In this paper, we design a robust resource allocation algorithm for a wireless-powered communication network (WPCN) taking into account residual hardware impairments (HWIs) at the transceivers, the imperfectness of the channel state information, and the non-linearity of practical radio frequency energy harvesting circuits. In order to ensure power-efficient secure communication, physical layer security techniques are exploited to deliberately degrade the channel quality of a multiple-antenna eavesdropper. The resource allocation algorithm design is formulated as a non-convex optimization problem for minimization of the total consumed power in the network, while guaranteeing the quality of service of the information receivers in terms of secrecy rate. The globally optimal solution of the optimization problem is obtained via a two-dimensional search and semidefinite programming relaxation. To strike a balance between computational complexity and system performance, a low-complexity iterative suboptimal resource allocation algorithm is then proposed. Numerical results demonstrate that both the proposed optimal and suboptimal schemes can significantly reduce the total system power consumption required for guaranteeing secure communication, and unveil the impact of HWIs on the system performance: (1) residual HWIs create a system performance bottleneck in the high transmit/receive power regimes; (2) increasing the number of transmit antennas can effectively reduce the system power consumption and alleviate the performance degradation due to residual HWIs; (3) imperfect CSI increases the system power consumption and exacerbates the impact of residual HWIs.