Hybrid Distribution Transformers (HDTs) offer a compelling alternative to traditional low-frequency transformers (LFTs), providing auxiliary services in addition to standard functionalities. By integrating LFTs with power converters, HDTs enhance the operational capabilities of the system. The specific configuration in which converters are connected to the transformer allows for the provision of multiple services. This can not only prevent network failures but also extend the lifespan of its components, an outcome that is highly desirable in a distribution grid. This article discusses an HDT developed to mitigate voltage fluctuations in the grid and to decrease the reactive power drawn from the secondary side of traditional LFTs. A finite-control-set model predictive control (FCS-MPC), in conjunction with linear controllers, is utilized for the effective management of the HDT converters. Two separate control loops are established to regulate voltage and reactive power on the secondary side of the transformer. Results from Hardware-in-the-Loop (HIL) testing affirm the proficiency of HDT in reducing grid voltage variations by 15% and in cutting reactive power consumption by up to 94%. The adopted control strategy and topology are demonstrated to be effective in stabilizing voltage and reactive power fluctuations while concurrently facilitating the charging of the converters' DC link directly from the grid.