The variability of the output power of distributed renewable energy sources (DRESs) that originate from the fast-changing climatic conditions can negatively affect the grid stability. Therefore, grid operators have incorporated ramp-rate limitations (RRLs) for the injected DRES power in the grid codes. As the DRES penetration levels increase, the mitigation of high-power ramps is no longer considered as a system support function but rather an ancillary service (AS). Energy storage systems (ESSs) coordinated by RR control algorithms are often applied to mitigate these power fluctuations. However, no unified definition of active power ramps, which is essential to treat the RRL as AS, currently exists. This paper assesses the various definitions for ramp-rate RR and proposes RRL method control for a central battery ESS (BESS) in distribution systems (DSs). The ultimate objective is to restrain high-power ramps at the distribution transformer level so that RRL can be traded as AS to the upstream transmission system (TS). The proposed control is based on the direct control of the ΔP/Δt, which means that the control parameters are directly correlated with the RR requirements included in the grid codes. In addition, a novel method for restoring the state of charge (SoC) within a specific range following a high ramp-up/down event is proposed. Finally, a parametric method for estimating the sizing of central BESSs (BESS sizing for short) is developed. The BESS sizing is determined by considering the RR requirements, the DRES units, and the load mix of the examined DS. The BESS sizing is directly related to the constant RR achieved using the proposed control. Finally, the proposed methodologies are validated through simulations in MATLAB/Simulink and laboratory tests in a commercially available BESS.