© 2019 IEEE. For the high luminosity upgrade of the CERN large hadron collider, lower β∗ quadrupole magnets based on advanced Nb3Sn conductors will be installed on each side of the ATLAS and compact muon solenoid (CMS) experiment insertion zones. As part of the technological developments needed to achieve the required field gradient of 132.6 T/m within a 150-mm aperture, short length model magnets, named MQXFS, are tested both at the CERN SM18 and Fermilab test facilities. The model magnets rely on two types of Nb3Sn conductors (restack rod process (RRP) and powder-in-tube (PIT)) and on an innovative bladders and keys design to provide mechanical support against the Lorentz forces. In 2016 and 2017, the powering tests of the first two models MQXFS3 (RRP) and MQXFS5 (PIT) proved that nominal performance (16.5 kA) could be reached with excellent memory of the quench current after thermal cycle. However both magnets showed a slow training behavior with clear observations of voltage disturbances before the quench. Besides, only MQXFS5 could reach ultimate current (17.9 kA) whereas erratic behavior was observed on MQXFS3 due to conductor local degradation at the head of one of the coils. In 2018, this limiting coil was changed and the applied azimuthal prestress increased. While ultimate current could then be reached, no stable current could be maintained due to identified defect on the outer layer of the new coil. Finally the outcome of the test of the new model MQXFS4, featuring the final RRP conductors that will be used for the series production and variation on the inner layer quench heater designs are here reported in details.