Integration Methods Used in Numerical Simulations of Transient Electromagnetic

Abstract

This paper made an analysis of some numerical integration methods that can be used in electromagnetic transient simulations. Among the existing methods, we analyzed the trapezoidal integration method (or Heun formula), Simpson's Rule and Runge-Kutta. These methods were used in simulations of electromagnetic transients in power systems, resulting from switching operations and maneuvers that occur in transmission lines. Analyzed the characteristics such as accuracy, computation time and robustness of the methods of integration.

Lumped‐parameter‐based electromagnetic transients simulation of non‐uniform single‐phase lines using state variable method

“…Numerical integration solutions based on the Runge–Kutta or trapezoidal rule of integration were used in many power system transient simulations [11, 12, 17, 18]. In the numerical integration, in order to determine the state vector at any time, the state of the system needs to be calculated in previous discrete time steps starting from an initial time, which is computationally time consuming and successive calculations may cause an error.…”

“…The state variable model based on distributed‐parameter line also exists [17, 18]. For the solution of the state equations, the numerical integration methods are generally used and in these techniques a voltage or current source with any type of variation can be adopted easily [11, 12, 17, 18]. However, to determine the state of the system at a time, it is required to determine the state vector at all previous time steps in an increment by numerical integration time step and thus, the interval of discrete‐time steps may affect the accuracy.…”