Due to massive transformations in the energy sector, the power grid of the future requires new solutions. One possible novel building block of the future grid is the energy router. Energy routers are power electronic devices that can bridge previously unconnected parts of the power grid, in order to increase the use of power line capacity and to increase the power grid’s resilience. Through the massive use of energy routers, the power grid will cease its traditional, hierarchical structure and transform into a ‘network of cells’, which requires new control approaches. This paper advances the Energy Packet Grid, an architecture of a future power grid, structured as a network of cells. The architecture is inspired by selected Internet design principles. In the Energy Packet Grid, all major power flows should be organized as energy packet transfers, short-term contracts between power electronic devices. This paper proposes the Time-Slotted Energy Packet Transfer Protocol (TEPT), a scheduling protocol that conducts energy packet transfers. Its goal is to efficiently use the power line capacity, to achieve fairness among competing transfers, and to sustain the power grid’s safety in case of communication failures. We evaluated TEPT with our simulator and with our real-world power electronic devices, demonstrating TEPT ’s feasibility on hardware.