Improving the time delay in the design of the damping controller with the aim of improving the stability of the power system in the presence of high penetration of renewable energy sources.

• New FWM design to compensate for the uncertainty caused by continuous and disruptive time delays. • Adapting the FWM method to the LMI in the form of an optimization problem. • Combined modeling of energy storage system with RES in large-scale power system. • Using state observer with FWM for better observability of closed-loop system poles in the design process. Due to the high penetration of renewable energy sources (RES) such as wind units in power systems, the need to check the stability of transmission networks has been given more attention than before. Therefore, in this paper, due to the importance of the topic, the wide area damping controller (WADC) has been used for the battery energy storage system (BESS) connected to the photovoltaic unit and the permanent magnet synchronous generator (PMSG) in the dc link. The WADC design is based on free weight matrices (FWM), which can solve a set of constraints based on the linear matrix inequality (LMI) based on the delay-dependent feedback control theory. The working method is that the constraints related to LMI are considered in such a way that it has the ability to tolerate the maximum amount of time delay. FWM has been used to communicate between LMI constraints and the maximum value of the time delay margin. FWM matrices are also based on an iterative algorithm based on linearization of the conical complement, which tries to search for the most optimal value for the control parameters. To implement the simulation results in MATLAB software, an improved power system of 16 machines has been used, the results of which are clearly analyzed and show the superiority of the proposed method compared to other mentioned methods. [ABSTRACT FROM AUTHOR]