An Abstract for a Poster at The Scalable Parallel Libraries Conference 6-8 October 1993

Parallel Differential Algebraic Equations (DAEs) Solver for Electrical Power System Transient Stability Analysis

by

Kamala Anupindi, Anthony Skjellum, Paul Coddington, Geoffrey Fox

Transient Stability Analysis examines the dynamic behaviour of a Power System for as much as several seconds following a power flow disturbance. The reaction of a single generator to variations in its load can be modeled using ODEs as follows

y = f(y,z)

However, there are multiple generators supplying power to the network and the generators are coupled through the power network. The power network can be modeled by non-linear algebraic equations as follows

0 = g(y,z)

and this entire system of DAEs must be solved simultaneously. Transient Stability Analysis is computationally intensive because the extremely large number of equations to be solved. The dynamics of each generator are individually modeled with as few as two and with as many as forty ODEs while the generators are coupled via the algebraic equations that describe the electrical network. This requires the solution of large systems of simultaneous sparse non-linear equations.

Real-time or faster-than-real-time power system transient stability simulations will have significant impact on the future design and operations of both individual electrical utility companies and large interconnected power systems. Several sequential DAEs solvers exist, that use various numerical techniques for solving the DAEs. Prominent among these are as follows:

1. LIMEX - an extrapolation integration technique. [1]

2. RADAU5 - an implicit Runge-Kutta method of order 5. [2]

3. RODAS - an embedded Rosenbrock technique of order(3)4. [2]

4. SODEX - an extrapolation technique based on linearly implicit mid-point rule. [2]

5. SEULEX - an extrapolation technique based on linearly implicit Euler method. [2] 6. DASSL - a multistep, backward differentiation formulas technique. [1]

7. LSODI - an implicit (will fill it up.)........

But to date, there has been no explicit mention in the power system transient stability analysis literature of application using public domain DAEs solvers. These solvers from the numerical analysis community often use higher order implicit Runge-Kutta integration techniques that yield more accurate solutions or permit larger time-steps. DAEs solvers exist that have been explicitly developed to handle discontinuities in functions – a condition encountered in transient stability calculations.

CDASSL [3] (Concurrent Dassl) is the only attempt that has been made at parallelizing these DAEs solvers. There is enormous potential for research in this field. Our research is examining the applicability of various DAEs solution techniques to parallel processing speedup. We have been analyzing the scalability and the possibility of implementing these solvers in parallel. Our research is concentrated on selecting the most suitable solver for the power system application. A parallel version of this DAEs solver will then be developed for use by, and not limited to, the power system community.

This poster session will describe the state of the art research on the DAEs solvers. We will describe our research on the parallelization of the selected DAEs solver, with reference to the power system problem. We will then present the performance data for the parallel DAEs solver using Multicomputer Toolbox [4] and Zipcode [5] for now, which will port to MPI next year and hence can run on all reasonable multicomputers.

References

[1] K.E. Brenan,S.L. Campbell, and L.R. Petzold. Numerical Solution of Initial Value Problems in Differential-Algebraic Equations. Elevier Science, 1989.

[2] E. Hairer and G. Wanner. Solving Ordinary Differential Equatios II – Stiff and Differential-Algebraic Problems. Springer-Verlag, New York, 1991.

[3] A. Skjellum. Concurrent Dynamic Simulation: Multicomputer Algorithms Research Applied to Ordinary Differential-Algebraic Process Systems in Chemical Engineering. PhD. Thesis, California Institute of Technology, Pasadena, CA, 1990.