Wind turbine upgrades have been spreading in the recent years in the wind energy industry, with the aim of optimizing the efficiency of wind kinetic energy conversion. This kind of interventions has material and labor costs and it is therefore fundamental to estimate realistically the production improvement. Further, the retrofitting of wind turbines sited in harsh environments might exacerbate the stressing conditions to which wind turbines are subjected and consequently might affect the residue lifetime. This work deals with a case of retrofitting: the testing ground is a multi-megawatt wind turbine from a wind farm sited in a very complex terrain. The blades have been optimized by installing vortex generators and passive flow control devices. The complexity of this test case, dictated by the environment and by the features of the data set at disposal, inspires the formulation of a general method for estimating production upgrades, based on multivariate linear modeling of the power output of the upgraded wind turbine. The method is a distinctive part of the outcome of this work because it is generalizable to the study of whatever wind turbine upgrade and it is adaptable to the features of the data sets at disposal. In particular, applying this model to the test case of interest, it arises that the upgrade increases the annual energy production of the wind turbine of an amount of the order of the 2%. This quantity is of the same order of magnitude, albeit non-negligibly lower, than the estimate based on the assumption of ideal wind conditions. Therefore, it arises that complex wind conditions might affect the efficiency of wind turbine upgrades and it is therefore important to estimate their impact using data from wind turbines operating in the real environment of interest.