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• Improving the voltage in a wind farm by a self-corrective static VAR compensator. • Considering the steady-state and transient modes under harsh faults in analysis. • Enhancing the system performance by employing an optimized Battery Energy Storage. • Reporting the results in different cases, with or without the mentioned equipment. Maintaining synchronism and voltage stability, especially in the presence of wind farms, has a crucial role in confirming the reliability requirements of the power grid, as the natural fluctuations of wind speed result in intermittency and uncontrollability of power generation. To this end, an optimized Battery Energy Storage System (BESS) was suggested to make an equilibrium between the generation and consumption in wind farms under harsh conditions. Additionally, the instability of wind farms is very likely after transmission line faults occur. To overcome this problem, in this paper, the impact of a constant capacitor bank, connected in parallel with the wind generators, is investigated. Also, a novel self-corrective Static Volt-ampere reactive Compensator (SVC) is proposed to overcome the variations of voltage and damp the reactive power oscillations after occurring the faults. The proposed SVC compares the network voltage profile as the reference voltage with the voltage deviations in a control block diagram. For this purpose, three similar wind farms of Permanent Magnet Synchronous Generator (PMSG) type are considered in a wind park. The simulation case studies are performed in Matlab/Simulink under different conditions of transient and steady-state voltage stabilities in the presence of proposed BESS including, only capacitor bank (without self-corrective SVC), and with self-corrective SVC. The results authenticate the ability of the proposed SVC strategy to correct the voltage deviations, and voltage stability improvement of the under study system. [ABSTRACT FROM AUTHOR]