Comparison of various robust and efficient load-flow techniques based on Runge–Kutta formulas

Abstract

Based on Continuous Newton’s method, any well-assessed numerical scheme can be adapted for solving the Load-Flow (LF) problem. So far, LF techniques based on 4th order Runge–Kutta formula (RK4) and Adams–Bashfort’s methods (AB) have been proposed. However, there is a huge variety of numerical methods whose adequacy for solving the LF problem has not been explored yet. This paper tries to fill this gap by proposing several LF solvers based on Runge–Kutta (RK) formulas. Thus, several LF techniques based on Midpoint (MP), 3rd order Heun (H3), Simpson 3/8 (S3/8) and an accelerated 3rd order Runge–Kutta (ARK3) formulas are proposed. The performance of the proposed LF techniques is assessed using several medium and large-scale ill-conditioned power systems. The proposed techniques are compared with RK4, AB and other robust LF methods. In addition, their scalability and influence of the loading level are analyzed. The obtained results prove that the proposed LF techniques are faster than RK4 and robust enough to successfully tackle medium and large-scale ill-conditioned power systems. As main conclusion, it is proved that lower order methods might be as robust as higher order ones but more efficient. Therefore, its usage with respect higher order methods (e.g. 4th order ones), should be frequently preferable.