We investigate the secrecy performance and energy-efficiency trade-offs associated to the secure communication between a full-duplex (FD) power beacon (PB) and an energy harvesting (EH) device, in the presence of an eavesdropper. Specifically, we analyze the feasibility of a jamming strategy implemented at the FD-PB under several practical constraints, such as imperfect self-interference (SI) cancellation, EH non-linearity, channel aging and energy-information correlation. The design of the optimal time-splitting factor for the simultaneous wireless information and power transfer (SWIPT) strategy, the adequacy of different beamforming strategies for proper system operation, and the impact of channel correlation between the energy and information transmission phases in SWIPT are thoroughly discussed. Results indicate that under practical constraints such as EH non-linearity and imperfect SI cancellation, the transmit powers at the FD-PB for the generation of energy and jamming signals are the key parameters to be optimized from both points of view: secrecy and energy efficiency. We also verify the positive impact of correlation between the energy and information links in wireless power transfer systems, from a physical layer security perspective.