Multiscale simulation of power system transients based on the matrix exponential function

Power system electro-magnetic transient programs (EMTP) have been popular among researchers and practitioners due to their detailed component modeling and high simulation accuracy for complex system operations. Despite broad applications in simulations with wide range of timescales, the small discretization step of these programs makes their use very time-consuming for system studies with long time span. Facing the increasingly complex power system transient characteristics and simulation demands, a multiscale algorithm that integrates the simulations of the electromagnetic and slower electromechanical transients is desirable. The multiscale simulation algorithm preserves the high fidelity of the EMTP and attains higher efficiency for the overall transient simulation. In this paper, we achieve this goal by exploiting the unique properties of the matrix exponential function. The proposed algorithm is capable of utilizing large step sizes to speed up the simulation of slow dynamics, whereas the fast transients are accurately reconstructed through efficient dense output mechanism, which is built upon the matrix exponential function computation. Numerical studies including a large-scale wind farm simulation are conducted to demonstrate the effectiveness of the proposed multiscale algorithm.