Homotopy Based Error Estimator for Adaptive Modified Euler in Transient Stability Simulations

Modified Euler is a well known solver for transient stability simulations even in commercial packages and adaptive step size is used to reduce the simulation run time. Multistage Homotopy Analysis Method (MHAM) comes under the semi-analytical methods for the solution of differential equations. This paper proposes MHAM to be used as an error estimator which can help to control the Local Truncation Error (LTE) at each integration step by adjusting the step size of a Modified Euler solver. It is shown that MHAM is able to give a good estimate of LTE and solves faster than a conventional adaptive step size Modified Euler solver. The proposed method is validated using systems from 10 generators 39 bus system to 4092 generators 13659 bus system, where full order generator models with saturation effects and composite load models are used. The accuracy of the proposed method is compared with a fixed step implementation of Modified Euler transient stability.