The integration of Renewable Energy Sources (RES), that use VSCs as the interface between the primary energy source and the grid, is rapidly decreasing the density of synchronous generators in power systems. Hence, power electronics will hold the lead role ensuring robustness, security and quality. The additional functionalities provided for this purpose are the so-called ancillary services, which concern voltage regulation, power quality and, especially, frequency regulation, among others. In three-phase systems, the concept of a VSG with Grid-Forming (GF) functionality has been studied. Nevertheless, in distribution networks, the base of the pyramid is composed by single-phase low-voltage networks, in which this modern functionality has been barely explored. Indeed, these networks are expected to experiment an intense PV penetration from actual and future prosumers, so it may be required those PV generators to also provide the mentioned ancillary services. This work is a continuation of the work done in a previous stay under the acronym CPHILT-GFVSC, which consisted in Control Hardware in the Loop (CHIL) and PHIL of VSG with GF-VSCs in islanded networks. In this second part, the grid-connected mode of GF-VSCs is addressed in PHIL mainly focusing on frequency control. The reference frame used is the rotating reference frame generated through a virtual axes dq in single-phase systems. These are obtained by means of a filter to the voltages and currents of the system. This makes it possible to implement classic control strategies based on PI controls. The evaluation and transfer of code between the User Group and the Host Group has been carried out using the following methodology: Simulations carried out by the User Group with the aim of validating the control of single-phase GF-VSCS in the hardware platform of the Host group. Transfer and adaptation of the User Group simulations to the Host Group simulation environment. The host group has a detailed simulation of the Triphase converter, device used in the experimental test-bed, which has been provided by Triphase. This simulation allows to integrate all the control blocks identically to the files used for the experimental validation. Experimental evaluation of the single-phase GF-VSC for different grids. The control is progressively validated from an initial open-loop test with an ideal grid to the final closed-loop test with a second VSG as the main grid. The experimental results have shown a good performance of GF-VSCS in single-phase networks to support the frequency control of the system in different types of grids. In addition, a methodology has been established for testing GF-VSCs, either three-phase or single-phase, in PHIL applications. This methodology allows to evaluate the response of GF-VSCs from simpler networks to more complex networks that integrate all the dynamics and characteristics of the grid. Finally, and as a result of this collaboration and the previous one between the Host group and the User group, lines of future work have been established to evaluate GF-VSCs in transitions between isolated and grid-connected mode.