The paper addresses the energy consumption minimization problem in wireless powered communication networks (WPCNs) and proposes a DT-SWIPT-assisted time allocation scheme, named DaTA, such that the wireless station can share the remaining energy after transmission to the HAP to those who have not transmitted to the HAP to minimize the energy consumption of the network. In addition to proposing a new frame structure, the paper also considers the SNR (Signal-to-Noise) constraint to guarantee that the HAP can successfully receive data from wireless stations. In the paper, the energy consumption minimization problem is formulated as a nonlinear programming model. We employ the SQP (Sequential Quadratic Programming) algorithm to figure out the optimal solution. Moreover, a heuristic method is proposed as well to obtain a near-optimal solution in a shorter time. Simulation results showed that the proposed scheme can have better performance than the related work in terms of energy consumption and energy efficiency.