Energy harvesting (EH) in wireless communications has become the focus of recent transmission technology studies. Herein, energy storage modeling is one of the crucial design benchmarks that must be treated carefully. Understanding the energy storage dynamics and the throughput levels is essential especially for communication systems in which the performance depends solely on harvested energy. While energy outages should be avoided, energy overflows should also be prevented in order to utilize all harvested energy. Hence, a simple, yet comprehensive, analytical model that can represent the characteristics of a general class of EH wireless communication systems needs to be established. In this paper, invoking tools from large deviation theory along with Markov processes, a firm connection between the energy state of the battery and the data transmission process over a wireless channel is established for an EH transmitter. In particular, a simple exponential approximation for the energy overflow probability is formulated, with which the energy decay rate in the battery as a measure of energy usage is characterized. Then, projecting the energy outages and supplies on a Markov process, a discrete state model is established and an expression for the energy outage probability for given energy arrival and demand processes is provided. Finally, under energy overflow and outage constraints, the average data service (transmission) rate over the wireless channel is obtained and the effective capacity of the system, which characterizes the maximum data arrival rate at the transmitter buffer under quality-of-service (QoS) constraints imposed on the data buffer overflow probability, is derived.