On the perturbation size of the finite difference method for trajectory sensitivity-based assessment of power system dynamics with non-smooth behavior

Abstract

Although a finite difference-based trajectory sensitivity (FDTS) has been widely used due to its robust availability in any environment, the accuracy of FDTS-based analyses could be influenced by the perturbation size of finite difference (FD), especially in non-smooth systems. This important yet overlooked issue has not been comprehensively addressed. Here, this paper thus investigates how the analysis accuracy varies depending on the perturbation size through case studies discussing whether the FDTS-based analysis could approximate the perturbation impact of multiple parameters. Case study results demonstrate that the approximation accuracy is notably dependent on the perturbation size, which is an interesting observation that the widely used small size cannot always guarantee the best performance. The underlying cause for our finding is understood through a comprehensive causal analysis: The result of FDTS-based studies could be affected by even small perturbations or interactions caused by perturbations at multiple remote locations. Further, this paper compares the accuracy and computing burden of first- and second-order approximations, advising that linear approximation is the most suitable for practical applications. The outcomes of this paper suggest that the reliability of FDTS-based analysis could be secured even in highly non-smooth power systems if the proper perturbation size is used.