The optimal design of a wind farm with the aim of increasing the exploitation rate and power production is one of the challenging problems in the field of renewable energies. In this paper, the effect of using different hub height wind turbines in a farm on total power is studied. An exact mathematical formulation is presented in terms of the interaction matrix for multi-turbine wake effects considering different hub height wind turbines, and a new mixed-integer quadratic optimization model is developed. Then, the model is generalized to include the changes in wind characteristics and uncertain parameters. The model is solved using the linearization technique and an iterative method. The performance of the model and solution algorithm is evaluated by solving different problems borrowed from the literature. The computation results show the possibility of having a high-quality solution in a reasonable time in almost all cases.