The increased utilisation of distributed renewable energy sources in low voltage grids leads to power quality problems such as overvoltages and voltage unbalance. This imposes challenges to the distribution system operators to maintain the power quality in their grids. To overcome these issues, energy storage systems could be integrated together with the distributed energy resources and the stored energy could be used when needed to better improve power quality and achieve better grid performance. However, integrating an energy storage system introduces additional cost, therefore, determining the right capacity is essential. In this article, an energy storage system is combined with the classical positive-sequence control strategy and the three-phase damping control strategy. The three-phase damping control strategy is able to mitigate the voltage unbalance by emulating a resistive behaviour towards the zero- and negative-sequence voltage components. This resistive behaviour can be set on different values such that the desired voltage unbalance mitigation is achieved. Hence, the three-phase damping control strategy, equipped with the energy storage system is investigated under different values of the resistive behaviour. Both control strategies are investigated under the same conditions and the impact of the different capacities of the energy storage systems is investigated.