A Numerical Solver Design for Extended-Term Time-Domain Simulation

Numerical methods play an important role in improving efficiency for power system time-domain simulation. Motivated by the need to perform high-speed extended-term time-domain simulation (HSET-TDS) for online purposes, this paper presents design principles for numerical solvers of differential algebraic systems associated with power system time-domain simulation, focusing on DAE construction strategies, integration methods, nonlinear solvers, and linear solvers. We have implemented a design appropriate for HSET-TDS, and we have compared the proposed integration method, Hammer-Hollingsworth 4 (HH4), with Trapezoidal rule in terms of computational efficiency and accuracy, using the New England 39-bus system, an expanded 8775-bus system, and PJM 13 029-bus system.

[1]  J.W. Feltes,et al.  Simulating fast and slow dynamic effects in power systems , 1992, IEEE Computer Applications in Power.

[2]  K. Karoui,et al.  A powerful tool for dynamic simulation of unbalanced phenomena , 1997 .

[3]  Fernando L. Alvarado,et al.  Testing of Trapezoidal Integration With Damping for the Solution of Power Transient Problems , 1983, IEEE Power Engineering Review.

[4]  P. Hammer,et al.  Trapezoidal methods of approximating solutions of differential equations , 1955 .

[5]  Siddhartha Kumar Khaitan,et al.  Fast parallelized algorithms for on-line extended-term dynamic cascading analysis , 2009, 2009 IEEE/PES Power Systems Conference and Exposition.

[6]  I. C. Decker,et al.  Conjugate gradient methods for power system dynamic simulation on parallel computers , 1996 .

[7]  A. Zecevic,et al.  A partitioning algorithm for the parallel solution of differential-algebraic equations by waveform relaxation , 1999 .

[8]  James Demmel,et al.  Making Sparse Gaussian Elimination Scalable by Static Pivoting , 1998, Proceedings of the IEEE/ACM SC98 Conference.

[9]  Daniel Tylavsky,et al.  Parallel Newton type methods for power system stability analysis using local and shared memory multiprocessors , 1991 .

[10]  V. Ajjarapu,et al.  A decoupled time-domain Simulation method via Invariant subspace partition for power system analysis , 2006, IEEE Transactions on Power Systems.

[11]  A. Bihain,et al.  The mixed Adams-BDF variable step size algorithm to simulate transient and long term phenomena in power systems , 1994 .

[12]  B. Stott,et al.  Power system dynamic response calculations , 1979, Proceedings of the IEEE.

[13]  Jiwu Shu,et al.  Parallel algorithm and implementation for realtime dynamic simulation of power system , 2005, 2005 International Conference on Parallel Processing (ICPP'05).

[14]  J.J. Sanchez-Gasca,et al.  Variable time step, implicit integration for extended-term power system dynamic simulation , 1995, Proceedings of Power Industry Computer Applications Conference.

[15]  James D. McCalley,et al.  Operational defence of cascading sequences , 2011, 2011 IEEE Power and Energy Society General Meeting.

[16]  Hermann W. Dommel,et al.  Fast Transient Stability Soultions , 1972 .

[17]  James Demmel,et al.  A Supernodal Approach to Sparse Partial Pivoting , 1999, SIAM J. Matrix Anal. Appl..

[18]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[19]  George Gross,et al.  An efficient algorithm for simulation on transients in large power systems , 1976 .

[20]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[21]  Alberto L. Sangiovanni-Vincentelli,et al.  The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits , 1982, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.