In this paper we present a new analysis of energy consumption in cellular network and we focus on the distribution of energy consumed by a base station. We first define the energy consumption model, in which the consumed energy is divided into two parts: the additive part and the broadcast part. The additive part is served to communicate with different users while the broadcast part is served to transmit the same information to all users in the cell. We then model user's activity as ON-OFF process in time. We also model user's mobility as a random process and we define the high mobility regime in which users move very fast. We are able to provide analytical expressions for statistics of consumed energy and bounds on the distribution of energy in motionless case. We then consider the impact of mobility and we mobility reduces moments and central moments of the additive part. We also show that high mobility regime, the variance of energy tends to zero. This is a strong result as it holds true for almost any mobility model. We are able to characterize the convergence decay rate of the variance in function of user's speed. We propose two applications of the model. The first one is to dimension cell radius in the economical point of view and the second one is to dimension cell battery in the sites that do not have access to electricity.