michael Griebel,et al.  Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences , 1998, Computing.

[24]  Xiang Ma,et al.  An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations , 2009, J. Comput. Phys..

[25]  Simon J. Julier,et al.  The scaled unscented transformation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[26]  Kai Strunz,et al.  Stochastic formulation of SPICE-type electronic circuit simulation with polynomial chaos , 2008, TOMC.

[27]  J.R. Hockenberry,et al.  Evaluation of uncertainty in dynamic simulations of power system models: The probabilistic collocation method , 2004, IEEE Transactions on Power Systems.

[28]  K Strunz,et al.  Stochastic Polynomial-Chaos-Based Average Modeling of Power Electronic Systems , 2011, IEEE Transactions on Power Electronics.

[29]  V. Vittal,et al.  Impact of Increased Penetration of DFIG-Based Wind Turbine Generators on Transient and Small Signal Stability of Power Systems , 2010, IEEE Transactions on Power Systems.