We describe a generalization of the coupled wake boundary layer (CWBL) model for wind farms that can be used to evaluate the performance of wind farms under arbitrary wind inflow directions, whereas the original CWBL model (Stevens et al., J. Renewable and Sustainable Energy 7, 023115 (2015)) focused on aligned or staggered wind farms. The generalized CWBL approach combines an analytical Jensen wake model with a ‘top-down’ boundary layer model coupled through an iterative determination of the wake expansion coefficient and an effective wake coverage area for which the velocity at hub-height obtained using both models converges in the ‘deep-array’ portion (fully developed region) of the wind farm. The approach accounts for the effect of the wind direction by enforcing the coupling for each wind direction. Here, we present detailed comparisons of model predictions with large eddy simulation results and field measurements for the Horns Rev and Nysted wind farms operating over a wide range of wind inflow directions. Our results demonstrate that two-way coupling between the Jensen wake model, and a ‘top-down’ model enables the generalized CWBL model to predict the ‘deep-array’ performance of a wind farm better than the Jensen wake model alone. The results also show that the new generalization allows us to study a much larger class of wind farms than the original CWBL model, which increases the utility of the approach for wind farm designers.