An efficient algorithm for simulation on transients in large power systems

The simulation of the transient response of a large interconnected power system involves the solution of a very large system of differential-algebraic equations under a great variety of initial conditions and disturbances. The demands imposed on a digital transient stability program to i) study larger power system interconnections, ii) provide a more detailed representation of the power system components, and iii) permit the simulation of longer time periods, have the effect of increasing the computing time. The importance of, and the need for, efficient computational schemes is apparent. The method presented in this paper makes detailed use of the structural properties of the differential-algebraic system representation. The nonlinear differential-algebraic system is split into a nonstiff part with long time constants coupled to a stiff part with a sparse Jacobian matrix whose longest time constant is shorter than that of the first part. These two parts are linear in their respective states, i.e., the system is semilinear. With the nonstiff part removed, a smaller set of stiff equations with a smaller conditioning number than the original system is obtained. Consequently, longer stepsizes can be used so as to reduce the computation time. The proposed multistep integration schemes exploit the stiffness and semilinearity properties. Numerical results on a small test problem indicate that these schemes operate with good accuracy at stepsizes as large as 100 times those necessary to ensure numerical stability by more conventional schemes.