Large-scale integration of inverter-based renewable generation leads to the reduction of power systems’ natural inertia. Therefore, the dynamics of the future power systems will be more sensitive than in the traditional systems with high-inertia rotating synchronous generators. This development is a potential risk for frequency stability and requires utilization of rapidly controllable resources for dynamic frequency stability support. Simultaneously, development of new synchronization and control methods for inverter-based resources is needed in order to ensure the frequency and synchronization stability of future power systems. In this paper, a grid-forming and supporting universal frequency-locked-loop -based control and grid synchronization for inverter-based resources is utilized to improve the frequency stability of a small high-voltage network. The simulations are done with PSCAD software and the main focus is on the battery energy storages to evaluate the effect of their location, enhanced control schemes as well as operation mode on frequency stability. In the studies, for example, the effect of battery storages location, active power response related control parameters, communication time delay and input frequency determination on frequency support are studied during charging and discharging of the batteries. Based on the simulations, also new solutions to improve the frequency stability of future variable inertia power systems with universal grid-forming battery storages are proposed.