Device-to-device (D2D) underlaid cellular network, enabled with radio frequency energy harvesting (RFEH), and enhanced interference management schemes is a promising candidate to improve spectral and energy efficiency of next generation wireless networks. In this paper, we propose a time division duplexing (TDD)-based protocol, in which allows the devices to harvest energy from the downlink transmissions of the base station, while controlling the interference among D2D and cellular communication in the uplink. We propose two schemes for transmission coordination, based on fixed transmission probability (FTP) and adaptive transmission probability (ATP), respectively. In FTP, the D2D transmitters that have harvested enough energy can initiate data transmission with a fixed probability. Differently from this, in ATP a device utilizes its sensing capability to get improved coordination and interference control among the transmitting devices. We evaluate the network performance by presenting an accurate energy model and leveraging tools from stochastic geometry. The results on outage probability and D2D sum-rate reveal the importance of transmission coordination on network performance. These observations led to a solution for choosing the parameters of the ATP scheme that achieves an optimal tradeoff between the D2D outage probability and number of transmitting users.