This paper presents a power control method for a hybrid electrical system, which enhances a conventional main AC grid by adding a DC sub-grid in parallel. In this system, each prosumer connects to the sub-grid via a couple of half-bridge inverters of a device called a power router. All of the power routers connected to the sub-grid are controlled such that they maintain the voltage of the sub-grid equally, which is an essential feature of peer-to-peer power accommodation without synchronization. This paper proposes an adaptive hysteresis current-control technique for controlling sub-grid-connected inverters that maintains the voltage of the sub-grid while accommodating a given power. The proposed control method also balances currents between positive and negative lines of the sub-grid simultaneously. The proposed control method is implemented on a high-speed FPGA-based digital controller and is evaluated on three prototypes of the power router. The experimental results show that the proposed method yields fast and stable responses and enables the power router to accommodate power with a high accuracy.