Using a floating vessel operating on its DP-system and using a motion-compensated pile gripper to install monopiles could be the installation method of the future. Therefore, this thesis focuses on this method. The main objective of this thesis project is to build a model that accurately describes the motions of the Stella Synergy, the monopile, and the motion-compensated gripper, depending on the environmental conditions. This model is built in Anysim, which is a time-domain simulation software program of MARIN based on the RK2 numerical method. The model considers the early pile driving phase because this phase is governing in terms of risk. The monopile acts as an inverted pendulum in this phase, and the motion-compensated pile gripper must guarantee the stability of the monopile. The vessel uses its DP-system for station keeping. The DP-system contains a position reference system, a filter, a control system, and a thruster allocation algorithm. The vessel describes the wind, current and wave forces on the monopile and vessel. The environmental conditions are assumed to be collinear, and wave spreading is added to the model for some simulations. The wave forces on the vessel are determined with diffraction calculations in Ansys AQWA. The diffraction calculation for the vessel is verified with a diffraction calculation of MARIN, and the diffraction calculation for the monopile considers the shielding effect and is verified with a calculation with the Morison equation. A motion-compensated pile gripper with two PD-controllers is built in Python. The gripper considers static and dynamic friction forces and a maximum delta force per numeric timestep to model the pressure build-up time of the hydraulic cylinders. Multiple 3-hour simulations are run to generate results. These simulations, which considers each a different sea condition, are tested by the six limitations of the model. First, the preferable incoming angle of environmental conditions is determined. The workability of the Stella Synergy is calculated operating at the North Sea using this preferable incoming angle of attack. Then, two adaptations to the model are tested to increase the workability. Using fast-rotating thrusters or changing the DP-gains result in the workability of 96.4%. The governing limitation is the pitch motion of the vessel. It is tested if using mooring lines in combination with the DP-system results in a footprint reduction. It is concluded that adding mooring lines could result in a footprint reduction, but it is crucial to gain insight into the optimal axial stiffness of the mooring lines. The monopile's influence on the vessel's motion is also tested. It is concluded that the vessel's surge, sway, roll and yaw motion increases significantly due to the environmental forces on the monopile, which are passed through the gripper to the vessel. Finally, the workability of the vessel during the worst-case single failure is determined. After improving the DP-gains for particular sea conditions, the workability for the worst-case single failure was 96.0%. The failure results thus in a minor difference in the workability.