In this paper, we analyze energy-efficient cellular networks that are based on renewable energy. We focus on hybrid energy base stations that are powered by renewable energy and power grid. This will provide the opportunity of obtaining green communication and integrating the renewable energy in the existing infrastructure at the same time. We propose a classification of the research problems and highlight different facets that need to be investigated. A new methodology is presented to specify the case study, where we classify the areas, describe different objectives and present several types of constraints. We provide an application of our framework to a specific case study and propose an algorithm for simple price-aware energy management (SPAEMA). The results show that there can be significant cost reduction using SPAEMA in comparison to the normal use of renewable energy. Moreover, this classification can serve as a basis for future work taking into account new cellular network techniques such as cell breathing.