The stability of future power systems will be challenged by high shares of converter-based generation technologies (CBGTs). To prevent instability problems, it is essential to explore new technologies and control strategies able to counteract the negative effects that CBGTs may have. In this regard, promising technologies are battery energy storage systems (BESSs), which can provide a wide range of benefits from a stability viewpoint. Current methodologies that quantify and allocate BESSs in electrical networks have been developed from an economic perspective considering a steady-state formulation of the system. Accordingly, these allocation approaches do not exploit all the benefits that BESSs can offer to system stability. This study proposes a novel optimisation methodology for efficient BESS allocation in systems with high levels of CBGTs. The model improves system stability by considering BESSs with voltage support capability during contingencies. The allocation is solved by a genetic algorithm considering transient voltages throughout the network busbars and their short circuit levels. The methodology was implemented in the 39-busbar New England system. Compared to traditional approaches, the proposed BESS allocation method enables significant improvements in the stability of the system during critical contingencies.