Fatigue damage of turbine components is typically computed by running a rain-flow counting algorithm on the load signals of the components. This process is not linear and time consuming, thus, it is non-trivial for an application of wind farm control design and optimisation. To compensate this limitation, this paper will develop and compare different types of surrogate models that can predict the short term damage equivalent loads and electrical power of wind turbines, with respect to various wind conditions and down regulation set-points, in a wind farm. More specifically, Linear Regression, Artificial Neural Network and Gaussian Process Regression are the types of the developed surrogate models in this work. The results showed that Gaussian Process Regression outperforms the other types of surrogate models and can effectively estimate the aforementioned target variables.