The present study investigates the effects of different parameters on the performance of a cold energy storage (CES) system based on spherical capsules using two- and three-dimensional numerical analyses. The effect of different arrangements of the capsules is studied using a 2D model. The impact of using nano-particles, diameter, and material of a spherical capsule and working parameters that affect the melting and solidification process are evaluated in a 3D model. The results revealed that the hexagonal arrangement compared to the triangular and rectangular arrangements, yields a lower charging time of 10.71% and 16.67%, respectively. Utilization of a 3% volume fraction of graphene nano-particles in the phase change material (PCM) reduces the charging and discharging process time by 11.11% and 22.22%, respectively. The diameter of the capsule is an effective parameter for the charging and discharging time, so the capsule with a diameter of 20 mm in comparison with a diameter of 40 mm reduces the charging and discharging time by 71.1% and 66.67%, respectively. Also, capsules made of graphite yield lower charging process time compared to plastic and glass capsules by 17.39% and 5%, respectively.