This paper considers a wireless powered communication network (WPCN), where multiple users harvest energy from a dedicated power station and then communicate with an information receiving station. Our goal is to investigate the maximum achievable energy efficiency (EE) of the network via joint time allocation and power control while taking into account the initial battery energy of each user. We first study the EE maximization problem in the WPCN without any system throughput requirement. We show that the EE maximization problem for the WPCN can be cast into EE maximization problems for two simplified networks via exploiting its special structure. For each problem, we derive the optimal solution and provide the corresponding physical interpretation, despite the non-convexity of the problems. Subsequently, we study the EE maximization problem under a minimum system throughput constraint. Exploiting fractional programming theory, we transform the resulting non-convex problem into a standard convex optimization problem. This allows us to characterize the optimal solution structure of joint time allocation and power control and to derive an efficient iterative algorithm for obtaining the optimal solution. Simulation results verify our theoretical findings and demonstrate the effectiveness of the proposed joint time and power optimization.