Exponential integration algorithm for large-scale wind farm simulation with Krylov subspace acceleration

Facing the increasingly complex power system transient characteristics, the electromagnetic transient simulation tools are gaining popularity, thanks to their detailed modeling of power system equipment and high fidelity simulation results. Consequently, the Electro-Magnetic Transient Programs are increasingly used in simulation studies of higher dimensions and wider range of scales, which challenges the circuit-based algorithmic design of these programs. This paper proposes to use explicit integration formulas based on the matrix exponential function in the transient simulations of large-scale wind farms, which possess both high efficiency of explicit methods and numerical stability of implicit methods. A Krylov subspace-based order reduction technique embedded into the integration formulas was developed to specifically address the simulation needs of high dimensional EMT model of detailed wind farms. Numerical studies are conducted based on a realistic large-scale wind farm, where the proposed state space modeling framework is established, and the matrix exponential-based algorithm is implemented and compared against a set of classical stiff ODE solvers. Simulation tests with different fault types and fault locations are presented, showing a superior computation speed for studies with both equivalent and detailed wind farm modeling. On the other hand, numerical errors of the new algorithm are shown to be at least one order of magnitude smaller than other solvers in the range of typical step sizes, under the same simulation setting. These properties ensure an efficient, reliable and highly scalable simulation capability for the computation challenges in the studies of large-scale wind farms.