We consider wireless-powered amplify-and-forward and decode-and-forward relaying in cooperative communications, where an energy constrained relay node first harvests energy through the received radio-frequency signal from the source and then uses the harvested energy to forward the source information to the destination node. We propose time-switching based energy harvesting (EH) and information transmission (IT) protocols with two modes of EH at the relay. For continuous time EH, the EH time can be any percentage of the total transmission block time. For discrete time EH, the whole transmission block is either used for EH or IT. The proposed protocols are attractive because they do not require channel state information at the transmitter side and enable relay transmission with preset fixed transmission power. We derive analytical expressions of the achievable throughput for the proposed protocols. The derived expressions are verified by comparison with simulations and allow the system performance to be determined as a function of the system parameters. Finally, we show that the proposed protocols outperform the existing fixed time duration EH protocols in the literature, since they intelligently track the level of the harvested energy to switch between EH and IT in an online fashion, allowing efficient use of resources.