Frequency domain relaxation of power system dynamics

A highly parallel frequency-domain waveform relaxation method is presented to solve transient dynamics of nonlinear systems. The method attempts to exploit parallelism offered by the frequency-domain matrix equations used to represent and solve the systems. A comparison with various other methods shows that this is a unique method in that it solves transient dynamics of nonlinear systems entirely in the frequency domain while being suitable for large-scale parallel computation. The method treats linear and nonlinear parts of the system individually. Linear blocks are easily solved in parallel in the frequency domain since superposition holds and each frequency can be handled independently of the other. Nonlinear blocks are approximated by polynomials and are solved in parallel using the describing function matrix technique. The frequency-domain-relaxation (FDR) has been used to solve for the transient response of two power system machine models. Results obtained by this method are compared to the results obtained by a conventional time-domain iteration method. It is observed that there is a reduction in the number of parallel steps required by the FDR method, which is dependent on the model and the ratio of data points required by the two methods to give solutions of comparable accuracy.<>