Numerical simulation and stability analysis of an islanded power network comprising 40 MW of hydropower, 20 MW of wind power and 60 MW of gas-fired power plant are investigated. First, the modeling of each power plant is fully described. The wind farm is modeled through an aggregated model approach of 10 wind turbines of 2 MW and comprises a stochastic model of wind evolution with wind gust. The hydraulic power plant comprises the upstream reservoir, a 1000 meters gallery, a surge tank, the 500 meters long penstock feeding a low specific speed pump-turbine and connected to the downstream tank through a 70 meters long tailrace water tunnel. The model of gas-fired power plant includes an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between. To predict the performance of the gas turbine engine, both at design and off-design conditions, performance maps are integrated in the modeling. Then, the capability of the hydraulic power plant to compensate wind power variations or load rejections is investigated using the EPFL simulation software SIMSEN to perform time domain simulation of the entire mixed islanded power network. This study shows the evolution of the response time of the hydraulic part as function of the penstock length and highlights the influence of the hydraulic layout on the power system stability. The dynamic performances of such hydraulic power plants are of highest interest for improving stability of mixed islanded power network, but require reliable simulation model of the entire network for safety and optimization purposes.