A Study on Energy Preservability of Runge-Kutta Methods in Power System Simulation

Runge-Kutta methods have been widely used in power system time-domain simulations. However, conventional Runge-Kutta methods can not preserve the total energy of the simulated system because they are not symplectic integrators. For the explicit Euler method and fourth-order Runge-Kutta method, this paper first finds explicit formulae on how the total energy of the simulated system trajectory can change with the integration time step by using the Hamiltonian system formulation of a single-machine-infinite-bus system. The formulae discover the existence of a critical time step for energy-preserving simulation. Then, the formulae are used to evaluate the error in observed damping of the system as well as the correction if the simulation is conducted for an extended period with a time step different from the critical time step. Finally, the formulae are applied to Kundur's two-area four-generator system regarding its dominant mode.