Storage technologies and storage integration are currently key topics of research in energy systems, due to the resulting possibilities for reducing the costs of renewables integration. Off-grid power systems in particular have received wide attention around the world, as they allow electricity access in remote rural areas at lower costs than grid extension. They are usually integrated with storage units, especially batteries. A key issue in cost effectiveness of such systems is battery degradation as the battery is charged and discharged. We present linear programming models for the optimal management of off-grid systems. The main contribution of this study is developing a methodology to include battery degradation processes inside the optimization models, through the definition of battery degradation costs. As there are very limited data that can be used to relate the battery usage with degradation issues, we propose sensitivity analyses to investigate how degradation costs and different operational patterns relate each others. The objective is to show the combinations of battery costs and performance that makes the system more economic.