We study the effects of a high share of wind generation on the frequency fluctuations of power grids on islands. We propose a dynamical model that includes conventional and variable renewable generation, as well as demand variations. Our model can assimilate load and generation data and reproduce frequency fluctuations with the current power mix with a high degree of accuracy, and it allows to simulate the frequency dynamics for different scenarios with a very high penetration of renewable energy. As a case study, we analyze the power grid of Gran Canaria island. We characterize the frequency fluctuations and propose a method to estimate the control needed to keep frequency deviations within reasonable limits.