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We present a grid of stellar models at super-solar metallicity (Z = 0.020) extending the previous grids of Geneva models at solar and sub-solar metallicities. A metallicity of Z = 0.020 was chosen to match that of the inner Galactic disk. A modest increase of 43% (=0.02/0.014) in metallicity compared to solar models means that the models evolve similarly to solar models but with slightly larger mass loss. Mass loss limits the final total masses of the super-solar models to 35 M$_\odot$ even for stars with initial masses much larger than 100 M$_\odot$. Mass loss is strong enough in stars above 20 M$_\odot$ for rotating stars (25 M$_\odot$ for non-rotating stars) to remove the entire hydrogen-rich envelope. Our models thus predict SNII below 20 M$_\odot$ for rotating stars (25 M$_\odot$ for non-rotating stars) and SNIb (possibly SNIc) above that. We computed both isochrones and synthetic clusters to compare our super-solar models to the Westerlund 1 (Wd1) massive young cluster. A synthetic cluster combining rotating and non-rotating models with an age spread between log10 (age/yr) = 6.7 and 7.0 is able to reproduce qualitatively the observed populations of WR, RSG and YSG stars in Wd1, in particular their simultaneous presence at log10(L/L$_\odot$) = 5-5.5. The quantitative agreement is imperfect and we discuss the likely causes: synthetic cluster parameters, binary interactions, mass loss and their related uncertainties. In particular, mass loss in the cool part of the HRD plays a key role., Comment: 15 pages, 12 figures. Accepted for publication in MNRAS