Next-generation communication networks will likely involve the energy-efficient transfer of information and energy over the same wireless channel, for which the physical layer will become more vulnerable to cyber attacks by potential multi-antenna eavesdroppers. To address this issue, this paper considers transmit time-switching (TS) mode, in which energy and information signals are transmitted separately in time by the BS. This protocol is not only easy to implement but also delivers the opportunity of multi-purpose beamforming, in which energy beamformers during wireless power transfer are useful in jamming the eavesdropper. In the presence of imperfect channel estimation and multi-antenna eavesdroppers, the energy and information beamformers and the transmit TS ratio are jointly optimized to maximize the worst-case user secrecy rate subject to UEs' harvested energy thresholds and a BS transmit power budget. New robust path-following algorithms, which involve one simple convex quadratic program at each iteration are proposed for computational solutions of this difficult optimization problem and also the problem of secure energy efficiency maximization. The latter is further complex due to additional optimization variables appearing in the denominator of the secrecy rate function. Numerical results confirm that the performance of the proposed computational solutions is robust against the channel uncertainties.