This paper presents a delay and a package drop compensator to address the variable latencies which arise in a wide area power system stabilizer (WAPSS). The vulnerability of data-driven control (DDC) based WAPSS to these latencies is specifically highlighted. The uniqueness of the proposed delay compensator (DC) is that it is designed to address not only the large deviations in delay mean value but also the variations around the mean value by careful reformulation of the delay in terms of its statistical features. Moreover, a new approach is proposed for package drop compensation, which considers nonlinearity in its formulation. The proposed package drop compensation uses the technique of dynamic linearization (DL) and pseudo partial derivative (PPD). Rigorous analysis is carried out to observe the effect of variable delay and package drop on the damping performance of DDC-WAPSS. It is shown that the damping performance of DDC-WAPSS improves when the proposed compensation techniques are used. The proposed DC and the nonlinear system based package drop compensator achieve improved compensation compared with the customary ones.