While research on wind-farm-atmospheric boundary layer interaction has primarily focused on local effects inside and above the farm, recent studies found that wind farms may affect the wind conditions several kilometres upstream of the farm via the excitation of atmospheric gravity waves. Such non-local effects can have strong implications for the wind-farm energy extraction but are currently overlooked in wind-farm design and operation and control strategies. In the present study, we employ a fast wind-farm boundary-layer model in combination with ERA5 reanalysis data to assess the potential impact of wind-farm induced gravity waves on the annual energy production of the Belgian-Dutch off shore wind-farm cluster in the North Sea. We estimate the annual energy loss due to the effect of self-induced gravity waves to be of the order of 4 to 6 %.