In recent years, energy harvesting has taken a considerable attention in wireless communication research. Nonetheless, the stochastic nature of renewable energy sources has become one of the research problems, and energy storage has been proposed as a solution to deal with it. Initially, researchers regarded a perfect battery model without energy losses during storage because of its simplicity and compatibility in wireless communication analysis. However, a battery model that reflects practical concerns should include energy losses. In this paper, we consider an energy harvesting wireless communication model with a battery that has energy losses during charging and discharging. We consider energy underflows (i.e., the energy level falls below a certain threshold in a battery) as the energy management concern, and characterize the energy underflow probability and provide a simple exponential formulation by employing the large deviation principle and queueing theory. Specifically, we benefit from the similarity between the battery and data buffer models. We further coin the available space decay rate at a battery as a parameter to indicate the energy consumption performance. We further outline an approach to set the energy demand policy to meet the energy management requirements that rule the energy underflow probability as a constraint. We finally substantiate our analytical findings with numerical demonstrations, and compare the transmission performance levels of a transmission system with a battery that has energy losses and a transmission system that consumes the energy as soon as it is harvested.