In this paper, an analytical framework is provided to analyze the energy coverage performance of unmanned aerial vehicle (UAV) energy harvesting networks with clustered user equipments (UEs). Locations of UEs are modeled as a Poisson Cluster Process (PCP), and UAVs are assumed to be located at a certain height above the center of user clusters. Hence, user-centric UAV deployments are addressed. Two different models are considered for the line-of-sight (LOS) probability function to compare their effects on the network performance. Moreover, antennas with doughnut-shaped radiation patterns are employed at both UAVs and UEs, and the impact of practical 3D antenna radiation patterns on the network performance is also investigated. Initially, the path loss of each tier is statistically described by deriving the complementary cumulative distribution function and probability density function. Following this, association probabilities with each tier are determined, and energy coverage probability of the UAV network is characterized in terms of key system and network parameters for UAV deployments both at a single height level and more generally at multiple heights. Through numerical results, we have shown that cluster size and UAV height play crucial roles on the energy coverage performance. Furthermore, energy coverage probability is significantly affected by the antenna orientation and number of UAVs in the network.