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Restoration objectives are to restore the system to normal operation as quickly as may be consistent with system security, minimizing the amount of disconnected loads. In the initial phase of restoration, operators are often concerned with load pickup problem. One of the important problems during load pickup is keeping frequency response in an allowable range. The aim of this paper is to investigate load pickup problem based on calculation frequency response of the power system. This paper considers hydro power plants for evaluating the stability and frequency response during load pickup in the early stages of power system restoration. Hydro power plants have capability of black start operation and can be used for early stages of power system restoration. Simulation results are highlighted based on an accurate proposed model of hydro power plant. The main characteristic of the developed model is to consider different parts of hydro power plant. The developed model shows a more detailed and precise calculation of the frequency response in the power system. This work proposes a linearized model that can be utilized instead of nonlinear hydro turbine model. This model is more appropriate for controller analysis using linear methods. Simulation results show that the proposed method helps determine the amount of load pickup during power system restoration.