When grid side converter (GSC) is connected to weak grid, the small signal instability can happen due to terminal characteristics of the GSC that are incompatible with the grid impedance. This issue is not of wide concern in previous studies of direct power control (DPC) of GSC. By small signal analysis, it is shown that the impedance characteristic of the conventional direct power control GSC is not compatible with the inductive grid impedance in weak grid due to its constant power load behavior. To solve the problem, instead of feeding the DPC controller with direct measured voltage and current, a Kalman filter (KF) is used to obtain filtered output current and a double second-order generalized integrator (DSOGI) is used to obtain filtered voltage at the point of common coupling (PCC). These strategies change the impedance characteristic of the GSC dramatically and make it suitable to operate in weak grid where SCR is 2, while the rapid power response is preserved. The proposed strategy is verified through simulation and controller hardware in loop (CHIL) tests.