Energy harvesting (EH) technology has imposed new constraints on the amount of time an energy-constrained relay node needs to use for EH and information forwarding. Moreover, EH techniques may increase vulnerability to eavesdropping, since a power receiver, as a potential eavesdropper, usually has a shorter access distance than an information receiver. Motivated by this issue, in this paper, we investigate a tradeoff between energy consumption and physical layer security in a wireless powered-untrusted cooperative communication (WPUCC) network consisting of one source-destination pair and multiple amplify-and-forward untrusted relays. To minimize the energy consumption of the network, we propose a secure adaptive relay-based cooperation approach. Moreover, a greedy battery-aware relay-selection scheme is proposed to minimize the power consumption in WPUCC systems. Using power-splitting-based energy accumulation, untrusted relays attempt to intercept the information intended to the legitimate destination while harvesting energy at the same time. To keep the information secure from potential eavesdropping, the source injects a jamming signal along with its data signal. By modeling the dynamic behavior of the relay battery as a finite-state Markov chain, we derive an analytical expression for the secrecy outage probability of our proposed secure adaptive harvest-use-store cooperative communication scheme and show that it is more secure than its direct transmission and pure two-hop transmission counterparts.