Mobile communications are a powerful contributor to social and economic development worldwide, including in less developed or remote parts of the world. However they are large users of electricity through their base stations, backhaul networks and Cloud servers, so that they have a large environmental impact when they use the electric grid. On the other hand, they could operate with renewable energy sources and thus reduce their CO2 impact and be accessible even in areas where the electric grid is unavailable or unreliable. The counterpart is that intermittent sources of energy, such as photovoltaic and wind, can affect the quality of service (QoS) that is experienced by mobile users. Thus in this paper we model the performance of mobile telecommunications that use intermittent and renewable energy sources. In such cases to analyse the performance of such systems, both the energy supply and the network traffic, can be modeled as random processes, and we develop mathematical models using the Energy Packet Network paradigm, where both data and energy flows are discretised. QoS metrics for the users are computed based on the traffic intensity and the availability of energy.