This paper provides evidence on how the variability of the power produced by a wind farm and its revenue are affected by implementing a ramp-rate limitation strategy and by adding a storage device to the system. The wind farm receives penalties whenever the ramp-rate limitations are not respected and may be supported by batteries to avoid this scenario. In this paper, we model the battery usage as a discrete time homogeneous Markov chain with rewards thanks to which it is possible to simulate the state of the charge of the battery and to calculate the amount of penalties suffered by the wind farm during any period. An application is performed considering the power produced by a hypothetical wind turbine located in Sardinia (Italy) using real wind speed data and electricity prices from a period of 10 years. We applied the concept of ramp-rate limitation on our hourly dataset, studying several limitation scenarios and battery capacities.