In this paper, we study a wireless powered communication network (WPCN) in a two-user interference channel, where two hybrid access-points (H-APs) support a user in each cell. In this two cell scenario, the H-APs first transmit the energy signal to charge both users in the downlink (DL) phase. Then, in the subsequent uplink (UL) phase, each user sends its information signal to the corresponding H-AP utilizing the harvested energy. Due to asynchronous time allocation of the DL and the UL between two cells, cross-link interference affects the overall performance. In this system, we aim to maximize the sum-rate by jointly optimizing the time durations for the DL and the UL phases of each cell, and the UL transmit power of all users. As the sum-rate maximization problem becomes non-convex, it is difficult to obtain an optimal solution. To solve this problem, we propose a new algorithm where the time allocation and the transmit power are alternatively updated based on the weighted sum-minimum mean square error criteria and the projected gradient method. In simulation results, we verify that the proposed algorithm for the asynchronous protocol outperforms conventional schemes.