As the penetration of Converter-Interfaced Distributed Renewable Energy Sources (CI-DRES) increases, several problems are revealed in electric power systems, e.g., power quality issues, reverse power flows and frequency instability. A solution to tackle these issues is the mitigation of high CI-DRES active power ramp-rates (RRs) by utilizing energy storage systems (ESS). In many grid-codes at transmission system (TS) level, it is specified that the CI-DRES limit their RRs, while also the utilization of a central ESS has been proposed to limit the RRs. Nevertheless, this approach involves only large energy market players. Although various RRL methods have been proposed for CI-DRES, a remaining gap is the evaluation of the RR of a Distribution Network (DN) containing CI-DRES and loads together with the influence of distributed ESS in the DN. Towards this direction, in this paper, this evaluation is performed in order to study the RRL capability of a low-voltage (LV) DN considering both central and distributed ESS. The analysis is conducted in the LV CIGRE DN via quasi-steady-state and RMS simulations in PowerFactory considering several techno-economic parameters, e.g., ESS size, type, per unit cost. This evaluation will help towards the integration of the RRL control in the grid codes in DNs so that it can be considered as a new ancillary service to be remunerated in respective markets where also small CI-DRES owners will be able to participate.